Magnetically Induced Polarization in Centrosymmetric Bonds.

We reveal the microscopic origin of electric polarization P[over →] induced by noncollinear magnetic order. We show that in Mott insulators, such P[over →] is given by all possible combinations of position operators r[over →][over ^]{ij}=(r[over →]{ij}^{0},r[over →]{ij}) and transfer integrals t[over ^]{ij}=(t_{ij}^{0},t_{ij}) in the bonds, where r[over →]{ij}^{0} and t{ij}^{0} are spin-independent contributions in the basis of Kramers doublet states, while r[over →]{ij} and t{ij} stem solely from the spin-orbit interaction. Among them, the combination t_{ij}^{0}r[over →]{ij}, which couples to the spin current, remains finite in the centrosymmetric bonds, thus yielding finite P[over →] in the case of noncollinear arrangement of spins. The form of the magnetoelectric coupling, which is controlled by r[over →]{ij}, appears to be rich and is not limited to the phenomenological law P[over →]∼ε_{ij}×[e_{i}×e_{j}] with ε_{ij} being the bond vector connecting the spins e_{i} and e_{j}. Using density-functional theory, we illustrate how the proposed mechanism works in the spiral magnets CuCl_{2}, CuBr_{2}, CuO, and α-Li_{2}IrO_{3}, providing a consistent explanation for the available experimental data.