Critical behavior and magnetocaloric effect in ${\mathrm{VI}}_3$

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 ${\mathrm{VI}}_3$ single crystals. The critical exponents $\beta =0.244\left(5\right)$ with a critical temperature $T_c=50.10\left(2\right)\mathrm{K}$ and $\gamma =1.028\left(12\right)$ with $T_c=49.97\left(5\right)\mathrm{K}$ are obtained from the modified Arrott plot, whereas $\delta =5.24\left(2\right)$ is obtained from a critical isotherm analysis at $T_c=50\mathrm{K}$. The magnetic entropy change $-\mathrm{\Delta }{S}_M(T,H)$ features a maximum at $T_c$, i.e., $-\mathrm{\Delta }{S}_M^{\max }\sim 2.64\left(2.27\right)\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ with out-of-plane (in-plane) field change of 5 T. This is consistent with $-\mathrm{\Delta }{S}_M^{\max }\sim 2.80\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ deduced from heat capacity and the corresponding adiabatic temperature change $\mathrm{\Delta }{T}_{\mathrm{ad}}\sim 0.96\mathrm{K}$ with out-of-plane field change of 5 T. The critical analysis suggests that the ferromagnetic phase transition in ${\mathrm{VI}}_3$ is situated close to a three- to two-dimensional critical point. The rescaled $\mathrm{\Delta }{S}_M(T,H)$ curves collapse onto a universal curve, confirming a second-order type of the magnetic transition and reliability of the obtained critical exponents.

Figure 1

(a) Single crystal x-ray diffraction (XRD) pattern of ${\mathrm{VI}}_3$. Inset shows the $ab$ plane structure and representative single crystal. (b) Refinement of synchrotron powder XRD data of ${\mathrm{VI}}_3$ at room temperature.

Figure 2

Temperature dependence of dc magnetic susceptibility $\chi$ for ${\mathrm{VI}}_3$ measured in various fields applied (a) in the $ab$ plane and (b) along the $c^{*}$ axis, respectively. (c) Field dependence of magnetization measured at $T=2\mathrm{K}$. (d) Ac susceptibility real part ${\chi }^{\prime }\left(T\right)$ as a function of temperature measured with oscillated ac field of 3.8 Oe and frequency of 499 Hz applied in the $ab$ plane and along the $c^{*}$ axis.

Figure 3

(a) Typical initial isothermal magnetization curves measured in out-of-plane fields from 40 to 60 K with a temperature step of 1 K for ${\mathrm{VI}}_3$. (b) The Arrott plot of $M^2$ vs $H/M$. The $M^{1/\beta }$ vs ${(H/M)}^{1/\gamma }$ plot with parameters of (c) 2D Ising, (d) 3D Ising, (e) 3D Heisenberg, (f) 3D XY, and (g) tricritical mean-field models. (h) Temperature dependence of the normalized slopes $NS=S\left(T\right)/S\left(T_c\right)$ for different models.

Figure 4

(a) Temperature dependence of the spontaneous magnetization $M_s$ (left) and the inverse initial susceptibility ${\chi }_0^{-1}$ (right) with solid fitting curves. Inset shows the ${log}_{10}M$ vs ${log}_{10}H$ collected at 50 K with linear fitting curve. (b) Scaling plots of $m^2$ vs $h/m$ with the scaled magnetization $m\equiv {\varepsilon }^{-\beta }M(H,\varepsilon )$ and the scaled field $h\equiv {\varepsilon }^{-(\beta +\gamma )}H$ below and above $T_c$ with critical exponents $\beta =0.244$, $\gamma =1.028$, and $\delta =5.24$ for ${\mathrm{VI}}_3$. Inset shows the rescaling of the $M\left(H\right)$ curves by $M{H}^{-1/\delta }$ vs $\varepsilon H^{-1/\left(\beta \delta \right)}$.

Figure 5

Temperature dependence of (a) the specific heat $C_p$, (b) the specific heat change $\mathrm{\Delta }{C}_p$, (c) the magnetic entropy change $-\mathrm{\Delta }{S}_M$, and (d) the adiabatic temperature change $\mathrm{\Delta }{T}_{\mathrm{ad}}$ for ${\mathrm{VI}}_3$ at the indicated out-of-plane fields.

Figure 6

Initial isothermal magnetization curves measured in (a) $\mathbf{H}\parallel {\mathbf{c}}^{*}$ and (b) $\mathbf{H}\parallel \mathbf{ab}$ with a temperature step of 2 K. The magnetic entropy change $-\mathrm{\Delta }{S}_M$ obtained from magnetization at indicated field changes with (c) $\mathbf{H}\parallel {\mathbf{c}}^{*}$ and (d) $\mathbf{H}\parallel \mathbf{ab}$, respectively. (e) Temperature dependence of $-\mathrm{\Delta }{S}_M^R$ obtained by rotating from the $ab$ plane to the $c$ axis in various fields. (f) Field dependence of the maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\max }$ (left) and the relative cooling power RCP (right) with power law fitting in red solid lines. The normalized $\mathrm{\Delta }{S}_M$ as a function of the rescaled temperature $\theta$ for (g) $\mathbf{H}\parallel {\mathbf{c}}^{*}$ and (h) $\mathbf{H}\parallel \mathbf{ab}$, respectively.