Magnetic anisotropy and entropy change in trigonal Cr$_{0.62}$Te

TL;DR

This study explores the magnetic anisotropy and magnetocaloric effects in trigonal Cr$_{0.62}$Te single crystals, revealing unique anisotropic transitions and potential for technological applications due to high $T_c$.

Contribution

It provides the first detailed analysis of anisotropic magnetic and magnetocaloric properties in Cr$_{0.62}$Te, highlighting the satellite transition $T^*$ and its field dependence.

Findings

Observation of magnetic-anisotropy-induced satellite transition $T^*$

Anomalous magnetization downturn similar to CrI$_3$

High $T_c$ makes Cr$_{0.62}$Te promising for nanofabrication

Abstract

We present a comprehensive investigation on anisotropic magnetic and magnetocaloric properties of the quasi-two-dimensional weak itinerant ferromagnet trigonal Cr$_{0.62}$Te single crystals. Magnetic-anisotropy-induced satellite transition $T^*$ is observed at low fields applied parallel to the $ab$ plane below $T_c$. The $T^*$ is featured by an anomalous magnetization downturn, similar to that in structurally related CrI$_3$, and shows a monotonous shift towards lower temperature with increasing field. Magnetocrystalline anisotropy is also reflected in magnetic entropy change $\Delta S_M(T,H)$ and relative cooling power RCP. Given the high $T_c$, Cr$_{0.62}$Te crystals are materials of interest for nanofabrication in basic science and applied technology.

Tables

Table 1. Table 1: Structural parameters for Cr 5 Te 8 obtained from synchrotron powder XRD at room temperature.

Chemical formula			Cr5Te8
Space grroup			$P\overline{3}m1$
$a$ (Å)			7.7951
$c$ (Å)			11.9766
atom	site	$x$	$y$	$z$	Occ.	Uiso (Å2)
Cr	Cr1	0	0	0	0.87	0.0019
Cr	Cr2	0.4920	0.5080	0.2515	1	0.0019
Cr	Cr3	0	0	0.2747	1	0.0019
Cr	Cr4	0.5	0	0.5	0.264	0.0019
Te	Te1	0.3333	0.6667	0.1164	1	0.00468
Te	Te2	0.3333	0.6667	0.6217	1	0.00468
Te	Te3	0.1652	0.8348	0.3816	1	0.00468
Te	Te4	0.8285	0.1715	0.1301	1	0.00468

Equations

$$\chi (k)=\sum _i\frac{N_i{S}_0^2}{k{R}_i^2}{f}_i(k,R_i)e^{-\frac{2R_i}{\lambda }}{e}^{-2k^2{\sigma }_i^2}sin[2k{R}_i+{\delta }_i(k)],$$

$$\Delta S_M(T,H)={\int }_0^H{\left(\frac{\partial S}{\partial H}\right)}_{T}dH={\int }_0^H{\left(\frac{\partial M}{\partial T}\right)}_{H}dH,$$

$$\Delta S_M(T_i,H)=\frac{{\int }_0^{H}M(T_i,H)dH-{\int }_0^{H}M(T_{i+1},H)dH}{T_i-T_{i+1}}.$$

$${\theta }_{-}=(T_{peak}-T)/(T_{r1}-T_{peak}),T<T_{peak},$$

$${\theta }_{+}=(T-T_{peak})/(T_{r2}-T_{peak}),T>T_{peak},$$

Full text

I INTRODUCTION

Achieving long-range magnetism at low dimensions as well as high temperature is of great importance for the development of next-generation spintronics. As stated in the Mermin-Wagner theorem,Mermin materials with isotropic Heisenberg interactions can not magnetically order in the two-dimensional (2D) limit. Strong magnetic anisotropy such as exchange anisotropy and/or single-ion anisotropy may remove this restriction. Recently, 2D long-range ferromagnetism was observed in van der Waals (vdW) CrI3 and Cr2Ge2Te6,McGuire ; Huang ; Seyler ; Fei ; Gong ; Lin ; Zhuang however the Curie temperature $T_{c}$ is significantly lowered when reducing to monolayer or few layers. The corresponding $T_{c}$ in monolayer and bilayer was only $\sim$ 45 K for CrI3 and 25 K in Cr2Ge2Te6, respectively. Therefore, high-$T_{c}$ ferromagnets with strong anisotropy are highly desirable.

