Co(II) single-ion magnets: synthesis, structure, and magnetic properties

Abstract

Magnetoactive coordination compounds exhibiting bi- or multistability between two or more magnetic stable states present an attractive example of molecular switches. Currently, the research is focused on molecular nanomagnets, especially single molecule magnets (SMMs), which are molecules, where the slow relaxation of the magnetization based on the purely molecular origin is observed. Contrary to ferromagnets, the magnetic bistability of SMMs does not require intermolecular interactions, which makes them particularly interesting in terms of application potential, especially in the high-density storage of data. This paper aims to introduce the readers into a basic understanding of SMM behaviour, and furthermore, it provides an overview of the attractive Co(II) SMMs with emphasis on the relation between structural features, magnetic anisotropy, and slow relaxation of magnetization in tetra-, penta-, and hexacoordinate complexes.

Graphical abstract

Introduction

Since their discovery in 1993 [1], the single molecule magnets (SMMs) have attracted considerable interest due to the possibility to store the magnetization within a single molecule, which means that new materials based on these compounds have high potential in modern applications and technologies. Especially data storage devices with extraordinary high capacity, optical imaging devices, or qubits for quantum computing are the examples worth mentioning [2]. When molecules of SMMs contain only one metal centre with significant magnetic anisotropy, they are called single-ion-magnets (SIMs).

One of the conditions required for storing information in a particle is the existence of magnetic hysteresis. The SMMs display field-induced hysteresis loop in M vs. field sweeps below the blocking temperature T_B. The remnant magnetization exists for a limited period called relaxation time τ. The blocking temperature of most molecule-based magnets is below 10 K, although cases up to 80 K can be found rarely [3,4,5]. To be considered decent SMMs, the compounds should show a large effective energy barrier against magnetization switch U_eff, the significant value of τ and high T_B. Therefore, the goal of current research in this field is to increase U_eff and T_B as much as possible [6, 7]. In other words, it is a great challenge for scientists to prepare nanomagnets that exhibit slow relaxation of the magnetization (SRM) at room temperature. The value of U_eff is connected to the values of magnetic anisotropy parameter D and total spin number S [vide infra, see Eqs. (7) and (8)]. If the value of the energy barrier of SMMs raises, both values D and S are increased, too. Hence, the first studies were focused on lifting the value of the total spin of the molecule and the synthesis efforts were concentrated on using a large amount of connected magnetic centres, where the 3d block elements were used heavily. However, recent investigations found that since D and S correlate to each other, it may be better to focus on boosting D value instead of the size of the S. This alternative approach considers Co(II) and lanthanide complexes as attractive candidates for further research [8]. In recent years, lanthanide based SMMs (Ln-SMMs) have become the most eye-catching and high-performance SMMs, although most of them are facing problems with air and moisture instability and their practical magnetic characterization becomes increasingly challenging [9].

Single molecule magnetism—a theoretical background

There are two characteristic indications that a molecule of SMM complex exhibits the SRM:

• 1. detection of maxima in the χ″ vs. f dependency (χ″ is out-of-phase AC (alternating current) magnetic susceptibility);

• 2. presence of a hysteresis loop in the magnetization vs. applied magnetic field response [10].

Unlike the case of the compounds with long-range magnetic ordering (ferromagnets, ferrimagnets), the maximum of out-of-phase AC susceptibility χ″ shifts to higher frequencies upon the temperature increase. This behaviour shows a typical feature of SMMs, where the maxima of χ″ are both frequency and temperature dependent and the relaxation time τ is shorter at higher temperatures. Furthermore, the hysteresis loop of SMMs is not smooth, and it rather exhibits steps characteristic of quantum tunnelling of magnetization (QTM), which correspond to positions of increased magnetization relaxation rates.

The alternating magnetic field is described by the following equation:

$$H\left(t\right)={H}_{\mathrm{DC}}+{H}_{\mathrm{AC}} \cdot \mathrm{cos}\left(\omega t\right),$$

(1)

where H_DC is a constant of DC (direct current) magnetic field, which is parallel to oscillating field H_AC and it can adopt zero as well as non-zero values. H_AC is defined as amplitude of AC magnetic field and ω goes for an angular frequency. The AC susceptibility measurements are used to analyse the dynamic susceptibility of sample by applying an oscillating magnetic field. For next calculations, the value of H_DC is set to zero. Because the alignment of magnetic moments of substance takes some time, the magnetization of the sample is not able to follow the applied external AC field. Therefore, the magnetization of the sample is delayed in comparison to magnetic field and the phase shifts by an angle φ [11] and Eq. (2) is valid.

$$M\left(t\right)={M}_{AC}\cdot \mathrm{cos}\left(\omega t-\varphi \right).$$

(2)

Equation (2) can be rewritten using the cosine addition formula into Eq. (3).

$$M\left(t\right)={M}_{\mathrm{AC}}\left[\mathrm{cos} (\varphi ) . \mathrm{cos} (\omega t) + \mathrm{sin }(\varphi ) . \mathrm{sin} (\omega t)\right].$$

(3)

The dynamic susceptibility is a complex quantity, hence it is expressed by the real χ′ (dispersion) and imaginary χ″ (absorption) components, which are dependent on the angular frequency of the AC field ω [11, 12]:

$$\chi ={\chi }^{^{\prime}} + i{\chi }^{^{\prime\prime} }= \frac{{M}_{\mathrm{AC}}}{{H}_{\mathrm{AC}}}\mathrm{cos}\left(\varphi \right)+i\frac{{M}_{\mathrm{AC}}}{{H}_{\mathrm{AC}}}\mathrm{sin}\left(\varphi \right).$$

(4)

Therefore, the time-dependent magnetization can be rewritten as follows:

$$M\left(t\right)={H}_{AC}\left[{\chi }^{^{\prime}} \mathrm{cos} (\omega t) + {\chi }^{^{\prime\prime} } \mathrm{sin} (\omega t)\right].$$

(5)

In the case of SMMs, the AC susceptibility contains the in-phase (χ′) as well as the out-of-phase (χ″) components. They are measured as a function of the AC frequency and as a function of temperature, leading to χ′ and χ″ vs. f and χ′ and χ″ vs. T plots, respectively (Fig. 1).

Fig. 1

χ′ and χ″ vs. f (a and c, respectively) and χ′ and χ″ vs. T (b and d, respectively) plots for Co(II) SMM [13]

The relaxation time can be determined by Eq. (6), which is valid at the peak maxima (out-of-phase component) or the inflexion point (in-phase component) in the frequency dependence of the AC susceptibility [2]:

$$\omega ={\tau }^{-1}.$$

(6)

In the presence of a large applied magnetic field, the m_s = − S state is stabilized more in comparison to m_s = + S state, which means that the spins of every molecule are aligned with the applied field and all of the molecules are in the m_s = − S state and the magnetization is saturated. After the field is switched off, the magnetization M is fixed because of the existence of the barrier and the return to the equilibrium value is happening very slowly. Therefore, a remanent magnetization is present. When the field reaches negative values, it causes the reduction of the barrier; hence it allows spins to “unfreeze” and the reversal of the magnetization is fast. Thus, a hysteresis loop is detected. The width of the hysteresis loop depends on the sweeping rate of the magnetic field as well as on the temperature. The value of magnetization projection can be positive as well as negative at zero field, which depends on the sample history and it is the principle of information storage in one single molecule [14].

Magnetic anisotropy means the preferential alignment of the magnetic axis along a specific direction. The phenomenon called zero-field splitting (ZFS) causes a single-ion anisotropy; therefore, it is essential for SMMs. It can occur in a system with S ≥ 1 ground state. Although it is known that the degeneracy of the m_s levels can be removed by the external magnetic field, ZFS means that the degeneracy in axial crystal field is removed even before the application of the magnetic field, the m_s =  ± 3/2 levels by 2D (where D is the axial ZFS parameter). Therefore, ZFS means that levels are separated in the absence of an applied magnetic field. Both the central atom and its coordination environment determine the size of the D parameter [14, 15]. In the systems with negative D (Fig. 2a), the m_s = ± S levels have the lowest energy (double well case). They are characterised by magnetic anisotropy along the easy axis, which means that flipping the molecule's spin along the z-axis takes some energy to reorient the spin via perpendicular m_s = 0 state [14]. The case of positive D (Fig. 2b) is called easy plane anisotropy and the relaxation of a system occurs fast from the m_s = − S state to the minimum value of spin projection. There are several methods to determine D and S, from which the most used ones are magnetic investigations at static (B_DC) magnetic field, EPR and far-infrared magnetic spectroscopy (FIRMS).

Fig. 2

Difference between easy axis (a) and easy plane (b) anisotropy [16]

In an applied external field parallel to the z-axis, the projection of magnetization, which is antiparallel to the field correlates with the levels of positive M_s and vice versa. The potential energy barrier value is proportional to axial ZFS parameter D and to the square of the ground state spin number according to Eqs. (7) and (8) for Kramers (non-integer spin number) and non-Kramers systems (even number of unpaired electrons), respectively:

$${U}_{\mathrm{eff}}= \left|D\right|\cdot {S}^{2},$$

(7)

$${U}_{\mathrm{eff}}= \left|D\right|\cdot {(S}^{2}-1/4).$$

(8)

Apart from the U_eff, another parameter, magnetic blocking temperature T_B, characterises the SMM complex. T_B is a specific temperature, below that the magnetic moments are frozen and above it, the spin reversal can go via thermally activated processes. Although three ways can define the T_B (vide infra), the second definition is often used, but it must be taken into consideration that the value of T_B highly depends on the sweep rate of the magnetic field [12]. The possible definitions of T_B are:

• temperature, at which a peak is identified in the out-of-phase susceptibility at a given frequency;

• the highest temperature, at which hysteresis curve is detected in a field vs. magnetization dependence;

• the highest temperature, at which a maximum in the zero-field cooled magnetization is recognized [12].

Although more processes of relaxation have been proposed, there are several most studied ones via which the system can return from the state of saturation of magnetization to equilibrium state, each of them has a characteristic temperature and DC field (H) dependence:

• Quantum Tunnelling of Magnetization (QTM);

• Thermally assisted QTM;

• Orbach process;

• Raman process;

• Direct process.

The QTM causes that the hysteresis loop of typical SMM is not smooth and some steps are noticed, while increasing the relaxation rate is observed. The origin of QTM has been investigated thoroughly to gain the ability to suppress it or use it to improve the quality of the SMMs. The quantum tunnelling can be observed between two levels of the same energy [14]. The presence of a small DC external magnetic field can remove the degeneracy of levels with opposite polarization of the magnetization, and hence, it can suppress the quantum tunnelling. This is the reason why the dynamic magnetic properties are very often studied at the applied static magnetic field. Figure 3a displays that at zero field, the m levels on the left and right are in resonance. Application of a magnetic field lifts this degeneracy and at certain field levels on the left and right come into resonance again [6]. For molecules with non-integer ground state, the situation is more interesting because of the existence of Kramers doublets in the absence of an applied magnetic field. Therefore, the molecule is not able to tunnel from m_s = − S to m_s = + S. The rate of QTM is related to ligand field distortion, hyperfine interaction, transverse fields [14] and it is temperature independent—see Eq. (9):

Fig. 3

Potential-energy diagram of an SMM and its changes as the magnetic field is swept from H = 0 to H = nD/gμ_B (a). Taken with permission from Ref. [14]. Thermally assisted QTM (b). Taken with permission from Ref. [17]

$${\tau }^{-1}={c}_{0}=\left(\frac{{b}_{1}}{1+{b}_{2}{H}^{2}}\right).$$

(9)

Tunnelling is possible to observe between the lowest energy states M_s = ± S as well as between pairs of degenerate excited states, which is called thermally assisted QTM. After the higher m_s states are populated via phonon absorption, the QTM may occur (Fig. 3b) [17].

