Article

# Topological chiral magnonic edge mode in a magnonic crystal

Physical review. B, Condensed matter (Impact Factor: 3.77). 04/2012; 87(17). DOI: 10.1103/PhysRevB.87.174427

Source: arXiv

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**ABSTRACT:**Magnetic excitations in ferromagnetic systems with a noncollinear ground state magnetization experience a fictitious magnetic field due to the equilibrium magnetic texture. Here, we investigate how such fictitious fields lead to thermal Hall effects in two-dimensional insulating magnets in which the magnetic texture is caused by spin-orbit interaction. Besides the well-known geometric texture contribution to the fictitious magnetic field in such systems, there exists also an equally important contribution due to the original spin-orbit term in the free energy. We consider the different possible ground states in the phase diagram of a two-dimensional ferromagnet with spin-orbit interaction: the spiral state and the skyrmion lattice, and find that thermal Hall effects can occur in certain domain walls as well as the skyrmion lattice.Physical review. B, Condensed matter 08/2012; 87(2). · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In the ferromagnetic insulator with Dzyaloshinskii-Moriya interaction, we theoretically predict and numerically verify a topological magnon insulator, where the charge-free magnon is topologically protected to transport along the edge while it is insulating in the bulk. Within the bulk band gaps, edge states form a connected loop as a $4\pi$- or $8\pi$-period M\"{o}bius strip in the wave vector space. As a consequence, the chiral energy current traveling along the corresponding edge is topologically protected from defects or disorders. Using the nonequilibrium Green's function method, we demonstrate that the energy current carried by magnons with energy in the bulk gap localizes at edges and prefers to travel along one edge in only one direction at nonequilibrium steady state. Our prediction about topological magnon insulator could be observed at a wide energy range in the thin film of the insulating ferromagnet, such as Lu$_2$V$_2$O$_7$.Physical review. B, Condensed matter 10/2012; 87(14). · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Based on a linearized Landau-Lifshitz equation, we show that two-dimensional periodic allay of ferromagnetic particles coupled with magnetic dipole-dipole interactions supports chiral spin-wave edge modes, when subjected under the magnetic field applied perpendicular to the plane. The mode propagates along a one-dimensional boundary of the system in a unidirectional way and it always has a chiral dispersion within a band gap for spin-wave volume modes. Contrary to the well-known Damon-Eshbach surface mode, the sense of the rotation depends not only on the direction of the field but also on the strength of the field; its chiral direction is generally determined by the sum of the so-called Chern integers defined for spin-wave volume modes below the band gap. Using simple tight-binding descriptions, we explain how the magnetic dipolar interaction endows spin-wave volume modes with non-zero Chern integers and how their values will be changed by the field.Physical review. B, Condensed matter 03/2013; 87(17). · 3.77 Impact Factor

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