Topological magnon insulator in insulating ferromagnet

Abstract

In the ferromagnetic insulator with the Dzyaloshinskii-Moriya interaction, we theoretically predict and numerically verify a topological magnon insulator, where the charge-free magnon is topologically protected for transporting along the edge/surface while it is insulating in the bulk. The chiral edge states form a connected loop as a 4π-or 8π-period Möbius strip in the spin-wave vector space, showing the nontrivial topology of magnonic bands. Using the nonequilibrium Green's function method, we explicitly demonstrate that the one-way chiral edge transport is indeed topologically protected from defects or disorders. Moreover, we show that the topological edge state mainly localizes around edges and leaks into the bulk with oscillatory decay. Although the chiral edge magnons and energy current prefer to travel along one edge from the hot region to the cold one, the anomalous transports are identified in the opposite edge, which reversely flow from the cold region to the hot one. Our findings could be validated within wide energy ranges in various magnonic crystals, such as Lu2V2O7.

Thermal Hall effect of spins in a paramagnet

“…4. A striking parallel of the topology of the magnon band structure to that of electronic bands responsible for quantized Hall effect was emphasized in several recent papers 9,10 . With a solid theoretical foundation and an experimental demonstration to back it up, the thermal Hall effect has become a powerful probe of the topological nature of magnon excitations in an ordered magnet.…”

“…14 Stimulated by their observations, we go beyond the existing magnon description of the thermal Hall effect [4][5][6][7][8][9][10] and formulate the phenomenon using the spin language entirely. It is then applied to discuss Hall effects of spin both in the paramgnetic as well as the ferromagnetic regime.…”

Tunable Magnon Weyl Points in Ferromagnetic Pyrochlores

“…In addition, the Chern numbers of magnon bulk bands are nonzero, and in accordance with the bulk-boundary correspondence [7,8] topological magnons are found at the edges of twodimensional kagome lattices [9,10]. Hence, systems featuring topological magnon states are dubbed 'topological magnon insulators' (TMIs) [9], because they exhibit many features of electronic topological insulators [11]. We recall that a pyrochlore lattice can be viewed as an alternating stacking of kagome planes along its [111] direction.…”

“…However, the present model relies on a ferromagnetic ground state and on the DM interaction; it is thus a natural extension of TMIs on kagome lattices [9,10] to three dimensions. Model and spin-wave analysis.…”

Quantum Anomalous Hall Effect

“…Effective topological band structure can be induced by the timedependent coupling, such as optical transition between different bands for an electron in external photon field. Beyond electron systems, the topological band structure leading to QAH effect has also been proposed and even realized in cold atom systems [105][106][107][108][109][110], photonic crystals [111][112][113][114] and magnonics [115][116][117].…”