Anisotropic magnetic entropy change in ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$

Intrinsic, two-dimensional (2D) ferromagnetic semiconductors are an important class of materials for spintronics applications. ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$ semiconductors show 2D Ising-like ferromagnetism, which is preserved in few-layer devices. The maximum magnetic entropy change associated with the critical properties around the ferromagnetic transition for ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6-\mathrm{\Delta }{S}_M^{\text{max}}\sim 5.05$ J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ is much larger than $-\mathrm{\Delta }{S}_M^{\text{max}}\sim 2.64$ J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ with an out-of-plane field change of 5 T. The rescaled $-\mathrm{\Delta }{S}_M(T,H)$ curves collapse onto a universal curve independent of temperature and field for both materials. This indicates similar critical behavior and 2D Ising magnetism, confirming the magnetocrystalline anisotropy that could preserve the long-range ferromagnetism in a few layers of ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6$.

Figure 1

Crystal structure of ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$ from (a) side and (b) top views. (c) Single-crystal x-ray diffraction (XRD) and (d) powder XRD patterns of ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$. The vertical tick marks represent Bragg reflections of the $R\overline{3}h$ space group.

Figure 2

(a) Temperature dependence of zero-field-cooling (ZFC) magnetic susceptibility $\chi$ (left axis) and corresponding $1/\chi$ (right axis) for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$ measured in in-plane and out-of-plane field of $H=10$ kOe. (b) Field dependence of magnetization measured at $T=2$ K.

Figure 3

Typical initial isothermal magnetization curves measured in (a,c) $\mathbf{H}\parallel \mathbf{ab}$ and (b,d) $\mathbf{H}\parallel \mathbf{c}$ around $T_c$ for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$.

Figure 4

Temperature dependence of the calculated anisotropy constant $K_u$, the estimated saturation field $H_s$, and the saturation magnetization $M_s$ (insets) below $T_c$ for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$.

Figure 5

Temperature dependence of isothermal magnetic entropy change $-\mathrm{\Delta }{S}_M$ obtained from magnetization at various magnetic fields change (a) in the $ab$ plane and (b) along the $c$ axis, respectively, for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$. (c) Temperature dependence of $-\mathrm{\Delta }{S}_M^R$ obtained by rotating from the $ab$ plane to the $c$ axis in various fields.

Figure 6

(a) Temperature dependence of the spontaneous magnetization $M_{\text{sp}}$ (left axis) and the inverse initial susceptibility ${\chi }_0^{-1}$ (right axis) in out-of-plane field with solid fitting curves for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$. The inset shows $\log M$ vs $\log H$ collected at $T_c$ with linear fitting curves. (b) Kouvel-Fisher plots of $M_{\text{sp}}{(d{M}_{\text{sp}}/dT)}^{-1}$ (left axis) and ${\chi }_0^{-1}{(d{\chi }_0^{-1}/dT)}^{-1}$ (right axis) with solid fitting curves.

Figure 7

(a) Field dependence of the maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\text{max}}$ and the relative cooling power (RCP) with power-law fitting in red solid lines for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$. (b) Temperature dependence of $n$ in various fields.

Figure 8

The normalized $\mathrm{\Delta }{S}_M$ as a function of the reduced temperature $\theta$ with (a) out-of-plane and (b) in-plane field for ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$. Scaling plot for (c) ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$ and (d) ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ based on the critical exponents $\beta$ and $\gamma$ obtained in out-of-plane field.