Magnetic-surface interactions in thin yttrium iron garnet films

Abstract

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 $\ensuremath{\delta}$ present at each surface of the film. The phase shifts are related to a surface-anisotropy energy ${E}^{s}(\ensuremath{\theta},\ensuremath{\varphi})$ which is expanded in terms of the angular momentum operators ${S}_{z}$, where the $z$ axis is normal to the film plane, such that ${E}^{s}=\ensuremath{\Sigma}\stackrel{}{q}{b}_{q}{S}_{z}^{q}.$ The angular dependence of the observed boundary condition can be expressed as $A=1\ensuremath{-}\ensuremath{\Sigma}\stackrel{}{q}{a}_{q}{P}_{q}(cos\ensuremath{\theta}),$where ${P}_{q}(cos\ensuremath{\theta})$ are Legendre polynomials. In the circular-precession approximation, which is a reasonable approximation for YIG at 24 GHz, the coefficients ${a}_{q}$ are shown to be directly related to the surface-anisotropy energy contributions ${b}_{q}$. Experimental evidence indicates the coefficients ${a}_{0}$ or ${b}_{0}$, due to an isotropic surface energy, and ${a}_{2}$ or ${b}_{2}$, 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.