Theory of two magnon scattering microwave relaxation and ferromagnetic resonance linewidth in magnetic thin films

Abstract

A detailed analysis of the two magnon scattering contribution to the microwave relaxation and ferromagnetic resonance linewidth in isotropic and anisotropic films and disks has been made. The analysis is based on the Sparks, Loudon, and Kittel (SLK) theory for the scattering of uniform mode magnons into degenerate spin wave states for isotropic spherical samples in the presence of magnetic inhomogeneities in the form of spherical voids or pores. The SLK theory has been extended to include: (i) thin film and thick film samples magnetized in an oblique out-of-plane direction; (ii) uniaxially anisotropic materials with either easy-axis or easy-plane anisotropy and an anisotropy axis perpendicular to the disk plane; (iii) a modified density of degenerate states to account for the nonzero relaxation rate of the scattered spin waves; and (iv) two limiting cases of the scattering interaction: (a) the original SLK case where the inhomogeneities are modeled as spherical voids and the coupling to the degenerate spin waves varies with the spin wave propagation direction and (b) an isotropic scattering model where the coupling is independent of the propagation direction. The formulation is valid for thick films for which the discrete nature of the spin wave modes may be neglected. The two magnon linewidth as a function of field orientation is calculated for three classes of material parameters corresponding to yttrium iron garnet and barium M-type and zinc Y-type hexagonal ferrites. The linewidth versus static field angle profiles show characteristic profiles which depend on the crystalline anisotropy, the sample dimensions, the nature of the scattering interaction, the inhomogeneity size, and the inhomogeneity volume fraction. These parameters, as well as the shape and evolution of the spin wave band as a function of the field angle under ferromagnetic resonance conditions, play critical roles in determining the linewidth versus angle profiles.

Low Gilbert damping in Co2FeSi and Fe2CoSi films

“…This nonlinear dependence of the FMR linewidth on frequency is a typical observation when two magnon scattering contributes significantly to the relaxation [22,23]. Two-magnon scattering is an extrinsic relaxation mechanism and can be induced by means of different scattering centers such as voids or pores [24], surface roughness [22] and grain size [25] or by network of misfit dislocations which causes scattering of the FMR mode (k=0) into propagating spin waves (k =0).…”

Determination of intrinsic damping of perpendicularly magnetized ultrathin films from time-resolved precessional magnetization measurements

“…In such case, a strong dependence on the external field would be observed for fields below Hkeff due to the variation in the orientation of the magnetization with the external magnetic field. At higher fields the dependence on the external field is expected to be moderate 35 .…”

“…The resultant additional linewidth broadening would then be regarded as an extrinsic contribution to the damping [34][35][36] . While in isotropic films which exhibit low crystalline anisotropy or in films having in-plane crystalline anisotropy, twomagnon scattering is maximized when the external field is applied in the film plane, in PMA films this is not necessarily the case and the highest efficiency of two-magnon scattering may be obtained at some oblique angle 35 .…”

Tunable magnetization relaxation of Fe2Cr1−xCoxSi half-metallic Heusler alloys by band structure engineering

“…The partial derivatives are evalued numerically at the resonance condition. The last term accounts for two magnon scattering (TMS) [53,54] activated by defects such as dislocations (See Supplemental Material Fig. S4 for TEM results), representing relaxation of the uniform mode to spin wave modes of non-zero wave vector (Fig.…”