1 Introduction

It is generally possible to substitute boron for cobalt in RCo5 to obtain the compounds Rn+1Co3n+5B2n, n = 0, 1, 2, 3, ∞, which form a unique series of crystal structures changing with n [1,2,3,4,5]. All these structures are derived from the CaCu5-type structure and differ in the ordering scheme of the B for Co substitution in RCo5. RCo4B compounds have been widely studied, first for their crystal structure and later because of their interesting physical properties [4, 6, 7]. A special interest in the magnetic properties results from the combination of rare-earth and transition-metal sublattices, which provide localized and itinerant magnetism, respectively.

The GdCo4B compound has been reported to crystallize in the CeCo4B-type crystal structure, obtained by an ordered substitution of B for Co on the 2c Wyckoff positions, thus leading to a doubling of the unit cell along the hexagonal c axis. The P6/mmm space group is retained. The GdCo4B compound has attracted much attention from a fundamental point of view. It was first investigated on polycrystalline samples [3, 4, 6,7,8,9,10], later a single crystal was produced [11, 12]. The crystal structure was determined from an X-ray study of a single crystal [13]. The magnetic properties have been investigated by a number of techniques, ranging from magnetization measurements [3, 4, 7, 10] through nuclear magnetic resonance spectroscopy [14] to high magnetic field studies [15, 16] and X-ray photoemission spectroscopy [17]. Pressure dependence of the magnetization curves has been explored as well [18, 19]. More recently, high-energy neutron scattering experiments and density functional calculations have been performed, aimed at the exchange interactions in GdCo4B [8].

A remarkable feature of GdCo4B is that it exhibits a first-order magnetization process when a magnetic field is applied perpendicularly to the six-fold symmetry axis. Another unusual feature of this compound is its easy-axis magnetic anisotropy. This is quite distinct from the behavior of the isotypic YCo4B compound, which exhibits a spin reorientation at Tsr = 155 K [11, 19, 20], the anisotropy being of the easy-plane type below that point and of the easy-axis type above it. The stronger positive anisotropy of GdCo4B has been attributed to the Gd sublattice, which is rather unusual for Gd. Generally Gd atoms are not expected to contribute to magnetocrystalline anisotropy, because their half-filled 4f shell has no orbital moment.

In this work we will first investigate the crystal structure of GdCo4B by X-ray diffraction and then focus on the study of its magnetocrystalline anisotropy. In order to extract the anisotropy parameters of the GdCo4B single crystal in the presence of a first-order magnetization process, we will extend the model previously proposed for magnets with an easy-plane anisotropy to the case of an easy-axis compound GdCo4B. Then temperature evolution of the anisotropy parameters and their pressure dependence will be determined.

2 Experimental

Single crystal of GdCo4B was grown using the Czochralski method. An initial polycrystalline GdCo4B sample was produced by arc-melting of a mixture of Gd (99.9%, CERAC Inc.), Co (99.8%, CERAC Inc.) and B elements (99.9%, Alfa Aesar). The obtained ingot was then placed in a tri-arc furnace on a water-cooled rotating copper hearth. It was subsequently melted with three electric arcs, which guaranteed homogeneity of the melt. Tungsten needle was used as a seed and a 10 mm long GdCo4B crystal was successfully obtained.

Composition of the obtained sample was verified with a scanning electron microscopy (SEM) technique using a JEOL JSM 7000F microscope. For the SEM analysis, a part of the grown monocrystalline sample was cut off, polished, and subsequently deposited on a carbon tape. The SEM data were normalized using spectra of the stoichiometric GdCo5 compound and the sample under study was found to feature the targeted Gd:Co ratio of 1:4 within the experimental error range. No secondary phases/inclusions were observed. Content of light B atoms was verified using monocrystalline synchrotron radiation diffraction experiment. For this a chipped GdCo4B single crystal with a size of ca. 150 × 150 × 150 µm3 was mounted on a glass pin. Data were collected on the Swiss-Norwegian beamlines BM01A at the ESRF synchrotron (Grenoble, France) using a KUMA6 diffractometer equipped with the TITAN CCD detector (62 µm pixel size) and a combination of ω- and φ-scans in 1° steps. The wavelength of the synchrotron radiation was set to 0.6987 Å. The experimental data were reduced using the CrysalisPro package [21] and refined with the SHELXL software [22].

The isothermal magnetization measurements have been undertaken on a single crystal sample in a wide temperature range from 2 to 300 K. The measurements have been carried out using the extraction magnetometer at the Néel Institute; the equipment employed has been described elsewhere [23]. In order to determine the ordering temperature and the compensation temperature, isofield magnetization measurements have been recorded above room temperature up to T = 650 K on a SQUID Quantum design ® apparatus.

