We proposed that in multiferroics, there exists a third long-range order besides the electric polarization and magnetic order. This long-range order reduces the symmetry of the spatial part of the wave functions of electrons. Thus the cancellation in the “spin-current” model can be avoided. As a result, the expectation value of electric polarization will be larger by an order of magnitude. We have derived a distinct form of electric polarization $\vec{P}\sim -\widehat{Q}\times \left({\widehat{s}}_j\times {\widehat{s}}_{j+1}\right)$, where $\vec{Q}$ is the wave vector of this long-range order.

• Received 26 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.224414