In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material.
[1][2] The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized.
Some promising applications of the ME effect are sensitive detection of magnetic fields, advanced logic devices and tunable microwave filters.
[4] The first example of a magnetoelectric effect was discussed in 1888 by Wilhelm Röntgen, who showed that a dielectric material moving through an electric field would become magnetized.
A mathematical formulation of the linear magnetoelectric effect was included in Lev Landau and Evgeny Lifshitz's Course of Theoretical Physics.
[7] Only in 1959 did Igor Dzyaloshinskii,[8] using an elegant symmetry argument, derive the form of a linear magnetoelectric coupling in chromium(III) oxide (Cr2O3).
Recently, technological and theoretical progress, driven in large part by the advent of multiferroic materials,[10] triggered a renaissance of these studies[11] and magnetoelectric effect is still heavily investigated.
which describes a linear response of the electric polarization to a magnetic field, and vice versa:[7] The tensor
The first material where an intrinsic linear magnetoelectric effect was predicted theoretically and confirmed experimentally was Cr2O3.
Multiferroics are another example of single-phase materials that can exhibit a general magnetoelectric effect[11] if their magnetic and electric orders are coupled.
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.
The main interaction between spins of transition metal ions in solids is usually provided by superexchange, also called symmetric exchange.
As the strength of symmetric exchange depends on the relative position of the ions, it couples the spin orientations to the lattice structure.
Coupling of spins to a collective distortion with a net electric dipole can occur if the magnetic order breaks inversion symmetry.
Thus, symmetric exchange can provide a handle to control magnetic properties through an external electric field.
[14] Thin film strategy enables achievement of interfacial multiferroic coupling through a mechanical channel in heterostructures consisting of a magnetoelastic and a piezoelectric component.
[15] This type of heterostructure is composed of an epitaxial magnetoelastic thin film grown on a piezoelectric substrate.
For this system, application of a magnetic field will induce a change in the dimension of the magnetoelastic film.
This process, called magnetostriction, will alter residual strain conditions in the magnetoelastic film, which can be transferred through the interface to the piezoelectric substrate.
In this case, the interface plays an important role in mediating the responses from one component to another, realizing the magnetoelectric coupling.
In light of this interest, advanced deposition techniques have been applied to synthesize these types of thin film heterostructures.
Molecular beam epitaxy has been demonstrated to be capable of depositing structures consisting of piezoelectric and magnetostrictive components.
[22] It was shown that in general case of cubic hexoctahedral crystal the four phenomenological constants approach is correct.
[23] The flexomagnetoelectric effect appears in spiral multiferroics[24] or micromagnetic structures like domain walls[25] and magnetic vortexes.
Existing symmetry classification[29] of magnetic domain walls was applied for predictions of electric polarization spatial distribution in their volumes.
[30][31] The predictions for almost all symmetry groups conform with phenomenology in which inhomogeneous magnetization couples with homogeneous polarization.
The total synergy between symmetry and phenomenology theory appears if energy terms with electrical polarization spatial derivatives are taken into account.