Exchange anisotropy: A ferromagnetic resonance study

A description of ferromagnetic resonance (FMR) modes is given for an exchanged (F)/(AF) bilayer thin films using the static-(AF) model. Included in the analysis are the exchange anisotropy field HE, the off-aligned exchange coupling angle {β}, the in-plane uniaxial, and the cubic magnetocrystalline anisotropies. The resonance field HR vs applied field angle {α} curves for an off-aligned exchange system are shifted with respect to the aligned (β=0) curve; from the experimental measure of the angle αₘᵢₙ corresponding to the curve minimum, a {β} value can be derived. The dispersion relation is described; depending on the frequency range and {β} values, up to three modes are expected in the cubic system while one mode at most will appear for the uniaxial one. The linewidth ΔH monotonically increases with H for free (F) layer and aligned exchanged F/AF; for β≠0, the ΔH vs H curves go through a minimum. A general formula for mode intensity, I, is derived. Taking the rf field h in plane, as the dc field is rotated in plane, the intensity is expected to vanish for an applied field angle α₁. A simple relation between α₁ and HE is found. For aligned exchange and low-{β} values, I decreases monotonically with increasing H, while for a 90^∘{} coupling and high-{β} values, the I vs H curves go through a maximum; for strong fields all FMR intensities tend to the same asymptotic value. At fixed frequency, the decrease of I with increasing HE for the 90^∘{}-coupling could be used as a means to distinguish the 90^∘{} coupling from the aligned exchange coupling case.