Magnetoelectric effect

The magnetoelectric effect (ME) is the phenomenon of inducing magnetic (electric) polarization by applying an external electric (magnetic) field. The effects can be linear or/and non-linear with respect to the external fields. In general, this effect depends on temperature. The effect can be expressed in the following form

where P is the electric polarization, M the magnetization, E and H the electric and magnetic field, and α and β are the linear and nonlinear ME susceptibilities. The effect can be observed in single phase and composite materials. Some examples of single phase magnetoelectrics are Cr₂O₃, and multiferroics materials which show a coupling between the magnetic and electric order parameters. Composite magnetoelectrics are combinations of magnetostrictive and electrostrictive materials, such as ferromagnetic and piezoelectric materials. The size of the effect depends on the microscopic mechanism. In single phase magnetoelectrics the effect can be due to the coupling of magnetic and electric orders as observed in some multiferroics. In composite materials the effect originates from interface coupling effects, such as strain. Some of the promising applications of the ME effect are sensitive detection of magnetic fields, advanced logic devices and tunable microwave filters.

The magnetoelectric effect was first conjectured by P. Curie in 1894 while the term "magnetoelectric" was coined by P. Debye in 1926. A more rigorous prediction of a linear coupling between electric polarization and magnetization was shortly formulated by L. D. Landau and E. Lifshitz in one book of their famous series on theoretical physics. Only in 1959, I. Dzyaloshinskii, using an elegant symmetry argument, derived the form of a linear magnetoelectric coupling in Cr₂O₃. The experimental confirmation came just few months later when the effect was observed for the first time by D. Astrov. The general excitement which followed the measurement of the linear magnetoelectric effect lead to the organization of the series of MEIPIC (Magnetoelectric Interaction Phenomena in Crystals) conferences. Between the prediction of I. Dzialoshinskii and the MEIPIC first edition (1973), more than 80 linear magnetoelectric compounds were found. Recently, technological and theoretical progress triggered a renaissance of these studies and magnetoelectric effect is still heavily investigated.

In crystals, spin-orbit coupling is responsible for single-ion magnetocrystalline anisotropies (provide link) which determine preferential axes for the orientation of the spins (such as easy axes). An external electric field may change the local symmetry seen by magnetic ions and affect both the strength of the anisotropy and the direction of the easy axes. Thus, single-ion anisotropy can couple an external electric field to spins of magnetically ordered compounds.

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