# Theory of standing spin waves in finite-size chiral spin soliton lattice

## TL;DR

This paper develops a theoretical model for standing spin waves in finite-size chiral spin soliton lattices, explaining experimental resonance phenomena in chiral helimagnets like CrNb3S6.

## Contribution

It generalizes existing theories to non-collinear helimagnets with surface pinning, identifying two distinct spin wave modes in chiral soliton lattices.

## Key findings

- Identification of Pincus and Kittel ripple modes in chiral soliton lattices.
- Theoretical explanation of double resonance profiles observed experimentally.
- Prediction of mode behavior depending on ac magnetic field orientation.

## Abstract

We present a theory of standing spin wave (SSW) in a monoaxial chiral helimagnet. Motivated by experimental findings on the magnetic field-dependence of the resonance frequency in thin films of Cr${}$Nb$_{3} $S${}_{6}$[Goncalves et al., Phys. Rev. B95, 104415 (2017)], we examine the SSW over a chiral soliton lattice (CSL) excited by an ac magnetic field applied parallel and perpendicular to the chiral axis. For this purpose, we generalize Kittel-Pincus theories of the SSW in ferromagnetic thin films to the case of non-collinear helimagnet with the surface end spins which are softly pinned by an anisotropy field. Consequently, we found there appear two types of modes. One is a Pincus mode which is composed of a long-period Bloch wave and a short-period ripple originated from the periodic structure of the CSL. Another is a short-period Kittel ripple excited by space-periodic perturbation which exists only in the case where the ac field is applied perpendicular the chiral axis. We demonstrate that the existence of the Pincus mode and the Kittel ripple is consistent with experimentally found double resonance profile.