3 Single crystal diffraction

The synchrotron radiation diffraction data has been analyzed in the P6/mmm space group, in excellent agreement with earlier reports [7, 11, 13]. 7619 Bragg reflections with − 9 ≤ h ≤ 9, − 9 ≤ k ≤ 9, − 14 ≤ l ≤ 14 have been collected, and the refinement was done against 336 independent reflections for 15 refined parameters. Summary of the structural refinement for GdCo4B is presented in Table 1. The refinement led to a Goodness-of-fit on F2 of 1.138 and final agreement factors of R1 = 0.0372, wR2 = 0.1017. All atomic sites, including that of B, were found to be fully occupied. We therefore conclude that the crystal studied in this work is of targeted GdCo4B composition and without secondary phases. The lattice parameters obtained at room temperature are as follows: a = 5.0970(3) Å, c = 6.9512(4) Å, α = β = 90°, γ = 120°. This yields a cell volume of 156.39(2) Å3 and a density of 8.574 g/cm3.

Table 1 Crystal data and structure refinement of GdCo4B single crystal, P6/mmm, a = 5.0970(3) Å, c = 6.9512(4) Å, V = 156.39(2) Å3, R1 = 0.0372 for data with I > 4σ(I) and R1 = 0.0390 for all data. U23 = U13 = 0 Å2 for all atoms
Full size table

The crystal structure obtained is shown in Fig. 1, it confirms the ordered substitution of B for Co and the consequent doubling of the unit cell as compared with the GdCo5 structure. The Co atoms in the 6i Wyckoff positions are located at z = 0.2874, indicating that this atomic plane is closer to the plane containing Gd2 atoms than to the one containing Gd1. The atomic coordinates are in excellent agreement with those reported earlier by Cordier et al. [13]. It is worth to note that anisotropic atomic displacement parameters have been determined. The refined values are essentially equivalent along the U11 and U33 directions, U12 being much smaller for all atomic positions. The Gd1 atoms on the 1a site exhibit larger U11 values than Gd2 on the 1b site. The obtained Uii values are rather close for B and Co2 atoms, but slightly larger values are found for Co1, in particular as regards U11 and U22.

Fig. 1 
figure 1

Schematic diagram of the GdCo4B crystal structure as derived from single crystal diffraction

Full size image

A typical Laue diffraction pattern is presented in Fig. 2 in order to illustrate the quality of the crystal. The observed Bragg peaks (in black on the film) are compared with the expected ones as derived from calculation (in red). A few Miller indexes are given. This Laue diffraction pattern has been recorded using a polychromatic beam in back scattered geometry from a tungsten anode X-ray tube. Figure 2 clearly confirms the hexagonal symmetry along the c axis in good agreement with the crystal structure derived above.

Fig. 2
figure 2

Laue diffraction pattern recorded on the GdCo4B single crystal with a tungsten anode

Full size image

4 Magnetic results and discussion

4.1 Magnetization measurements

Figure 3 shows thermal evolution of magnetization in a weak magnetic field (0.01 T) applied along the easy axis. The data were taken while cooling down to room temperature. Two prominent features can be observed. The first one is the ferromagnetic ordering at a Curie temperature of TC = 564 K, accompanied by a dramatic growth of magnetization. As temperature continues to descend, the magnetization reaches a maximum then decreases, changing sign at a compensation point of Tcomp = 474 K. This is a temperature where the magnetization is nil since the moments of the Gd and Co sublattices cancel each other out. The applied field was set particularly low (0.01 T) in order to trick the system into a metastable (undercooled) state with negative magnetization just below Tcomp. At a yet lower temperature the magnetization becomes positive again, as the system eventually leaves the metastable state for the stable one. Note that Tcomp corresponds to the higher-temperature crossing-point since the data presented in Fig. 3 were collected while cooling down. If they were measured while heating up Tcomp would be the lower-temperature crossing-point. When plotted together, the curves corresponding to both scenarios should form a bowtie-shaped hysteresis loop centered about Tcomp, as sketched in the inset. Slightly different values of TC and Tcomp may have been reported in the literature [4, 6, 10], however, the present values have been determined on a stoichiometric GdCo4B single crystal and can be regarded as more reliable.

Fig. 3
figure 3

Thermal evolution of the magnetization of GdCo4B in a field of 0.01 T applied along the easy axis

Full size image

The spontaneous magnetization reported by Thang et al. [11] for a single crystal is 3.36 µB/f.u. at T = 5 K, a value close to 3.25 µB/f.u. derived by Burzo et al. [4]. Here, we obtain a similar value of 3.33 µB/f.u. by extrapolation of the saturated part of the magnetization curve to zero field (see Fig. 4). Thang et al. [11] showed that the easy magnetization direction in GdCo4B is the c axis and reported a first-order magnetization process (FOMP) in the magnetization curves recorded along the b axis. Such a feature is also present in our magnetization curves (see Fig. 5) taken at low temperatures; it disappears progressively as temperature is raised.

