Magnetotransport properties in the noncentrosymmetric itinerant ferromagnet ${\mathrm{Cr}}_{11}{\mathrm{Ge}}_{19}$

We have investigated the anomalous Hall effect and magnetoresistance of the noncentrosymmetric itinerant ferromagnet ${\mathrm{Cr}}_{11}{\mathrm{Ge}}_{19}$. We have found a characteristic temperature ($\sim 30$ K) below the ferromagnetic transition temperature $T_{\mathrm{C}}=85$ K. While a conventional anomalous Hall conductivity that is proportional to the magnetization smoothly grows below $T_{\mathrm{C}}$, the anomalous Hall conductivity shows an additional enhancement below the characteristic temperature. Concomitantly, the AMR emerges and the magnitude of negative magnetoresistance begins to increase toward low temperature. Because there is no anomaly in the temperature dependence of magnetization around the characteristic temperature, the origin of these observations in transport properties is ascribed to some electronic structure with the energy scale of 30 K. We speculate this is caused by the spin splitting due to breaking of spatial inversion symmetry.

Figure 1

Temperature dependence of (a) magnetization at 0.1 T and 1.5 T for $H\perp c$ and $H\left|\right|c$, (b) saturation magnetic fields for $H\perp c$ and $H\left|\right|c$, and (c) zero field resistivity for $I\perp c$ and $I\left|\right|c$. Inset in (b) shows magnetization curves for $H\left|\right|c$ and $H\perp c$ at 10 K.

Figure 2

Magnetic field dependence of Hall resistivity at various temperatures.

Figure 3

(a) Temperature dependence of Hall conductivity ${\sigma }_{\mathrm{xy}}$ (blue dots) and magnetization (green dashed line) around 1.5 T. The inset shows the ${\sigma }_{\mathrm{xy}}$ data plotted against ${\sigma }_{xx}^2$. The black dashed line shows the ${\sigma }_{xx}$ dependence expected in the case of coexistence of skew scattering and intrinsic mechanisms (see main text). (b) Temperature dependence of $\mathrm{\Delta }{\rho }_{\mathrm{neg}}/\rho$ for $I\perp c$ and $I\left|\right|c$. (c) Temperature dependence of $\mathrm{\Delta }{\rho }_{\mathrm{AMR}}/\rho$ for $I\perp c$ and $I\left|\right|c$.

Figure 4

(a), (b) Magnetic field dependence of magnetoresistance $\mathrm{\Delta }\rho /\rho =({\rho }_{xx}\left(H\right)-{\rho }_{xx}(H=0))/{\rho }_{xx}(H=0)$ for (a) $I\perp c$ and (b) $I\left|\right|c$ in the magnetic fields parallel and perpendicular to $c$ axis at various temperatures.

Figure 5

(a) Magnetic field dependence of $\mathrm{\Delta }\rho /\rho$ for $I\left|\right|c$ and $H\perp c$ at 2 K, 5 K, and 10 K. (b) Magnetic field dependence of $\mathrm{\Delta }\rho /\rho$ at 2 K with various configurations of current and magnetic field. (c) Magnetic field dependence of $\mathrm{\Delta }\rho /\rho$ for $I\left|\right|c$ in the magnetic fields parallel and perpendicular to $c$ axis at 10 K. Dashed line shows vertically shifted $\mathrm{\Delta }\rho /\rho$ for $H\left|\right|c$. $\mathrm{\Delta }{\rho }_{\mathrm{pos}}/\rho$ and $\mathrm{\Delta }{\rho }_{\mathrm{AMR}}/\rho$ indicate the estimated components of positive magnetoresistance and AMR. (d) $\mathrm{\Delta }{\rho }_{\mathrm{pos}}/\rho$ at 7 T, $\mathrm{\Delta }{\rho }_{\mathrm{neg}}/\rho$ at 7 T, and $\mathrm{\Delta }{\rho }_{\mathrm{AMR}}/\rho$ for $I\left|\right|c$ plotted against ${\sigma }_{xx}$.