Easy-cone magnetic structure in (Cr_0.9B_0.1)Te

Cr_1−x Te compounds have attracted increasing attention since the discovery of their ferromagnetism. Different crystalline and magnetic Cr_1−x Te phases have been reported for $0<x<0.4$⁠. Different Cr contents x also result in a different Curie temperature (T_C) and saturation magnetization.¹ Cr_1−x Te has a hexagonal structure similar to binary CrTe, which has T_C = 340 K. However, although the Te layers are fully occupied in both cases, Cr_1−x Te has Cr vacancies in every second Cr layer. The Cr vacancies induce small deviations from the hexagonal symmetry, leading to monoclinic Cr₃Te₄, trigonal Cr₂Te₃, and trigonal and monoclinic Cr₅Te_8.² In particular, Cr₅Te₈ is a strong uniaxial ferromagnet.^3,4 However, at higher Cr concentrations, the magnetic structure is more complicated. For instance, a canted ferromagnetic structure was observed at low temperature by neutron diffraction^5,6 and magnetization measurements.¹ Although the tendency to create vacancies makes the synthesis of stoichiometric CrTe difficult, the defects determine the magnetic moment of Cr and the magnetic structure of Cr_1−x Te, leading to a lower saturation magnetization and T_C.

The present work reports the magnetic and electronic properties of (Cr_0.9 B_0.1)Te single crystals, where the Cr vacancies are filled by B, stabilizing the hexagonal structure as well as shifting the Fermi energy and melting point. Measurements of the structural and magnetic properties are compared with ab initio calculations.

Single crystals of (Cr_0.9 B_0.1)Te were grown by a step-by-step annealing process. Pure Cr (99.99%), Te (99.9999%), and B (99.999%) were ground into small pieces and mixed in an alumina tube. The alumina tube was sealed in a quartz tube filled with 20 kPa Ar. To reduce the evaporation of Te, the latter tube was heated gradually in the series: annealing to 873 K for 3 days, 1073 K for 1 day, and 1473 K for 5 days. Then, because a fast cooling is of vital importance, as a slow cooling would lead to the precipitation of Cr, the tube was cooled by immersion into ice water. The composition has been characterized by both energy-dispersive x-ray spectroscopy (EDS) and wavelength-dispersive x-ray spectroscopy (WDS). The samples have a homogeneous Cr_45.8 B_3.4 Te_50.9 composition that, using Te as the reference, corresponds to Cr_0.9 B_0.07 Te_1.0. This is in agreement with their nominal composition within the uncertainty of the methods used.

X-ray diffraction (XRD) and Laue patterns of the powder, taken at room temperature with Cu $Kα$ radiation, are shown in Fig. 1. As seen, the hexagonal structure is confirmed. Binary CrTe crystallizes in the $B81$ structure (prototype: NiAs, hP4, $P 63mmc$⁠, 194)⁷ with Cr and Te layers alternating. For (Cr_1−x B_x)Te with $x≪1$⁠, it is assumed that B replaces only Cr atoms of every second Cr layer. Consequently, Cr atoms are in two different environments: the Cr atoms in the unperturbed layer are labeled Cr^I and those in the layer with substituted B are labeled Cr^II. The resulting Cr_1−x B_x (⁠$x≪1$⁠) structure belongs to space group $P 3¯m1$ (164), with Cr^I (97.3%) in Wyckoff position 1a (0,0,0) (in brackets, the site occupations from Rietveld refinement are given) and Te (98.6%) in 2d (2/3,1/3,1/4). Site 1 b (0,0,1/2) is partially occupied by Cr^II (79.6%) and randomly distributed B (19.9%). The lattice constants a = 4.0184 Å and c = 6.2684 Å are in agreement with the values previously reported for similar compounds.^1,7

The electronic and magnetic structures were calculated from first principles in the local spin density approximation using the SPRKKR⁸ computer program in its full potential, fully relativistic mode. In this mode, instead of using a perturbational approach to the spin–orbit interaction, the spin-polarized Dirac equation with the 4-component Kohn–Sham wavefunction is solved. In particular, the generalized gradient approximation of Perdew et al.⁹ was used for the parametrization of the exchange-correlation functional. In the calculations for (Cr_0.9 B_0.1)Te, the random occupation of the 1 b sites in the Cr–B layer was modeled through the coherent potential approximation implemented in SPRKKR. It should be noted that the calculations did not converge when B replaced Cr in both layers.

The fully relativistic electronic structure calculated is shown in Fig. 2. The smearing and broadening of the dispersion is a result of the chemical disorder scattering caused by the random distribution of Cr^II and B on site 1 b. The density of states reveals the exchange splitting of the Cr 3d valence states. The density of the minority states exhibits a minimum at the Fermi energy (ϵ_F) resulting from a pseudogap.