Relaxation via Orbach process is described as follows: first, the molecule is able to change its state from m_s = − S to m_s = − S + 1 by absorption of one quantum, correlating to the difference in energy between those states. The action can be repeated until m_s = 0 is achieved. From this state the energy of spin can be lost due to phonon emission and state m_s = + S can be reached, although the system can return to m_s = − S state. The longitudinal relaxation rate for Orbach process describes Eq. (10):

$${\tau }^{-1}={\tau }_{0}^{-1}\mathrm{exp}(-{U}_{\mathrm{eff}}/{k}_{\mathrm{B}}T).$$

(10)

Raman process is process similar to Orbach in terms of understanding but unlike the Orbach process, this process consists of absorption of a phonon, which excites the molecule to a so-called virtual state. Often it is dominant over direct process for not too low temperatures and it is described by the Eq. (11). The Raman process is ion dependent, which means that the exponent n usually adopts value of 7 and 9 for non-Kramers and Kramers systems, respectively. It is worth to note, that because it depends also on the energy of the ground state, all values of 4 and larger are considered as reasonable ones [12]:

Fig. 4

Out-of-phase peaks (a–c) and the Cole–Cole plots (d–f) for one, two, and three relaxation channels at various temperatures. Solid lines present the fits [13, 21]

$${\tau }^{-1}=C{T}^{n}=d\left(\frac{1+e{H}^{2}}{1+f{H}^{2}}\right){T}^{n}.$$

(11)

Direct process of relaxation involves absorption of one phonon, which triggers a spin-flip (and the emission of the phonon) [18]. The frequency of the emitted or absorbed phonon is very short and limited by the phonon density of states [14]. The relaxation rate is proportional to temperature—see Eq. (12) and like Raman process, this mechanism is related to a nature of involved ions; therefore, the value of exponent m usually equals 2 and 4 for non-Kramers and Kramers system, respectively. The direct process is important mainly at very low temperatures, while the importance of Raman and Orbach processes becomes more significant at higher temperatures [18]:

$${\tau }^{-1}=A{H}^{m}T.$$

(12)

Particular knowledge of the various mechanisms is crucial for the understanding the dynamics of magnetization relaxation. Since there is usually more than one process present for one SMM, the global relaxation rate is frequently described by the Eq. (13), where a combination of these mechanisms is taken into the consideration [19]:

$${\tau }^{-1}={\tau }_{0}^{-1}\mathrm{exp}\left(-\frac{{U}_{\mathrm{eff}}}{{k}_{\mathrm{B}}T}\right)+C{T}^{n}+A{H}^{m}T+ {c}_{0}={\tau }_{0}^{-1}\mathrm{exp}\left(-\frac{{U}_{\mathrm{eff}}}{{k}_{\mathrm{B}}T}\right)+d\left(\frac{1+e{H}^{2}}{1+f{H}^{2}}\right){T}^{n}+A{H}^{m}T+\left(\frac{{b}_{1}}{1+{b}_{2}{H}^{2}}\right).$$

(13)

The a, b₁, b₂, d, e, f, and n stand for reduced parameters, which are connected to the different relaxation pathways [20] and the together with the relaxation parameters $A, {\tau }_{0}, {U}_{\mathrm{eff}}, C$ (vide supra) have the essential effect on the overall relaxation time τ at the given temperature, hence the understanding of their connection with the structural characteristics of SMMs are one of the crucial challenges in the area of molecular magnetism.

When comes to the AC susceptibility measurements, from experimental point of view, the sample is installed between two coils, where the current circulates at various frequencies. The sample response after application of a tiny oscillating magnetic field, which includes a small magnetization in a substance, is detected by secondary coils. The frequency of external oscillating magnetic field varies yielding in the in-phase (χ′) and out-of-phase (χ″) AC susceptibility signals. An out-of-phase (χ″) peak is detected when the rate the working frequency of the AC field is nearby the flipping rate of the magnetic moment of the molecule [1]. The energy barrier ${U}_{\mathrm{eff}}$ is acquired through fitting the in-phase (χ′) and out-of-phase (χ″) AC susceptibility data using Debye model [12]. For a single relaxation process characterised by one relaxation time, the Eqs. (14) and (15), where χ_S and χ_T act as the adiabatic (ω → ∞) and isothermal (ω → 0) susceptibility, respectively [14], are valid:

$${\chi }^{\mathrm{^{\prime}}}\left(\omega \right)={\chi }_{s}+\frac{({\chi }_{T}-{\chi }_{s})}{1-{\omega }^{2}{\tau }^{2}},$$

(14)

$${\chi }^{^{\prime\prime} }\left(\omega \right)=\frac{({\chi }_{T}-{\chi }_{s})\omega \tau }{1+{\omega }^{2}{\tau }^{2}}.$$

(15)

Nevertheless, due to some differences across the SMM molecules, the relaxation process is usually characterised by a distribution of relaxation times. Thus, a distribution parameter α, which is a measure of the distribution of relaxation processes and its value ranges from 0 to 1, is introduced. A narrow distribution of relaxation times results in a small α value [12]. If there is only one peak in the χ″ vs. f plot (Fig. 4), one relaxation channel occurs and one-set Debye model (Eqs. (16) and (17)) are used to obtain fitting parameters:

$${\chi }^{\mathrm{^{\prime}}}\left(\omega \right)={\chi }_{s}+\left({\chi }_{T}-{\chi }_{s}\right)\frac{1+{\left(\omega \tau \right)}^{\left(1-\alpha \right)}\mathrm{sin}\left(\frac{\pi \alpha }{2}\right)}{1+2{\left(\omega \tau \right)}^{\left(1-\alpha \right)}\mathrm{sin}\left(\frac{\pi \alpha }{2}\right)+{\left(\omega \tau \right)}^{\left(2-2\alpha \right)}},$$

(16)

$${\chi }^{^{\prime\prime} }\left(\omega \right)=\left({\chi }_{T}-{\chi }_{s}\right)\frac{{\left(\omega \tau \right)}^{\left(1-\alpha \right)}\mathrm{cos}\left(\frac{\pi \alpha }{2}\right)}{1+2{\left(\omega \tau \right)}^{\left(1-\alpha \right)}\mathrm{sin}\left(\frac{\pi \alpha }{2}\right)+{\left(\omega \tau \right)}^{\left(2-2\alpha \right)}}.$$

(17)

On the other hand, if two peaks of upper mentioned dependence are detected, two relaxation channels (Fig. 4)are involved and the fit of the χ′ and χ″ using two-set Debye model leads to Eqs. (18) and (19). The in-phase (χ′) and out-of-phase (χ″) components of AC susceptibility are fitted simultaneously and χ_S, χ_T, α_i and relaxation times τ_i are obtained [12]:

$$\begin{gathered} \chi ^{\prime}(\omega ) = \chi_{S} + \left( {\chi_{T1} - \chi_{S} } \right)\frac{{1 + (\omega \tau_{1} )^{{(1 - \alpha_{1} )}} sin(\pi \alpha_{1} /2)}}{{1 + 2(\omega \tau_{1} )^{{(1 - \alpha_{1} )}} sin(\pi \alpha_{1} /2) + (\omega \tau_{1} )^{{(2 - 2\alpha_{1} )}} }} \hfill \\ \, + \left( {\chi_{T2} - \chi_{T1} } \right)\frac{{1 + (\omega \tau_{2} )^{{(1 - \alpha_{2} )}} sin(\pi \alpha_{2} /2)}}{{1 + 2(\omega \tau_{2} )^{{(1 - \alpha_{2} )}} sin(\pi \alpha_{2} /2) + (\omega \tau_{2} )^{{(2 - 2\alpha_{2} )}} }}, \hfill \\ \end{gathered}$$

(18)

$$\begin{gathered} \chi ^{\prime\prime}(\omega ) = \left( {\chi_{T1} - \chi_{S} } \right)\frac{{(\omega \tau_{1} )^{{(1 - \alpha_{1} )}} cos(\pi \alpha_{1} /2)}}{{1 + 2(\omega \tau_{1} )^{{(1 - \alpha_{1} )}} sin(\pi \alpha_{1} /2) + (\omega \tau_{1} )^{{(2 - 2\alpha_{1} )}} }} \hfill \\ \, + \left( {\chi_{T2} - \chi_{T1} } \right)\frac{{(\omega \tau_{2} )^{{(1 - \alpha_{2} )}} cos(\pi \alpha_{2} /2)}}{{1 + 2(\omega \tau_{2} )^{{(1 - \alpha_{2} )}} sin(\pi \alpha_{2} /2) + (\omega \tau_{2} )^{{(2 - 2\alpha_{2} )}} }}. \hfill \\ \end{gathered}$$

(19)

The Argand (Cole–Cole) plot is commonly used for quantification of the distribution of the relaxation times width. The larger value of α produces the flatter the Argand plot and if the range of α is narrow and system displays only one relaxation channel, the Argand diagram is fitted combining equations of one-set Debye model very accurately.

The χ″ maximum of semicircle of one channel in the Cole–Cole plot occurs at

$${\chi }^{\mathrm{^{\prime}}}={\chi }_{s}+\frac{1}{2\left({\chi }_{T}-{\chi }_{s}\right)},$$

(20)

and its value can be determined by Eq. (21):

$${\chi }_{\mathrm{max}}^{^{\prime\prime} }=\frac{1}{2\left({\chi }_{T}-{\chi }_{s}\right)\mathrm{tan}\left(\frac{\uppi }{4\left(1-\alpha \right)}\right)}.$$

(21)

Tetracoordinate Co(II) complexes

Rechkemmer et al. [22] have studied a Co(II) single-ion magnet with very high energy barrier of spin reversal and value of D parameter. The reaction of acetonitrile solutions of Co(BF₄)₂·6H₂O and H₂L1 (molecular structures of all mentioned ligands and their IUPAC names listed in Table 1) in the presence of base NEt₃ resulted in formation of tetracoordinate Co(II) compound 1 ((NHEt₃)₂[Co(L1)₂]). The central ion is surrounded by four nitrogen atoms of two ligand anions L1²⁻ aligned perpendicularly to each other (Fig. 5a). The coordination geometry adopts a shape of distorted tetrahedron with the N–Co–N angles of the values 80.59° and 80.70° and the lengths of Co–N bonds acquire values from 2.00 to 2.01 Å. The variable temperature DC magnetic susceptibility data revealed the room temperature value of product function χT = 3.14 cm³ K mol⁻¹, which is higher than the expected spin only value for a system with S = 3/2. With decreasing temperature, χT stays relatively constant down to 130 K, when begins to drop, suddenly reaching value near 2.50 cm³ K mol⁻¹ at low temperatures, which is an indication of a large anisotropy (Fig. 5b). The magnetization at 1.8 K and high fields (up to 7 T) saturated to value of 2.56 μ_B, which is significantly lower than expected for this system (3.90 μ_B) and it also suggests the presence of pronounced ZFS. The obtained D value from fitting of the static magnetic data according to spin Hamiltonian was − 115 cm⁻¹ and g = 2.20, g_||= 3.03, which is one of the largest published value for tetracoordinate Co(II) ion so far and it indicates a large uniaxial anisotropy of the compound 1 (all mentioned compounds, their general molecular formulas, ZFS and relaxation parameters are listed in Table 2). Investigation of the slow relaxation of magnetization was carried out via AC susceptibility measurements at several temperatures and frequencies. The compound 1 displays significant magnetic relaxation, which confirms an SMM behaviour, even in the absence of DC field (Fig. 5c). The relaxation times τ at different temperatures obtained by fitting the Argand plots to a generalized one-set Debye model were used to construct Arrhenius plot of ln τ vs. T⁻¹. The linear regime observed in the high-temperature regions of the dependency refers to a temperature range, where the relaxation goes via an Orbach process. In contrast, the other—QTM, Raman and direct processes created a curvature of the plot at the low temperatures. The fitting of the linear regime at high temperatures to the Arrhenius law gave values of U_eff = 170 K and τ₀ = 3.9 × 10^–8 s, which authors reported as the highest value of effective energy barrier amongst previously reported tetracoordinate Co(II) complexes, exhibiting SMM behaviour at the zero DC field [23,24,25]. Nevertheless, this value is still significantly lower as it would be obtained from calculation according to Eq. (8) with the experimental D value, obtained from static magnetic measurements. Therefore, the authors performed far-infrared transmission measurements at various static fields, and the data revealed an apparent field-dependent absorption near 230 cm⁻¹ (Fig. 5d) allowed to determine the energy barrier of spin reversal U_eff = 230 K experimentally. This value was fixed within the fitting procedure of Orbach and Raman processes and resulted in the best fitted values C = 0.09, n = 3.65 and τ₀⁻¹ = 9.1 × 10⁹ s⁻¹.

Table 1 List of reported ligands

Fig. 5

Molecular structure of the complex anion of 1. Colour code: Co—blue, O—red, S—yellow, N—violet, C—grey. Hydrogen atoms have been omitted for the sake of clarity (a) χT vs. T plots of 1 at 1000 Oe (T < 50 K) and 10,000 Oe (T > 40 K). The red line = spin Hamiltonian fit (D = –115 cm⁻¹, g = 2.20, g_||= 3.03). The dashed blue line = simulation according to the correlated calculations. The inset = magnetic hysteresis at T = 1.8 K (b). The out-of-phase AC susceptibility at zero DC field for 1 as a function of the frequency. c Normalized far-infrared absorption spectra of 1 at T = 4 K (d) [22] (colour figure online)

Table 2 List of reported Co(II) compounds

Inspired by bidentate motive of H₂L1, the same research group prepared redox active tetrasulfonamido-benzene bis-bidentate bridging ligand, which allows strong exchange couplings between the neighbouring coordination centres. Albold et al. [26] have reported synthesis, structural and magnetic investigation of the dinuclear Co(II) radical-bridged compound 2 ((K‐18‐c‐6)₃[{(H₂L2²⁻)Co^II}₂(μ‐L2³⁻)]), where H₄L2 corresponds to tetrakis(methanesulfonamido)benzene. This compound is highly appealing due to pronounced hysteresis and unusually long relaxation times at low temperatures. The synthesis of mentioned coordination compound starts with the deprotonation of H₄L2 with KOtBu and following reaction with 18‐crown‐6 in acetonitrile. In the next, the complexation with Co(BF₄)₂⋅6 H₂O takes place and following oxidation with pure oxygen results in the formation of coordination polymer 2. The single‐crystal X‐ray diffraction measurements displayed that compound crystallizes in the monoclinic space group P2₁/c and the supramolecular structure of the complex (Fig. 6a) contains two different couples of 18‐crown‐6-ethers encased potassium counterions incorporated in the crystal structure, two of them interconnect neighbouring complex anions into a polymeric chain and next two are connected to complex anions terminally. In addition, the compound contains two distorted tetrahedral coordinated Co(II) centres, surrounded by four nitrogen atoms from the ligand and one centre of inversion, which is placed at the middle of the molecule.

