Anisotropic magnetocaloric effect and critical behavior in ${\mathrm{CrSbSe}}_3$

We report anisotropic magnetocaloric effect and critical behavior in a quasi-one-dimensional ferromagnetic ${\mathrm{CrSbSe}}_3$ single crystal. The maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\max }$ is 2.16 J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for the easy $a$ axis (2.03 J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for the hard $b$ axis) and the relative cooling power RCP is 163.1 J ${\mathrm{kg}}^{-1}$ for the easy $a$ axis (142.1 J ${\mathrm{kg}}^{-1}$ for the hard $b$ axis) near $T_c$ with a magnetic field change of 50 kOe. The magnetocrystalline anisotropy constant $K_u$ is estimated to be 148.5 kJ ${\mathrm{m}}^{-3}$ at 10 K, decreasing to 39.4 kJ ${\mathrm{m}}^{-3}$ at 70 K. The rescaled $\mathrm{\Delta }{S}_M(T,H)$ curves along all three axes collapse onto a universal curve, respectively, confirming the second-order ferromagnetic transition. Further critical behavior analysis around $T_c\sim 70\mathrm{K}$ gives that the critical exponents $\beta =0.26\left(1\right)$, $\gamma =1.32\left(2\right)$, and $\delta =6.17\left(9\right)$ for $H\parallel a$, while $\beta =0.28\left(2\right)$, $\gamma =1.02\left(1\right)$, and $\delta =4.14\left(16\right)$ for $H\parallel b$. The determined critical exponents suggest that the anisotropic magnetic coupling in ${\mathrm{CrSbSe}}_3$ is strongly dependent on orientations of the applied magnetic field.

Figure 1

(a) Crystal structure of ${\mathrm{CrSbSe}}_3$ and (b) representative single crystals on a millimeter-grid paper. (c) Powder x-ray diffraction (XRD) pattern of ${\mathrm{CrSbSe}}_3$. (d) Temperature-dependent magnetization $M\left(T\right)$ measured in $H=1$ kOe with zero-field cooling (ZFC) and field-cooling (FC) modes along all three axes (left axis) and inverse average magnetization $1/M_{\mathrm{ave}}=3/(M_a+M_b+M_c)$ (right axis) fitted by the Curie-Weiss law. Inset shows the field-dependent magnetization $M\left(H\right)$ at 2 K.

Figure 2

(a)–(c) Typical initial isothermal magnetization curves measured along all three axes with temperature ranging from 10 to 100 K. (d)–(f) The corresponding calculated magnetic entropy change $-\mathrm{\Delta }{S}_M\left(T\right)$ at various fields change.

Figure 3

(a)–(c) Normalized magnetic entropy change $\mathrm{\Delta }{S}_M$ as a function of the reduced temperature $t$ along all three principal crystallographic axes of ${\mathrm{CrSbSe}}_3$. Insets show the evolution of the reference temperatures $T_1$ and $T_2$. (d) Temperature dependence of the magnetocrystalline anisotropy constant $K_u$, the saturation field $H_s$, and the saturation magnetization $M_s$ (insets) estimated from the hard $b$ axis below $T_c$ for ${\mathrm{CrSbSe}}_3$. (e) Field dependence of the maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\max }$ and the relative cooling power (RCP) with power-law fitting in solid lines along all three axes for ${\mathrm{CrSbSe}}_3$.

Figure 4

The Arrott plot of $M^2$ vs $H/M$ (a)–(c) and the modified Arrott plot of $M^{1/\beta }$ vs ${(H/M)}^{1/\gamma }$ (d)–(f) with indicated $\beta$ and $\gamma$ for the $a$, $b$, and $c$ axes, respectively.

Figure 5

(a) Temperature dependence of the spontaneous magnetization $M_s$ (left) and the inverse initial susceptibility ${\chi }_0^{-1}$ (right) with solid fitting curves for ${\mathrm{CrSbSe}}_3$. Inset shows the ${\log }_{10}M$ vs ${\log }_{10}H$ at 70 K with linear fitting curve. (b) Kouvel-Fisher plots of $M_s{(d{M}_s/dT)}^{-1}$ (left) and ${\chi }_0^{-1}{(d{\chi }_0^{-1}/dT)}^{-1}$ (right) with solid fitting curves for ${\mathrm{CrSbSe}}_3$.

Figure 6

Scaling plots of renormalized $m={M\left|\varepsilon \right|}^{-\beta }$ vs $h={H\left|\varepsilon \right|}^{-(\beta +\gamma )}$ above and below $T_c$ for ${\mathrm{CrSbSe}}_3$.