Theory Of Standing Spin Waves In A Finite-Size Chiral Spin Soliton Lattice

We present a theory of standing spin waves (SSW) in a monoaxial chiral helimagnet. Motivated by experimental findings on the magnetic-field dependence of the resonance frequency in thin films of CrNb3S6 [Goncalves et al., Phys. Rev. B 95, 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 a noncollinear helimagnet with the surface end spins, which are softly pinned by an anisotropy field. Consequently, we found that there appear two types of modes. One is a Pincus mode that 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 in which 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 the experimentally found double resonance profile.