Origin of nonlinear magnetoelectric response in rare-earth orthoferrite perovskite oxides

We report a theoretical study of the nonlinear magnetoelectric response of $\mathrm{Gd}\mathrm{Fe}{\mathrm{O}}₃$ through an analytical approach combined with a Heisenberg model, which is fitted against first-principles calculations. Our theory reproduces the nonlinear change of polarization under applied magnetic field reported experimentally such that it allows us to analyze the origin of the large responses in different directions. We show that the nonlinear character of the response in these materials originates from the fact that the antiferromagnetic order of Gd atoms changes nonlinearly with respect to the applied magnetic field. Our model can be generalized to other materials in which the antiferromagnetic ordering breaks inversion symmetry.