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The ferroelectricity of multiferroics induced by spin order is commonlyexplained by considering either purely electronic or ion-displacementcontribution. However, there is no general model which includes both effectssimultaneously. Here, we suggest a realistic model to describe theion-displacement part of the ferroelectricity based on the spin-latticecoupling Hamiltonian. Combining this model with our previous pure electronicmodel for spin-order induced polarization, we propose a unified model thatincludes both effects. By applying the unified model to representativemultiferroics where the electronic and ion-displacement contributions varywidely, we find that this model can not only reproduce the first-principlesresults, but also provide insight into the origin of ferroelectricity.

Unified Model of Ferroelectricity Induced by Spin Order