Transverse complex magnetic susceptibility of single-domain ferromagnetic particles with uniaxial anisotropy subjected to a longitudinal uniform magnetic field

The infinite hierarchy of differential-recurrence relations for the equilibrium transverse correlation functions appropriate to magnetic relaxation of single-domain ferromagnetic particles with uniaxial anisotropy subjected to a uniform external magnetic field $H_0$ is derived by averaging Gilbert’s equation. Exact expressions in terms of matrix continued fractions for the transverse complex magnetic susceptibility are obtained with the aid of linear-response theory by solving the infinite hierarchy. The principal features of the spectra are emphasized in figures showing the real and imaginary parts of the complex magnetic susceptibility. The accuracy and the range of the applicability of analytical results based on the effective eigenvalue method is established. It is shown that this method provides in general a good approximation to the exact solution with the exception of the range of low-to-intermediate barrier heights of the anisotropy potential where at small $H_0$ there exists essentially a spread of the precession frequencies of the magnetization.