image: An example of a scheme of virtual excitations corresponding to the coupling of spins of chromium and iron ions with an electric field. The iron ion, due to the interaction with the electric field, transfers from the ground state 5 Eθ to the excited state 5 Eξ , which then interacts with the ground states of three chrome ions through the oxygen ion 2. At the final (third) stage of the process, the iron ion passes into the ground state due to the spin-orbit interaction.
The authors, Kirill Vasin and Mikhail Eremin, contribute to the theory of electronic and structural properties of FeCr2O4 ferrimagnet. Due to the specific quantum state and the symmetry of FeO4 fragment, it has unusual electric and magnetic properties. Below TOO~150K, it lowers the symmetry with the macroscopic deformations due to the cooperative Jahn-Teller effect. The coupling between macroscopic deformation of the crystal FeCr2O4 and its inner ions shifts was revealed. The team enhanced the microscopic crystal field theory for 3D electrons with Kleiner's correction - the effect of penetrating charges density. It allows to have better prediction of electron-deformation coupling parameters, which is important for magnetostriction applications and critical temperature TOO. A FeO4 fragment has no inversion symmetry, therefore, the magnetization couples to the electric field (magnetoelectric coupling) via a crystal field from the nearest oxygen ions. Experimentally it was discovered by Chinese and German physicists, however, the nature of this effect had been mysterious.
The researchers developed a microscopic theory of magnetoelectric effect involved Fe2+ and Cr3+ spins. They found two effective mechanisms: the single-ion which demands at least a short-range order of Fe spins (spin-liquid or spin-glass, for instance), and the two-ions mechanism, where the canting between Fe and Cr spins is required. Both reproduce the existing experimental data on the electric polarization measurements by the order of the magnitude and the optical absorption spectrum.
Multiferroics are fascinating multifunctional materials which have a wide range of applications in electronics and spintronics, such as actuators, new types of non-volatile energy efficient memory, electric valves driven by magnetic field. etc. Putting this simply, we can magnetize the medium using electric field and vice versa. Magnetoelectric coupling depends on many competing interactions, and the theory is still unclear. The paper provides a method of calculations of the magnetoelectric and electron-deformation coupling parameters for 3D ions. The latter is also used to calculate magnetostriction, which is important for building sensors (like sonars) and actuators.
One of the important consequences is that the magnetic anisotropy can maintain not only the magnetic "memory", but also the electric "memory" of the material. The spin structure must have no inversion symmetry to maintain the electric polarization in the ground state. Also, the interplay of electric and magnetic domains may have a significant impact on electric polarization. To solve these issues, it is necessary to study the magnetic subsystem more accurate as well, which is unclear due to the lack of the experimental data and the complexity of the compound.