Annealing and doping effects on magnetism for T$^{*}$-type (La, Eu, Sr)$_2$CuO$_{4-y}$F$_y$ cuprates

Abstract

The magnetic behavior of T$^{*}$-phase cuprates in the underdoped region has been studied through zero-field muon spin rotation/relaxation ($\mu$SR) measurements. By examining the manner in which the superconducting transition temperature changes with increased fluorine substitution, we demonstrate the possibility of achieving an underdoped region in T$^{*}$-La$_{1-x/2}$Eu$_{1-x/2}$Sr$_{x}$CuO$_{4-y}$F$_{y}$ (LESCOF). For as-grown (AS) samples, the onset temperature for development of spin correlation is determined by $\mu$SR measurement. We observed a substantial enhancement from $\sim$ 7 K (x = 0.18, y = 0) to $\sim$ 80 K (x = 0.18, y = 0.15) with an appearance of a magnetic order below $\sim$ 55 K. Thus, the magnetic order can be stabilized by underdoping in AS T$^{*}$-LESCOF, similar to T-phase La$_{2-x}$Sr$_x$CuO$_4$. However, the damping of spin precession in the $\mu$SR time spectra appears to be significant than in La$_2$CuO$_4$ (LCO), suggesting the presence of inhomogeneous magnetism. In addition, the unrecovered normalized time spectrum to 1/3 along the time axis indicates a dynamical nature of magnetism. These magnetic behavior disappears with oxidation annealing, even in the lightly hole-doped sample. The absence of static magnetism in the oxidation-annealed T$^{*}$-LESCOF could be attributed to the structural effect, as the physical properties of the T$^{\prime }$-phase cuprates has been discussed in terms of oxygen coordination around the Cu ion.

1 Introduction

In the past 30 years, the study of copper-based high-temperature superconductivity (HTSC) continues to attract the attention of researchers. The emergence of superconductivity in the CuO$_2$ plane has gained widespread consensus. In addition, numerous studies have also highlighted the close connection between the local structure and SC state in cuprates, such as the coordination number and distance between the apical oxygen and Cu [1,2,3]. Interestingly, the antiferromagnetic (AFM) and superconducting (SC) ground state of $Re_2$CuO$_4$ (Re = rare earth elements) cuprate family have been reported as distinct between their isomers. In the T$^{\prime }$-phase cuprates (CuO$_4$ coordination), a so-called undoped SC behavior without standard doping has been reported [4,5,6]. Further theoretical and experimental studies have shown that in the T$^{\prime }$-phase of cuprates, removing excess oxygens at apical site collapses the charge-transfer gap. This leads to the simultaneous presence of mobile electrons and holes [7,8,9]. This behavior has attracted our attention to the physical nature of the apical oxygen, which plays an essential role in HTSC cuprates.

In addition to the T-phase (CuO$_6$ coordination) and T$^{\prime }$-phase, the so-called T$^{*}$-phase (CuO$_5$ coordination) cuprates have been long out of the main race. The crystal structure of T$^{*}$-phase cuprates is formed by alternate stacks of T-phase-like and T’-phase-like layers along the c-axis. The first T$^{*}$-phase was established in the Nd-Ce system with $T_c$ $\sim$ 33 K and requires oxidation annealing (O-AN) to repair the apical oxygen vacancies [10, 11]. Given this behavior, the oxygen content at the apical site can be more easily controlled than in the other two phases through different annealing processes. Several studies, including angle-resolved photoemission spectroscopy (ARPES) and muon spin rotation/relaxation ($\mu$SR), were conducted in the early years. However, the unstable crystal structure impairs further discussion [12,13,14]. Therefore, the physical nature such as superconductivity, spin correlation, band structure, etc. correlated to the apical oxygen in T$^{*}$-phase cuprates remains unknown.