Fig. 6

Scheme of 2 (a). χT vs. T plot for 2 in an applied field of 1000 Oe (blue), red line—the fit, green line—the ab initio calculation of susceptibility, yellow symbols—twice the χT value of 1 with the addition of a 0.375 cm³ K mol⁻¹ as a contribution for the radical. The inset—low-temperature region (b). The out-of-phase AC susceptibility for 2 as a function of frequency (c). ln(1/τ) vs. 1/T plot for 1 (red) and 2 (blue) (d). Taken with permission from Ref. [26] (colour figure online)

Authors reported complete magnetic characterization of 2. The room temperature χT values of 6.36 cm³ K mol⁻¹ is in accordance with the expected value for one Co(II) ion and one unpaired electron of radical (6.14 cm³ K mol⁻¹). The χT product increases gradually as the temperature is reduced to 100 K, reaching a maximum of 7.60 cm³ K mol⁻¹. Further cooling causes a slow downturn up to the temperature of 10 K when there is a rapid decline (Fig. 6b). This curve shape is explained by high magnetic anisotropy of Co(II) centres and the antiferromagnetic exchange interactions. The χT vs. T function was fitted according to spin Hamiltonian, which resulted in best fit values D = − 115 cm⁻¹, g_∥ = 2.85 and g_⊥ = 2.09, and they correspond to those obtained by theoretical calculations. The AC susceptibility measurements were performed on a powder sample of the complex to investigate the dynamic magnetic behaviour. Under a zero external magnetic field, there was an apparent frequency‐dependent out‐of‐phase signal up to 25 K (Fig. 6c). The frequency and temperature-dependent data can be reasonably fitted to the extended one-set Debye model to extract the relaxation times at different temperatures. The linear nature of the ln(τ) vs. T⁻¹ plot at temperatures higher than 20 K displays an exponential temperature dependence of the relaxation time. The overall non-linear nature of the ln(τ) vs. T⁻¹ dependency (Fig. 6d) suggests that the relaxation pathway is governed not only via single Orbach process but also the Raman term must be involved in the fitting procedure, which resulted in values τ₀ = 2.4 × 10⁻¹⁰ s, U_eff = 267 K, C = 0.9 s⁻¹ K^−1.20, and n = 1.20. The obtained energy barrier is in perfect agreement with the value expected from the D parameter, which was found by fitting the DC susceptibility. In addition, compound 2 exhibits an evident hysteresis at temperatures up to 15 K, which is relatively rare in Co(II) SMMs [27,28,29,30]. The hysteresis was the widest at fields between 100 Oe and 20,000 Oe, indicating that magnetisation's relaxation is slower at that region than under a zero field. Concerning this, authors also performed relaxation studies of saturated sample of 2 at applied various DC fields that belong to the wider hysteresis region. At first, the compound was exposed to a high magnetic field to reach the saturation, and then the field was rapidly decreased down to desired end value from the range 500 Oe–10000 Oe and the decay of magnetization was measured in the progress of time. The data of magnetization decay fitting confirmed that the relaxation time values are growing notably with the strength of the external field. The longest relaxation time was reached at the external DC magnetic field 1500 Oe with an unusually high value of 32,000 s.

Mitsuhashi et al. [31] have studied hydrogen-bonding interactions and magnetic relaxation dynamics in tetracoordinate Co(II) SIMs. Three tetracoordinate Co(II) complexes with a series of asymmetric (N and O-donor) bidentate ligands were synthesized and characterized. The authors reported that even though the static magnetic properties of the compounds are comparable, their dynamic magnetic properties are significantly different, and depend indirectly on intermolecular hydrogen-bonding interactions. The complexes 3 ([Co(L3)₂]·CH₃OH), 4 ([Co(L4)₂]), and 5 ([Co(L5)₂]), where L3 = 2-(1H-imidazol-2-yl)phenolate, L4 = 2-(4,5-dihydro-1H-imidazol-2-yl)phenolate, and L5 = 2-(1,4,5,6-tetrahydropyrimidin-2-yl)phenolate were prepared via reaction of Co(II) salt and corresponding ligand in the 1:2 ratio in methanol (3 and 4) or ethanol (5). According to single crystal X-ray analysis, the Co(II) ion is surrounded by two oxygen and two nitrogen atoms of bidentate ligands (Fig. 7a). The coordination geometry diverges from ideal tetrahedral geometry.

Fig. 7

Molecular structure of 5. Colour code: Co—blue, O—red, N—violet, C—grey (a). Temperature dependence of the χT product for 5 in an applied DC field of 5000 Oe (red circles). The inset—field dependence of the magnetization for 5 at 2, 4, 6, and 8 K. The solid points—the experimental data, solid line—fit (b). Temperature dependence of out-of-phase AC susceptibility at 1.9–8.0 K 5 in the absence of the DC field. Lines—guide to the eye (c). Temperature dependence of the relaxation time τ in the absence and presence of the DC field for 5. The dashed lines—fitted lines for a single relaxation process of Raman, Orbach, and QTM. The solid black line—the sum of the relaxation processes (d). Taken with permission from Ref. [31] (colour figure online)

The careful investigation of supramolecular structures of 4 and 5 revealed the formation of 1D chains created by double hydrogen bonds between O and N(H) donor atoms of neighbouring complex molecules. On the other hand, the 2D network formed via hydrogen bonds of complex and methanol molecules was found in the crystal structure of 3. The intersheet distances in the 3 (7.51 Å) are considerably shorter than those observed in the 4 and 5 (ca 9 Å), causing that each molecule of 3 is surrounded by more paramagnetic Co(II) ions in comparison with the complex molecules of 4 and 5. Such paramagnetically rich neighbourhoods in 3 can propagate the noticeable dipolar interactions which support the QTM process. The temperature dependence of magnetic susceptibility displayed similar features for all three complexes. The values of χT product at temperature 300 K were near 2.50 cm³ K mol⁻¹, which is more than the expected value for the S = 3/2 system (1.875 cm³ K mol⁻¹). Nevertheless, these values are still within the conventional range for Co(II) ions with the orbital contribution. Upon lowering the temperature, the χT values remained constant until 70 K and then, the sudden drop was observed, which can be explained by large magnetic anisotropy of the Co(II) centre (Fig. 7b). The magnetization data do not saturate at high fields, which is an implication of the existence of ZFS. The g-factors and the axial ZFS parameters were evaluated by the simultaneous fitting of the temperature and field dependence of magnetization according to the spin Hamiltonian. The acquired parameters showed that D parameters of all complexes are of negative value (− 42 cm⁻¹ for 3, − 38 cm⁻¹ for 4, − 35 cm⁻¹ for 5) and the g_x, g_y values lie in the range of 2.11–2.15, while the g_z values are near 2.50. The dynamic magnetic measurements confirmed the field induced SMM behaviour in all complexes 3–5. For 3, the temperature dependence of τ was satisfactorily fitted with a combination of the phonon-bottleneck-limited direct and Raman processes (τ⁻¹ = BT² + CTⁿ, C = 1.4 × 10^–3 s⁻¹ K⁻⁸, n = 8 and B = 1.84 s⁻¹ K⁻²). Contrarily, complexes 4 and 5 exhibited pronounced frequency dependence on both in-phase and out-of-phase susceptibilities in the presence and absence of an external DC field (Fig. 7c). This slow magnetic relaxation under the zero field is uncommon for tetrahedral Co(II) complexes; however, it is not rare, since it has been already reported for the few tetrahedral complexes [26, 32,33,34,35]. Analysis of dynamic magnetic behaviour of both complexes 4 and 5 at zero field revealed the dominant contribution of QTM mechanism to the SRM. However, this feature was suppressed by the exposure of optimal static magnetic field 400 Oe (4) and 800 Oe for (5). The temperature dependence of τ was successfully fitted to Raman process (compound 4, C = 1.2 × 10^–2 s⁻¹ K^−6.6, n = 6.6) and to combination of the Orbach and Raman processes (compound 5, U_eff = 89 K and τ₀ = 6.4 × 10^–10 s, C = 6.18 × 10^–4 s⁻¹ K^−6.3, n = 6.3, Fig. 7d). It is worth noting that the value of the effective energy barrier for 5 is in good agreement with expected values calculated from D parameter (U_eff = 101 K). Since the static magnetic measurements confirmed similar magnetic anisotropy or the exchange interactions for complexes 3–5, the significant differences in relaxation of magnetisation were brought the attention. Authors attributed such divergent dynamic magnetic properties at zero and non-zero static magnetic fields to the different intermolecular interactions forming the above mentioned 1D and 2D hydrogen bonded networks. Such different supramolecular architecture has a strong influence on the mechanisms of the SRM in structurally similar SIMs 3–5.

Yang et al. [36] have studied the field induced slow magnetic relaxation behaviour in the phosphine oxide ligand-based tetrahedral Co(II) complexes modified by terminal ligands. The authors synthesized two isostructural mononuclear Co(II) complexes 6 and 7 of the formula [Co(L6)(NCS)₂] and [Co(L6)(NCO)₂], respectively, where L6 = 9,9-dimethyl-4,5-bis(diphenylphosphinyl)xanthene. The number of tetrahedral Co(II) SMMs based on ligand L6 or similar phosphine ligands have been already reported [37, 38], although this kind of ligands is more commonly used in the field of lanthanide luminescence complexes [39,40,41]. Complexes 6 and 7 were prepared by the complexation of ligand L6 with Co(ClO₄)₂·6H₂O and KNCS or KNCO, respectively, in a mixture of acetonitrile and THF (1:2). Both complexes contain distorted tetrahedral coordination environments, where the central ion is coordinated by two oxygen atoms of bidentate ligand L6 and two nitrogen atoms from terminal NCS⁻ or NCO⁻ ligands (Fig. 8a). In addition, no significant intermolecular H‐bonds and π–π interactions were found in the crystal structures of complexes. The DC magnetic measurements were performed and the temperature dependence of magnetic susceptibility under an external magnetic field of 0.1 T showed the room temperature χT values of 2.62 and 2.75 cm³ K mol⁻¹ for 6 and 7, respectively. These values are considered to be larger than the spin‐only values for a high‐spin Co(II) ion with S = 3/2 and g = 2, which can be explained by the notable spin‐orbit coupling of the tetrahedral Co(II) centres. The curve of χT product constantly declines upon cooling to 40 K, where is observed a sudden drop down to values of 1.69 and 1.72 cm³ K mol⁻¹ for 6 and 7, respectively (Fig. 8b). Isothermal field-dependent magnetization measurements were collected at temperatures of 2, 3, and 5 K. The magnetization does not show the saturation at high fields, the largest values of magnetization at the lowest temperature are 2.65 and 2.56 μ_B for 6 and 7, respectively. The static magnetic data are similar for both complexes and indicate significant magnetic anisotropies. The data were fitted to spin Hamiltonian and the best fits revealed values g = 2.29 and D = − 7.1 cm⁻¹ for 6 and g = 2.39 for and D = 12.6 cm⁻¹ for 7. Therefore, the axial magnetic anisotropy for 6 and transverse magnetic anisotropy for 7 was suggested. The calculated ab initio values of D and g are in good agreement with experimental data. Although the AC magnetic data confirmed field induced SMM behaviour in the case of both complexes (Fig. 8c), the field induced SRM displays different anisotropies for the complexes. The temperature and frequency AC susceptibility data were fitted to the modified one-set Debye model, since only one peak of the out-of-phase AC susceptibility was observed. Authors claim that relaxation features of 6 are comparable with the slow relaxation of already reported similar similar SIMs 8 [37] of the structure [Co(L7)(NCS)₂] (L7 = 9,9-dimethyl-4,5-bis(diphenylphosphino)xanthene), for which were obtained ZFS parameters g = 2.27, D = − 16.2 cm⁻¹ and parameters of Orbach process U_eff = 30 K and τ₀ = 6.2 × 10⁻⁶ s. In the next, the authors report that temperature dependence of τ of 7 can be fitted using the combination of Raman and Orbach processes with the values of U_eff = 39 K, n = 4, C = 24 and τ₀ = 1.1 × 10⁻¹¹ s (Fig. 8d). It is worth mentioning that the experimental energy barrier against the magnetization switch corresponds with the calculated value (U_eff = 42 K). The study was investigating the reason why dynamic magnetic data were so different for the structurally similar complexes 6 and 7 and the authors explained that although the complexes are isostructural, there are some minor differences present. For instance, while the Co−O and Co−N distances of 6 and 7 (1.95 Å) are similar, the angles between N−Co−O bonds differ significantly for the complexes. Therefore, the geometry of complex 7 is closer to a tetrahedral symmetry compared to 6. As it has been already reported [24, 25, 42,43,44], the magnetic anisotropy of tetrahedral Co(II) complexes is highly responsive to the strength of the ligand field and, thus, the ZFS parameters can be easily modified by substituting terminal ligands. In the case of the reported work, the substitution from NCS⁻ to NCO⁻ changes the sign of D parameter from negative to positive. Therefore, those findings demonstrate attempts for the rational strategy to modify the magnetic anisotropies of Co(II) SIMs.

