Critical behavior and magnetocaloric effect in VI$_3$.

We investigated critical properties and magnetocaloric effect connected with ferromagnetic transition in VI$_3$ single crystals. We obtained 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 from the modified Arrott plot, whereas critical isotherm analysis resulted in $\delta = 5.24(2)$ at $T_c = 50$ K. This suggests that the ferromagnetic phase transition in VI$_3$ follows the tricritical mean-field model and that it is situated close to a two- to three-dimensional tricritical point. Futhermore, the magnetic entropy change $-\Delta S_M$ features a maximum at $T_c$, i.e., $-\Delta S_M^{max} \sim$ 2.64 J kg$^{-1}$ K$^{-1}$ with out-of-plane field change of 5 T. This is consistent with the $-\Delta S_M^{max}$ $\sim$ 2.80 J kg$^{-1}$ K$^{-1}$ deduced from the 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 rescaled $\Delta S_M(T,H)$ curves collapse onto a universal curve, indicating a second-order type of the magnetic transition.