Polaronic transport and thermoelectricity in ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystals

We carried out a comprehensive study of the structural, electrical transport, thermal, and thermodynamic properties in ferrimagnetic ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystals. Mn and Te $K$-edge x-ray absorption spectroscopy and synchrotron powder x-ray diffraction were measured to provide information on the local atomic environment and the average crystal structure. The dc and ac magnetic susceptibility measurements indicate a second-order paramagnetic to ferrimagnetic transition at $T_c\sim 74$ K, which is further confirmed by the specific heat measurement. ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ exhibits semiconducting behavior along with a large negative magnetoresistance of $-87\%$ at $T_c$ and a relatively high value of thermopower up to $\sim 10$ mV/K at 5 K. Besides the rapidly increasing resistivity $\rho \left(T\right)$ and thermopower $S\left(T\right)$ below 20 K, the large discrepancy between the activation energy for resistivity $E_{\rho }$ and thermopower $E_S$ above 20 K indicates the polaronic transport mechanism. Furthermore, the thermal conductivity $\kappa \left(T\right)$ of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ is notably rather low, comparable to ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$, and is strongly suppressed in the magnetic field across $T_c$, indicating the presence of strong spin-lattice coupling, also similar with ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$.

Figure 1

Crystal structure of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ (space group $P\overline{3}1c$) shown from the (a) side view and (b) top view, respectively. (c) Normalized Mn and Te $K$-edge x-ray absorption near edge structure (XANES) spectra. (d) Fourier transform magnitudes of the extended x-ray absorption fine structure (EXAFS) oscillations (symbols) for the Te $K$ edge with the phase shift correction. The model fits are shown as solid lines. Insets show the corresponding filtered EXAFS (symbols) with $k$-space model fits (solid lines). (e) Refinement of synchrotron powder XRD data of ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ at room temperature, confirming the main phase of ${\mathrm{Mn}}_{2.97}{\mathrm{Si}}_2{\mathrm{Te}}_6$ ($93\%$) with tiny impurities $\mathrm{Si}{\mathrm{Te}}_2$ ($4\%$) and $\mathrm{Mn}{\mathrm{Te}}_2$ ($3\%$).

Figure 2

(a) Temperature dependence of zero-field-cooling (ZFC) and field-cooling (FC) dc magnetization $M\left(T\right)$ measured at $H=1$ kOe with both $\mathbf{H}\parallel \mathbf{ab}$ and $\mathbf{H}\parallel \mathbf{c}$ for the ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystal. The inset shows the FC $1/M\left(T\right)$ vs $T$ curves fitted by the Curie-Weiss law from 250 to 350 K. (b) The isothermal magnetization $M\left(H\right)$ measured at $T=5$ K for both directions. (c) Temperature dependence of ac susceptibility real part $m^{\prime }\left(T\right)$ and imaginary part $m^{\prime \prime }\left(T\right)$ (inset) measured in an ac field of 3.8 Oe and with a frequency of 499 Hz. (d) The Arrott plot $M^2$ vs $H/M$ with $\mathbf{H}\parallel \mathbf{ab}$.

Figure 3

(a) Temperature dependence of in-plane resistivity $\rho \left(T\right)$ of a ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystal in 0 and 9 T. The inset shows the field-dependent $\rho \left(T\right)$ at 10 K. (b) The $\ln (\rho /T)$ vs $1/k_{B}T$ curve fitted by an adiabatic small polaron hopping model $\rho \left(T\right)=ATexp(E_{\rho }/k_{B}T)$ with $E_{\rho }$ being the activation energy. (c) Temperature dependence of in-plane thermopower $S\left(T\right)$ of the ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystal in 0 and 9 T. The inset shows the field-dependent $S\left(T\right)$ at 10 K. (d) The $S\left(T\right)$ vs $1/k_{B}T$ curve fitted by the formula $S\left(T\right)=(k_B/e)(\alpha +E_S/k_{B}T)$ with $E_S$ being the activation energy.

Figure 4

Temperature dependence of (a) specific heat $C_p\left(T\right)$ and (b) the low-temperature part fitted by using $C_p\left(T\right)=\gamma T+\beta T^3+\delta T^{3/2}$ for the ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystal. Insets in (a) show the $C_p\left(T\right)$ near $T_c$ in 0 and 9 T, and the estimated magnetic contribution $C_m\left(T\right)$ (left axis) and derived magnetic entropy (right axis). (c) Temperature dependence of in-plane thermal conductivity $\kappa \left(T\right)$. Insets show the estimated $zT=S^{2}T/\kappa \rho$ and the differential scanning calorimetry (DSC) curve for the ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$ single crystal. (d) The $\kappa \left(T\right)$ in 0 and 9 T at low temperatures.