Magnetic-surface interactions in thin yttrium iron garnet films

The spin-wave spectra in an annealed yttrium iron garnet (YIG) thin film deposited on a gadolinium-gallium-garnet substrate is discussed in terms of generalized magnetic-boundary conditions comprised of various surface-anisotropy energies. The allowed propagation constants and mode intensities of the spin-wave spectra are evaluated in terms of a spin-wave phase shift δ present at each surface of the film. The phase shifts are related to a surface-anisotropy energy Eˢ(θ,φ) which is expanded in terms of the angular momentum operators Sz, where the z axis is normal to the film plane, such that Eˢ=ΣqbqSzq. The angular dependence of the observed boundary condition can be expressed as A=1-ΣqaqPq(cosθ),where Pq(cosθ) are Legendre polynomials. In the circular-precession approximation, which is a reasonable approximation for YIG at 24 GHz, the coefficients aq are shown to be directly related to the surface-anisotropy energy contributions bq. Experimental evidence indicates the coefficients a₀ or b₀, due to an isotropic surface energy, and a₂ or b₂, due to a uniaxial surface-anisotropy energy, present at each surface of the film are sufficient to account for the out-of-plane angular dependence of the observed spin-wave spectra. The variation of these coefficients with temperature and the measurement of a photoinduced surface-anisotropy energy present at temperatures below 100 K are observed to be consistent with a proposed microscopic interaction. A small phase shift having a fourfold symmetry in the plane of a (100)-oriented film is also reported.