Abstract
We develop a quantum theory of magnetic skyrmions and antiskyrmions in a spin-1/2 Heisenberg magnet with frustrating next-nearest neighbor interactions. Using exact diagonalization we show numerically that a quantum skyrmion exists as a stable many-magnon bound state and investigate its quantum numbers. We then derive a phenomenological Schr\"odinger equation for the quantum skyrmion and its internal degrees of freedom. We find that quantum skyrmions have highly unusual properties. Their bandwidth is exponentially small and arises from tunneling processes between skyrmion and antiskyrmion. The bandstructure changes both qualitatively and quantitatively when a single spin is added or removed from the quantum skyrmion, reflecting a locking of angular momentum and spin quantum numbers characteristic for skyrmions. Additionally, while for weak forces the quantum skyrmion is accelerated parallel to the force, it moves in a perpendicular direction for stronger fields.
Highlights
Magnetic skyrmions are textures in the magnetization which can be characterized by a topological winding number
Magnetic skyrmions were first discovered in the chiral cubic magnet MnSi [1] and subsequently in a wide range of chiral magnets, magnetic monolayers, and layered magnetic systems with sizes ranging from nanometers to micrometers [2,3,4,5,6,7,8,9]
Viewing the skyrmion as a classical particle is justified in most experimental situations: the skyrmions are often large objects involving a large number of spins and the coupling to electrons in a metal or to thermal magnons will destroy effects of quantum coherence
Summary
Magnetic skyrmions are textures in the magnetization which can be characterized by a topological winding number. The ground-state properties of a single quantum skyrmion in a chiral magnet are (at least to leading order approximation) rather obvious: as their dynamics is governed by a large magnetic field, the ground state is localized in a Landau level with edge channels at the sample boundary Corrections to this picture arise from an exponentially small lattice potential which gives rise to a band structure [15,16]. Skyrmion states in frustrated magnets were first investigated by Ivanov et al [21] and more recently by Okubo et al [22], Leonov and Mostovoy [23], Lin and Hayami [24], and Zhang and coworkers [25,26]. In a second step we develop a phenomenological theory of skyrmion motion investigating both the coupling to the helicity d.o.f. and the skyrmionantiskyrmion tunneling
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