Previously, we reported on the systematic magnetism research of the T$^{*}$-phase La$_{1-x/2}$Eu$_{1-x/2}$Sr$_x$CuO$_4$ (LESCO) for as-grown (AS) and O-AN samples using the $\mu$SR technique for the first time [15]. However, because of the crystal structure’s instability (as previously mentioned), we could not synthesize the sample with $x<0.14$. In addition, early research on the T$^{*}$-phase SmLa$_{1-x}$Sr$_x$CuO$_4$ indicates that $T_c$ increases monotonically up to x = 0.10 with decreasing the value of x, suggesting that the sample is in the overdoped region, similar to what is observed with LESCO [16]. In other words, the magnetic nature of the underdoped region for T$^{*}$-phase cuprates remains unknown. In this study, we used a fluorine substitute as an alternative method to reduce the value of hole concentration ($n_h$). We performed $\mu$SR measurements to clarify the magnetic behavior but extended them to the lightly doped region to complement the previous research.

2 Experiment

A pristine T$^{*}$-phase cuprate La$_{0.91}$Eu$_{0.91}$Sr$_{0.18}$CuO$_4$ (LESCO) sample was prepared by the solid-state reaction method as in our previous study [15]. The sample quality was assessed through X-ray diffraction (XRD), and the lattice constant was determined using the Rietveld method; the sample closely resembled our previously used sample. The pristine sample was then mixed with NH$_4$F and heated to 550 $^{\circ }$C for 12 h to obtain the fluorinated samples (La$_{0.91}$Eu$_{0.91}$Sr$_{0.18}$CuO$_{4-y}$F$_{y}$, LESCOF). The O-AN sample was prepared by heat sample to 500 $^{\circ }$C for 72 h under high oxygen pressure (over 45 MPa). The quality of the fluorinated sample was also evaluated by XRD and the lattice constant with the pristine sample shown in Table 1.

Table 1 Lattice constant for as-grown (AS) and oxidation annealed (O-AN) La$_{0.91}$Eu$_{0.91}$Sr$_{0.18}$CuO$_{4-y}$F$_{y}$ with y = 0 (LESCO) and 0.15 (LESCOF)

The variation of the a- (or b-) and c-lattice constant could be observed after both O-AN and fluorination processes. The slight decrease in the a- (or b-) axis after O-AN could be attributed to the structural change following repair of the oxygen vacancies and the increase in size of the c-axis. However, fluorination caused the a- (or b-) and c-axes to increase and decrease in size, respectively. Considering previous studies on the fluorination T$^{\prime }$-phase La$_{1.8}$Eu$_{0.2}$CuO$_4$, the reduced size of the c-axis could be attributed to the substitute process on the rare-earth oxygen site, where the ionic radius is shorter for F$^{-1}$ [17]. The increase in the size of the a- (or b-) axis more likely derived from the decrease in the hole doping level, which caused a reduction in Cu valence similar to the evolution in the La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) [18].

In this study, the magnetic susceptibility was measured by the magnetometer of a superconducting quantum interference device (SQUID) at the Low-temperature Materials Science, Institute for Materials Research (IMR), Tohoku University. The zero-field (ZF) $\mu$SR time spectrum of the fluorinated sample was measured from 2 K to 300 K with a single pulsed $\mu ^+$ beam at the RIKEN-RAL Muon Facility (RAL) in the UK and at the Materials and Life Science Experimental Facility (MLF) in J-PARC, Japan.

3 Results and discussion

3.1 Magnetic susceptibility

Figure 1 shows the magnetic susceptibility of the fluorinated samples with different y. Compared to the Ar-annealed T$^{*}$-phase cuprates, which had increased oxygen vacancies, the deficiency in AS LESCOF could be considered comparable to that of the pristine samples [19]. However, the spin-glass (SG)-like feature remained absent on the as-grown LESCOF samples. Given the evolution of the lattice constant and combined with early research, some F$^-$ ions are likely to be inserted near the apical site. This could disrupt the Cu spin, leading to the disappearance of the SG state [20]. By contrast, all O-AN samples showed SC nature as well as an onset $T_c$ evolution from $\sim$ 24 K for y = 0.02 to $\sim$ 29 K for y = 0.05. They then decreased to $\sim$ 22 K with further increasing y to 0.15. Indeed, the limited number of experimental points did not ensure a dome-shaped evolution of superconductivity as observed in other hole-doped cuprates. However, considering the progressive electron doping observed in fluorine-substituted T$^{\prime }$-phase La$_{1.8}$Eu$_{0.2}$CuO$_4$ (LECO) [17], we could reasonably attribute a similar process to our research in which hole concentration decreased progressively with fluorine doping. In other words, due to the decrease in the hole concentration, the LESCOF passed through a dome-like feature and eventually reached an underdoped region when $y=0.15$.