Fig. 8

Structure of complex 7 with hydrogen atoms omitted for clarity (a). Temperature-dependent χT of 6 (black) and 7 (red) under a 1000 Oe applied DC field. Open circles = experimental data, solid lines = fit (b). Frequency-dependent in-phase and out-of-phase AC susceptibility plots for 7 under a DC field of 800 Oe. Solid lines = fit (c). Temperature-dependent relaxation time of complex 7 (solid line = fit) (d). Taken with permission from Ref. [36] (colour figure online)

Hrubý et al. [45] were investigating Co(II) based SIMs with organometallic ligand L8 (1,1′-ferrocenediyl-bis(diphenylphosphine)). The authors were focusing on the preparation, spectral and magnetic characterization of two heterobimetallic Fe(II)–Co(II) coordination compounds 9 and 10 of the formulas [Co(L8)Cl₂], [Co(L8)Br₂]. The complexes were synthesized by the reaction of the ferrocene ligand L8 and corresponding Co(II) salt. Although the structure of complex 10 is new, the synthesis and structure of 9 have been reported previously [46, 47]. In all three compounds, the central Co(II) ion is surrounded by two P atoms from diphenylphosphine groups of ligand L8 and two halide terminal ligands (Fig. 9a). The compounds 9 and 10 crystallize in the triclinic space group P1̅ and they are both isostructural with each other with the distorted tetrahedral coordination geometry of complexes. Since both structures lack significant non-covalent interactions and the closest Co⋯Co distances are 9.61 and 9.68 Å in 9 and 10, respectively, the presence of magnetic exchange coupling or the dipolar interactions are not likely present. The high-frequency electron paramagnetic resonance (HF-EPR) spectroscopy data were collected (Fig. 9b) and after the ab initio simulations procedure revealed the values of zero-field splitting parameters and g-tensor are D = − 12.0 cm⁻¹, E/D = 0.10, and g_x = 2.20, g_y = 2.20, g_z = 2.28 for the complex 9 and D = − 11.2 cm⁻¹, E/D = 0.09, and g_x = 2.22, g_y = 2.22, g_z = 2.31 for 10. DC magnetic measurements revealed similar magnetic behaviour for both complexes 9 and 10. At room temperature, the values of the effective magnetic moment (4.4–4.5 μ_B) are larger than spin only value for this system (3.87 μ_B). Upon cooling, the values remain constant until 20 K and then they exhibit a rapid drop to a minimal value of 3.5 and 3.7 μ_B for 9 and 10, respectively. Such a sudden decrease can be explained by the large magnetic anisotropy of the Co(II) ion (Fig. 9c). The magnetic data were fitted to spin Hamiltonian, which confirmed the axial magnetic anisotropy in compounds 9 and 10, and the values of D and g parameters were following calculated values as well as those obtained from HF-EPR measurements. Dynamic magnetic measurements revealed field-induced SMM behaviour for both complexes 9 and 10 and thus, the AC susceptibility was measured at B_DC = 0.1 T (Fig. 9d). Then, the data were fitted by the one-component Debye model, because there was only one frequency-dependent peak of the out-of-phase magnetic susceptibility. The temperature dependency of relaxation times was successfully analysed with the single Orbach process in both cases with the parameters τ₀ = 5.2 × 10⁻⁹ s, U_eff = 33 K for 9, and τ₀ = 1.8 × 10⁻⁹ s, U_eff = 29 K for 10. It is worth noting that the values of U_eff are in very good agreement with the calculated from the HF-EPR analysis as well as with the experimental magnetic data. What is further interesting about this publication, the authors performed deposition of the 10 on surfaces, such as Au(111), glass, and acetate. This deposition is important from the technological point of view in the further development of devices based on SMMs. They used two techniques: a thermal sublimation in high-vacuum and a drop-casting under an inert nitrogen atmosphere. While they deposited the complex by drop-casting under inert nitrogen atmosphere successfully, the technique of thermal sublimation was not fully successful due to partial decomposition of the complex, which was moisture sensitive. Therefore, the authors suggested that the nano-structuration of these systems should be operated by introducing functional groups allowing the chemisorption from diluted solution and promoting the formation of monolayers on surfaces [45].

Fig. 9

Molecular structure of 9 (a). HF-EPR spectra of 9 (b). DC magnetic data of 9 (c). AC susceptibility data for 9 (d) [45]

Vaidya et al. [48] studied structural characterization and magnetic properties in the series of mononuclear four-coordinate thiourea Co(II) complexes. Four complexes 11 ([Co(L9)₄](NO₃)₂), 12 ([Co(L10)₄](ClO₄)₂), 13 ([Co(L11)₄](ClO₄)₂), and 14 ([Co(L12)₄](ClO₄)₂), where L9 = thiourea, L10 = 1,3-dibutylthiourea, L11 = 1,3-phenylethylthiourea, and L12 = 1,1,3,3-tetramethylthiourea, were prepared by the reaction of Co(NO₃)₂·6H₂O or Co(ClO₄)₂·6H₂O and corresponding ligand in ethyl acetate or alcoholic solution. Single crystal X-ray diffraction measurements revealed that complexes 11 and 14 crystallise in the monoclinic space groups Pc and P2₁/c, respectively, whereas the remaining complexes 12 and 13 crystallize in the triclinic space group P1̅. Furthermore, all complexes adopt a distorted tetrahedral geometry with the central ion surrounded by four sulphur atoms of monovalent ligands (Fig. 10a), where the Co−S distances range from 2.30 to 2.31 Å for the series. DC magnetic susceptibility measurements at room temperature give values of χT = 3.10, 3.03, 3.08, and 2.60 cm³ K mol^–1 for compounds 11–14, respectively, which are clearly higher than the expected spin-only value for mononuclear Co(II) system. χT data for all complexes display a downturn at low temperature, suggesting the presence of significant magnetic anisotropy. The low-temperature magnetization measurements at various applied DC fields were performed at 2, 4, and 8 K, saturating to values of 2.25, 1.99, 1.95, and 2.07 μ_B for 11–14, respectively, at the lowest temperature and high fields, which also suggest the significant ZFS (Fig. 10b). The values of D extracted from fitting of magnetic data were found to be negative in the range from –21.3 cm⁻¹ for 14 to – 80.7 cm⁻¹ for 12. Temperature- and frequency-dependent AC susceptibility data were collected to confirm SMM behaviour of all four compounds. The χ′′ signal for 11–13 was observed even in the absence of an applied DC field, while 14 was proved to be a field-induced SIM. The data of 11 show two relaxations processes, a fast one is operative below 3 K and slow one in the temperature range 3.5 and 10 K (Fig. 10c). The authors attributed the fast process to QTM, whereas the slower one is identified as a thermally activated process in which the relaxation is governed via Orbach process with parameters U_eff = 28 K and τ₀ = 7.6 × 10^–7 s of comparable values to already reported values for tetracoordinated Co(II) complexes [24, 25, 49]. Compound 12 also exhibits two relaxation processes at the zero DC field, although the values of an effective energy barrier and relaxation time estimated from the Arrhenius plot are larger (U_eff = 46 K and τ₀ = 2.2 × 10^–6 s). Since both compounds 11 and 12 show some intermolecular hydrogen bonding networks, which may affect the relaxation features, the diluted samples (solid solutions of 10% Co(II) samples with 90% of the corresponding Zn(II) analogues) were prepared to supress fast QTM and bring more light to the relaxation dynamics. In both cases, the analysis showed that intermolecular interactions effectively contribute to quenching the QTM in the absence of DC field (Fig. 10d). The peaks of the thermally activated processes were better resolved and the increase of the energy barrier values to 47 K and of 89 K for 11 and 12, respectively, was observed. The AC data for compound 13 differ considerably from the other reported complexes and they reveal more out-of-phase susceptibility peaks in the absence of DC field, which are not resolved and this led to collecting data at 2000 Oe DC field to find more resolved peaks. After extraction from the Arrhenius plot, the effective energy barrier and the relaxation time were detected to be U_eff = 27 K and τ₀ = 1.6 × 10^–6 s. Unlike the compounds 11–13, the AC measurements of 14 did not show out-of-phase susceptibility without the presence of DC field. After analysis of the AC data collected at 0.2 T field, effective energy barrier and relaxation time were found to be of the values 19 K and 3.2 × 10^–8 s. Since there are more relaxation mechanisms, such as Raman and QTM, the experimental energy barriers are lower than theoretically expected values for all four complexes.

Fig. 10

Molecular structure of complex cation of 11. Colour code: Co—blue, S—yellow, N—violet, C—grey (a). DC magnetic data for 11 (b). Frequency-dependent out-of-phase susceptibility data for 11 in the absence DC field (c). Frequency-dependent out-of-phase susceptibility data for 10% diluted sample of 11 in the absence of DC field (d). Taken with permission from Ref. [48] (colour figure online)

Pentacoordinate and hexacoordinate Co(II) complexes

The group of Richeson [50] studied SMM behaviour enhanced through peripheral ligand modification. They used tridentate bis(imino)pyridine pincer ligands in conjunction with two isothiocyanate ligands to prepare two mononuclear Co(II) complexes. The rigid and planar pincer ligands favour a square pyramidal geometry rather than trigonal bipyramid. That would induce a larger zero-field splitting D parameter. Furthermore, the scientists introduced phenyl substituents in the imine positions expecting that this step can affect the geometry of the coordination environment by inducing of higher degree of distortion and pulling of the Co(II) ion out of the basal plane. According to authors, the Co(NCS)₂ reacted directly with ligands L13 (2,6-bis[1-[(2,6-diisopropylphenyl)imino]ethyl]pyridine) or L14 (2,6-bis[1-[(2,6-diisopropylphenyl)imino]benzyl]pyridine). Nearly quantitative yields of green compound 15 of formula [Co(L13)(NCS)₂] and brown–green compound 16 of formula [Co(L14)(NCS)₂] were prepared. The pentacoordinate Co(II) ion adopts distorted square pyramidal geometries (Fig. 11a) in both compounds. In 15, the central atom sits above the basal plane by 0.39 Å. Introduction of phenyl substituents in 16 caused more visible distortion with the metal centre lying out of the basal plane by 0.52 Å. Neither of the prepared complexes shows relevant intermolecular contacts; however, compound 16 displays an interesting packing arrangement. Although Co(II) ions are separated by 8.67 Å, the S2 atom of apical isothiocyanate is oriented towards the open face of the adjacent metal centre along the C-axis (Fig. 11b). The methyl analogue does not show that kind of long-distance interaction, and the shortest metal–metal distances were found to be 9.90 Å.

