Magneto-electric couplings in Sr_1−xMn_xTi_1−yMn_yO₃

We study the interactions between Mn impurities substituting for different cations in the incipient ferroelectric perovskite SrTiO₃. Using the LSDA+U and many-body perturbation theory, we show that magnetic interactions J between off-centered Mn²⁺_A ions substituting for Sr and inducing ferroelectric instability in the system is negligible. For the nearest neighbours |J_AA/k_B| < 5 K. We show that the interactions involving Mn⁴⁺_B ions substituting for Ti are much larger (J_AA ≪ J_AB ≪ J_BB). The dependence of J_AB on Mn²⁺_A position contributes to magnetoelectricity of the system. These findings are in accordance with recent experimental observations, and provide the key for understanding microscopic mechanisms of magnetoelectricity in manganese doped incipient ferroelectrics.