Critical behavior and magnetocaloric effect in VI$_3$

Layered van der Waals ferromagnets are promising candidates for designing new spintronic devices. Here we investigated the critical properties and magnetocaloric effect connected with ferromagnetic transition in layered van der Waals VI$_3$ single crystals. The critical exponents $\beta = 0.244(5)$ with a critical temperature $T_c = 50.10(2)$ K and $\gamma = 1.028(12)$ with $T_c = 49.97(5)$ K are obtained from the modified Arrott plot, whereas $\delta = 5.24(2)$ is obtained from a critical isotherm analysis at $T_c = 50$ K. The magnetic entropy change $-\Delta S_M(T,H)$ features a maximum at $T_c$, i.e., $-\Delta S_M^{max} \sim$ 2.64 (2.27) J kg$^{-1}$ K$^{-1}$ with out-of-plane (in-plane) field change of 5 T. This is consistent with $-\Delta S_M^{max}$ $\sim$ 2.80 J kg$^{-1}$ K$^{-1}$ deduced from heat capacity and the corresponding adiabatic temperature change $\Delta T_{ad}$ $\sim$ 0.96 K with out-of-plane field change of 5 T. The critical analysis suggests that the ferromagnetic phase transition in VI$_3$ is situated close to a three- to two-dimensional critical point. The rescaled $\Delta S_M(T,H)$ curves collapse onto a universal curve, confirming a second-order type of the magnetic transition and reliability of the obtained critical exponents.