Spin chirality, Berry phase, and anomalous Hall effect in a frustrated ferromagnet

An electron hopping on non-coplanar spin sites with spin chirality obtains a complex phase factor (Berry phase) in its quantum mechanical amplitude th at acts as an internal magnetic field, and is predicted to manifest itself in the Hall effect when it is not cancelled. The present combined work of t ransport measurement, neutron scattering, and theoretical calculation provi des evidence that the gigantic anomalous Hall effect observed in Nd2Mo2O7, a pyrochlore ferromagnet with geometrically frustrated Lattice structure, i s mostly due to the spin chirality and the associated Berry phase originati ng from the Mo spin tilting.