Magnetization was measured using a vibrating sample magnetometer (MPMS 3, Quantum Design). The magnetic properties of (Cr_0.9 B_0.1)Te single crystals are summarized in Fig. 3. The Curie temperature found is $TC=336$ K. The magnetic moment at 2 K is 2.8 $μB$⁠, which results in an average total magnetic moment per Cr atom of $mCr=3.11 μB$⁠. The ab initio calculations result in spin (m_s) and orbital (m_l) magnetic moments per Cr atom, which are $msI=3.706 μB, mlI=0.007 μB$ for Cr^I and $msII=3.717 μB, mlII=0.009 μB$ for Cr^II. The overall magnetic moments in the four-site primitive cell are $ms=6.483 μB$ and $ml=−0.016 μB$⁠. The negative value of the overall orbital moment results from polarization of the Te atoms. However, as seen, the orbital moments are negligible. The magnetic moments calculated for the Cr atoms are rather site-independent although they are higher than the average ones obtained experimentally.

The dependence of the magnetization along the c- and a-axes on the temperature is shown in Figs. 3(a) and 3(b), respectively, for different applied magnetic fields. At an applied field of 1 T, the saturation magnetization M_s increases to 90 Am²/kg. At a low temperature and low field, a kink caused by spin reorientation appears, shifting in temperature with the size of the applied field. At a low magnetic field (0.01 T), the transition temperature T_SR is approximately 140 K, decreasing rapidly as the field along the c-axis increases, dropping to 118 K at 0.1 T. Conversely, it increases slightly to 142 K under a 0.45 T field along the a-axis. The spin reorientation is also observed in the AC susceptibility measurements of Fig. 3(c). Besides the Hopkinson effect¹⁰ observed near $TC$⁠, the AC susceptibility drastically decreases below 140 K to almost zero when the field is along the c-axis, while it slightly increases at temperatures below T_SR when the field is along the a-axis. The magnetization curves for both field directions at 300 and 2 K after correction of the demagnetizing factor are shown in Figs. 3(d) and 3(e), respectively. At 300 K, the magnetization of the crystal saturates at a small field along the c-axis, whereas a field of up to 0.44 T is required to saturate the sample along the a-axis. This is a typical easy-axis-type behavior. Therefore, the in-plane anisotropy can be assumed to be negligible. At 2 K, the magnetization along c saturates fast, similar to the 300 K case. However, at approximately 0.22 T along the a-axis, it displays a sudden curvature that does not exist in the linear curve of 300 K. This is because of the spin reorientation caused by the applied magnetic field. The coercivity along the c-axis at 2 K and 300 K is 0.011 T and lower than 0.003 T, respectively. Note that, below T_SR, the saturation magnetic field $Hsat$ along the a-axis, i.e., the anisotropy field H_a, decreases gradually for decreasing temperature, different from normal easy-axis magnets. The magnetocrystalline anisotropy, calculated as explained in Ref. 11, is shown in Fig. 3(f). The anisotropy constant K₁ decreases from 240 kJm⁻³ at 200 K to −100 kJm⁻³ at 2 K, whereas K₂ increases from −40 kJm⁻³ at high temperature to 100 kJm⁻³ at 2 K. The negative K₁ and $K2>−K1$/2 indicate an easy-cone-type structure with the cone angle given by $sin (θ)=−K1/2K2$⁠.^11,12

To determine the relation between the tilt angle and temperature, the magnetization of a single crystal is measured under a rotating magnetic field of 0.05 T, as shown in Fig. 3(g). Because the sample is cubic, it has a uniformly shaped anisotropy. Above T_SR, the angular dependence of the magnetization has a sinusoidal shape, with the largest value obtained along c. However, below T_SR, the curve gradually becomes asymmetric because of hysteresis, as shown from the evolution of the tilt angle with the temperature shown in Fig. 3(h). The tilt angle can be identified from the shoulders of the magnetization, which are indicated by arrows in Fig. 3(g). As seen, it decreases gradually from approximately $30°$ at 2 K to $0°$ at T_SR. The asymmetric shape of the magnetization curves is a result of non-equivalent directions. One is closer to the initial magnetization direction than the other. The angles obtained from the shoulders agree with those deduced from K₁ and K₂. The value in Fig. 3(g) is smaller than that in Fig. 3(a) under 0.05 T, because of the cooling history. Figure 3(a) originates from a field cooling process, while the sample in Fig. 3(g) was cooled without the applied field and then magnetized initially along the a axis. The coercivity at low temperature is of the same order as the applied field (0.05 T) and influences the measured value too. Figure 3(i) illustrates the alignment of the magnetization in the remanent state. At high temperature, the spins as well as the remanence (M_r) are parallel to the c-axis. Below T_SR, the major component along the c-axis is compensated to reduce the stray field, whereas the minor component in the basal plane is not completely compensated, leading to a net M_r. When the field is lower than the coercivity—as is the case in the AC susceptibility measurements—the domain wall motion is forbidden; as a result, the AC susceptibility becomes zero. At moderate fields, instead, the behavior is that of an easy-axis magnet.

