Unified Model of Ferroelectricity Induced by Spin Order

The ferroelectricity of multiferroics induced by spin order is commonly explained by considering either purely electronic or ion-displacement contribution. However, there is no general model which includes both effects simultaneously. Here, we suggest a realistic model to describe the ion-displacement part of the ferroelectricity based on the spin-lattice coupling Hamiltonian. Combining this model with our previous pure electronic model for spin-order induced polarization, we propose a unified model that includes both effects. By applying the unified model to representative multiferroics where the electronic and ion-displacement contributions vary widely, we find that this model can not only reproduce the first-principles results, but also provide insight into the origin of ferroelectricity.