Hard-axis ferromagnetic-resonance-driven energy dissipation in a uniaxial single-domain ferromagnet: A closed-form geometrical drive-coupling factor in the linear regime

Microwave power absorbed at ferromagnetic resonance (FMR) is conventionally described by the imaginary part of the dynamic susceptibility. For a uniaxial single-domain ferromagnet biased along its hard axis, however, that general formulation does not by itself display in a compact form how the field-induced ellipticity of the eigenmode changes coupling to a linearly polarized rf field. Here, we derive a closed-form on-resonance result to leading order in damping within the linear regime and explicitly connect it to the conventional susceptibility description; the finite-damping correction is quantified separately. The mass-specific spin-dissipation power separates into a damping-controlled scale and a dimensionless geometrical drive-coupling factor. As the hard-axis field approaches the anisotropy field from below, the precession ellipse collapses toward a line perpendicular to the rf-drive direction and the coupling factor decreases from one half to zero; above hard-axis saturation, the resonance reopens and the factor increases again toward one half. The same factor equals the drive-direction fraction of the Gilbert-loss kinetic term and the squared projection of the transverse eigenmode onto the rf-field direction. Frequency-dependent calculations and direct time-domain Landau–Lifshitz–Gilbert integration validate the result for weak drive. The closed-form factor provides an easy-to-use spin-dissipation source term for interpreting bias-field-dependent FMR heating and microwave absorption in anisotropic single-domain particles. For thermally fluctuating or randomly oriented nanoparticle ensembles, the present macrospin result is a baseline to be combined with orientational, thermal, and interaction averaging.