Induced magnetization in ferroelectric-antiperovskite heterostructure

We theoretically predict the linear magnetoelectric effect (ME) in ferroelectric-antiperovskite PbTiO$_{3}$/Mn$_{3}$GaN heterostructure. The effect is caused by the recently reported piezomagnetic nature of the Mn$_{3}$GaN. Elastic deformations in the Mn$_{3}$GaN are due to the surface strain and the soft mode atomic displacements from~ferroelectric to the antiperovskite (AP) phase. Both mechanisms lower the symmetry of the AP component, which results in the induced magnetization. Reversal of the polarization direction in the ferroelectric phase results in the magnetization reversal in Mn$_{3}$GaN, thus the observed effect is linear. We study few interface geometries to account for the electrostatic complementarity at the surface. Those interfaces, which are electrostatically incompatible exhibit strong tetragonal distortion of the cell. The induced magnetization depends on the termination of the components of the heterostructure, and ranges from 0.25 $\mu _{B}$ to 0.6 $\mu _{B}$ per unit cell of Mn$_{3}$GaN. All calculations were performed by projector augmented wave method.