Amplitude and phase of perpendicular standing spin waves via VNA-FMR in sputtered Py/Ta films

The first observation of perpendicular standing spin waves via ferromagnetic resonance in thin films dates back to the mid `50s. However, phase-sensitive, broad-band FMR methods have only recently been developed with sufficient signal-to-noise to examine the dependence of spin-wave phase on mode index. We measured field-swept complex spectra of perpendicular standing spin waves (PSSWs) up to wavenumber 2x10$^{6}$ cm$^{-1}$ (30 GHz) in Py/Ta films of different thickness with vector-network-analyzer FMR with coplanar waveguide excitation. The spectra are fitted simultaneously with multiple complex susceptibilities to account for inter-mode interference. The spin-wave stiffness constant D and the pinning-parameter $\varepsilon $ are determined from a quadratic fit of the exchange field to the mode number. For all film thickness, $\varepsilon $ is indicative of weak pinning. Mode amplitude vs. excitation direction points to a dead layer at the Py/Ta interface. We observe strong inter-mode phase variations, especially for thinner (\textless 100 nm) films. Results are compared to a 1-d electrodynamic model that simultaneously solves the Maxwell and Landau-Lifshitz equations. The observed phase shifts are not expected if substrate conductivity is ignored.