Microscopic origin of magnetoelectric coupling in noncollinear multiferroics

An universal microscopic mechanism to understand the interplay between the electric and magnetic degrees of freedom in noncollinear multiferroics is developed. In a system with a strong spin-orbit coupling, we show that there is a pure electric mechanism that the ferroelectricity is generated by noncollinear magnetism through an electric current cancellation process, which saves the pure electric energy. This mechanism provides a simple estimation and sets a physical limitation of the value of ferroelectricity in noncollinear multiferroic materials.