Laboratoire de Physique Théorique
Toulouse - UMR 5152

We considered the exact calculations of the magnetoelectric effect realized by means of Katsura-Nagaosa-Balatsky(KNB) mechanism for S=1/2 XXZ-chain with DM-term and for XX-chain with DM-terms and three-spin interaction. The KNB mechnism connects the local polarization with the cross product of two spin from adjacent sites. Thus, the DM-term have an interpretation as an interaction between local polarization and external electric field. We apply the quantum transfer matrix(QTM) and non-linear integral equation(NLIE) technique for exact description of the mutual influence of magnetic and dielectric properties at finite temperature for XXZ-chain. For the XX-chainand the Jordan-Wigner fermionization is applied. We obtain the exact plots of polarization(magnetization) dependence on magnetic(electric) filed as well as temperature dependence of the magnetielectric tensor. The results, particularly, show several possible regimes of polarization, linear, square-root, quadratic and some combination of them for XXZ-chain. The switching between different regimes can be easily performed by adjusting the magnetic field. In case of XY-chain with three-spin interaction which can be formally considered as a phenomenological interaction between local dipole and magnetic moment the plots exhibit non-trivial magnetoelectric effect, i.e. the induction of polarization(magnetization) by magnetic(electric) field at zero electric(magnetic) field.