Fig. 1

Magnetic susceptibility measured by SQUID for LESCOF for the (a) as-grown (AS) $y = 0.15$ sample with both ZF cooling (ZFC) and field cooling (FC) and (b) oxidation annealed (O-AN) $y = 0.02 - 0.15$ samples with ZFC

3.2 ZF $\mu$SR results

To gain deeper insight into the magnetic behavior associated with the annealing effect in the underdoped region, we conducted ZF $\mu$SR measurements. The normalized ZF $\mu$SR time spectra of AS and O-AN LESCOF $y = 0.15$ are plotted in Fig. 2. In the AS sample, as temperature decreased, the spectral change from Gaussian-like to exponential depolarization suggested the development of Cu spin correlation. The onset temperature for this type of spin correlation seemed to be much higher than that of the pristine samples, which was $\sim$ 7 K for 0.14 $\le x \le$ 0.28. [15]. In contrast, no trace of the spectrum evolution from Gaussian-like to exponential depolarization for the O-AN SC sample until 2 K indicated a paramagnetic behavior.

For a quantitative understanding of the magnetic behavior, we analysed the results using the following equation:

$$\begin{aligned} A(t)=A_0e^{-\lambda _0t}G_z(\Delta ,t)+A_1e^{-\lambda _1t}+A_{BG} \end{aligned}$$

(1)

where,

$$\begin{aligned} G_z(\Delta ,t)=1/3+2/3(1-\gamma _\mu ^2\Delta ^2t^2)e^{-1/2\gamma _\mu ^2\Delta ^2t^2} \end{aligned}$$

(2)

where $A_0$ and $A_1$ are the initial asymmetries with $A_0+A_1=1$ in which $A_{BG}$ is the temperature-independent background and $\lambda _0(\lambda _1)$ is the slow (fast) depolarization rate. The (2) is the static ZF Kubo–Toyabe function, where $\gamma _\mu$ (2$\pi \times 13.55$kHz/G) is the gyromagnetic ratio of $\mu ^+$ and $\Delta$ describing the half-width of the nuclear dipole field distributed at the muon site. The corresponding parameters of $A_0$ and $\lambda _0$ plotted with the pristine sample are shown in Fig. 3. The parameter $A_0$ shown in Fig. 3(a) could reflect the thermal evolution of the magnetism, and we defined $T_m$ as the estimated onset temperature at which $A_0$ decreased from 1. Enhancement of $T_m$ following fluorination from $\sim$7 K to $\sim$80 K was confirmed. In addition, the depolarization rate $\lambda _0$ exhibited a peak-like behavior with the maximum at $\sim$ 55 K, suggesting a magnetic transition. Although the peak-shape was not very prominent, we defined the position of this peak as $T_N$. By contrast, no clear peak features were observed on the pristine sample, which may have been located at an even lower temperature in our measurements.

Fig. 2

Normalized ZF $\mu$SR time spectra for (a) as-grown (AS) and (b) oxidation-annealed (O-AN) La$_{0.91}$Eu$_{0.91}$Sr$_{0.18}$CuO$_{3.85}$F$_{0.15}$

3.3 Magnetism in the doped T$^{*}$-phase cuprates

Based on the aforementioned results, we concluded that fluorination reduced the value of $n_h$ in T$^{*}$-phase cuprates. However, the actual doping number remains difficult to determine in this process. The evolution of $T_c$ with respect to the value of y demonstrated that LESCOF $y=0.15$ entered the underdoped region. With this established, we further explored the magnetic properties of T$^{*}$-phase cuprates influenced by annealing. Comparing the static magnetism of the SC sample with other 214-type cuprate families would be worthwhile. An early $\mu$SR study on LSCO revealed that magnetism still developed in the underdoped region [21]. In addition, the T-phase La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (T-LESCO), which contains the low-temperature tetragonal (LTT) structure in a wider $n_h$ region, exhibits more stable static magnetism as compared with LSCO [16, 22]. Thus, the absence/existence of static magnetism could be ascribed to the crystal structure with different oxygen coordination.

