A mechanism of spin structure-driven anomalous Hall effect (AHE) in tilted ferromagnetic metals is proposed by taking account of the $d$-orbital degree of freedom. We find that a conduction electron acquires a Berry phase due to the complex $d$-orbital wave function, in the presence of noncollinear spin structure and the spin-orbit interaction. The AHE driven by this orbital-derived Berry phase is much larger than the AHE induced by spin chirality, and it naturally explains the salient features of spin structure-driven AHE in pyrochlore ${\text{Nd}}_2{\text{Mo}}_2{\text{O}}_7$. Since the proposed AHE can occur even for coplanar spin orders $\left(M_z=0\right)$, it is expected to emerge in other interesting geometrically frustrated systems.

• Received 4 February 2009

DOI:https://doi.org/10.1103/PhysRevB.80.100401