Anisotropic magnetocaloric effect in single crystals of CrI$_3$

We report a systematic investigation of dc magnetization and ac susceptibility, as well as anisotropic magnetocaloric effect in bulk CrI$_3$ single crystals. A second-stage magnetic transition was observed just below the Curie temperature $T_c$, indicating a two-step magnetic ordering. The low temperature thermal demagnetization could be well fitted by the spin-wave model rather than the single-particle model, confirming its localized magnetism. The maximum magnetic entropy change $-\Delta S_M^{max} \sim 5.65$ J kg$^{-1}$ K$^{-1}$ and the corresponding adiabatic temperature change $\Delta T_{ad} \sim 2.34$ K are achieved from heat capacity analysis with the magnetic field up to 9 T. Anisotropy of $\Delta S_M(T,H)$ was further investigated by isothermal magnetization, showing that the difference of $-\Delta S_M^{max}$ between the $ab$ plane and the $c$ axis reaches a maximum value $\sim$ 1.56 J kg$^{-1}$ K$^{-1}$ with the field change of 5 T. With the scaling analysis of $\Delta S_M$, the rescaled $\Delta S_M(T,H)$ curves collapse onto a universal curve, indicating a second-order type of the magnetic transition. Furthermore, the $-\Delta S_M^{max}$ follows the power law of $H^n$ with $n = 0.64(1)$, and the relative cooling power RCP depends on $H^m$ with $m = 1.12(1)$.