Magnetoelectric effect

In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. 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. A material where such a coupling is intrinsically present is called a magnetoelectric. In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. 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. A material where such a coupling is intrinsically present is called a magnetoelectric. Historically, the first and most studied example of this effect is the linear magnetoelectric effect. Mathematically, while the electric susceptibility χ e {displaystyle chi ^{e}} and magnetic susceptibility χ v {displaystyle chi ^{v}} describe the electric and magnetic polarization responses to an electric, resp. a magnetic field, there is also the possibility of a magnetoelectric susceptibility α i j {displaystyle alpha _{ij}} which describes a linear response of the electric polarization to a magnetic field, and vice versa: The tensor α {displaystyle alpha } must be the same in both equations. Here, P is the electric polarization, M the magnetization, E and H the electric and magnetic fields. The SI Unit of α is which can be converted to the practical unit by =1.1 x10−11 εr . For the CGS unit, = 3 x 108 /(4 x π) The first material where an intrinsic linear magnetoelectric effect was predicted theoretically and confirmed experimentally is Cr2O3. This is a single-phase material. Multiferroics are another example of single-phase materials that can exhibit a general magnetoelectric effect if their magnetic and electric orders are coupled. Composite materials are another way to realize magnetoelectrics. There, the idea is to combine, say a magnetostrictive and a piezoelectric material. These two materials interact by strain, leading to a coupling between magnetic and electric properties of the compound material. Some promising applications of the ME effect are sensitive detection of magnetic fields, advanced logic devices and tunable microwave filters. 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. The possibility of an intrinsic magnetoelectric effect in a (non-moving) material was conjectured by P. Curie in 1894, while the term 'magnetoelectric' was coined by P. Debye in 1926.A mathematical formulation of the linear magnetoelectric effect was included in L. D. Landau and E. Lifshitz famous book 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, driven in large part by the advent of multiferroic materials, triggered a renaissance of these studies and magnetoelectric effect is still heavily investigated. If the coupling between magnetic and electric properties is analytic, then the magnetoelectric effect can be described by an expansion of the free energy as a power series in the electric and magnetic fields E {displaystyle E} and H {displaystyle H} : Differentiating the free energy will then give the electric polarization P i = − ∂ F ∂ E i {displaystyle P_{i}=-{frac {partial F}{partial E_{i}}}} and the magnetization M i = − ∂ F ∂ H i {displaystyle M_{i}=-{frac {partial F}{partial H_{i}}}} .Here, P s {displaystyle P^{s}} and M s {displaystyle M^{s}} are the static polarization, resp. magnetization of the material, whereas χ e {displaystyle chi ^{e}} and χ v {displaystyle chi ^{v}} are the electric, resp. magnetic susceptibilities. The tensor α {displaystyle alpha } describes the linear magnetoelectric effect, which corresponds to a polarization induced linearly by a magnetic field, and vice versa. The higher terms with coefficients β {displaystyle eta } and γ {displaystyle gamma } describe quadratic effects. For instance, the tensor γ {displaystyle gamma } describes a linear magnetoelectric effect which is, in turn, induced by an electric field. The possible terms appearing in the expansion above are constrained by symmetries of the material. Most notably, the tensor α {displaystyle alpha } must be antisymmetric under time-reversal symmetry. Therefore, the linear magnetoelectric effect may only occur if time-reversal symmetry is explicitly broken, for instance by the explicit motion in Röntgens' example, or by an intrinsic magnetic ordering in the material. In contrast, the tensor β {displaystyle eta } may be non-vanishing in time-reversal symmetric materials.