Anomalous Hall effect in the trigonal ${\mathrm{Cr}}_5{\mathrm{Te}}_8$ single crystal

We report anomalous Hall effect (AHE) and transport properties of trigonal ${\mathrm{Cr}}_5{\mathrm{Te}}_8$ (tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8)$ single crystals. The electrical resistivity as well as the Seebeck coefficient show a clear kink at the paramagnetic-ferromagnetic transition of tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$, which is also confirmed by the heat capacity measurement. The scaling behavior between anomalous Hall resistivity ${\rho }_{xy}^A$ and longitudinal resistivity ${\rho }_{xx}$ is linear below $T_c$. Further analysis suggests that the AHE in tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$ is dominated by the skew-scattering mechanism rather than the intrinsic or extrinsic side-jump mechanism.

Figure 1

Crystal structure of tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$ from (a) side and (b) top view. (c) X-ray energy-dispersive spectroscopy of tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$. Inset shows a photograph of tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$ single crystal on a 1 mm grid.

Figure 2

Temperature dependence of (a) in-plane resistivity $\rho \left(T\right)$, (b) Seebeck coefficient $S\left(T\right)$, and (c) heat capacity $C_p\left(T\right)$ of tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$ single crystal measured in zero field. Insets in (a) show the low-temperature part fitted by $\rho \left(T\right)={\rho }_0+a{T}^{3/2}+b{T}^2$ (solid line), in comparison with $\rho \left(T\right)={\rho }_0+b{T}^2$ (dashed line), and the $d\rho /dT$ vs $T$ curve. Inset in (c) exhibits the low-temperature $C_p\left(T\right)/T$ vs $T^2$ curve fitted by $C_p\left(T\right)/T=\gamma +\beta T^2$.

Figure 3

(a) Effective field dependence of magnetization $M\left({\mu }_0{H}_{\mathit{eff}}\right)$ and (b) Hall resistivity ${\rho }_{xy}\left(B\right)$ as a function of magnetic induction $B$ for tr-${\mathrm{Cr}}_5{\mathrm{Te}}_8$ single crystal at indicated temperatures with out-of-plane fields. The red dashed lines are linear fits of $M\left({\mu }_0{H}_{\mathit{eff}}\right)$ and ${\rho }_{xy}\left(B\right)$ at high-field region.

Figure 4

Temperature dependence of (a) ordinary Hall coefficient $R_0\left(T\right)$ (left axis), derived carrier concentration $n_a\left(T\right)$ (right axis), and (b) anomalous Hall coefficient $R_s\left(T\right)$ fitted from ${\rho }_{xy}(B,T)$ using ${\rho }_{xy}=R_{0}B+R_s{\mu }_{0}M$. (c) Anomalous Hall conductivity ${\sigma }_{xy}^A$ (left axis) and scaling coefficient $S_H\left(T\right)$ (right axis) as a function of temperature. (d) Plot of ${\rho }_{xy}^A$ vs ${\rho }_{xx}$ with a linear fit (solid red line) below $T_c$.