Long Range orders in multiferroics

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 new form of electric polarization \vec{P} -\vec{Q}\times(\vec{s_i}\times\vec{s_{j+1}}) where \vec{Q} is the wave vector of this long range order

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