Brillouin Light Scattering from Quantized Spin Waves in Nanowires with Antisymmetric Exchange Interactions

Abstract

Antisymmetric exchange interactions are used to stabilize magnetic textures and lead to non-reciprocal spin-wave propagation [1-2]. As a result, left and right propagating waves at the same energy have different wavelengths. Thus, interference between counter-propagating spin waves does not lead to standing waves; instead, confined modes have a time-dependent phase, i.e., their phase is modulated at a rate determined by the Dzyaloshinskii–Moriya interactions (DMI) [3].We report on a Brillouin light scattering (BLS) study of confined spin waves in Co/Pt nanowires with strong DMI, whose widths range from 100 to 400 nm [4]. Two different scattering geometries were used: a transverse geometry where the incident light is perpendicular to the nanowire, as illustrated in Fig. 1(a), and a longitudinal geometry, where the incident light is parallel to the nanowire. Fig. 1(b) shows a SEM image of a nanowire array. Fig. 2(a-d) show sample BLS spectra for both scattering geometries. Fig. 2(e) shows spin-wave quantization in narrow (<200nm width) wires dramatically reduces the frequency shift between BLS Stokes and anti-Stokes lines in the transverse geometry. In contrast, the frequency shift associated with the longitudinal geometry 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. Our results show that, in contrast to the BLS frequency shift in the longitudinal scattering geometry, which enables direct determination of the DMI, the BLS frequency shift in the transverse scattering geometry is not directly related to the DMI.  Fig. 1 (a) Schematic of spin waves in a confined geometry with chiral magnetic interactions. (b) A SEM image of the nanowire array consisting of 100 nm width Co/Pt nanowires with 100 nm spacing.  Fig. 2 (a)-(d) BLS spectra for Stokes and anti-Stokes processes for both positive and negative fields on nanowire arrays with different widths. (e) The absolute value of the frequency shift on nanowire arrays with different widths in the longitudinal (k∥L) and transverse (k⊥L) scattering geometries.