Critical behavior and magnetocaloric effect in ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$

The critical properties and magnetocaloric effect of semiconducting ferrimagnet ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystals have been investigated by bulk magnetization and heat capacity around $T_c$. Critical exponents $\beta =0.41\pm 0.01$ with a critical temperature $T_c=74.18\pm 0.08\mathrm{K}$ and $\gamma =1.21\pm 0.02$ with $T_c=74.35\pm 0.05\mathrm{K}$ are deduced by the Kouvel-Fisher plot, whereas $\delta =4.29\pm 0.05(3.40\pm 0.02)$ is obtained by a critical isotherm analysis at $T=74\left(75\right)\mathrm{K}$. The magnetic exchange distance is found to decay as $J\left(r\right)\approx r^{-4.79}$, which lies between the mean-field and 3D Heisenberg models. Moreover, the magnetic entropy change $-\mathrm{\Delta }{S}_M$ features a maximum at $T_c$, i.e., $-\mathrm{\Delta }{S}_M^{\max }\sim 2.53\left(1.67\right)\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ with in-plane (out-of-plane) field change of 5 T, confirming large magnetic anisotropy. The heat capacity measurement further gives $-\mathrm{\Delta }{S}_M^{\max }\sim 2.94\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and the corresponding adiabatic temperature change $\mathrm{\Delta }{T}_{ad}\sim 1.14\mathrm{K}$ with out-of-plane field change of 9 T.

Figure 1

(a) Crystal structure and (b) representative single crystal of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$. (c) Powder x-ray diffraction (XRD) and (d) single-crystal XRD patterns of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ at room temperature. The vertical tick marks represent Bragg reflections of the $P\overline{3}1c$ space group.

Figure 2

Temperature dependence of dc magnetic susceptibility $\chi$ and corresponding $d\chi /dT$ for ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ measured in the magnetic field $H=1$ and 50 kOe applied (a),(c) in the $ab$ plane and (b),(d) along the $c$ axis, respectively. Insets: field dependence of magnetization measured at $T=5\mathrm{K}$.

Figure 3

(a) Typical initial isothermal magnetization curves measured in $\mathbf{H}//\mathbf{ab}$ from 5 to 90 K for ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$. (b) the modified Arrott Plot around $T_c$ for the optimum fitting with $\beta =0.41$ and $\gamma =1.21$.

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 $\log M$ vs $\log H$ collected at 74 and 75 K with linear fitting curves. (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.

Figure 5

Scaled magnetization $m$ vs scaled field $h$ below and above $T_c$ for ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$. Inset: the rescaling of the $M\left(H\right)$ curves by $M{H}^{-1/\delta }$ vs $\varepsilon H^{-1/\left(\beta \delta \right)}$.

Figure 6

(a) The magnetic entropy change $-\mathrm{\Delta }{S}_M$ obtained from magnetization at various magnetic fields change in the $ab$ plane. (b) Normalized $\mathrm{\Delta }{S}_M$ as a function of the rescaled temperature $\theta$. Inset: magnetic field dependence of the maximum magnetic entropy change $-\mathrm{\Delta }{S}_M^{\max }$ with power law fitting in red solid line.

Figure 7

Temperature dependences of (a) the specific heat change $\mathrm{\Delta }{C}_p$, (b) the magnetic entropy change $-\mathrm{\Delta }{S}_M$, and (c) the adiabatic temperature change $\mathrm{\Delta }{T}_{ad}$ for ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ at the indicated fields. Inset shows the temperature dependence of specific heat $C_p$.