Unconventional Anomalous Hall Effect Enhanced by a Noncoplanar Spin Texture in the Frustrated Kondo Lattice ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$

We have investigated the Hall effect in the geometrically frustrated Kondo lattice ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. In its spin-liquid-like paramagnetic regime, the Hall resistivity ${\rho }_{xy}$ is found to increase logarithmically on cooling. Moreover, in this low temperature region, the field dependence of the Hall conductivity ${\sigma }_{xy}$ shows a large enhancement up to $30{\Omega }^{-1}{\mathrm{cm}}^{-1}$ as well as a nonmonotonic change with the magnetization. Our results are far different from the anomalous Hall effect due to the spin-orbit coupling observed in ordinary magnetic conductors. We discuss the possible spin-chirality effect in the Ir $5d$ conduction band due to the noncoplanar texture of Pr $⟨111⟩$ Ising-like moments.

Figure 1

Temperature dependence of the Hall resistivity ${\rho }_{xy}$ ($T$) under a field of $B=0.3\mathrm{T}$ along the [111] direction. Inset: the Hall coefficient $R_H$ vs the susceptibility $4\pi M/B$ under a field of $B=0.3\mathrm{T}$ along the [111] direction.

Figure 2

Temperature dependence of the anomalous Hall coefficient $R_s$ ($T$) (left) and the longitudinal resistivity ${\rho }_{xx}$ ($T$) (right) under a field of $B=0.3\mathrm{T}$ along the [111] direction. Inset: ${\rho }_{xy}$ vs $M$ plot at $T=0.5\mathrm{K}$ for different field directions.

Figure 3

Field dependence of (a) the Hall conductivity ${\sigma }_{xy}(B)$ and (b) the magnetization $M(B)$ at $T=0.5\mathrm{K}$ for different field directions. Inset: field dependence of the anisotropy of the Hall conductivity ${\sigma }_{xy}^{[100]}/{\sigma }_{xy}^{[110]}$ and the magnetization $M^{[100]}/M^{[110]}$ at $T=0.5\mathrm{K}$.

Figure 4

Configurations of the Pr spins (green arrows) for the “2-in, 2-out” and “1-in, 3-out” states and the corresponding internal fields at the Ir sites (blue arrows) under the high field limit along the (a) [100] and (b) [111] directions. Open black and closed red arrows denote the directions of external and fictitious magnetic fields, respectively.