Ferrimagnetic Resonance Modes in Spheres

Abstract

The magnetostatic solutions of ferrimagnetic resonance in ferrite spheres are briefly derived. General and specific solutions are given for values of n up to five for the magnetostatic potentials, rf distributions of magnetization, and fields for resonance. Some experimental results are given and compared with the theory.

Magnetic spheres in microwave cavities

“…In this regime, higher angular momentum eigenmodes of the dielectric sphere participate and the scattering shows s-as well as p-wave character. We thereby transcend studies that focus on dipolar spin waves in a magnetostatic framework [30,31] by considering propagation effects via the full Maxwell equation. Our study might be useful in designing optimal conditions to design cavities in which YIG spheres are coherently coupled to, e.g., superconducting qubits, in microwave cavities for coherent quantum information transfer [21].…”

“…This is basically again a one-dimensional problem that can be treated semianalytically and has other advantages as well, such as a homogeneous dipolar field and simple boundary conditions. The eigenmodes of magnetic spheres have been studied in the "magnetostatic" approximation [30,31], in which the spins interact by the magnetic dipolar field, disregarding exchange as well as propagation effects, which may be done when λ a, where a is the radius of the sphere and λ the wavelength of the incident radiation. Arias et al [32] treated the interaction of magnetic spheres with microwaves in the weak-coupling regime.…”

Dispersive readout of ferromagnetic resonance for strongly coupled magnons and microwave photons

“…This indicates that the strong coupling regime g ≫ κ, γ is achieved, with a cooperativity (g 2 /κγ) of around 200. In addition to the uniform mode, other non-uniform magneto-static modes in the sphere 28,29 couple to the resonator due to the radial dependence of microwave field in the cavity. One of In addition a number of other spin wave modes in the sphere couple to the cavity; the strongest is indicated by the green arrow.…”

Theory of collective spin-wave modes of interacting ferromagnetic spheres

“…More relevant to the present analysis is the paper by Fletcher and Bell. 11 These authors consider the special case of the sphere in detail, providing analytic formulae for the characteristic equations from which frequencies of the various normal modes can be determined. They also describe the response of the sphere to an external microwave field, so in fact from their paper one can construct the response function defined in Eq.…”

“…A careful and remarkably complete discussion of this mode spectrum can be found in the paper by Fletcher and Bell. 11 Most of these modes may be described as high order multipole modes, characterized by rather large values of the indices l , m in the discussion of Sec. II A.…”