Spin Chirality, Berry Phase, and Anomalous Hall Effect in a Frustrated Ferromagnet

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Abstract
An electron hopping on non-coplanar spin sites with spin chirality obtains a complex phase factor (Berry phase) in its quantum mechanical amplitude that 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 transport measurement, neutron scattering, and theoretical calculation provides evidence that the gigantic anomalous Hall effect observed in Nd 2 Mo 2 O 7 , a pyrochlore ferromagnet with geometrically frustrated lattice structure, is mostly due to the spin chirality and the associated Berry phase originating from the Mo spin tilting.