Binary chromium tellurides Cr1-xTe are such promising candidates with high-$T_{c}$ ranging from 170 to 360 K depending on different Cr vacancies.Herbert ; Street ; Akram ; Huang1 ; Huang2 The carriers of magnetism in CrI3 and Cr2Ge2Te6 are Cr3+ ions with spin $S=3/2$ which are octahedrally coordinated by Te ligands and form a honeycomb magnetic lattice in the $ab$ plane. Cr1-xTe crystallizes in a defective NiAs structure, showing similarities in crystal structure, magnetic ion, and magnetic ordering. The mechanism of FM in this system could be attributed to the dominant FM superexchange coupling between half-filled Cr $t_{2g}$ and empty $e_{g}$ states via Te $p$ orbitals, against the AFM direct exchange interactions of Cr $t_{2g}$ states. The saturation magnetization in Cr1-xTe is observed as $1.7\sim 2.5$ $\mu_{B}$, which is much smaller than the expected moment value of Cr using ionic model due to the spin canting, itinerant nature of the $d$ electrons and the existence of mixed valence Cr.Andresen The electronic structure of Cr1-xTe has further been studied by photoemission spectroscopy,Shimada showing the importance of electron-correlation effect. Here we focus on trigonal Cr5Te8 with $x=0.375$, which has a higher $T_{c}$ of 230 K compared with monoclinic space group.Lukoschus ; Xiao ; XiaoH ; YuLIU ; YL0 Strong magnetic anisotropy with out-of-plane easy $c$ axis has been confirmed.Akram Critical behavior analysis of trigonal Cr5Te8 illustrates that the ferromagnetic state below $T_{c}$ conforms to three-dimensional (3D) Ising model,YuLIU holding a high potential for establishing long-range magnetic order when thinned down to 2D limit. Anisotropic anomalous Hall effect (AHE) was recently observed in trigonal Cr5Te8.YL0 ; Wang Calculations of band structure is desired to explain its origin, calling for precise structural information.

Magnetocaloric effect (MCE) in the FM vdW materials provides important insight into the magnetic properties. The magnetocrystalline anisotropy constant $K_{u}$ is found to be larger for Cr2Si2Te6 when compared to Cr2Ge2Te6, resulting in larger rotational magnetic entropy change at $T_{c}$.yuliu CrI3 also exhibits anisotropic $-\Delta S_{M}^{max}$ with values of 4.24 and 2.68 J kg*-1* K*-1* at 5 T for $\mathbf{H\parallel c}$ and $\mathbf{H\parallel ab}$, respectively.YULIU Intriguingly, there is an anisotropic magnetic anomaly $T^{*}$ just below $T_{c}$ in low fields;McGuire ; YULIU the origin of $T^{*}$ is still unknown.

In this work we investigate the anisotropy of magnetic and magnetocaloric properties in trigonal Cr5Te8 single crystal. A satellite transition $T^{*}$ below $T_{c}$ was observed, at which the huge magnetic anisotropy emerges. We assign its origin to the interplay among magnetocrystalline anisotropy, temperature and magnetic field. Whereas the anisotropic magnetic entropy change $\Delta S_{M}$ in Cr5Te8 is small, the magnetocrystalline anisotropy constant $K_{u}$ is found to be temperature-dependent and comparable with CrI3 and Cr2Ge2Te6. As a result of high-$T_{c}$ in Cr5Te8, it would be of interest to design low-dimensional FM heterostructures.

