Polarization-resolved measurement of forward volume spin waves by micro-focused Brillouin light scattering

Abstract

We show how the micro-focused BLS signal of forward volume spin waves is formed and why it remains observable despite symmetry-based "suppression" expectations. A reciprocity-theorem based model with vectorial diffraction-limited focusing identifies the nonnegligible longitudinal focal-field component as the key element responsible for BLS sensitivity in the forward volume geometry. We further demonstrate that full polarization analysis, implemented through polarizer-analyzer maps of coherently excited spin waves, provides information beyond the conventional crossed polarizer-analyzer readout. In a BiYIG thin film, the measured maps exhibit Stokes/anti-Stokes polarization asymmetries and nontrivial patterns that stem from quadratic magneto-optical coupling terms. Fitting the data with a model including Voigt and Cotton-Mouton contributions yields an effective Cotton-Mouton constant and shows that the quadratic response is comparable to the linear Voigt contribution.

Figures (4)

• Figure 1: Schematics of the used micro-focused Brillouin light scattering setup. The polarization of the linearly polarized incoming laser can be rotated by motorized $\lambda/2$ plate. The beam then passes through two non-polarizing beam splitters and is focused on the sample by microscope objective with NA = 0.8. The scattered light then passes through a rotatable polarizer before is fed into a tandem Fabry--Perot interferometer. An additional LED light source and CCD camera are used to control the positioning of the laser beam on the sample in the vicinity of the microstrip antenna. The biasing magnetic field can be applied both, in-plane and out-of-plane.
• Figure 2: Measured µBLS spectra in the FV geometry for 7 different polarizer angles $\theta$ with the analyzer angle set to $\phi = 150^\circ$. Spectra are offset by 6000 counts from each other for clarity.
• Figure 3: (a) Absolute values of the transfer function components $T_{yz}, T_{zy}, T_{yx}$, and $T_{xy}$ at $k_y=0$ for positive $k_x$ in the crossed polarizer--analyzer scheme ($\theta=0^\circ$, $\phi=90^\circ$). (b) BLS signal in the BV, DE, and FV geometry assuming magnetization dynamics with identical amplitudes of the circular spin precession. The spin waves were measured at $k=10$ rad/µm for FV and $k=0.7$ rad/µm for DE and BV, marked by color dots in the plots.
• Figure 4: Polarization-dependent BLS amplitude maps of the fundamental magnon mode peak in the experimental data (red colormaps, columns 1 and 3) and fitted using the semi-analytical model (green colormaps, columns 2 and 4). The Stokes (first two columns) and anti-Stokes (last two columns) peaks were analyzed in two fundamental spin-wave geometries: forward volume (a-d) and Damon--Eshbach (e-h).