X-ray absorption spectra (XAS) were measured at the TPS45A beamline¹³ of the NSRRC synchrotron (Taiwan). The Cr $L2,3$ XAS spectra measured at 300 K for (Cr_0.9 B_0.1)Te and Cr₂O₃, which were used as a reference, are shown in Fig. 4. The spectrum of (Cr_0.9 B_0.1)Te is less structured and is shifted to lower energy by approximately 2–3 eV relative to Cr₂O₃. This is attributed to the metallic nature of (Cr_0.9 B_0.1)Te and to a change in the multiplet structure, i.e., to a different coupling of the 2p corehole with the 3d valence states of Cr. The energy shift can be understood by an increased covalence or a decrease in the charge transfer from oxygen to tellurium, which results in a gradual decrease in the charge transfer energy.

X-ray magnetic circular dichroism (XMCD) was measured to obtain a deeper understanding of the magnetic properties. The measurements were carried out at 10 K under a magnetic field of 6 T and at 100% circular polarization at the DEIMOS beamline of the SOLEIL synchrotron (France). Figure 4(b) shows the results of the measurements. For comparison, the results of the first principles calculations are reported in Fig. 4(c). The measured and calculated data are in agreement with a previous report on the Cr–Te system.¹⁴ As seen, the ab initio calculations reproduce the shape of the experimental spectra. The Cr 2p binding energies for the first Cr atom are calculated to be $E3/2I=−549.02$ eV and $E1/2I=−557.66$ eV and only 37 meV higher for the second Cr atom. For both atoms, the spin–orbit splitting is $ΔSO≈8.6$ eV, in agreement with the calculated value. The difference between the experimental and calculated spectra is caused by the secondary electron background in the measurements, which is not present in the calculations. However, further deviations may appear because of incomplete photon polarization or magnetization in the experiment.

To obtain the spin magnetic moment, the spin sum rule is commonly used.¹⁵ However, a strong overlap between the L₂ and L₃ edges leads to a large underestimation of the spin moment.^16–18 Therefore, atomic ligand-field multiplet calculations were performed using the XTLS code.¹⁹ The CrTe₆ cluster parameters were set to U_dd = 5.5 eV, U_pd = 7.0 eV, $Δ=1.0$ eV, $10Dq=1.0$ eV, $V(t2g)=1.56$ eV, $V(eg)=2.94$ eV, and H_ex = 0.02 eV along the z direction. The Slater integrals were scaled to 75% of the Hartree-Fock values. In the multiplet calculations, the charge transfer energy Δ needed to be reduced from 5.2 eV for Cr₂O₃²⁰ to 1.0 eV for (Cr_0.9 B_0.1)Te. This accounts for the increased covalence, corresponding to a lower charge transfer energy, when comparing Te with O. As shown in Fig. 4(d), the multiplet calculations, similar to the ab initio ones, reproduce the measured XMCD spectra of Fig. 4(b). The spin and orbital moments of Cr obtained from the multiplet calculation are 2.98 $μB$ and 0.09 $μB$⁠, respectively. This leads to a total moment of 3.07 $μB$⁠, in good agreement with the measurements. Instead, the orbital moment obtained from XMCD is larger than the one obtained from the fully relativistic ab initio calculations by a factor 10.

In the current work, the structural and magnetic properties of synthesized (Cr_0.9 B_0.1)Te single crystals have been investigated. The structural, electronic, and magnetic measurements, including the XMCD ones, have been discussed and compared with ab initio calculations. From our detailed magnetic investigations, it is concluded that (Cr_0.9 B_0.1)Te has a collinear spin structure with an easy axis along c at high temperature. Below 140 K, the magnetic moments localized at the Cr atoms gradually tilt away from the c-axis. The tilt angle is field- and temperature-dependent, having its maximum of $30°$ at 2 K.

This research was partially supported by ERC Advanced Grant (No. 742068) TOPMAT. Support from the Max Planck-POSTECH-Hsinchu Center for Complex Phase Materials is gratefully acknowledged.