The connection between the in-plane superexchange effect and apical oxygen has been investigated using the resonant inelastic X-ray scattering method [23]. The research revealed that the in-plane higher-order magnetic exchange is stronger with higher split-off energy of the $3d_{z^{2}}$ orbital. In other words, it is affected by the local coordination and distance between the apical oxygen and Cu (identified as Cu-O$_{ap }$). Subsequent theoretical studies of the Sr$_2$CuO$_3$ and La$_2$CuO$_4$ suggested that longer Cu-O$_{ap }$ lead to larger nearest-neighbor Cu-Cu coupling [24]. In T$^{*}$-phase cuprates, the Cu-O$_{ap }$ is only $2.2 - 2.3$ Å  resulting in lower Cu-O hopping that suppresses the AFM.

Fig. 3

Temperature dependence of (a) initial asymmetry $A_0$ of the slow fluctuation states of the Cu spins, and (b) the slow depolarization rate $\lambda _0$ for the as-grown (AS) La$_{0.91}$Eu$_{0.91}$Sr$_{0.18}$CuO$_{4-y}$F$_{y}$ with y = 0.15. For reference, the results of the pristine samples taken from Ref.  [15] are overplotted

The annealing effect that correlates to the apical deficiency presents further information on magnetism, leading us to consider it from two viewpoints. First, based on experiments, the value of $n_h$ on the AS sample should be lower [25]. Considering the drastic enhancement of $T_m$ and $T_N$, we can reasonably hypothesize the value of $n_h$ is approximately 0 for an AS fluorinated sample. However, the time spectrum at the lowest temperature does not recover to 1/3, suggesting that the dynamical behavior of magnetism is included and the well-defined oscillations component are absent. This considerably faster damping of the procession in the LESCO is similar to the doped region of $\sim x =0.10 - 0.18$ for the T-LESCO, which can be attributed to the significant spacial inhomogeniety in the sublattice magnetization. Therefore, whether this behavior could reflect the physical nature of the ideal T$^{*}$-phase cuprates is unclear. Given the effects of excess oxygen on the electronic structure in the T$^{\prime }$-phase [9], apical oxygen vacancies could also cause local defects, resulting in localized carriers and partial recovery of AFM. Similar behavior is supported by our $\mu$SR study for pristine samples in Ref. [15], where the local defects could slow down the Cu spin fluctuation. Therefore, the AFM state with the higher $T_m$ and $T_N$ in T$^{*}$-phase cuprates likely originates from the same source as the T$^{\prime }$-phase, indicating that effects of chemical defect are crucial.

We should also note that several issues remain with the current results. First, early studies reported the dynamically disordered canting of CuO$_5$ pyramids caused by apical vacancies and the T$^{*}$ structure itself, which in turn affected the AFM state [11, 26]. The effects of defect before and after O-AN were unclear. Indeed, we could assume the defects were lower after O-AN, but we could not qualitatively study the relation between the AFM and effects of chemical defect. Second, the effective doping level against the SC and AFM state remained vague; X-ray absorption spectroscopy estimated the doping number of pristine T$^{*}$ LESCO, showing that the $n_h$ was lower than the chemical value [25]. Finally, we could not rule out the additional suppression of AFM from the fluorine ion, which may have formed the Cu-F bond, as claimed in Ref. [20]. We are currently addressing these issues, and the results will be published in the near future.

4 Conclusion

In this study, we investigated for the first time the magnetic behavior of the underdoped region for T$^{*}$-phase cuprates. We performed a ZF $\mu$SR study of fluorine substitute as-grown and oxidation-annealed T$^{*}$-phase cuprate samples. The dome-like evolution of the $T_c$ suggested this process could be realized, where the sample is forced to the underdoped region. The O-AN SC sample did not exhibit magnetic depolarization; it was drastically enhanced on the AS sample but in disordered magnetism. We concluded that both structural and electronic effects occurred that altered the AFM state, whereby lower Cu-O$_{ap }$ in T$^{*}$-phase cuprates resulted in weaker spin correlations between nearest-neighbour Cu ions. Considering the local defects, we can assume that the magnetism probably derived from a partially recovered AFM state. Further research on these unsolved issues is ongoing and we will publish our results in the future.