Spin Chirality Fluctuations and Anomalous Hall Effect in Itinerant Ferromagnets

The anomalous Hall effect due to the spin chirality order and fluctuation is studied theoretically in a Kondo lattice model without the relativistic spin-orbit interaction. Even without the correlations of the localized spins, ${\sigma }_{xy}$ can emerge depending on the lattice structure and the spin anisotropy. We reveal the condition for this chirality-fluctuation driven mechanism for ${\sigma }_{xy}$. Our semiquantitative estimates for a pyrochlore oxide ${\mathrm{N}\mathrm{d}}_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$ give a finite ${\sigma }_{xy}\sim 10{\Omega }^{-1}{\mathrm{c}\mathrm{m}}^{-1}$ together with a high resistivity ${\rho }_{xx}\sim {10}^{-4}–{10}^{-3}\Omega \mathrm{c}\mathrm{m}$, in agreement with experiments.

Figure 1

Low-temperature spin structure of the Mo itinerant spins and the Nd localized spins in a unit cell for ${\mathrm{N}\mathrm{d}}_2{\mathrm{M}\mathrm{o}}_2{\mathrm{O}}_7$.

Figure 2

Black lines represent numerical results in the local moment limit of the localized spins for $⟨s^z⟩$, $⟨s^{\perp }⟩$, ${\sigma }_{xx}$, and ${\sigma }_{xy}$ after rescaling [27]. $J_{fd}=80\mathrm{K}$ [21] and $⟨n_i⟩=0.7$ are adopted. Grey lines represent experimental results for ${\sigma }_{xy}$ and ${\sigma }_{xx}$ by Taguchi et al. [18].

Figure 3

Diagrammatic representation of $V_{j,j^{\prime }}(\mathbf{q})$. Solid lines, dashed lines, and dots represent the electron Green’s function $G_{i,i^{\prime }|\alpha ,{\alpha }^{\prime }}(\mathbf{k},\omega )$, spin correlation function $T{\chi }_{j,j^{\prime }}(\mathbf{q})$, and the coupling $2J_{fd}{v}_{\mathbf{q},i,j}\overrightarrow{\sigma }·{\overrightarrow{n}}_j{\delta }_{i,i^{\prime }}$. The irreducible vertex corresponds to the dashed line with two dots at the ends.

Figure 4

Black lines represent numerical results after rescaling [27] where correlations of the localized spins are taken account. $J_{fd}=40\mathrm{K}$ [21] and $⟨n_i⟩=2/3$ are adopted. Grey lines represent experimental results for ${\sigma }_{xy}$ and ${\sigma }_{xx}$ [18].