II EXPERIMENTAL DETAILS

Plate-like single crystals of Cr5Te8 were fabricated by the self-flux method and the surface is the $ab$ plane.YuLIU ; YL0 The structure was characterized by powder x-ray diffraction (XRD) in the transmission mode at 28-D-1 beamline of the National Synchrotron Light Source II (NSLS II) at Brookhaven National Laboratory (BNL). Data were collected using a 0.5 mm2 beam with wavelength $\lambda\sim$ 0.1668 Å. A Perkin Elmer 2D detector (200 $\times$ 200 microns) was placed orthogonal to the beam path 990 mm away from the sample. The x-ray absorption spectroscopy measurement was performed at 8-ID beamline of NSLS II (BNL) in fluorescence mode. The x-ray absorption near edge structure (XANES) and the extended x-ray absorption fine structure (EXAFS) spectra were processed using the Athena software package. The extracted EXAFS signal, $\chi(k)$, was weighed by $k^{2}$ to emphasize the high-energy oscillation and then Fourier-transformed in a $k$ range from 2 to 12 Å*-1* to analyze the data in $R$ space. The magnetization data as a function of temperature and field were collected using Quantum Design MPMS-XL5 system in temperature range 200 $\sim$ 280 K with a step of 4 K on cleaved crystals in order to remove surface contamination of residual Te flux droplets on the surface.

III RESULTS AND DISCUSSION

Rietveld powder diffraction analysis was carried out on data obtained from the raw 2D diffraction data integrated and converted to intensity versus $Q$ using the Fit2d software where $Q=4\pi sin\theta/\lambda$ is the magnitude of the scattering vector.Hammersley The refinement was performed using GSAS-II modeling suite.Toby Figure 1(a) shows the refinement result (goodness of fit $\sim 4\%$) of Cr5Te8 (0.885 by weight) and residual Te flux impurity (0.115 by weight). The crystal structure of trigonal Cr5Te8 can be well refined in the $P\bar{3}m1$ space group with four crystallographically different sites for both Cr and Te atoms, leading to the formation of a five-layer superstructure of the CdI2 type.Bensch The detailed structural parameters are summarized in Table I. The superstructure is composed of three types of Cr layers with a stacking sequence abcba. Cr2 and Cr3 occupy the vacancy-free atomic layers, while Cr1 and Cr4 distribute in the metal-deficient layers [inset in Fig. 1(b)]. The average Cr-Te bond distances in vacancy-free layers range from 2.701 to 2.805 Å, match well with the reported values for Cr2(Si,Ge)2Te6 (2.741 - 2.803 Å) and CrTe3 (2.700 - 2.755 Å).Bensch However, the Cr-Te bond distances in metal-deficient layers are shorter with values of 2.673 - 2.681 Å. The shortest Te-Te interatomic separations range from 3.664 to 3.779 Å, significantly shorter than the sum of their anionic radii 4.2 Å, indicative of weak bonding interactions with a quasi-2D character.

Figures 1(b) and 1(c) show the normalized Cr K-edge XANES spectra and Fourier transform magnitudes of EXAFS spectra of Cr5Te8, respectively. The XANES spectra is close to that of Cr2Te3 with Cr3+ state.Ofuchi The prepeak feature is due to a direct quadrupole transition to unoccupied $3d$ states that are hybridized with Te $p$ orbitals. In the single-scattering approximation, the EXAFS could be described by the following equation:Prins

[TABLE]

where $N_{i}$ is the number of neighbouring atoms at a distance $R_{i}$ from the photoabsorbing atom. $S_{0}^{2}$ is the passive electrons reduction factor, $f_{i}(k,R_{i})$ is the backscattering amplitude, $\lambda$ is the photoelectron mean free path, $\delta_{i}$ is the phase shift of the photoelectrons, and $\sigma_{i}^{2}$ is the correlated Debye-Waller factor measuring the mean square relative displacement of the photoabsorber-backscatter pairs. The corrected main peak around $R\sim 2.7$ Å in Fig. 1(b) corresponds to the Cr-Te bond distances [Cr2-Te1: 2.70(1) Å, Cr2-Te4: 2.74(2) Å, Cr4-Te2: 2.683(1) Å] extracted from the model fit in the range 2 Å to 3 Å, only slightly modified when compared with the average bond distances. The peaks in high R range are due to longer Cr-Cr (3.01 Å $\sim$ 3.29 Å) and Te-Te (3.66 Å $\sim$ 3.78 Å) bond distances and multiple scattering effects.