Fig. 11

Structure and selected atom numbering scheme of compounds 15 (a—left) and 16 (b—right). Hydrogen atoms and co-crystallized solvents omitted for clarity (a). The intermolecular interactions for compound 16 (b). Taken with permission from Ref. [50] (colour figure online)

The variable temperature DC susceptibility for both compounds was measured at a field of 1000 Oe and over the temperature range 2–300 K (Fig. 12a). According to expectations, the χT value remained constant up to 100 K, and then started to decrease with decreasing temperature. Such continual decrease up to 2 K was observed for 15 and is related with ZFS. However, the χT value of complex 16 reaches the lowest value 2.48 cm³ K mol⁻¹ at 12 K, then starts to increase up to 3.21 cm³ K mol⁻¹ at 3 K and again drops down to 3.03 cm³ K mol⁻¹ at 2.5 K. Such magnetic behaviour is attributed to ferromagnetic exchange coupling mediated through intermolecular interactions, which can be suppressed by dilution of sample. Thus, compound 16 was dissolved in THF and further DC susceptibility measurements were performed on a frozen solution below 50 K (Fig. 12a, red dots). The 16-S curve is in accordance with expectations, it shows a smooth decrease in χT with decreasing temperature reaching 2.1 cm³ K mol⁻¹ at 2.5 K. The absence of increase of χT in the measurement of dissolved sample proves that observed behaviour in the solid state sample of 16 has origin in the intermolecular interactions between the highly anisotropic spin carriers. The field dependence of the magnetization of 15, 16, and 16-S shows no apparent saturation, which can be caused by the presence of magnetic anisotropy. Unfortunately, the authors report that several attempts to fit the reduced magnetization data were unsuccessful, and more sophisticated software needs to be employed to achieve proper fits. On the other hand, the susceptibility data can be fitted assuming a simple zero-field splitting effect [51, 52], which leads to D values of − 28.1 cm⁻¹ for 15 and − 28.2 cm⁻¹ for 16, suggesting a considerable uniaxial anisotropy. To confirm SMM behaviour, temperature and frequency dependence of the AC susceptibility were measured in the temperature range from 2 to 10 K for both compounds. The optimum fields of 700 and 2000 Oe for 15 and 16, respectively, were found. However, to bring more light in comparison of energy barriers of both complexes, further AC measurements were performed under the same 2000 Oe field for all samples (Fig. 12b–d). The fitting procedure according to a thermally activated Orbach process resulted in following parameters: U_eff = 16 K, τ₀ = 3.6 × 10^–6 s for 15, U_eff = 24 K, τ₀ = 5.1 × 10^–7 s for 16, and U_eff = 25 K, τ₀ = 6.6 × 10^–6 s for 16-S. Similar data obtained from solid 16 and frozen solution 16-S confirmed that SRM has a molecular origin.

Fig. 12

Temperature dependence of the χT product at 1000 Oe for complexes 15 (blue) and 16 (black), red dots 16-S are for a THF solution sample of 16 (a). Variable-frequency out-of-phase AC susceptibility data collected over the temperature range 2–10 K under an applied field of 2000 Oe for 15 (b), 16 (c), 16-S (d). Taken with permission from Ref. [50] (colour figure online)

The group of Konar [44] also published an article dealing with the impact of the ligand field and coordination geometry on the magnetic anisotropy of pentacoordinate Co(II) based SIMs. The idea was to tune the magnetic anisotropy and dynamics of relaxation processes by variation of terminal ligand anions around the metal centre. Complexes 17, 18, and 19 of formulas [Co(L15)Cl₂]·(MeOH), [Co(L15)(NCS)₂], and [Co(L15)Br₂]·(MeOH), respectively, were synthesized via complexation of ligand L15 (2,6-bis(2-benzimidazol-1-yl)pyridine) with corresponding Co(II) salts and all reactions yielded green crystals after slow evaporation of the solvent. The structural analysis shows that the five-coordinate Co(II) centres adopt geometries which are best defined as distorted square pyramid for 17 and 19 and as trigonal bipyramid for 18. Both complexes 17 and 19 are isostructural with each other, the crystal structure of 18 presents Fig. 13a. Magnetic susceptibility studies (Fig. 13b) were carried out for all complexes under a 1000 Oe field. At 300 K, the χT values of 2.57, 2.39, and 2.28 cm³ K mol^–1 were observed for 17, 18, and 19, respectively, which are higher than the expected spin-only value for the HS Co(II) centres. The typical values for anisotropic Co(II) complexes are in the range of 2.1–3.4 cm³ K mol^–1 [53]. Upon the cooling, the χT values are stable up to 60 K, below which there is a sudden drop caused by ZFS, reaching values of 1.69, 1.52, and 1.46 cm³ K mol^–1, for 17, 18, and 19, respectively, at 2 K. Reduced magnetization data values are lower than the theoretical saturation for an S = 3/2 system and do not saturate at high fields. Density functional theory (DFT) calculations give positive D parameters (11.1 cm⁻¹, 8.4 cm⁻¹, and 7.8 cm⁻¹ for 17, 18, and 19, respectively), which are matching with the experimental ones (14.5 cm⁻¹,10.7 cm⁻¹, and 8.4 cm⁻¹ for 17, 18, and 19, respectively). According to authors, those values differ from the most of to date reported SMM, where D parameter is negative. The AC susceptibility data (Fig. 13c) of all complexes revealed the SMM behaviour, although the signal was not detected at a zero DC field. The data were fitted by one-set Debye model. The effective energy barrier and relaxation times were calculated using the Arrhenius equation for thermally activated process and give U_eff of 17, 18, and 19 of 20 K, 10 K, and 8 K, respectively. The relaxation times τ₀ are on the order of 10^–5 s, which are typical for Co(II) HS complexes. ln(1/τ) vs. 1/T plot for complex 18 as well as best fits of the Arrhenius equation is in Fig. 13d.

Fig. 13

Molecular structure of complex 18 (a) χT vs. T plots measured at 1000 Oe for 18 (b). The out-of-phase AC susceptibility for 18 as a function of the frequency (c). ln(1/τ) vs. 1/T plot for complex 18. The red line is the best fit of the Arrhenius relationship (d). Taken with permission from Ref. [44] (colour figure online)

Similarly, the group of Boča [54] has prepared, structurally and magnetically characterized two complexes of [Co(L15)X₂]·DMF type. Tridentate N-donor ligand L15 has been synthesized via reaction of pyridine-2,6-dicarboxylic acid and o-phenylenediamine in phosphoric acid. Reported complexes in polycrystalline form were prepared by the complexation of L15 with corresponding anhydrous Co(II) salt in THF and the single crystals of both complexes were grown from DMF solvent. Both complexes are isostructural and isomorphic with each other and crystallize in monoclinic crystal P2₁/n space group. In the crystal structures, the π−π stacking with centroid distances ca. 3.6 Å between the pyridine rings can be found. The τ₅ parameter equals 0.02, which means that the coordination chromophore adopts shape close to square pyramid. The molecular structure of [Co(L15)Cl₂]·DMF (20) is shown on Fig. 14. Although the structure and static magnetic properties of 20 were already reported before [55, 56], the authors measured it again for the sake of better comparison with the data of 21. Two effects are visible in the temperature dependency of μ_eff for complex 21. Upon the cooling from room temperature, μ_eff slightly decreases due to the presence of temperature-independent paramagnetism. Such decrease becomes more pronounced in the low temperature region (< 50 K), where the ZFS effect becomes visible. The field-dependent magnetization was measured at constant temperature of 2.0 and 4.6 K, respectively. The magnetization per formula unit at T = 2.0 K and high fields saturates to the value of 2.26 μ_B. This is lower than expected value of 3 μ_B which can be addressed again to zero-field-splitting. The values of calculated D parameter by ZFS fitting model are 58.4 cm^–1 and + 47.0 cm⁻¹ for 20 and 21, respectively.

Fig. 14

Molecular structure of complex 20 (a). DC magnetic data for 20. The lines are fitted by ZFS model (b). Taken with permission from Ref. [54]

Fig. 15

AC susceptibility and as function of the frequency at B_DC = 0.2 T (top a) and B_DC = 0.4 T (bottom a) and ln τ as a function of 1/T (b) for 20. The out-of-phase susceptibility component (c) and the Arrhenius-like plot (d) for 22. Solid lines are fitted using a two-set Debye model. Taken with permission from Ref. [54]

Interesting findings concerning the SRM of 20 were reported. Since the highest response of out-of-phase component $\chi^{\prime\prime}$ of AC susceptibility varies with the applied static magnetic field, the frequency- and temperature-dependent AC susceptibility measurement was investigated at two different static fields − 2000 and 4000 Oe (Fig. 15). Furthermore, the $\chi^{\prime\prime}$ component of AC susceptibility as function of frequency displays two maxima, which means that magnetization relaxes via two low-frequency (LF) and high-frequency (HF) relaxation channels. Therefore, dynamic magnetic data were analysed using two-set Debye model, which allowed to evaluate two different relaxation times τ(LF) and τ(HF). The observed two relaxation processes behave differently while increasing temperature. Although the faster HF branch of relaxation time diminishes with temperature, the τ(LF) of slower LF channel retains almost constant with the temperature. To bring more light into the relaxation processes, the doped complex 22 ([Co_0.37Zn_0.63(L15)Cl₂]·DMF) containing the solid solution of 20 with Zn(II) diamagnetic analogue has been prepared. Such dilution with diamagnetic matrix causes the isolation of Co(II) complex molecules from each other and it abrogates the intermolecular interactions between the paramagnetic centers in that way. Surprisingly, the appearance of the LF relaxation channel in 22 was significantly suppressed which proves that its origin is conditioned by the intermolecular interactions and it does not have a molecular origin. Authors reported that both studied complexes 20 and 21 exhibit field-supported single-molecule magnet behaviour with values of effective barrier U_eff around 30 K and relaxation time τ₀ of the order of 10^–8 s, which is in agreement of characteristic values for HS Co(II) complexes.

The previously mentioned papers [44, 54,55,56] have been investigating structure and magnetic properties of pentacoordinate Co(II) complexes with the same tridentate N donor ligand L15 and two halido or pseudohalido terminal ligands. The complexes 17 together with 20 and 19 together with 21 have the same molecular structure, the only difference is the presence or absence of solvent molecule in the crystal structure. Furthermore, the complexes 17, 20, 19, and 21 are isostructural with each other. The calculated Addison parameters τ₅ [57] are in the range from 0.02 to 0.27 and suggest that coordination polyhedra adopt the shape of distorted square pyramid. The experimental values of D parameter are positive for all complexes, although the D for complex 20 and 21 were found to be significantly higher (58.4 and 47.0 cm⁻¹) than for complexes 17 and 18 (14.5 and 10.7 cm⁻¹, respectively). Nevertheless, the relaxation properties reported in those papers differ significantly. The authors agreed that the Orbach process is not enough for describing of their dynamic magnetic behaviours and other processes should be taken into the consideration. Moreover, Rajnák et al. [54] found two relaxation channels in the complexes 20 and 21, where the slow LF relaxation channel has been connected with the presence of intermolecular interactions.

The same group has studied structural and magnetic properties of five pentacoordinate 2,6-bis(pyrazol-1-yl)pyridine–cobalt(II) complexes exhibiting field-induced slow magnetic relaxation [58,59,60]. The halogenated tridentate ligand 4-iodo-2,6-bis(pyrazol-1-yl)pyridine (L16) has been employed for the Sonogashira cross-coupling reaction which allowed to form ligands L16–L20 bearing the n-pentylacetylene, n-octylacetylene, n-decylacetylene, and n-dodecylacetylene substituents on 2,6-bis(pyrazol-1-yl)pyridine moiety. Then complexes were prepared via following procedure: the corresponding ligand and CoCl₂·6H₂O were stirred and heated in acetonitrile solution and the blue crystals were grown by slow evaporation. Structural analysis revealed solvent-free structures of complexes 23 ([Co(L16)Cl₂]) and 27 ([Co(L20)Cl₂]), although complexes 24 ([Co(L17)Cl₂]), 26 ([Co(L19)Cl₂]), and 25 ([Co(L18)Cl₂]) consist of the neutral complex molecules together with one, two and three CH₃CN solvent molecules, respectively. All complexes crystallize in monoclinic space group P2₁/c except 26, which belongs to the orthorhombic crystal system (Pbca). The supramolecular properties of these compounds are also worth mentioning. 23, 24, and 27 form supramolecular dimers through short π–π contacts, while remaining two form infinite chains that are held by π–π stacking. There is no clear correlation of supramolecular interactions with the length of the alkyl tail of the antenna-like ligand. These pentacoordinate complexes adopt the shape of a square pyramid and the τ₅ parameter ranges from 0.01 to 0.15 in terms of complexes 23, 24, 27 and from 0.35 to 0.45 relating to 25 and 26. The crystal packing of some complexes is viewed on Fig. 16. The value of effective magnetic moment for 25 and 27 remained steady while decreasing temperature. However, below 100 K the curve drops due to the ZFS of Co(II) centers and then it arises again because of ferromagnetic interactions. This kind of behaviour is similar to complex 24, although opposite to the magnetic data observed for 23 and 26. The DC magnetic data were fitted using an isotropic exchange model with single-ion anisotropy. The calculated D parameters for these complexes range from − 119 to 44.2 cm⁻¹. The AC susceptibility measurements confirm that the SMM behaviour of reported complexes is observed. Two relaxation channels were observed for all compounds.

Fig. 16

Crystal packing of complex 23—linked dimers (a) and 25—infinity network through π–π stacking (b). Colour code: Co—blue, I—purple, N—violet, C—grey, Cl—green. DC magnetic data of complex 23 (c) and complex 25 (d). Taken with permission from Ref. [58] (colour figure online)

The Fig. 17a, c shows AC data of complexes 23 and 24, respectively. An extended one-set Debye model was used in to fit the frequency dependence of the AC magnetic susceptibility. As it can be seen from Fig. 17, the observed two relaxation processes are behaving differently while increasing temperature. According to expectations, the peak of faster branch of relaxation time decreases with temperature. However, the slower relaxation channel initially tends to reduce its value with the temperature and then sudden recovery occurs. The faster relaxation time was characterized using Orbach, direct and Raman processes. In opposite to slower relaxation time, it exhibits typical features of SRM for related complexes. The effective barriers U_eff range from 15 to 41 K and the relaxation times τ₀ for the Orbach processed are of the order of 10^–7 s.

