Hall Effect of Spin Waves in Frustrated Magnets

Abstract

We examine a possible spin Hall effect for localized spin systems with no charge degrees of freedom. In this scenario, a longitudinal magnetic field gradient induces a transverse spin current carried by spin wave excitations with an anomalous velocity which is caused by a topological Berry-phase effect associated with spin chirality, in analogy with anomalous Hall effects in itinerant electron systems. Our argument is based on a semiclassical equations of motion applicable to general spin systems. Also, a microscopic model of frustrated magnets which exhibits the anomalous spin Hall effect is presented. PACS numbers:Introduction -Spin transport phenomena in condensed matter systems have been attracting much interest because of potential applications to spintronics [1,2], and also because of their fundamental relation with the notion of topologically-induced spin currents [3,4,5]. For semiconductors and metals with spin-orbit interactions, the spin Hall effect (SHE) in the absence of magnetic fields was predicted theoretically [1], and later experimentally realized [2]. This effect allows for topological interpretation in terms of the Berry phase; the spinorbit interaction gives rise to the Berry curvature associated with the Bloch wave function, which results in the nonzero anomalous velocity producing a transverse force even in the absence of the Lorentz force [3]. This leads to the anomalous Hall effect (AHE) for the case without time-reversal symmetry [3,4,5,6,7], and the SHE for the case with time-reversal symmetry [1]. On the other hand, it was shown by several authors that the anomalous velocity is also generated by spin textures accompanying spin chirality, and the AHE occurs in itinerant electron systems coupled with localized spins, the orientation of which possesses spin chirality order [8]. In this letter, we propose a possible analogue of this phenomenon for localized spin systems with no charge degrees of freedom. We demonstrate that, in analogy with metallic systems, the topological Berry-phase effect associated with spin chirality raises the dissipationless spin Hall current induced by a longitudinal magnetic field gradient: i.e. Hall effect of spin waves.

Magnonic quantum Hall effect and Wiedemann-Franz law

“…As in Refs. [14,42,44,61], a gradient along, say, the x direction, of a magnetic field B perpendicular to the xy plane (Fig. 1) acts [15,[62][63][64][65] as a driving force for magnons like an electric field for charged particles.…”

Photon Thermal Hall Effect

“…In semiconductors, metals or high-Tc superconductors it is the Lorentz force acting on the free electrons which is responsible for a transversal heat current. In ferromagnetic materials, magnons (spin waves) [3][4][5] currents have been shown to be the source of thermal Hall effect. Recently, a phonon mediated themal Hall effect [6,7] has been highlighted in neutral objects of zero electrical charge.…”

The Hall effect and its analogs

“…The theory of the magnon (and, in principle, of the spinon) Hall effect was considered in [76,77]. The theory of the magnon (and, in principle, of the spinon) Hall effect was considered in [76,77].…”