Temperature dependence of zero field cooling (ZFC) and field cooling (FC) magnetization $M(T)$ taken at various magnetic fields for Cr5Te8 is presented in Fig. 2. We observe an interesting anisotropic magnetic response for fields applied along the $c$ axis and in the $ab$ plane, respectively. In Fig. 2(a), for $\mathbf{H\parallel c}$ at 10 kOe, a typical increase in $M(T)$ on cooling from high temperature corresponds well to the reported paramagnetic (PM) to FM transition.Lukoschus An appreciable thermomagnetic irreversibility occurs between the ZFC and FC curves in lower fields [Figs. 2(b)-2(d)], in the magnetically ordered state, indicating magnetocrystalline anisotropy. On the other hand, for $\mathbf{H\parallel ab}$, an anomalous peak feature is observed. The ZFC and FC magnetization in fields ranging from 10 kOe to 10 Oe are virtually overlapping in the whole temperature range [Figs. 2(f)-2(i)]. A similar magnetization downturn below $T_{c}$ is also seen for Cr2(Si,Ge)2Te6 and Cr(Br,I)3,Casto ; Richter at which the strong magnetic anisotropy emerges. Since the ZFC curve might be influenced by the domain wall motion, we summarize the field dependence of $T_{c}$ (the minimum of $dM/dT$) and $T^{*}$ (the maximum of $dM/dT$) from FC magnetization. As shown in Figs. 2(e) and 2(j), both $T_{c}$ and $T^{*}$ are field-dependent but with an opposite tendency, i.e., with increasing field the $T_{c}$ increases whereas the $T^{*}$ gradually decreases.

Isothermal magnetization $M(H)$ for $\mathbf{H\parallel c}$ exhibits a clear FM behavior at low temperatures and a linear PM behavior with small slope at 300 K [Fig. 3(a)]. The mild hysteresis for both orientations indicates the behavior expected for a soft ferromagnet. The observed saturation magnetization of $M_{s}\approx$ 1.8 $\mu_{B}$/Cr for $\mathbf{H\parallel c}$ at 5 K which is smaller when compared to the expected value for Cr free ion (3 $\mu_{B}$/Cr), indicating weak itinerant nature of Cr or canted FM in Cr5Te8.YuLIU The saturation field $H_{s}$ could be derived from the $x$ component of the intercept of two linear fits, one being a fit to the saturated regime at high fields and one being a fit of the unsaturated linear regime at low fields. As we can see, the magnetization is much easier to saturate for $\mathbf{H\parallel c}$ [Fig. 3(a)] than for $\mathbf{H\parallel ab}$ [Fig. 3(b)], indicating that the $c$ axis is the easy magnetization direction. The large disparity of $H_{s}$ for two orientations can be explained by easy (hard) natures of the domain wall motion along different $c$ (ab) axes. Figures 3(c) and 3(d) present the temperature dependence of ZFC ac susceptibility measured with oscillated ac field of 3.8 Oe and frequency $f$ = 499 Hz. A pronounced broad peak is observed at $T_{c}$ in the real part $m^{\prime}$, i. e. at 238 K for $\mathbf{H\parallel ab}$ and at 231 K for $\mathbf{H\parallel c}$. An additional anomaly occurs just below $T_{c}$, as seen in an obvious hump in the imaginary part $m^{\prime\prime}$ at 199 K for $\mathbf{H\parallel c}$, further confirming the anisotropic magnetic response.

