Magnetoelectricity

Freeman, A. J. Schmid, H. (eds) (1975) Magnetoelectric Interaction Phenomena in Crystals, Gordon Breach, New York. 

F erromagnetoelectric Magnetoelectric coefficients Magnetic field and electric field CrjOj... 

Dt, electric displacement Pi AT, pyroelectric effect Ky Ej, permittivity Ky Hj, magnetoelectric polarizability dyic rSjk, piezoelectric effect... 

Bh magnetic induction q AT, pyromagnetic effect Xji Ej, converse magnetoelectric effect Pij Hj, magnetic permeability Qijk <3jk, piezomagnetic effect... 

The magnetoelectric polarizability [X, ] of a crystalline material gives rise to a magnetic moment I (Tan axial vector, or T( 1 )ax) when the crystal is placed in an electric field E (Aa polar vector, or T( 1)). Its transpose [T/ ] describes the converse magnetoelectric effect in which the roles of Y and X are interchanged. To find the structure of K = [T, ], we look for IRs which have components of both xy z and Rx Ry Rz as bases. 

If we can combine ferroelectrically polarizable guest molecules with PCPMs, then we can obtain new types of multiferroic materials, where ferroelectricity and ferromagnetism coexist. Such multifunctional materials have recently aroused increasing interest from the viewpoint of the development of new materials with very large magnetoelectric effects. [Mn3(HCOO)6] EtOH is considered to be the first ferroelectric PCP.182 Because the desolvated compound [Mn3(HCOO)6] shows a very small and almost temperature-independent dielectric constant, irrespective of the direction of the electric field,183 the observed ferroelectric property is considered to come mainly from the guest EtOH molecules. 

Sohmid, H. 1975 Magnetoelectric Interaction Phenomena in Crystals (ed. H. J. Freeman H. Schmid) New York Gordon and Breach. 

Fig. 5 Magnetocapacitance and magnetoelectric effects in Tb MnCri, Magnetic field-induced change in the dielectric constant (a) and (b), electric polarization along the c and a axes, respectively (c) and (d). Magnetic fields are applied along the b axis. The data for (d) were collected after magnetic field cooling. The numbers in (d) denote the order of measurements at 9 K (from ref. 14).

These new molecular tensors seem very promising, as they are related to other spectroscopic parameters. A periodic magnetic field induces an electric field at the nuclei, which can be described in terms of an electromagnetic shielding tensor [15]. This is related to the intensity of absorption bands in vibrational circular dichroism (VCD) [16, 20]. Also, in the presence of a periodic electric field, the nuclei are acted upon by an induced magnetic field. This leads to the definition of magnetoelectric shielding [15]. 

Some molecular tensors (electric dipole polarizability, electric and magnetoelectric shielding) are origin independent, as can be immediately found by inspection of definitions (87)-(112). Other tensors depend on the origin assumed for the multipole expansion. For instance, in a change of origin... 

Pirson, S.J., 1981. Significant advances in magnetoelectrical exploration. In B.M. Gottlieb (ed.). Unconventional Methods in Exploration for Petroleum and Natural Gas II. Southern Methodist University Press, Dallas, pp. 169-196. 

Fig. 19 Hamiltonian, definition of magnetoelectric coefficients a, and theoretical calculations of the magnetoelectric coefficients temperature dependences (simplified model) [37]...

Magnetoelectric coefficient a y and its derivative daxy/dT vs. temp>erature for TbP04. a) Ebcperimental b) thecweticaL... 

Fig. 20 The experimental and theoretical data for the magnetoelectric coefficients of TbP04 crystal according to [39]...

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