Anisotropic magnetocaloric effect and critical behavior in CrSbSe$_3$

We report anisotropic magnetocaloric effect and critical behavior in quasi-one-dimensional ferromagnetic CrSbSe$_3$ single crystal. The maximum magnetic entropy change $-\Delta S_M^{max}$ is 2.16 J kg$^{-1}$ K$^{-1}$ for easy $a$ axis (2.03 J kg$^{-1}$ K$^{-1}$ for hard $b$ axis) and the relative cooling power $RCP$ is 163.1 J kg$^{-1}$ for easy $a$ axis (142.1 J kg$^{-1}$ for 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 m$^{-3}$ at 10 K, decreasing to 39.4 kJ m$^{-3}$ at 70 K. The rescaled $\Delta S_M(T,H)$ 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 K gives that the critical exponents $\beta$ = 0.26(1), $\gamma$ = 1.32(2), and $\delta$ = 6.17(9) for $H\parallel a$, while $\beta$ = 0.28(2), $\gamma$ = 1.02(1), and $\delta$ = 4.14(16) for $H\parallel b$. The determined critical exponents suggest that the anisotropic magnetic coupling in CrSbSe$_3$ is strongly dependent on orientations of the applied magnetic field.