Using the Stoner-Wolfarth model a value for the magnetocrystalline anisotropy constant $K_{u}$ can be estimated from the saturation regime in the isothermal magnetization curve. Figures 4(a) and 4(b) present the magnetization isotherms with field up to 5 T in the temperature range from 200 to 280 K for both $\mathbf{H\parallel ab}$ and $\mathbf{H\parallel c}$. When $\mathbf{H\parallel ab}$, where the anisotropy becomes maximal, the saturation field $H_{s}$ is associated with the magnetocrystalline anisotropy constant $K_{u}$ and the saturation magnetization $M_{s}$ with $\mu_{0}$ being the vacuum permeability: $2K_{u}/M_{s}=\mu_{0}H_{s}$.Cullity Figure 4(c) exhibits the temperature dependence of derived $K_{u}$ for Cr5Te8, which is about 94 kJ cm*-3* at $T$ = 160 K. The $K_{u}$ in Cr5Te8 is larger than those for Cr2(Si,Ge)2Te6 and CrBr3,yuliu ; Richter which most likely results in a more apparent magnetization downturn anomaly in Cr5Te8 [Figs. 2(f)-2(i)]. Here we propose that the origin of this downturn in the magnetization curve for $\mathbf{H\parallel ab}$ is a continuous reorientation of the magnetization direction as a result of an interplay between the magnetocrytalline anisotropy, field and temperature. The magnetocrytalline anisotropy favors a magnetization direction perpendicular to the $ab$ plane, which for $\mathbf{H\parallel ab}$ the field wants to align the magnetization direction parallel to the field. Assuming an external field $H_{1}$ is higher than the anisotropy field $H^{*}$ at temperature $T_{1}$ below $T^{*}$, the magnetization vector is aligned along the external field direction. By reducing the external field to a value $H_{2}$ below $H^{*}$ at fixed $T_{1}$, a tilting of the magnetization vector towards the easy $c$ axis will be achieved. The tilting in turn leads to a reduction of the magnetization component parallel to the field. This is like the spin-flop mechanism that usually is observed in an AFM ordered state. Such feature is also presented in the field-dependent magnetization in the hard $ab$ plane [Fig. 3(b)] at 5 and 100 K.

Furthermore, the magnetocrytalline anisotropy $K_{u}$ for Cr5Te8 is found to be temperature-dependent [Fig. 4(c)], gradually increasing with decreasing temperature. This tendency arises solely from a large number of local spin clusters fluctuating randomly around the macroscopic magnetization vector and activated by a nonzero thermal energy.Zener ; Carr In a simple classical theory, $\langle K^{(n)}\rangle\propto M_{s}^{n(n+1)/2}$, where $\langle K^{(n)}\rangle$ is the anisotropy expectation value for the $n^{th}$ power angular function,Zener ; Carr in the case of uniaxial anisotropy $n$ = 2 and of cubic anisotropy $n$ = 4, leading to an exponent of 3 and 10, respectively. The temperature-dependent $M_{s}/M_{s}(160K)$, $[M_{s}/M_{s}(160K)]^{3}$, and $[M_{s}/M_{s}(160K)]^{10}$ are also plotted. The comparison in Fig. 5(c) points to the predominant uniaxial anisotropy with some deviation to cubic anisotropy in Cr5Te8. As discussed above, reducing the external field from $H_{1}$ passing $H^{*}$ to $H_{2}$ at $T_{1}$ ($<T^{*}$) results in a tilting of the magnetization vector towards the easy $c$ axis. The observed temperature-dependent $K_{u}$ gives a reduction of magnetic anisotropy when increasing temperature to $T_{2}$ ($>T^{*}$). Then the alignment along the magnetic easy axis becomes less favorable upon warming, which leads to a stronger tilting of the magnetization vector towards the $ab$ plane and an increased experimentally observed $ab$-component magnetization. Therefore, the spin configuration of Cr5Te8 below $T_{c}$ is supposed to be an out-of-plane FM order with in-plane AFM components, calling for further neutron scattering measurement. This canted FM configuration might arise from the ordered Cr-vacancies induced modification of local structure and indicates competing exchange interactions exist in Cr5Te8.