Fig. 17

AC susceptibility data for 23 (a, b) and 25 (c, d) at B_DC = 0.2 T. Taken with permission from Ref. [58]

Murugesu and co-workers [61] investigated influence of the ligand field on the SRM along with spin crossover (SCO) effect in mononuclear Co(II) complexes. They were mostly interested in the systems, with the possibility of performing fine-tuning of the ligand field by controlling of the number of coordinated terpyridine ligands (L21) and remaining terminal ligands to induce SIM or SCO behaviour. The authors prepared two pentacoordinated complexes [Co(L21)Cl₂] (28), [Co(L21)(NCS)₂] (29) and one hexacoordinated compound [Co(L21)₂](NCS)₂∙1.5H₂O (30). This offered a great opportunity to compare magnetic properties in penta- and hexacoordinated Co(II) compounds. The complex 28 was prepared by direct reaction of anhydrous CoCl₂ and L21 in THF solution and the green prisms suitable for X-ray measurements were obtained by recrystallization from dichloromethane solution. Compounds 29 and 30 were prepared by reaction of Co(NCS)₂ and L21 in dichloromethane and this reaction resulted in green precipitate and brown solution. The green powder was dissolved in DMF/acetone mixture and the slow diffusion of ether allowed the formation of single crystals of 29. The remaining brown solution was used for slow diffusion of cyclohexane, which resulted in the formation of single crystals of 30.

In complex 28, the Co(II) ion is elevated with respect to the plane formed by three N atoms of ligands L21 and coordination polyhedron forms distorted square based pyramid. On the other side, the metal centre in 29 is placed within the plane of L21 causing trigonal bipyramidal shape. The six-coordinate compound 30 adopts distorted octahedral geometry (Fig. 18).

Fig. 18

Molecular structures of [Co(L21)Cl₂] (28) (a); [Co(L21)(NCS)₂] (29) (b); [Co(L21)₂]²⁺ (30) (c). Hydrogen atoms, counterions, and solvent molecules are omitted for the sake of clarity. The plane, which is composed of the three N atoms of L21 (28 and 29) along with the polyhedron around the Co(II) ion (30), is displayed shaded (right). Taken with permission from Ref. [61]

In compounds 28 and 30, the intermolecular π–π stacking of distance between aromatic rings 3.79 Å and 3.70 Å, respectively, is observed. Complex 29 shows a parallel alignment of Co(II) centres with a length of 3.66 Å between terpyridine ligands centroids. DFT calculations revealed HS ground state for complexes 28 and 29. On the other hand, coordination compound 30 containing the complex cation [Co(L21)₂]²⁺ with two tridentated ligands is stabilized in the low-spin state at low temperatures and above 100 K exhibits the gradual SCO, which does not reach the high-spin plateau at high temperatures (Fig. 19). The χT reaches 1.39 cm³ K mol⁻¹ at 350 K corresponding to 68% of Co(II) metal centres in HS state. Thus, the SRM in 30 is not expectable.

Fig. 19

a Temperature dependence of the magnetic susceptibility for complexes 28 (blue), 29 (green), and 30 (black). Fitted lines are red. b Powder EPR spectra and simulations for complexes 28 (a) and 30 (b); Exp. 1 (blue) was performed at 2.5 K; Exp. 2 (red) was completed several months later on the same powder pellet, at 20 K. Inset: Expanded view of the spectra. Taken with permission from Ref. [61] (colour figure online)

χT vs. T plot proves the high-spin state behaviour of pentacoordinate complexes 28 and 29 (Fig. 19), where the low temperature decrease of χT function is attributed to the presence of high magnetic anisotropy [53, 62]. The values at 300 K are 3.34 cm³ K mol⁻¹ and 2.66 cm³ K mol⁻¹ for 28 and 29, respectively. The M vs. H and M vs. HT⁻¹ plots shows no saturation for 28 and 29, which can be explained by the presence of high magnetic anisotropy (Fig. 20). In addition, high-frequency EPR measurements were performed on 28 and 30 (Fig. 19b). While the spectra obtained for 28 span a broad field range indicating high magnetic anisotropy, the spectrum of 30 does not indicate anisotropic metal centre. Values of g for 30 are 2.03–2.19 for S = 1/2, which agrees with results of the magnetic measurements. Moreover, g values for 28 are associated with HS S = 3/2 Co(II) ions.

Fig. 20

Magnetization (M) as a function of field (H) plotted as M vs. H and M vs. HT⁻¹ for complex 28 (a) and 29 (b). Taken with permission from Ref. [61]

The AC magnetic measurements confirmed SMM behaviour of 28 and 29 (Fig. 21), while according to expectations, no slow relaxation dynamics were observed for 30. Furthermore, complexes 28 and 29 exhibit the relaxation of magnetization through two pathways—fats and slow relaxation channels. The relaxation parameters U_eff and τ₀ of the following values were extracted: U_eff = 28 K, τ₀ = 1.1 × 10^–6 s (28) and U_eff = 17 K, τ₀ = 5.9 × 10^–6 s (29) for fast relaxation processes and U_eff = 4 K, τ₀ = 7.4 × 10^–2 s (28) and U_eff = 3 K, τ₀ = 0.1 s (29) for slow relaxation processes. As it apparent from AC data, the change of Cl⁻ ligands for NCS⁻ ligands causes a significant decrease in the energy barrier.

Fig. 21

Frequency (f) dependence of the out‐of‐phase magnetic susceptibility, χ′′, at the indicated applied fields (H) and temperature ranges for 28 (a) and 29 (b). Taken with permission from Ref. [61]

The output of this study revealed that it is possible to control physical and magnetic properties, such as effective anisotropy barrier by tuning ligand field strength around the metal centre as well as its geometry.

The paper of Brachňaková et al. [63] deals with the stereochemistry of coordination polyhedra and its influence on SRM in penta- and hexacoordinate complexes with tridentate N-donor rigid ligands. Authors have prepared a ligand L22 and used it for the synthesis of three neutral pentacoordinate Co(II) complexes and one hexacoordinate Co(II) ionic compound. The L22 was synthesized by the following procedure: L15 (bzimpy) reacted with 3,5-di-tert-butylbenzyl bromide in DMSO solution to form two products (L22 and the minor product L23), which were separated using column chromatography. Complexes 31–33 were prepared by complexation of L22 with corresponding Co(II) salt in acetonitrile solution, whereas 34 was prepared in MeOH solution. Moreover, the authors used small excess of L22 to prevent formation of pentacoordinate complex in the synthesis of hexacoordinate complex compound 34. Single crystal X-ray analysis confirmed the structure of compounds 31–34. The structure of complex 33 is shown in Fig. 22a. The asymmetric unit of structures 31–33 consists of complex represented by the general formula [Co(L22)X₂], where X = NCS⁻, Cl⁻, and Br⁻ for 31, 32, and 33, respectively. The complexes 32 and 33 are isomorphic and isostructural with each other. The asymmetric unit of 34 is expressed by the formula of [Co(L22)₂]Br₂·2CH₃OH·H₂O. The authors studied the geometry of coordination polyhedra of compounds by the continuous symmetry measure methodology. The square pyramidal or vacant octahedral geometries were found to be the closest one for 31. On the other hand, 32 and 33 adopt geometry close to trigonal bipyramid. Moreover, values of τ₅ distortion parameter were calculated (τ₅ = 0.3 for 31, τ₅ = 0.46 for 32, τ₅ = 0.41 for 33) to indicate intermediate geometry between the square pyramidal and trigonal bipyramidal, slightly closer to square pyramidal (τ₅ = 0). Compound 34 exhibits a notable distortion from a perfect octahedral geometry that was determined by angular distortion parameter ∑ = 136.4° [64, 65], calculated from 12 cis angles of the hexacoordinate polyhedron acquiring zero values if ideal octahedral geometry is present. The obtained value is typical for HS hexacoordinate Co(II) complexes with terpy-like N-donor ligands. Authors also reported that crystal structures of 31– 33 contain several π–π interactions between aromatic moieties of neighbouring molecules forming the pseudodimeric couples.

Fig. 22

Molecular structure of 33. Hydrogen atoms, uncoordinated anions and lattice solvent molecules are omitted for the sake of clarity. Colour code: C—grey; N—blue; Cl—green; Br—brown; S—yellow (a). Magnetic data for 33 are shown as the temperature dependence of the effective magnetic moment and as the isothermal magnetizations in the insets. The empty symbols represent the experimental data and red solid lines represent the fitted data (b). Frequency-dependent out-of-phase χ′′ components of AC susceptibility for compound 33 recorded at an applied static magnetic field 3000 Oe. Solid lines represent the fits using the two-component Debye model (c). Temperature dependency of the resulting relaxation times τ₁ of the LF channel and τ₂ of the HF channel recorded at fields 2000 and 3000 Oe. The fits of the resulting relaxation times τ₂ with the combination of the direct and Orbach processes using are viewed as dashed lines and the combination of the Raman and direct processes are viewed as solid lines (d) [63] (colour figure online)

Fig. 23

Molecular structure of 35 (a). Temperature dependence of the effective magnetic moment and molar magnetization measured at B = 0.1 T in the inset, and isothermal reduced magnetizations measured at T = 2 and 5 K. Empty circles: experimental data. Red and full blue lines: calculated data (b). HFEPR spectra of 1 at 5 K and different frequencies (in GHz) (c). Out-of-phase molar susceptibilities for 35 at B_DC = 0.1 T. Full points—experimental data, full lines—fitted data (d). Taken with permission from Ref. [66] (colour figure online)

Magnetic characterization at static magnetic field allowed to evaluate ZFS parameters for all three pentacoordinate complexes. The obtained temperature and field-dependent magnetization data were analysed with respect to spin Hamiltonian and parameters D and E were determined (Fig. 22b). The best fits for pentacoordinate complexes 31–33 were acquired with D in the range from 25 to 39 cm⁻¹ and large rhombicity. Although the positive D parameter usually suggests easy-plane magnetic anisotropy, the large value of E/D indicates that the easy-axis magnetic anisotropy can be present. Indeed, this indication was confirmed by CASSCF/NEVPT2 calculations, which showed axial character of magnetic anisotropy. On the other hand, the ZFS parameters of hexacoordinate Co(II) compound 34 was not possible to determine from the static magnetic measurements. Authors claim that spin Hamiltonian approach is not operative for this system.

The dynamic magnetic measurements confirmed that 31–34 exhibit field-induced slow magnetic relaxation. The collected sets of $\chi ^{\prime}$ and $\chi^{\prime\prime}$ susceptibilities for complexes 31, 32, and 34 were fitted using one-set Debye model, since frequency-dependent susceptibility measurements revealed single-relaxation process. In 31 and 32, however, the low frequency out-of-phase signal suggests the presence of poorly resolved second relaxation channel. The extracted temperature dependencies of relaxation time were fitted to relaxation Eq. (13) aiming the combination of Orbach and direct processes. The best fit parameters U_eff = 24.6 K, τ₀ = 5.9 × 10^–7 s for 31 and U_eff = 18.9 K, τ₀ = 2.9 × 10^–7 s for 32, respectively, are typical for pentacoordinated Co(II) SIMs. The dynamic magnetic data of 33 show the presence of two relaxation channels (Fig. 22c) and they were analysed using the two-set Debye model. The AC susceptibility of complex 33 was measured at four different static magnetic fields to better understand both low-frequency (LF) and high-frequency (HF) channels. In addition, the single HF process obtained at lower fields was analysed using one-set Debye model. The appearance of LF relaxation channel in compound 33 was diminished in the sample dispersed with diamagnetic eicosane and thus, its origin can be connected with the presence of intermolecular interactions. The values of effective barrier and extrapolated relaxation times for 33 were found to be U_eff = 19.1 K, τ₀ = 9.2 × 10^–8 s at 0.05 T and U_eff = 21.22 K, τ₀ = 4.8 × 10^–6 s at 0.3 T (Fig. 22d). They are highly comparable with those obtained for the isostructural chlorido complex 32. The AC susceptibility data for 34 revealed single channel relaxation, which was possible to analyse with the single Orbach process with the values of U_eff and τ₀ are 9.5 K and 6.7 × 10^–7 s, respectively. The authors also mentioned that to bring more light to relaxation processes, they attempted to prepare Zn(II) doped compounds 31–34. Unfortunately, in all four cases the suspension of dissolved Co(II) complex and precipitated hexacoordinated Zn(II) complex was found.

