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.
| Original language | English |
|---|---|
| Article number | 064414 |
| Journal | Physical Review B |
| Volume | 99 |
| Issue number | 6 |
| DOIs | |
| State | Published - Feb 13 2019 |
Funding
Research by R.S.F. was sponsored by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. T.R. would like to acknowledge support from the Estonian Ministry of Education and Research with institutional research funding IUT23-3, and the European Regional Development Fund Project No. TK134. R.d.S. acknowledges financial support from NSERC (Canada) through its Discovery program (RGPIN-2015-03938). This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.