Normal Modes of a Spin Cycloid or Helix

Abstract

Although spin cycloids and helices are quite common, remarkably little is known about the normal modes of a spin cycloid or helix with finite length on a discrete lattice. Based on simple one-dimensional lattice models, we numerically evaluate the normal modes of a spin cycloid or helix produced by either Dzyaloshinskii-Moriya (DM) or competing exchange (CE) interactions. The normal modes depend on the type of interaction and on whether the nearest-neighbor exchange is antiferromagnetic (AF) or ferromagnetic (FM). In the AF/DM and FM/DM cases, there is only a single Goldstone mode; in the AF/CE and FM/CE cases, there are three. For FM exchange, the spin oscillations produced by non-Goldstone modes contain a mixture of tangential and transverse components. For the DM cases, we compare our numerical results with analytic results in the continuum limit. Examples are given of materials that fall into all four cases.

10 pages, 6 figures

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• Magnetically driven ferroelectric order in Ni${}_3$V${}_2$O${}_8$
• Incommensurate magnetic order in the alpha-Fe(Te,Se) superconductor systems
• Optical coupling to spin waves in the cycloidal multiferroic BiFeO3
• Competing exchange interactions on the verge of a metal-insulator transition in the two-dimensional spiral magnet Sr${}_3$Fe${}_2$O${}_7$
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Cited by in corpus (5)

• Modelling spin waves in noncollinear antiferromagnets: spin-flop states, spin spirals, skyrmions and antiskyrmions
• Symmetry analysis of magnetoelectric effects in perovskite-based multiferroics
• Dimensional reduction and incommensurate dynamic correlations in the $S=\frac{1}{2}$ triangular-lattice antiferromagnet Ca${}_3$ReO${}_5$Cl${}_2$
• Competing long-range interactions and spin vector chirality in spin-chains
• ${\mathbb{Z}}_2$ Vortex Crystals in Tetrahedral Antiferromagnets: Fractional Charges and Topological Magnons