Topological energy bounds for frustrated magnets

Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search for hopfions in real physical systems has been ongoing for nearly half a century, starting with the seminal work of Faddeev. However, so far, realizations in bulk solids are missing. Here, we show that hopfions appear as emergent particles of the classical Heisenberg model with competing exchange interactions. This requires going beyond the model approach used in prior work and deriving a general micromagnetic energy functional directly from a spin-lattice Hamiltonian. We present a definite parameter space in which the existence of hopfions is possible. This opens a concrete vista to combine computational approaches such as density functional theory with material informatics to find magnetic crystals that can host hopfions. As proof of principle, we show how zero-field hopfions can be visualized by the means of off-axis electron holography in a transmission electron microscope.

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Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

Speight

Winyard

2020

Phys. Rev. B

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A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, H 0 < 1/4, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged sigma model in a fixed background gauge, allowing the construction of stable isolated Skyrmions, and stable multi-Skyrmion clusters, which approach the conical ground state at spatial infinity. Owing to the spatial anisotropy induced by the ground state, these Skyrmions exhibit only discrete symmetries, and are of neither Néel nor Bloch type. These Skyrmions are continuously connected to the more familar solutions in the high field regime (H 0 > 1/4), acquiring axial symmetry in the limit H 0 → 1/4. The propagation of small amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both H 0 and propagation direction relative to the ground state. In contrast to spin waves in the high field regime (H 0 > 1/4) there is no spectral gap: waves may propagate with any angular frequency. *

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Topological energy bounds for frustrated magnets

Cited by 4 publications

References 18 publications

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Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

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