Observation of Phase-Modulated Quantized Spin Waves in Nanowires with Antisymmetric Exchange Interactions

Antisymmetric exchange interactions lead to non-reciprocal spin-wave propagation. As a result, spin waves confined in a nanostructure are not standing waves; they have a time-dependent phase, because counter-propagating waves of the same frequency have different wave lengths. We report on a Brillouin light scattering (BLS) study of confined spin waves in Co/Pt nanowires with strong Dzyaloshinskii Moriya interactions (DMI). Spin-wave quantization in narrow (<200 nm width) wires dramatically reduces the frequency shift between BLS Stokes and anti-Stokes lines associated with the scattering of light incident transverse to the nanowires. In contrast, the BLS frequency shift associated with the scattering of spin waves propagating along the nanowire length is independent of nanowire width. A model that considers phase-modulated confined modes captures this physics and predicts a dramatic reduction in frequency shift of light scattered from higher energy spin waves in narrow wires, which is confirmed by our experiments.