The physics of magnetic resonance in the proximity of energy instability

We are investigating the magnetization dynamics of a ferromagnetic system in the proximity of an unstable equilibrium. The test system utilized is permalloy in thin film and nano-scale dot geometries with the magnetization along the film normal at fields close to saturation (4$\pi $M$_{eff})$. For sub-critical fields (H$_{appl.}$ = 4$\pi $M$_{eff})$, the magnetization equilibrates at some angle $\theta $, but has no energy minumum in the azimuthal angle $\phi $, therefore no resonance condition exists. Slight misalignment of the field removes the degeneracy in $\phi $ resulting in an energy minimum in both the $\theta $ and $\phi $ directions. This produces finite resonances at sub-critical fields. This sub-critical energy minimum resembles an asymmetrical `bowl' that changes shape with field and misalignment angle. We model measured frequency/field dispersion curves in terms of the Landau-Lifshitz equations of motion about the equilibrium position and interpret the results in terms of the `bowl' geometries. We also explain the observance of a local minimum, close to 4$\pi $M$_{eff}$, resulting in the three resonances in a constant frequency/swept field scan.