Light scattering by magnons in whispering gallery mode cavities

Abstract

Brillouin light scattering is an established technique to study magnons, the elementary excitations of a magnet. Its efficiency can be enhanced by cavities that concentrate the light intensity. Here, we theoretically study inelastic scattering of photons by a magnetic sphere that supports optical whispering gallery modes in a plane normal to the magnetization. Magnons with low angular momenta scatter the light in the forward direction with a pronounced asymmetry in the Stokes and the anti-Stokes scattering strength, consistent with earlier studies. Magnons with large angular momenta constitute Damon-Eschbach modes which are shown to inelastically reflect light. The reflection spectrum contains either a Stokes or anti-Stokes peak, depending on the direction of the magnetization, a selection rule that can be explained by the chirality of the Damon-Eshbach magnons. The controllable energy transfer can be used to manage the thermodynamics of the magnet by light.

Coherent Conversion Between Microwave and Optical Photons—An Overview of Physical Implementations

“…The inclusion of optical cavity modes in the form of WGMs has not led to a significant improvement, principally because of the small overlap between the spatially uniform Kittel mode, which occupies the entire YIG sphere, and the WGMs, which are confined to the equator, giving a small magnon–photon coupling. Possible routes to improve this include using higher‐order magnetostatic modes, which are concentrated near the surface of the sphere (although these are harder to excite with microwaves), or use a ferromagnetic disc or oblate spheroid (although this is likely to have negative consequences for the linewidth of the magnetic modes). Alternatively, Mie resonances in magnetic dielectrics with length scales similar to the optical wavelength could be used instead of WGMs, with the increased filling factor improving the coupling to spin waves …”

Orbital angular momentum conservation in Brillouin light scattering within a ferromagnetic sphere

“…Let us now see that the total orbital angular momentum is conserved in the Brillouin scattering process. The thorough treatment of the Brillouin scattering by magnons in WGMs can be found in [16]. In the following, we emphasize the role of orbital angular momenta in the Brillouin scattering process.…”

“…Phenomenologically, magnetooptical effects can be captured by ˜( ) t , the macroscopic dielectric tensor [32]. For a magnetized cubic crystal, the dielectric tensor ˜( ) t in the Cartesian basis can be written [16,17,33] as is responsible for the vector light shift (Faraday effect) and is the first order in the magnetization M . Here the M s stands for the saturation magnetization.…”

“…To overcome the weakness of the spin-light interaction, cavity optomagnonics has been investigated [10][11][12][13][14][15][16][17]. In cavity optomagnonics, the density of states of optical modes are engineered with an optical cavity to enhance spin-light interaction.…”

“…where the first two terms represent the Faraday effect and the last two terms represent the Cotton-Mouton effect. The irrelevant terms in(16) which give no contribution to the Brillouin scattering are neglected.…”