Anisotropic magnetocaloric effect and critical behavior in ${\mathrm{CrCl}}_3$

We report anisotropic magnetocaloric effect and magnetic critical behavior in the van der Waals crystal ${\mathrm{CrCl}}_3$. The maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\max }\sim 14.6$ J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and the relative cooling power $\text{RCP}\sim 340.3$ J ${\mathrm{kg}}^{-1}$ near $T_c$ with a magnetic field change of 5 T are much larger when compared to ${\mathrm{CrI}}_3$ or ${\mathrm{CrBr}}_3$. The rescaled $\mathrm{\Delta }{S}_M(T,H)$ curves collapse onto a universal curve, confirming the second-order ferromagnetic transition. Further critical behavior analysis around $T_c$ presents a set of critical exponents $\beta =0.28\left(1\right)$ with $T_c=19.4\left(2\right)\mathrm{K}$, $\gamma =0.89\left(1\right)$ with $T_c=18.95\left(8\right)\mathrm{K}$, and $\delta =4.6\left(1\right)$ at $T_c=19\mathrm{K}$, which are close to those of the theoretical tricritical mean-field model.

Figure 1

(a) X-ray diffraction (XRD) pattern in logarithmic scale of a ${\mathrm{CrCl}}_3$ single crystal. ${\mathrm{BiI}}_3$-type structure (b) at low temperature and representative single crystals (c). (d) Temperature dependence of zero-field-cooling (ZFC) normalized magnetization (left axis) $M/H$ and (right axis) $H/M$ of ${\mathrm{CrCl}}_3$ at $H=10$ Oe applied along in-plane and out-of-plane directions. Inset shows the field dependence of magnetization $M\left(H\right)$ at 2 K.

Figure 2

Temperature dependence of zero-field-cooling (ZFC) and field-cooling (FC) dc magnetization $M(T,H)$ of ${\mathrm{CrCl}}_3$ measured at the indicated (a),(c) in-plane and (b),(d) out-of-plane magnetic fields. Temperature dependence of the ac susceptibility real part $m^{\prime }\left(T\right)$ and the imaginary part $m^{″}\left(T\right)$ measured with an oscillated ac field of 3.8 Oe and frequency of 499 Hz applied (e) in plane and (f) out of plane.

Figure 3

Representative magnetization isothermals at various temperatures around $T_c$ for (a) in-plane and (b) out-of-plane magnetic fields. Temperature dependence of the derived magnetic entropy change $-\mathrm{\Delta }{S}_M$ at various (c) in-plane and (d) out-of-plane magnetic fields.

Figure 4

Normalized $\mathrm{\Delta }{S}_M/\mathrm{\Delta }{S}_M^{\max }$ as a function of the rescaled temperature $\theta$ for (a) in-plane and (b) out-of-plane fields. Insets show the evolution of the reference temperatures $T_1$ and $T_2$. Field dependence of the maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\max }$ and the relative cooling power RCP with power-law fitting in red solid lines for (c) in-plane and (d) out-of-plane fields.

Figure 5

The modified Arrott plots $M^{1/\beta }$ vs ${(H/M)}^{1/\gamma }$ for in-plane fields with parameters of (a) 2D Ising, (b) 3D Heisenberg, (c) 3D Ising, (d) 3D $XY$, (e) mean field, and (f) tricritical mean-field models. (g) Temperature dependence of the normalized slopes $\text{NS}=S\left(T\right)/S\left(T_c\right)$ for different theoretical models.

Figure 6

(a) Temperature dependence of the spontaneous magnetization $M_s$ (left) and the inverse initial susceptibility ${\chi }_0^{-1}$ (right) with solid fitting curves for ${\mathrm{CrCl}}_3$. Inset shows the ${\log }_{10}M$ vs ${\log }_{10}H$ at $T_c=19\mathrm{K}$ with linear fitting curve. (b) Kouvel-Fisher plots of $M_s{(d{M}_s/dT)}^{-1}$ (left) and ${\chi }_0^{-1}{(d{\chi }_0^{-1}/dT)}^{-1}$ (right) with solid fitting curves for ${\mathrm{CrCl}}_3$. (c) Scaling plots of renormalized $m={M\left|\varepsilon \right|}^{-\beta }$ vs $h={H\left|\varepsilon \right|}^{-(\beta +\gamma )}$ above and below $T_c$ for ${\mathrm{CrCl}}_3$. Inset shows the Arrott plot of $m^2$ vs $h/m$ for ${\mathrm{CrCl}}_3$.