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Spin-electric interactions and magnetoelectric properties of triangular rare-earth molecular nanoclusters are investigated by the example of Dy 3 . The effective spin-electric Hamiltonian is derived on the base of a developed quantum-mechanical model of the cluster spin structure. It is shown that a toroidal (anapole) moment is induced in such clusters with magnetic field exceeding some threshold value or with crossed electric and magnetic fields (or an electric current). Due to the considerable relaxation time of the state with non-zero toroidal moment, it is possible to observe the non-equilibrium quantum linear magnetoelectric effect.

We study the quantum dynamics of polygonal rare-earth molecular clusters with Ising-type ion magnetization. It is shown that the ground state of such systems is a non-magnetic quasi-doublet of states with oppositely twisted ion spins. The states differ in sign of toroidal moment, which is a natural physical quantity to characterize the spin chirality of the clusters. The possibility of macroscopic quantum tunneling of toroidal moment between the states is predicted. The effects of an external current is considered, both in equilibrium and in the frames of the Landau-Zener-Stückelberg tunneling model. The special treatment is given for the most important case of triangular rare-earth clusters.The model. -We consider a spin ring, a system of N non-Kramers rare-earth ions located in the apices of a regp-1 arXiv:1009.0371v2 [cond-mat.mes-hall]

Magnetoelectric properties of a molecular crystal formed by dysprosium triangular clusters are investigated. The effective spin-electric Hamiltonian is derived on the base of developed quantum mechanical model of the cluster spin structure. The magnetoelectric contribution to the free energy of the crystal is calculated. The analysis reveals several distinctive features of the magnetoelectric effect, which are not typical for conventional paramagnetic systems at low temperatures. The peculiarities are explained by the chirality of the dysprosium core of the molecules. PACS numbers: 75.85.+t -Magnetoelectric effects, multiferroics; 75.45.+j -Macroscopic quantum phenomena in magnetic systems arXiv:1108.1460v1 [cond-mat.mes-hall]

The magnetoelectricity of garnets is considered by means of a symmetry and quantum mechanical combined analysis. It is shown, that the magnetoelectric effect is not realized in most garnets although the necessary condition of the crystal magnetic structure antisymmetry in them is held at low temperatures. Nevertheless, the effect can be observed in some garnets as well as other odd effects, namely, piezomagnetic effect, magnetic field evoked piezoelectric one, etc. It is also discovered that magnetic fields can induce specific antiferroelectric structures in garnet crystals and produce electric polarization in epitaxial films. The polarization can also be caused in a bulk crystal by an inhomogeneous magnetic field.