To further characterize the anisotropic magnetic properties in Cr5Te8, we investigate the anisotropic magnetic entropy change:

[TABLE]

where $\left(\frac{\partial S}{\partial H}\right)_{T}$ = $\left(\frac{\partial M}{\partial T}\right)_{H}$ is based on Maxwell’s relation.Pecharsky In the case of magnetization measured at small discrete field and temperature intervals,

[TABLE]

Figures 5(a) and 5(b) show the calculated $-\Delta S_{M}(T,H)$ as a function of temperature in selected fields up to 5 T with a step of 1 T applied in the $ab$ plane and along the $c$ axis, respectively. All the $-\Delta S_{M}(T,H)$ curves feature a broad peak in the vicinity of $T_{c}$. The value of $-\Delta S_{M}$ increases monotonically with increasing field; the maximal value reaches 1.39 J kg*-1* K*-1* in the $ab$ plane and 1.73 J kg*-1* K*-1* along the $c$ axis, respectively, with field change of 5 T. Most importantly, the values of $-\Delta S_{M}$ for the $ab$ plane are negative at low temperatures in low fields, however, all the values are positive along the $c$ axis. The field dependence of $-\Delta S_{M}(T,H)$ at low temperature [inset in Fig. 5(a)] shows a clear sign change for $\mathbf{H\parallel ab}$. This behavior is similar with that in CrI3,YULIU in which the magnetic anisotropy originates mainly from the superexchange interaction.Lado The calculated magnetocrytalline anisotropy decreases with increasing temperature [Fig. 4(c)], whereas the magnetization may exhibit opposite behavior. At low fields, the magnetization at higher temperature could be larger than that at lower temperature [Figs. 2(f)-(i) and 3(b)], which gives a negative $-\Delta S_{M}$. The rotational magnetic entropy change $\Delta S_{M}^{R}$ can be calculated as $\Delta S_{M}^{R}(T,H)=\Delta S_{M}(T,H_{c})-\Delta S_{M}(T,H_{ab})$. As shown in Fig. 5(c), the temperature dependence of $-\Delta S_{M}^{R}(T,H)$ also features a peak at $T_{c}$ with the field change of 0.2 T, however, the temperature of the maximum $-\Delta S_{M}^{R}(T,H)$ moves away from $T_{c}$ to lower temperature with increasing field. When $T\leq T_{c}$, the field dependence of $-\Delta S_{M}^{R}(T,H)$ increases rapidly at low field and changes slowly at high field [Fig. 5(d)]. This possibly reflects the anisotropy field in Cr5Te8, which decreases with increasing temperature and gradually disappears when $T\geq T_{c}$. The obtained $-\Delta S_{M}$ of Cr5Te8 is significantly smaller than those of well-known magnetic refrigerating materials, such as Gd5Si2Ge2, LaF13-xSix, and MnP1-xSix,GschneidnerJr however, comparable with those of Cr(Br,I)3 and Cr2(Si,Ge)2Te6.yuliu ; Xiaoyun ; YS

For a material displaying a second-order transition,Oes the field-dependent maximum magnetic entropy change should be $-\Delta S_{M}^{max}\propto H^{p}$.VFranco Another important parameter is the relative cooling power $RCP=-\Delta S_{M}^{max}\times\delta T_{FWHM}$.Gschneidner The $-\Delta S_{M}^{max}$ is the maximum entropy change near $T_{c}$ and $\delta T_{FWHM}$ is the full-width at half maximum of $-\Delta S_{M}$. The RCP also depends on the field with $RCP\propto H^{q}$. Figure 6(a) displays the temperature dependence of $p(T)$ in various out-of-plane fields. At low temperatures, well below $T_{c}$, $p$ has a value which tends to 1. On the other side, well above $T_{c}$, $p$ approaches 2 as a consequence of the Curie-Weiss law. At $T=T_{c}$, $p$ reaches a minimum. Figure 6(b) summarized the field dependence of $-\Delta S_{M}^{max}$ and RCP. The RCP is calculated as 131.2 J kg*-1* with out-of-plane field change of 5 T for Cr5Te8, which is comparable with that of CrI3 (122.6 J kg*-1* at 5 T).YULIU Fitting of the $-\Delta S_{M}^{max}$ and RCP gives $p=0.667(2)$ and $q=1.12(2)$.

