Hosho Katsura

Spin Current and Magnetoelectric Effect in Noncollinear Magnets

A new mechanism of the magnetoelectric effect based on the spin supercurrent is theoretically presented in terms of a microscopic electronic model for noncollinear magnets. The electric polarization P(ij) produced between the two magnetic moments S(i) and S(j) is given by P proportional e(ij) X (S(i) X S(j)) with e(ij) being the unit vector connecting the sites i and j. Applications to the spiral spin structure and the gauge theoretical interpretation are discussed.

Quantum spin Hall effect in a transition metal oxide Na2IrO3.

We study theoretically the electronic states in a 5d transition metal oxide Na2IrO3, in which both the spin-orbit interaction and the electron correlation play crucial roles. A tight-binding model analysis together with the first-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Because of the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.

Nearly Flatbands with Nontrivial Topology

We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flatband aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

Observation of the Magnon Hall Effect

Observing the Magnon Hall Effect The anomalous thermal Hall effect occurs when transverse heat transport is generated in the absence of an external magnetic field. The transport may be mediated by free carriers, phonons, or spin waves (magnons). Onose et al. (p. 297) observed this effect in an insulating ferromagnet and were able to rule out free carriers and phonons as the mediators of the thermal transport. Instead, the observations are consistent with a theory ascribing its origin to magnon propagation. This thermal magnon Hall effect is caused by the spin-orbit interaction, which acts in a fashion similar to the magnetic field in the conventional Hall effect. Its observation in an insulator may enable the elimination of losses in spintronic applications. Spin excitations in an insulating ferromagnet exhibit an anomalous thermal Hall effect. The Hall effect usually occurs in conductors when the Lorentz force acts on a charge current in the presence of a perpendicular magnetic field. Neutral quasi-particles such as phonons and spins can, however, carry heat current and potentially exhibit the thermal Hall effect without resorting to the Lorentz force. We report experimental evidence for the anomalous thermal Hall effect caused by spin excitations (magnons) in an insulating ferromagnet with a pyrochlore lattice structure. Our theoretical analysis indicates that the propagation of the spin waves is influenced by the Dzyaloshinskii-Moriya spin-orbit interaction, which plays the role of the vector potential, much as in the intrinsic anomalous Hall effect in metallic ferromagnets.

Dynamical magnetoelectric coupling in helical magnets.

We develop a theory of collective mode dynamics in the helical magnets coupled to electric polarization via spin-orbit interaction. The low-lying modes associated with the ferroelectricity are not the transverse optical phonons, but are the spin waves hybridized with the electric polarization. This hybridization leads to the Drude-like dielectric function epsilon(omega) in the limit of zero magnetic anisotropy. There are two additional low-lying modes: phason of the spiral and rotation of helical plane along the polarization axis. Role of these low-lying modes in the neutron scattering and antiferromagnetic resonance is revealed, and a novel experiment to detect the dynamical magnetoelectric coupling is discussed.

Theory of the Thermal Hall Effect in Quantum Magnets

We present a theory of the thermal Hall effect in insulating quantum magnets, where the heat current is totally carried by charge-neutral objects such as magnons and spinons. Two distinct types of thermal Hall responses are identified. For ordered magnets, the intrinsic thermal Hall effect for magnons arises when certain conditions are satisfied for the lattice geometry and the underlying magnetic order. The other type is allowed in a spin liquid which is a novel quantum state since there is no order even at zero temperature. For this case, the deconfined spinons contribute to the thermal Hall response due to Lorentz force. These results offer a clear experimental method to prove the existence of the deconfined spinons via a thermal transport phenomenon.

Localization and fractality in inhomogeneous quantum walks with self-duality.

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-binding model with a quasiperiodic potential. When the period of coin operators is incommensurate to the lattice spacing, we rigorously show that the limit distribution of the quantum walk is localized at the origin. We also numerically study the eigenvalues of the one-step time evolution operator and find the Hofstadter butterfly spectrum which indicates the fractal nature of this class of quantum walks.

Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators

We have investigated the thermal Hall effect of magnons for various ferromagnetic insulators. For pyrochlore ferromagnetic insulators Lu

Entanglement in an SU(n) valence-bond-solid state

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Extreme sensitivity of a frustrated quantum magnet: Cs2CuCl4

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