Electric field dependence of the magnetic anisotropy energy in magnetite (Fe3O4)

Abstract

The application of a static magnetic field to a single crystal of synthetic magnetite (${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$) at 4.2°K is found to induce a static electric polarization which is a nonlinear function of the components of the magnetic field and exists even in the absence of an applied electric field. A newly modified thermodynamic theory shows that these nonlinear magnetoelectric effects arise from the electric field dependence of the macroscopic magnetic anisotropy energy. No such dependence has been observed previously at any temperature in any material. The values of the electric field derivatives of two of the anisotropy constants are determined by means of experiments in saturating magnetic fields. With the use of these two values, and without the use of adjustable parameters, the modified thermodynamic theory successfully predicts the measured curves of (a) the induced electric polarization as a function of the orientation of a nonsaturating magnetic field of constant magnitude and (b) the induced electric polarization as a function of the magnitude of a sufficiently large magnetic field of constant orientation. After a brief discussion of the microscopic origin of the electric field derivatives of the anisotropy constants, appropriate symmetry arguments are used in conjunction with the experimental data to show for the first time that the point group of the crystallographic space group of magnetite at 4.2°K is the group 1.