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• W2799709073 abstract "We apply the equations for the magnetization $stackrel{Pvec}{M}$ and field $stackrel{Pvec}{H}$ to study their coupled modes for a semi-infinite ferromagnet, conductor, or insulator with magnetization ${M}_{0}$ and field ${H}_{0}$ normal to the plane (perpendicular resonance) and wave vector normal to the plane, which makes the modes doubly degenerate. With dimensionless damping constant $ensuremath{alpha}$ and dimensionless transverse susceptibility ${ensuremath{chi}}_{ensuremath{perp}}={M}_{0}/{H}_{e}phantom{rule{0.28em}{0ex}}({H}_{e}ensuremath{equiv}{H}_{0}ensuremath{-}{M}_{0})$, we derive an analytic expression for the wave vector squared, showing that $stackrel{Pvec}{M}$ and $stackrel{Pvec}{H}$ are nearly decoupled only if $ensuremath{alpha}ensuremath{gg}{ensuremath{chi}}_{ensuremath{perp}}$. This is violated in the ferromagnetic regime, although a first correction is found to give good agreement away from resonance. Emphasizing the conductor permalloy as a function of ${H}_{0}$ we study the eigenvalues and eigenmodes and the dissipation rate due to absorption both from the total effective field and from the Joule heating. (We include the contribution of the nonuniform exchange energy term, needed for energy conservation.) Using these modes we then apply, for a semi-infinite ferromagnet, a range of boundary conditions (i.e., surface anisotropies) on ${M}_{ensuremath{perp}}$ to find the reflection coefficient $R$ and the reflectivity ${|R|}^{2}$. As a function of ${H}_{0}$, absorption is dominated by the the skin depth mode (primarily $stackrel{Pvec}{H}$) except near the resonance and at a higher-field ${H}_{d}$ associated with a dip in the reflectivity, whose position above the main resonance varies quadratically with the surface anisotropy ${K}_{s}$. The dip is driven by the boundary condition on $stackrel{Pvec}{M}$; the coefficient of the (primarily) $stackrel{Pvec}{M}$ mode becomes very small at the dip, being compensated by an increase in the amplitude of the $stackrel{Pvec}{M}$ mode, which has a Lorentzian line shape of height $ensuremath{sim}{ensuremath{alpha}}^{ensuremath{-}1}$ and width $ensuremath{sim}ensuremath{alpha}$." @default.
• W2799709073 created "2018-05-17" @default.
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• W2799709073 date "2018-05-10" @default.
• W2799709073 modified "2023-09-27" @default.
• W2799709073 title "Strongly coupled modes of M and H for perpendicular resonance" @default.
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• W2799709073 doi "https://doi.org/10.1103/physrevb.97.174411" @default.
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