Antiferromagnetic spin cantings as a driving force of ferroelectricity in multiferroic Cu₂OSeO₃

Ferroelectric properties of cubic chiral magnet Cu₂OSeO₃ can emerge due to the spin noncollinearity induced by antiferromagnetic cantings. The cantings are the result of the Dzyaloshinskii-Moriya interaction and in many ways similar to the ferromagnetic cantings in weak ferromagnets. An expression for the local electric polarization is derived, including terms with gradients of magnetization [Formula: see text]. When averaged over the crystal the electric polarization has a non-vanishing part associated with the anisotropy of the crystal point group 23. In the framework of the microscopic theory, it is shown that both scalar and vector products of spins, [Formula: see text] and [Formula: see text], can give contributions of the same order of magnitude into the electric polarization.