In general, according to previously mentioned papers, the pentacoordinate Co(II) complexes with tridentate N-donor ligands adopt coordination geometry of distorted square pyramid or close to trigonal bipyramid. The D parameters usually lie in the range of − 100 to + 100 cm⁻¹. The effective anisotropy barriers adopt values near 50 K and relaxation times τ₀ are generally of the order of 10^–7 s. Overall, there are several relaxation processes (Orbach, Raman, and direct) usually found in Co(II) SMMs and this makes the magnetic measurements and data extracting very complex. So far, no relations between the coordination geometry, ZFS parameters and AC parameters data were found, although it is clear that even a tiny change of geometry causes the change in dynamic magnetic properties.

Nemec et al. [66] studied field-induced SRM in a mononuclear pentacoordinate Co(II) compound. Although the most pentacoordinate Co(II) SIMs consist of tridentate heterocyclic N-donor ligand and two halido or pseudohalido ligands [60, 61], in this work, the authors reported SMM behaviour of Co(II) complex consisting of bidentate N-donor ligand L24 and three monodentate ligands. The crystal structure and synthesis of compound 35 with the formula [Co(L24)(DMSO)Cl₂] was already published and well described [67]. The authors obtained X-ray quality crystals after dissolving of compound [Co(L24)Cl₂] in DMSO and by slow diffusion of diethylether. In the structure, bond lengths of coordination polyhedron are notably dependent on the nature of the coordinated ligand and vary from 2.052 to 2.356 Å for C–N and C–Cl. Based on the value of Addison parameter τ₅ = 0.54, the shape of coordination polyhedron was found to be somewhere in the middle of the Berry pseudorotation pathway, which describes the transformation square pyramid to trigonal bipyramid. The crystal structure contains weak non-covalent intermolecular interactions, such as π–π stacking and hydrogen bonds. The compound was first characterized at static magnetic field and results of experimental fits were supported by ab initio calculations. The effective magnetic moment adopts significantly higher values (4.84 μ_B) than the expected spin only value for HS Co(II) (3.87 μ_B), which can be explained by the strong contribution of spin–orbit coupling to the ground state magnetic moment. There is a continuous drop of μ_eff below 50 K due to ZFS and both temperature- and field-dependent magnetic data were successfully fitted with negative D parameter (− 17 cm⁻¹) and large rhombicity (E/D = 0.24). The calculated parameters (D = − 17.7 cm⁻¹, E/D = 0.31) are in very good agreement with experimental parameters. Moreover, the g-tensor values were obtained as g₁ = 2.18, g₂ = 2.32, g₃ = 2.46 (g_iso = 2.32). To bring a better estimation of g tensors and D parameter, the HF EPR spectra were recorded although; the authors could not have determined the value of D. The best fits were for E/D = 0.33, g_z = 2.6, g_y = 2.4, g_z = 2.3. The AC susceptibility investigation revealed field-induced SRM with a single relaxation channel. Temperature dependency of relaxation time was successfully analysed by Orbach process with parameters U_eff = 10.4 K, τ₀ = 5.69 × 10^–9 s. The value of the effective anisotropy barrier was found to be much lower than theoretical predictions (U_eff ≈ 55 K), which is considered as common disagreement and it was also observed in a plethora of other reported pentacoordinate Co(II) SIMs [31, 60, 61]. A possible explanation is that lowering U_eff is affected by QTM, which is connected to large rhombicity. In summary, several relaxation processes (Orbach, Raman and direct) are usually found in Co(II) SIMs, making them very complex (Fig. 23).

Woods et al. [68] studied relaxation dynamics of identical bipyramidal Co(II) compounds with different local symmetries and packing arrangements. They reported a family of isostructural, mononuclear Co(II) compounds with trigonal bipyramidal coordination geometry. Tetradentate ligand L25 tris(2-pyridylmethyl)amine was chosen to provide a rigid backbone for Co(II) centres as well as leave one free coordination place. The complexes of formula [Co(L25)(CH₃CN)₆](BF₄)₂ (36), [Co(L25)Cl]Cl (37), [Co(L25)Br]Br (38), and [Co(L25)I]I (39) were reported in the mentioned work, while the ligand L25 and complex 36 were published earlier [69, 70]. Furthermore, by different synthetic approaches was possible to prepare cubic (marked with “c”) and triclinic (marked with “t”) polymorphic phases of 37 and 38. Synthesis of compounds was performed under the dry and inert conditions, where one equivalent of L25 and corresponding Co(II) salt were dissolved in acetonitrile (36, 37c, 38c, and 39) or methanol (37t and 38t). Then, X-ray quality single crystals were obtained by slow diffusion of diethyl ether vapours into the filtrate (36) or by layering with diethylether (37t, 38t, 38c, and 39) with over toluene (37c). Compound 36 crystallizes in the monoclinic space group P2₁/c, 37c and 38c crystallize in cubic space group P2₁3 and 37t, 38t, and 39 crystallize in triclinic space group P1̅. The shapes of coordination polyhedra are distorted trigonal bipyramides and consist of four nitrogen atoms from ligand L25 and the remaining coordination place is occupied either with one nitrogen atom of acetonitrile molecule or corresponding halido donor atom. All reported compounds show similar magnetic properties recorded at the static magnetic field (Fig. 24b). The room temperature χT values are higher than expected for S = 3/2 system with g = 2, which is an indication of orbital momentum contribution to the overall magnetization of compounds. The decrease of χT values is apparent in the low temperature region, which is the fingerprint of ZFS. M vs. H measurements at 1.8 K did not saturate at the highest available field, which is another indication of the high anisotropy of the systems. The fitting procedures along with ab initio calculations resulted in a positive D and small rhombicity for 36 and negative D values for compounds 37–39 (see Table 2). Dynamic magnetic measurements revealed obvious SMM behaviour in the compounds 36, 37c, and 38c in the presence of applied DC field. Moreover, the compound 37c shows a weak out-of-phase signal at zero DC field, which does not reach the maximum at the highest measured frequency of AC field. The one-set Debye model was used to analyse magnetic data for 36, 37c, and 38c and two-set Debye model for data of 37c. From the Arrhenius plot, the relaxation parameters U_eff and τ₀ of the following values were extracted. U_eff = 21.6 K, τ₀ = 1.7 × 10^–8 s (at 1000 Oe), U_eff = 21.6 K, τ₀ = 2.98 × 10^–8 s (at 400 Oe), and U_eff = 17.7 K, τ₀ = 8.06 × 10^–8 s (at 1600 Oe) for 36, 37c, and 38c, respectively. At the applied field, the triclinic polymorphs 37t, 38t, and 39 show some signal in $\chi^{\prime\prime}$ at high frequencies, but no maximum was observed at the highest measured frequency. Such behaviour of AC susceptibility can be explained by the presence of shorter intermolecular Co…Co separations allowing strong dipolar interactions and, therefore, fast spin relaxation.

Fig. 24

Molecular structure of compound 37c emphasizing the trigonal bipyramidal geometry (purple polyhedron) with the equatorial plane defined by the three pyridine N atoms of L25. Colour code: Co—pink, Cl—green, N—blue, C—grey. Hydrogen atoms have been omitted for clarity (a). The plot of χT vs. T under a 1000 Oe applied field for compounds 36–39 (b). Magnetic data (AC) for 37c, and at different temperatures (c). Arrhenius plots for 37c. The black line is the fit to the Arrhenius equation (d). Taken with permission from Ref. [68] (colour figure online)

Fig. 25

Molecular structure of compound 40. Colour code: Co—blue, Cl—green, N—violet, C—grey. Hydrogen atoms have been omitted for clarity (a). DC magnetic data for 40. Lines indicate the fits with the ZFS model (b). Out-of-phase AC susceptibility component for 40 (c). Arrhenius‐like plot for 40. The solid lines are fitted (d). Taken with permission from Ref. [71] (colour figure online)

Rajnák et al. [71] studied field-supported slow magnetic relaxation in two mononuclear hexacoordinate Co(II) complexes containing four equatorial 4-benzylpyridine (L26) and two axial chlorido or thiocyanato ligands. The coordination polyhedron of 40 [Co(L26)₄Cl₂] corresponds to elongated tetragonal bipyramid because of long Co–Cl axial distances (2.44 Å) relative to equatorial Co–N distances (average distance 2.21 Å). On the other hand, the axial tiocyanato terminal ligands in complex 41 ([Co(L26)₄(NCS)₂]) form shorter bonds which resulted in the compressed tetragonal bipyramidal shape of coordination polyhedron. DC magnetic measurements revealed that effective magnetic moment for 40 adopts room-temperature value of 4.97 μ_B, which gradually decreases upon cooling until it reaches μ_eff = 3.6 μ_B at T = 1.9 K. The molar magnetization saturates at 2.16 N_A/μ_B at T = 2 K and B = 7 T. This is lower value than expected one for S = 3/2 system and it indicates a substantial ZFS. The magnetic functions for 41 show similar behaviour. Field dependence of the molar magnetization and temperature dependence of the molar magnetic susceptibility were fitted simultaneously to the model of spin Hamiltonian, which yielded D of + 106 and + 90.5 cm⁻¹ for 40 and 41, respectively. These values are in good agreement with the averaged ZFS parameters predicted by ab initio calculations. The AC magnetic data confirmed a fast magnetic relaxation in the absence of the magnetic field; however, reported complexes show a field-induced slow magnetic relaxation mediated through multiple relaxation channels. For both compounds, there is a dominant relaxation process in the high-frequency region (around τ(HF) = 0.8 ms) of AC magnetic susceptibility recorded at T = 1.9 K and 2000 Oe. The second channel appears as a satellite peak at the low-frequency region of out-of-phase component with τ(LF) ≈ 40 ms. In addition, this peak splits at H_DC = 4000 Oe, and therefore, the increase of static field causes appearance of the third relaxation channel. Both compounds show similar evolution of the in-phase and out-of-phase magnetic susceptibility data, which were fitted by three-set Debye model and temperature dependency of τ(HF) relaxation times were analysed concerning the extended relaxation equation. For complex 40, the authors obtained the best fits by considering a single Raman process with parameter C = 4.16 T⁻⁵ K⁻¹ s⁻¹ at H_DC = 4000 Oe. However, the unusual feature was observed at low temperatures for 41. Upon the heating, τ(HF) relaxation time increases with the temperature, passes through a round maximum around 3 K and then decreases. Such unexpected behaviour did not allow successful analysis of Arrhenius-like plot at the low temperature region. The quantitative parameters resulting from the data fitting of the high temperature region of τ(HF) are not comparable with 40. At 4000 Oe, the lnτ vs. 1/T function was analysed with Orbach process, which resulted in parameters U_eff = 27.7 K and τ₀ = 0.3 × 10^–6 s. According to the authors, the existence of the LF branch is conditioned by intermolecular interactions. Those interactions are disrupted by increasing temperature and the LF branch disappears progressively with increasing temperature. This is probably the origin of a higher separation of LF and HF components with an increasing magnetic field (Fig. 25).