Fig. 4
figure 4

Isothermal magnetization curve along the b axis of GdCo4B recorded at T = 3 K

Full size image
Fig. 5
figure 5

Comparison of the magnetization curves along the b axis of GdCo4B recorded at T = 100, 200 and 310 K

Full size image

4.2 Determination of anisotropy parameters from a first-order magnetization process

The anisotropy energy of a uniaxial crystal is written as follows:

$$ E_{a} = K_{{1}} {\text{sin}}^{{2}} q + K_{{2}} {\text{sin}}^{{4}} q, $$
(1)

where K1 and K2 are anisotropy parameters, often called anisotropy constants even though they depend on temperature. Below we shall determine these parameters for GdCo4B as functions of temperature using a new approach.

Indeed, at low temperatures the GdCo4B magnetization curves recorded along the hard direction (H⊥[001]) have an anomaly (a jump) characteristic of a first-order reorientation transition (FOMP). According to Asti and Bolzoni [24, 25], this FOMP is of type I: the jump begins at certain critical magnetization and magnetic field, Mcr and Hcr, and ends in a state of technical saturation, M = Ms, Ms being the spontaneous magnetization. In this case the standard Sucksmith-Thompson technique [27] is inefficient because only a small initial portion of the magnetization curve—well below the FOMP anomaly—can be used for the determination of K1 and K2. In an earlier work on Tb2Fe17 [26], it was proposed to express K1 and K2 directly in terms of Mcr and Hcr (as well as mcr = Mcr/Ms). Unlike Tb2Fe17, GdCo4B is an easy-axis magnet, therefore, the equations derived in Ref. [26] have to be modified accordingly. The modification concerns only the expression for K1, which now becomes

$$ K_{1} = \frac{{1 + 2m_{{{\text{cr}}}} + 3m_{{{\text{cr}}}}^{2} }}{{2m_{{{\text{cr}}}} \left( {1 + m_{{{\text{cr}}}} } \right)^{2} }}\mu_{0} M_{{\text{s}}} H_{{{\text{cr}}}} , $$
(2)

whereas the formula for K2 remains unchanged,

$$ K_{2} = - \frac{{\mu_{0} M_{{\text{s}}} H_{{{\text{cr}}}} }}{{2m_{{{\text{cr}}}} \left( {1 + m_{{{\text{cr}}}} } \right)^{2} }}. $$
(3)

Equations (2) and (3) were used to process the magnetization curves taken at T ≤ 100 K, where the FOMP is clearly visible. The so-obtained values of K1 and K2 are plotted against T in Fig. 6, and the values are listed in Table 2 for selected temperatures. At T ≥ 100 K, K1 and K2 were determined by the usual Sucksmith-Thompson technique [27] and the values obtained by both methods match at T = 100 K (Fig. 6).

Fig. 6
figure 6

Thermal evolution of the anisotropy parameters K1 and K2 of GdCo4B

Full size image
Table 2 Experimental values of K1 and K2 of GdCo4B at P = 0 derived from the FOMP by using Eqs. (2, 3)
Full size table

Turning now to compensation temperature, we present the thermal dependence of the spontaneous magnetization of GdCo4B as follows:

$$ M_{{\text{s}}} \left( T \right) = 7{\upmu }_{{\text{B}}} {\text{B}}_{7/2} \left( {\frac{{7{\upmu }_{{\text{B}}} B_{{\text{ex }}} f\left( {T/T_{{\text{C}}} } \right)}}{kT}} \right) - M_{{{\text{Co}}}} \left( 0 \right) f\left( {T/T_{{\text{C}}} } \right). $$
(4)

Here B7/2(x) is the Brillouin function for J = 7/2, Bex is the exchange field on Gd produced by the Co sublattice, and MCo(0) = 3.67 µB/f.u. is the Co sublattice moment at T = 0, chosen so as to reproduce the spontaneous magnetization measured at low temperatures, Ms(0) = 3.33 µB/f.u. Further, f(T/TC) stands for a function describing the thermal dependence of the Co sublattice magnetization [28, 29]:

$$ f\left( {T/T_{{\text{C}}} } \right) = \left[ {1 - s\left( {T/T_{{\text{C}}} } \right)^{3/2} - \left( {1 - s} \right)\left( {T/T_{{\text{C}}} } \right)^{5/2} } \right]^{1/3} . $$
(5)

The compensation temperature is determined from an obvious condition, Ms(Tcomp) = 0. It should be noted that the resulting value of Tcomp depends essentially on Bex only. The form of the function f(T/TC) and the values of the parameters s and TC have only a minor effect on Tcomp. By linearizing the Brillouin function, \({\mathrm{B}}_{7/2}\left(x\right)\approx \frac{3}{7} x\), one can eliminate the factor f(T/TC) from the condition for Tcomp, which then becomes directly proportional to Bex,

$$k{T}_{\mathrm{comp}}=21{\upmu }_{\mathrm{B}}^{2}{M}_{\mathrm{Co}}^{-1}\left(0\right){B}_{\mathrm{ex}}$$
(6)

