Anomalous Hall effect in the weak-itinerant ferrimagnet ${\mathrm{FeCr}}_2{\mathrm{Te}}_4$

We carried out a comprehensive study of electronic transport, thermal, and thermodynamic properties in $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ single crystals. It exhibits bad-metallic behavior and anomalous Hall effect (AHE) below a weak-itinerant paramagnetic-to-ferrimagnetic transition $T_c\sim 123$ K. The linear scaling between the anomalous Hall resistivity ${\rho }_{xy}$ and the longitudinal resistivity ${\rho }_{xx}$ implies that the AHE in $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ is most likely dominated by an extrinsic skew-scattering mechanism rather than an intrinsic KL or an extrinsic side-jump mechanism, which is supported by our Berry phase calculations.

Figure 1

(a) Temperature-dependent heat capacity $C_p\left(T\right)$ for $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$. Inset shows the low temperature $C_p\left(T\right)/T$ vs $T^2$ curve fitted by $C_p\left(T\right)/T=\gamma +\beta T^2$. (b) Seebeck coefficient $S\left(T\right)$ and (c) in-plane resistivity ${\rho }_{xx}\left(T\right)$ for $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ single crystal. Inset in (c) shows data below 100 K fitted by $\rho \left(T\right)={\rho }_0+a{T}^{3/2}+b{T}^2$ (solid line) in comparison with $\rho \left(T\right)={\rho }_0+c{T}^2$ (dashed line).

Figure 2

Out-of-plane field dependence of (a) DC magnetization $M\left({\mu }_{0}H\right)$ and (b) Hall resistivity ${\rho }_{xy}\left({\mu }_{0}H\right)$ for $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$ at indicated temperatures. (c) Temperature dependence of ordinary Hall coefficient $R_0$ (left axis) and anomalous Hall coefficient $R_s$ (right axis) fitted from the ${\rho }_{xy}$ vs ${\mu }_{0}H$ curves using ${\rho }_{xy}=R_0{\mu }_{0}H+R_{s}M$.

Figure 3

Temperature dependence of the carrier concentration (a) and the anomalous Hall conductivity ${\sigma }_{xy}^A={\rho }_{xy}^A/({\rho }_{xx}^2+{\rho }_{xy}^2)$ (b). Scaling behavior of the anomalous Hall resistivity (c) and the coefficient $S_H={\mu }_0{R}_s/{\rho }_{xx}^2$ (d).

Figure 4

(a) Crystal structure, Brillouin zone (BZ), and electronic structure of $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$. The red vectors in the crystal structure represent the directions of the magnetic moments on Fe and Cr. The high symmetric $k$ paths in the BZ are shown. The $x, y$, and $z$ directions of the Cartesian coordinate are along the lattice vectors $a, b$, and $c$, respectively. The Fermi energy is set to zero. Calculated (b) Seebeck coefficient $S$ and (c) anomalous Hall conductivity ${\sigma }_{xy}$ of $\mathrm{Fe}{\mathrm{Cr}}_2{\mathrm{Te}}_4$. The calculated $S$ in low temperature shows good agreement with the experiment. The ${\sigma }_{xy}$ at the Fermi level (zero) is $\sim 127$ ($\mathrm{\Omega }$ cm)${}^{-1}$, much larger than the measured value of 22 ($\mathrm{\Omega }$ cm)${}^{-1}$.