Shi et al. [73] studied syntheses, structures and magnetic properties of three two-dimensional Co(II) SMMs with octahedral geometry. Although each compounds crystallize in different space groups, they all have similar 2D structures, where the two Co(II) centres are bridged by the ligand 4,4’dipyridyl sulfide (L27). The coordination geometry of the Co(II) centres adopts a general CoN₄X₂ octahedral environment formed by four equatorial N atoms from four ligands L27 and two axial X⁻ atoms (X = Cl⁻, Br⁻, or O). This work aimed to synthesize 2D coordination polymers with different axial coordination atoms and to study structural and magnetic changes caused by these differences. The flexible organic spacer L27 that they used is capable of forming 2D frameworks and preventing magnetic interactions between Co(II) ions. The compound of formula [Co(L27)₂Cl₂]_n (42), [Co(L27)₂Br₂]_n (43), and [[Co(L27)₂(H₂O)₂]I₂·(H₂O)₄]_n (44) were synthesized as follows: a mixture of L27 and corresponding Co(II) salt were dissolved in methanol (42) or methanol/acetonitrile (43, 44), stirred and then kept still for slow evaporation to form pink (42, 43) or orange (44) crystals suitable for X-ray diffraction. The structure of compound 42 (Fig. 26a) was already reported previously [72], yet the authors measured it for the sake of consistency. The crystal systems and space groups are monoclinic P2₁/_C for 42, orthorhombic Pccn for 43 and Pbca for 44. All compounds 42–44 have similar 2D framework structures, where the Co(II) centres are placed in distorted octahedra and bridged by long spacer ligands L27. The Co–N_eq bond lengths vary from 2.13 to 2.28 Å. The N_eq–Co–N_eq bond angles for 42–44 are very close to each other, while X_axial–Co–X_axial (X = Cl, Br, O) bond angles are very close to 180°. The Co–O_axial lengths in 44 (2.09 Å) are significantly shorter than Co–Cl_axial in 42 and Co–Br_axial in 43, which are of lengths 2.42 Å and 2.57 Å for 42 and 43, respectively. As far as magnetic properties are going, the χT values at room temperature for 42–44 vary from 3.08 to 3.41 cm³ mol⁻¹ K and they are higher than expected values for an isolated HS d⁷ Co(II) cation (S = 3/2). By lowering the temperature, the values decrease smoothly and then it is a sudden drop below 100 K to reach values of range 1.76–2.05 cm³ mol⁻¹ K at 2 K (Fig. 26b). This drop is mainly caused by the magnetic anisotropy of Co(II) ions and ZFS. In addition, the field-dependent magnetization data for 42–44 were measured at 2 K, 3 K, and 5 K. At 2 K, the magnetization saturates at the high magnetic field to value 2.31–2.42 μ_B, which is below the expected saturation value for the single HS Co(II) centre. Nevertheless, all these data support the presence of significant magnetic anisotropy originating from the spin–orbit coupling and orbital contribution. The magnetic data were further analysed and experimental values of D were obtained as D = 27.2, 28.0, and 9.5 cm⁻¹ for 42–44. However, the calculation results suggest very strong spin–orbit coupling, and therefore, the description of their magnetic properties using the spin Hamiltonian seems meaningless. There was no out-of-phase susceptibility signal observed under a zero DC field, which indicates fast relaxation of magnetization due to the quantum tunnelling of magnetization (QTM) that is observed in the majority of Co(II) based SIMs. However, all compounds displayed $\chi^{\prime\prime}$ a peak in the presence of a small DC field (Fig. 26c), which makes them field induced SIMs. The AC magnetic data were fitted using a generalized one-set Debye model and the temperature-dependent relaxation time was then analysed to extract the effective energy barrier U_eff. The high temperature linear regime of the Arrhenius plot (ln(τ) vs. T⁻¹) was fitted using the Arrhenius equation (Orbach process; Fig. 26d) giving the energy barrier U_eff = 12.43, 27.0, and 28.8 K with relaxation times τ₀ = 2.4 × 10^–5, 4.8 × 10^–6, and 1.4 × 10^–6 s for 42–44, respectively. The deviation from Arrhenius behaviour at low-temperature region is often connected to multiple relaxation pathways, such as QTM, direct, Raman, and Orbach relaxation processes. The best fit parameters considering these processes gave the energy barriers U_eff = 15.8, 41.6, and 36.4 K for 42–44, respectively, and they are more significant than barriers considering only the thermally activated relaxation process. To sum it up, the authors report that although the axial coordination atoms have an obvious influence on their structures and thus the magnetic properties, there is still no clear conclusion on the relations between the magnetic anisotropy and axial ligands based on the results obtained in this work.

Fig. 26

Molecular structure of 42. Hydrogen atoms are omitted for the sake of clarity. Colour code: Co—pink, S—yellow, N—blue, C—grey (a). Magnetic data for 42 Insets: Field-dependent magnetization M(H) plots at different temperatures. The red lines in the χT curves and the lines in all the M(H) curves are fits, while the blue lines in the χT curves correspond to the ab initio calculations. b Frequency-dependent in-phase and out-of-phase χ′′ components of AC susceptibility for compound 42 recorded at an applied static magnetic field 1500 Oe. c Arrhenius plot for 42. The red lines show the fits of the data to the Arrhenius law assuming the Orbach relaxation mechanism; green lines are fits assuming multiple relaxation pathways (d). Taken with permission from Ref. [73] (colour figure online)

Rajnák et al. [74] studied an effect of the distant substituent on the slow magnetic relaxation in the mononuclear Co(II) complex with pincer-type ligands. A hexacoordinated complex 45 of formula [Co(L28)₂](mdnbz)₂ (mdnbz = 4-methyl-3,5-dinitrobenzoate, Fig. 27a) was prepared by mixing of stoichiometric amounts of Co(OAc)₂·4H₂O, 2,6-dimethanolpyridine (L28), and 4-methyl-3,5-dinitrobenzene acid in hot water. Then, light pink X-ray quality crystals were grown and collected after slow evaporation. Authors compared properties of 45 with already reported analogous complex 46 [Co(L28)₂](dnbz)₂, where dnbz = 3,5-dinitrobenzoate anion [75], which possesses a non-methylated counter anion and identical complex cation. Compound 45 crystallizes in the monoclinic space group C2/c and molecular structure consists of one complex dication which charge is balanced by two uncoordinated mdnzbz anions. Hexacoordinate coordination polyhedron of compressed tetragonal bipyramidal shape consists of two pyridine N axial and four hydroxyl O equatorial donor atoms from each of two neutral tridentate L28 ligands. The one complex cation [Co(L28)₂]²⁺ and two mdnbz anions are connected through (O–H…O) hydrogen bonds into a 1D supramolecular chain (Fig. 27a). Furthermore, the supramolecular structure is extended into the 3D network via another O–H…O hydrogen bond formed between neighbouring molecules' carboxylic and alcohol groups. On the other hand, the complex 46 crystallizes in space group P1̅, and it does not form any supramolecular chains.

Fig. 27

Molecular structure of 45 with unsymmetrical hydrogen bonds between anionic part of carboxylic acids and a complex cationic unit (a). DC magnetic data for 45. The solid lines denote fitting by the ZFS model. The dashed lines resemble ab initio calculation (b) frequency-dependent in-phase and out-of-phase χ′′ components of AC susceptibility for compound 45 recorded at an applied static magnetic field 2500 Oe (c). Arrhenius‐like plot for 45. The dashed lines are a guide to the eye (d). Taken with permission from Ref. [74]

Compound 45 was characterized by static and dynamic magnetic measurements. At T = 300 K, the effective magnetic moment adopts a value of μ_eff = 4.70 μ_B, which slightly decreases with decreasing temperature down to 4.48 μ_B at T = 100 K (Fig. 27b). Upon further cooling, the decrease of μ_eff is more pronounced, which is related to ZFS phenomenon always present in hexacoordinated Co(II) complexes. The effect of ZFS is also confirmed by the value of magnetization per formula unit, which saturates to 2 N_Aμ_B at T = 2 K and high magnetic fields. The magnetic susceptibility and magnetization data fitting resulted in the D = 50 cm⁻¹ and E = 10.2 cm⁻¹. Contrary to this, the ZFS parameters obtained from ab initio show significantly different values D = − 69.0 cm⁻¹, E = 0.19 and the average g_iso = 2.38. The experimental value of D parameter is positive and the authors report that it is more realistic than the calculated one, as it can be seen from a comparison of fitted and calculated magnetic functions in Fig. 27b. AC magnetic measurements confirmed at least two peaks visible at frequency dependence of the out-of-phase magnetic susceptibility, indicating that slow magnetic relaxation has a multi-channel nature (Fig. 27c). Therefore, the dynamic magnetic properties were analysed by the extended three-set Debye model. By help of extracted isothermal susceptibilities was possible to determine the mole fractions of corresponding relaxation channels x(LF) = 0.19, x(IF) = 0.45, and x(HF) = 0.37. The Arrhenius-like plot lnτ vs. T⁻¹ visualizes the thermal development of the individual relaxation times (Fig. 27d). Interestingly, the low frequency relaxation time at T = 1.9 K is by order of magnitude higher for 45 relative to 46 (τ_LF = 282 vs. 29 ms for 45 and 46, respectively) at a similar external field. This is an indication that even small modifications of the SIMs are important for the slow magnetic relaxation.

García López et al. [76] conducted research dealing with field-induced SRM in a mononuclear Co(II) complex with 2,6-bis(pyrazol-1-yl)pyridine ligands functionalized with a carboxylic group (L29). The bis-chelated Co(II) complex 47 (Fig. 28a) of the tridentate ligand L29 of formula [Co(L29)₂](ClO₄)₂·2Me₂CO was prepared by mixing acetone solutions of L29 (which was previously prepared according to literature method [77]) and corresponding Co(II) salt. The red–orange prismatic crystals of compound 47 suitable for X-ray diffraction measurements were obtained by slow diffusion of diethyl ether into this solution. The compound 47 crystallizes in the monoclinic space group P2₁/c. The central Co(II) ion is coordinated by six N atoms from the two tridentate ligand L29. The distorted octahedron consists of two shorter Co–N axial bonds formed with the central pyridine rings (2.07 and 2.08 Å) and four longer equatorial Co–N bonds of pyrazole moieties (from 2.11 to 2.15 Å). These distances are typical for hexacoordinated Co(II) HS complexes. The pyrazol rings of two neighbouring complex cations [Co(L29)₂]²⁺ create face-to-face π–π and edge-to-face CH–π interactions which are responsible for the formation of 1D supramolecular chain along the a axis. Moreover, those chains are linked through C–O, CH–O, and CH–π intermolecular contacts into the second direction leading to the formation of layers of complexes in the a–c plane alternating with a layer of perchlorate counter ions and acetone solvent molecules. This kind of weak intermolecular interactions is responsible for the loss of solvent molecules after extracting the crystals from the mother liquor. The thermal dependence of the product of the molar magnetic susceptibility times the temperature (χT) shows a value of 2.47 cm³ K mol⁻¹ at 300 K, which is in accordance with expected values for HS Co(II) with some orbital momentum contribution. While cooling, this value decreases continuously with a sudden drop below 100 K due to single-ion anisotropy and reaches value of 1.70 cm³ K mol⁻¹ at 2 K. The magnetization at 5 T and 2 K saturates to value of 2.14 μ_B and it is significantly lower than the expected saturation for a system with S = 3/2 and g > 2 (Fig. 28b). Fitting of DC magnetic data results in the values of D = 51.6 cm⁻¹, g = 2.41, and E/D = 0.28, which are similar to values found in related compounds [78, 79]. The AC measurements revealed no signal in out-of-phase magnetic susceptibility in the absence of DC field, which is common behaviour in mononuclear Co(II) SMMs and it is usually attributed to QTM, dipolar interactions or hyperfine interactions [80]. The AC data under small applied static field show single relaxation channel (Fig. 28c) and analysed with one-set Debye model. The highest temperature relaxation times were fitted to the Arrhenius expression for a thermally activated Orbach process (Fig. 28d) leading to parameters U_eff = 16 K and τ₀ = 2.7 × 10^–6 s. This effective barrier is lower than experimental energy gap between both Kramer doublets, which indicates the contribution of other relaxation mechanisms.

Fig. 28

Molecular structure of cationic complex in 47. Colour code: Co—dark blue, O—red, N—light blue, C—black (a). Temperature dependence of the product of the magnetic susceptibility times the temperature at 0.1 T. Inset: isothermal magnetizations measured at T = 2, 5, and 10 K. Empty circles: experimental data. Full lines: simulated curves using best simultaneous fit (b). Frequency dependence of out-of-phase molar susceptibilities for 47 at 3000 Oe (c). Thermal dependence of the relaxation time and best fit (d). Taken with permission from Ref. [76] (colour figure online)

Conclusions

Although the field of Ln-SMMs has been catching attention in recent years heavily, from this review, it is apparent that there is still a lot to explore in the topic of Co(II) SIMs. Numerous recent works have studied the correlation between magnetic properties and structural parameters. By understanding this correlation, the controlled tuning of the magnetic anisotropy simply by choice of the ligand could be available.

Nevertheless, the situation in Co(II) complexes is more complicated than in other transition metals, such as Ni(II), since the structural distortions from the ideal shapes of coordination polyhedra are more complex. As Titiš et al. [81] reported in 2013, “The only steps forward are representing by synthesising a more numerous set of coordination compounds and subject them to a magnetochemical investigation by contemporary hardware and software.” [81]. Nowadays, in this review, we sum up some of the most significant studies, which have been committed to the design and synthesis of novel Co(II) SIMs via several synthetic strategies and investigations of magnetic properties.

In the case of tetracoordinate Co(II) complexes, the highest value of parameters D, as well as U_eff, was acquired by compound 2 [26], where Albold et al. used the strategy of creating a strongly coupled multispin system to suppress the existence of undesirable relaxation parameters that are not influenced by U_eff, such as QTM and Raman process. They took as inspiration the multispin metal radical complex 1. It can be said that their approach was successful by the means that also the value of relaxation time at low temperatures and the field of 1500 Oe reached 32,000 s, which is undoubtedly the highest reported one in this review. Furthermore, so far, these values are the highest reported overall.

The largest U_eff in the case of penta- and hexacoordinate compounds was reported in the hexacoordinate compound 46 (44 K) [75]. In contrast, the highest experimental as well calculated parameter D was reported in the pentacoordinate Co(II) complex 24 (D > 100 cm⁻¹) [58]. Although it is generally established that since the positive value of the D parameter has a ground state of M = 0, and therefore, there should be no U_eff found, the SMM behaviour can still be observed in those systems. In addition, indeed, complex 24 was proven to be field-induced SMM with the characteristics of SRM typical for pentacoordinate Co(II) complexes.

Although there is still not a complete understanding of tuning the SRM in Co(II) complexes, the most recent results suggest that the approach of the incorporation the strong exchange couplings in the transition–metal–radical systems could be particularly fruitful in terms of increasing the magnetic anisotropy as well as the values of effective barrier U_eff and relaxation time τ.