Transmission resonance in ferromagnetic gadolinium

A theoretical expression for the amplitude of a microwave magnetic field transmitted through a thin ferromagnetic Gd foil as a function of the dc magnetic field applied normal to the foil surface is derived. This expression includes the effects of the exchange energy, Bloch--Bloembergen, and Landau damping terms. The boundary condition on the magnetization is discussed and the mixed form is used in the derivation of the theoretical signal expression. This expression is compared with experimental results using a nonlinear least-squares curve fitting procedure to determine parameters such as saturation magnetization, relaxation time, skin depth, and exchange stiffness constant for three temperatures, 181, 259, and 2730K. The fittings indicate that the exchange term has negligible effect, that Landau damping is not applicable, and that Bloch damping is at least partially correct. Comparison between the fits for ferromagnetic Gd and paramagnetic Gd at 3130K suggests there may be an additional damping process for ferromagnetic Gd