Excitation of Spin Waves in Ferromagnets: Eddy Current and Boundary Condition Effects

The boundary condition for the transverse magnetization is derived when there is a surface anisotropy field $H_s$. Writing the transverse magnetization as $\alpha sinkz+\beta cos\mathrm{kz}$, we have $\frac{\alpha }{\beta }=-\frac{1}{2}ka+\left(\frac{H_s}{H_e\mathrm{ak}}\right),$ where $H_e$ is the exchange field and $a$ the lattice constant. A similar result is found when there is an antiferromagnetic surface layer. For $H_s\ne 0$ spin-wave modes can be excited by a uniform rf field in a ferromagnet. The power absorbed in each mode in an insulator is calculated as a function of the surface anisotropy field. The excitation of the exchange modes is calculated for a metal with eddy-current damping. The eddy currents are found to have a large effect only on long wavelength spin waves. The line shape in a thick metal plate is calculated for $H_0$ normal to the plate.