This relation is however an approximate one. This is because at the compensation point, the argument of the Brillouin function is x ~ 1, rather than x <  < 1 as required for the linearization to be accurate. We therefore prefer finding Bex from Eqs. (4) and (5). The values of TC and Tcomp are then taken from the experiment, while the parameter s is fixed at s = 0.7, like in YCo5 [28]. Firstly, s = 0.7 is a value typical for ferromagnets [29]. Secondly, as stated above, varying s rather than having it fixed does not change Tcomp very much. The result is Bex = 131 T.

4.3 Discussion

The values of K1 and K2 obtained at T = 2 K are 60 and − 22 J/kg, respectively. Whereas K1 changes rather little with temperature, becoming about 52 J/kg at T = 155 K, K2 experiences a much faster decay, from − 22 J/kg at T = 2 K to practically zero at T = 155 K. The anisotropy parameters obtained here from the FOMP are in good agreement with the values found previously by fitting magnetization curves [11]. This validates the theoretical approach described above and provides a new method to determine the magneto-crystalline anisotropy parameters in compounds exhibiting a FOMP.

Z. Arnold et al. have reported the pressure dependence of the magnetization curves for a GdCo4B single crystal [19]. Their study revealed that the FOMP observed for GdCo4B is highly sensitive to the application of external pressure to the compound. We used the experimental data of Ref. [19] to derive the anisotropy parameters by the method described in the previous section; those data had been recorded at different pressures but under the same conditions and in the identical pressure cell [19]. From the 30 K data set of Ref. [19], we deduced K1 = 64 J/kg and K2 = − 25.6 J/kg at P = 6.1 kbar, as well as K1 = 61.6 J/kg and K2 = − 22.8 J/kg at P = 0. The zero-pressure anisotropy parameters are slightly different from those obtained in the previous section, because single crystals of different provenance were used. It is interesting to note that at T = 30 K, which is below the minimum in K1(T) situated at T = 60 K, both K1 and K2 are strengthened by the pressure. On the contrary, at temperatures above 60 K both K1 and K2 are reduced under pressure. Thus, at T = 90 K, we got K1 = 58.9 J/kg and K2 = − 18.9 J/kg at P = 6.5 kbar, as against K1 = 59.8 J/kg and K2 = − 19.2 J/kg at P = 0. At T = 30 K the pressure derivatives of the anisotropy parameters are estimated to be ∂K1 /∂P = 0.41 J kg−1 kbar−1 and ∂K2/∂P = − 0.46 J kg−1 kbar−1. At T = 90 K both derivatives have changed sign and become about three times smaller in magnitude.

Using the characteristic temperatures of our GdCo4B single crystal, Tcomp = 474 K and TC = 564 K, we find from Eqs. (4, 5) an exchange field of Bex = 131 T. This value is in excellent agreement with that obtained from inelastic neutron scattering measurements, 130(10) T [8]. This is a further confirmation of the reliability of the theoretical approach described in the present work. Calculations using smaller values of Tcomp and TC, taken from the literature [15, 16], yielded a much smaller exchange field. DFT calculations [8] have predicted a significantly larger exchange field on the 1a site than on the 1b one. This is not surprising if one considers that Gd(1a) have 6 more cobalt atoms as nearest neighbors than Gd(1b) have. However, only a mean exchange field can be estimated from our experimental studies, corresponding to an average value for the two gadolinium sites. Similarly, the limited resolution of inelastic neutron scattering in Ref. [8] did not allow to distinguish between the two inequivalent Gd positions.

5 Conclusions

A single crystal of GdCo4B has been synthesized and its crystal structure investigated by X-ray diffraction. Investigation of the magnetic properties has yielded Tcomp = 474 K and TC = 564 K for the compensation temperature and the Curie temperature, respectively. Hence the mean exchange field experienced at the Gd atomic positions, Bex = 131 T (at T = 0). At low temperatures, a first-order magnetic transition (FOMP) occurs when recording the magnetization along the hard magnetization direction. A theoretical model permitting to access the anisotropy parameters has been adapted for this kind of FOMP. This approach, employed originally for easy-plane compounds, is found to perform well for GdCo4B, as judged from the comparison with earlier published results [11]. The method is applicable to both easy-plane and easy-axis materials with a FOMP and is complementary to the well-known Sucksmith-Thomson technique, which is disadvantageous for such materials.

The effect of pressure on the anisotropy parameters K1 and K2 has been investigated using the same method and earlier published magnetization curves [19].