Longitudinal Resonance for Thin Film Ferromagnets with Random Anisotropy

At the microscopic level, individual spins in ferromagnets with random anisotropy tip transversely with distinct local angles relative to the magnetization Μ. When driven by an rf field along the equilibrium M₀, which changes dΜ = Μ_{0 ‘} dM, the transverse tippings rotate about Μ₀, corresponding to a new macroscopic collective angle Ø about Μ_0. The coupling of dM and ø leads to a new longitudinal mode, which in bulk has a frequency that is largely independent of field Η. A longitudinal mode has been observed in thin films of ferromagnets with random anisotropy, but its frequency is Η-dependent; for Η at angle θ to the film normal and fixed resonator frequency f, Η cos θ was constant to angles of 80^°, with Η saturating for larger angles. When the demagnetization field is included the theory yields such as Η vs θ for θ <80^°, thus providing evidence for the predicted angle θ. However, lower frequency resonators are needed to manifest the predicted macroscopic anisotropy energy.