  We consider a simple integrable model of a spin chain exhibiting the
Magnetoelectric Effect (MEE). Starting from the periodic S=1/2 XXZ-chain with
Dzyaloshinskii-Moriya terms, which we consider as a local electric polarization
in the spirit of the Katsura-Nagaosa-Baladsky (KNB) mechanism, we perform the
mapping onto the conventional XXZ-chain with twisted boundary conditions. Using
the techniques of Quantum Transfer Matrix (QTM) and Non-Linear Integral
Equations (NLIE) we obtain the magnetization, electric polarization and
magnetoelectric tensor as functions of magnetic and electric field for
arbitrary temperatures. We investigate these dependencies as well as the
thermal behavior of the above mentioned physical quantities, especially in the
low-temperature regime. We found several regimes of polarization. Adjusting the
magnetic field one can switch the system from one regime to another. The
features of the critical properties connected with the MEE are also
illustrated.
