Magneto-electric Coupling In Multiferroics And Mott Insulators

In multiferroics, magnetism and ferroelectricity coexist simultaneously and there is coupling between the electric polarization and magnetization. This novel cross-coupling in many kinds of recent found materials has evoked response in researches toward the fundamental origin of magneto-electric coupling as well as the potential application of these multiferroics to devices. The advantage of multiferroics lies the controlling of electric polarization though magnetic field as well as the magnetiza-tion though electric field. In this decade there are a lot of studies in the spin-driven ferroelectricity both in the theoretical and experimental research. In the spin-driven ferroelectric materials, the ferroelectricity is induced by the spatial inversion symme-try breaking magnetic order. Furthermore in some recent found ferroaixal materials the origin of magneto-electric coupling is still unknown. On the other hand, recent re-searches show that in Mott insulator, even the electric degree of freedom is suppressed, the delocalization of electrons still exists. This electron delocalization will lead to the emergence of electric dipole in frustrated Mott insulator. In this dissertation we will study the effect of octahedron rotation in mulferroics on the electric polarization and also the effect of spin orbit coupling on the electric dipole in Mott Insulator. In the first chapter we will review the known magneto-electric coupling in multiferroics and Mott insulator from the fundamental and potential industrial application aspects.In the second chapter we study the spin-orbital ferroelectricity in ferroaxial ma-terials. In this kind of materials the electrical polarization is induced by the com-bination of orbital order which comes from the octahedron of oxygen ligands rota- tion among neighboring transition metals and the magnetic order. Based on the spin current mechanism we also study the transition metal-ligand-transition metal clus-ter in 1D chain. We introduced the local frame to describe the local orbital at dif-ferent transition metal site. We find that the electric polarization is proportional to ei,i+1×(e-2αi,i+1lxei×e2αi,i+1lxei+1), where ei and ei+1 are unit spin direction vector at site i and i+1, respectively. Here ei,i+i is the unit vector connecting site i and i+1, αi,i+1 is the relative titled angle among the octahedron, and lx is the x component gen-erator in the SO(3) algebra. Then we apply this formula to different kinds of magnetic order. In the collinear case, there is a net electric polarization in contrast to the vanish-ing one in spin current mechanism. And in the cycloidal magnetic order, the electric polarization is not confined in the spin rotation plane. As also there are corrections to the canonical magnetic order.In chapter 3 we study the effect of spin orbit coupling on the delocalization of electrons in frustrated Mott insulator. Th charge redistribution in a triangle unit will induce the charge dipole. Due to the spin orbit coupling, there are some novel phe-nomena of charge dipole in the frustrated Mott insulator. Employing the perturbation canonical expansion, we can obtain the low temperature effective charge density and current operator. When the DM interaction is normal to the triangle plane, in the cy-cloidal magnetic order the electric polarization will in the spiral rotation plane and normal to the spiral propagation vector. Also when the DM interaction is in the tri-angle plane and normal to bond, the proper-screw magnetic order will induce a net electric polarization. From the aspect of symmetry, our result is consistent with the ionic spin current mechanism and the ionic one proposed by Arima. But the electric polarization we discussed is a electronic one.