Scaling analysis of $-\Delta S_{M}$ can be built by normalizing all the $-\Delta S_{M}$ curves against the respective maximum $-\Delta S_{M}^{max}$, namely, $\Delta S_{M}/\Delta S_{M}^{max}$ by rescaling the reduced temperature $\theta_{\pm}$ as defined in the following equations,Franco

[TABLE]

[TABLE]

where $T_{r1}$ and $T_{r2}$ are the temperatures of two reference points that corresponds to $\Delta S_{M}(T_{r1},T_{r2})=\frac{1}{2}\Delta S_{M}^{max}$. Following this method, all the $-\Delta S_{M}(T,H)$ curves in various fields collapse into a single curve [Fig. 6(c) and inset]. The values of $T_{r1}$ and $T_{r2}$ depend on $H^{1/\Delta}$ with $\Delta=\beta+\gamma$ [inset in Fig. 6(d)].Franco In the phase transition region, the scaling analysis of $-\Delta S_{M}$ can also be expressed as $-\Delta S_{M}/a_{M}=H^{n}f(\varepsilon/H^{1/\Delta})$, where $a_{M}=T_{c}^{-1}A^{\delta+1}B$ with A and B representing the critical amplitudes as in $M_{s}(T)=A(-\varepsilon)^{\beta}$ and $H=BM^{\delta}$, respectively, and $f(x)$ is the scaling function.Su If the critical exponents are appropriately chosen, the $-\Delta S_{M}(T)$ curves should be rescaled into a single curve, consistent with normalizing all the $-\Delta S_{M}$ curves with two reference temperatures ($T_{r1}$ and $T_{r2}$). This is indeed seen in Fig. 6(d) by using the values of $\beta$ = 0.315 and $\gamma$ = 1.81,YuLIU confirming that the critical exponents for Cr5Te8 are intrinsic and accurately estimated. As is well known, the critical exponents $\beta$ = 0.25, $\gamma$ = 1.75 and $\beta$ = 0.325, $\gamma$ = 1.24 are expected for 2D and 3D Ising models, respectively. The spatial dimension extends from $d$ = 2 to $d$ = 3 passing through $T_{c}$ confirms that trigonal Cr5Te8 features quasi-2D character. The spin dimension of Ising-type $n$ = 1 implies strong uniaxial magnetic anisotropy, which is of high interest for establishing long-range magnetism down to 2D limit.YL

IV CONCLUSIONS

In summary, we have studied in detail the anisotropy of magnetic and magnetocaloric properties of trigonal Cr5Te8 with a high-$T_{c}$ of 230 K. A satellite transition $T^{*}$ is confirmed below $T_{c}$, featuring an anomalous magnetization downturn when low field applying in the hard $ab$ plane. A canted out-of-plane FM configuration with in-plane AFM components is supposed for Cr5Te8, suggesting the existence of competing exchange interactions. Intrinsic magnetocrystalline anisotropy in trigonal Cr5Te8 is established and also reflected in anisotropic magnetic entropy change. Taken its high-$T_{c}$ and strong anisotropy, Cr5Te8 is a promising material to gain further insight into low-dimensional ferromagnetism and is of high interest or nanofabrication that could led to ferromagnetic heterostructures devices.

Acknowledgements

This work was funded by the Computation Material Science Program (Y.L. and C.P.). This research used the 28-ID-1 and 8-ID beamlines of the National Synchrotron Light Source II, a U.S. DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704.