Three-dimensional critical behavior and anisotropic magnetic entropy change in quasi-two-dimensional ${\mathrm{LaCrSb}}_3$

The critical properties and magnetic entropy change of quasi-two-dimensional ${\mathrm{LaCrSb}}_3$ single crystals have been systematically investigated. The ferromagnetic transition is determined to be of a second order. Critical exponents $\beta =0.298\left(7\right)$ with a critical temperature $T_c=132.0\left(2\right)$ K and $\gamma =1.277\left(9\right)$ with $T_c=132.5\left(3\right)$ K are yielded by the modified Arrott plot, whereas $\delta =5.28\left(9\right)$ is deduced by a critical isotherm analysis at $T=132$ K. The critical exponents of quasi-two-dimensional ${\mathrm{LaCrSb}}_3$ exhibit a three-dimensional critical behavior. The magnetic interaction is found to be of a long range and the magnetic exchange distance decays as $J\left(r\right)\approx r^{-4.9}$, which lies between the mean-field model and 3D Heisenberg model. Furthermore, the magnetic entropy change $-\mathrm{\Delta }{S}_M$ features a maximum around $T_c$, i.e., $-\mathrm{\Delta }{S}_M^{\text{max}}\sim 3.4$, 5.9, and $5.8 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for a field change of 5 T applied the $H//a, b$, and $c$ axes, respectively. The rotating magnetic entropy change $\mathrm{\Delta }{S}_M^R(T,H)$ between the $a$ and $b$ axes (the $a$ and $c$ axes) reaches a maximum value of $2.55 \left(2.49\right) \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ around $T_c$, exhibiting strong anisotropic features. However, $\mathrm{\Delta }{S}_M^R(T,H)$ between the $b$ and $c$ axes is $\sim 0 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ at $T>T_c$ displaying a nearly isotropic behavior, and is less than $0.3 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ at $T<T_c$ showing weak anisotropy.

Figure 1

(a) Left: Temperature dependence of magnetization curves under $H=1$ kOe applied along three different axes. Right: plots of $1/(\chi -{\chi }_c)$ vs $T$ under a 1 kOe field applied along three different axes. The linear lines display the fitting by the Curie-Weiss law. Inset: Crystal structure of ${\mathrm{LaCrSb}}_3$. (b) $M\left(H\right)$ curves along three different axes at $T=2\mathrm{K}$.

Figure 2

(a) The field dependence of isothermals $M\left(H\right)$ measured under $H\parallel b$ from $T=118$ to 144 K. (b) The Arrott plots of $M^2$ vs $H/M$ for $H\parallel b$.

Figure 3

The isotherms plotted as $M^{1/\beta }$ vs ${(H/M)}^{1/\gamma }$ with a (a) 2D Ising model, (b) 3D Ising model, (c) 3D Heisenberg model, and (d) tricritical mean-field model.

Figure 4

Plots of normalized slopes $S_N=S\left(T\right)/S\left(T_c\right)$ vs $T$ for diverse universal theoretical models. Inset: The modified Arrott plot of $M^{1/\beta }$ vs ${(H/M)}^{1/\gamma }$.

Figure 5

(a) The spontaneous magnetization $M_s$ (left) and the inverse initial susceptibility $1/{\chi }_0$ (right) as a function of the temperature with solid fitting curves for ${\mathrm{LaCrSb}}_3$. Inset: Plots of $M$ vs $H$ at $T_c=$ 132 K in ${\log }_{10}-{\log }_{10}$ scale with a linear fitting. (b) The Kouvel-Fisher plot of temperature-dependent $M_s{(d{M}_s/dT)}^{-1}$ (left) and ${\chi }_0^{-1}{(d{\chi }_0^{-1}/dT)}^{-1}$ (right). The $T_c$ and critical exponents are deduced by linear fits (red lines). (c) Scaling plots of ${M\left|\varepsilon \right|}^{-\beta }$ vs ${H\left|\varepsilon \right|}^{-(\beta +\gamma )}$ in ${\text{log}}_{10}\text{−}{\text{log}}_{10}$ scale. (d) Renormalized plots of $M\left(H\right)$ curves by $M{H}^{-1/\delta }$ vs $\varepsilon H^{-1/\left(\beta \delta \right)}$.

Figure 6

Effective exponent ${\gamma }_{\text{eff}}$ vs $\varepsilon =(T-T_c)/T_c$ above $T_c$.

Figure 7

Dependence of (a) $\beta$ and (b) $\gamma$ on the fitted maximum magnetic field.

Figure 8

(a)–(c) Calculated magnetic entropy change of ${\mathrm{LaCrSb}}_3$ for the magnetic field along three different axes, respectively. (d)–(f) Calculated rotating magnetic entropy change of ${\mathrm{LaCrSb}}_3$ between the (d) $a$ and $b$ axes, (e) $a$ and $c$ axes, and (f) $b$ and $c$ axes, respectively.

Figure 9

(a) The field dependence of $\mathrm{\Delta }{S}_M^{\text{max}}$ and RCP for $H\parallel b$. Inset (i): Field-dependent $T_{r1}$ and $T_{r2}$; (ii) the temperature dependence of $n$ under various fields. (b) The normalized magnetic entropy change $\mathrm{\Delta }{S}_M/\mathrm{\Delta }{S}_M^{\text{max}}$ as a function of the reduced temperature $t$. Inset: Scaling of $\mathrm{\Delta }{S}_M\left(T\right)$ under the obtained critical exponents.

Figure 10

(a) The temperature dependence of the anisotropy constant $K_u$ (left axis) and the ratios of ${[M_s/M_s\left(67K\right)]}^{n(n+1)/2}$ with $n=1$, 2, and 4 (right axis).