Static And Dynamical Magnetoelectric Effects In Multiferroics

Multiferroic materials, in which ferroelectric and magnetic ordering are in presence simultaneously, exhibit unprecedented physical properties due to the coupling between electric and magnetic order parameters. The significant cross-coupling effects in the newly found materials have invigorated research in multi-ferroics as they offer a new route toward fundamental understanding of how the spin and lattice degrees of freedom interact to produce macroscopic phenomena. Furthermore, the emergence of multiple functional properties in those materi-als has stimulated the application in next generations of novel devices in which polarization can be controlled by a magnetic field or vice versa. Recently, the study for an enhanced coupling between dual parameters has brought in discov-eries of new class of materials called magnetism-driven ferroelectrics. In those materials, the ferroelectricity is induced by a fundamental new mechanism, by which magnetic orders with broken symmetry result in ferroelectric distortion. This dissertation focuses on the study of static and dynamical magnetoelectric coupling in multiferroic materials. In the first chapter, we make a brief overview of history, progress, and current status of magnetoelectric effects and multifer-roics. The main theoretical studies and original results of this dissertation work are listed as follows:In chapter2, we study the bond distortion effect on electric polarization in spiral multiferroics magnets based on cluster and chain models. The bond distor-tion breaks inversion symmetry and modify the d-p hybridization. Consequently, it will affect electric polarization which can be divided into spin-current part and lattice-mediated part. The spin current polarization can be written in terms of ei,j×(ei×ej) and the lattice-mediated polarization exists only when the M-O-M bond is distorted. The electric polarization for three-atom M-O-M and four-atom M-O2-M clusters is calculated. We also study possible electric ordering in three kinds of chains that consists of different clusters. The electric polarization of the systems may be ferroelectric or ferrielectric ordered that is closely related to the geometry of the bond. Then, we apply our theory to multiferroics copper oxides and find that our results agree with experimental observations. The effect of bond-distortion on the magnetic-driven polarization provides a clue to clarify the anisotropy of the electric polarization observed in LiCuV04and LiCu2O2and to elucidate the puzzle of non-multiferroicity in NaCu2O2.In chapter3, we investigate the dynamical magnetoelectric coupling of multi-ferroic materials. We study conically spiral multiferroic magnets by generalizing the spin current model. We show that a conically spiral multiferroics shows unique dynamical magnetoelectric property which differs from a conventional cycloidal magnet. We found that the magnon mode at q=0remains gapless and the doubly degenerate gapful modes at q=±Q are lifted. In contrast to the in-plane cycloidal spiral situation where only one electromagnon is observed, the hybridized collective excitation, the called electromagnon, splits into two branches. The theoretical results agree with the existing experiments well and we make predictions for other compounds. Our theoretical investigations will provide a clue for experimentalists to elucidate the novel multiferroic excitation in conically multiferroic materials.In chapter4, we extend our investigation of the dynamical magnetoelectric effects to a class of spiral multiferroics including an easy-axis anisotropy. This single-ion anisotropy perturbs the perfect spin helix adding higher-order harmon-ics. We calculate the spin wave excitations and show that the coupling between spin and electric polarization induces an effective spin anisotropy resulting in an additional gapped mode. In analogy to the perfect cycloidal spin structure, the electromagnon can be assigned to the spin wave modes of the distorted he-limagnets at the ordering wave vector Q. It is shown that the electromagnon in the distorted helimagnets is indeed affected by the helix distortion which can be experimentally controlled. This provides a possibility to manipulate electro-magnons via doping or applying external magnetic field.