Spin-Wave Effects in the Magnetization Reversal of a Thin Ferromagnetic Film

The influence of spin waves on rapid rotational magnetization reversal (switching) in a thin ferromagnetic film is investigated by means of a semiclassical, continuum theory which includes external, anisotropy, exchange, and magnetostatic (dipolar) fields. To simplify the magnetostatic field, a "thin-film approximation" is introduced, in which the magnetization is replaced by its average over the film thickness. From a stochastic model for the microstructure of a polycrystalline film, the equilibrium magnetization configuration M(T)is derived. Planar fluctuations of M from its mean direction rrT are found which o have the characteristics of "longitudinal ripple," namely, wave vectors k parallel torn and wavelengths -4 .° greater than an exchange cutoff 2irX ~ 10 cm. Components with wave vectors in directions other than ±m are attenuated by magnetostatic forces, while exchange forces attenuate components with wavelengths less than 2irA . The magnetization dispersion 6 [ rms angular deviation of M(T) from m ] is also calculated. A brief discussion is given of the uniform rotational switching mode (without spin waves), with particular attention to undamped and overdamped cases. From the spin-wave equations of motion, the spectrum applicable to a parallel resonance situation (external field in the film plane) is first obtained, and long-wavelength magnetostatic distortion is noted. Then the transient spin-wave response is calculated for a switching field H suddenly turned on at t = 0. It is found that if m (t) rotates faster than — • P ° longitudinal spin waves [ k 11 m (0)] can relax, the magnetization goes through a transient state of high ° 2. magnetostatic energy, and a spin-wave reaction torque (proportional to 6 ) is exerted on the uniform mode. If H is less rhan a critical field H , the reaction torque at some point in the switching process is greater than the reversing torque and the uniform mode becomes locked; rotational reversal cannot proceed until initially longitudinal spin waves have relaxed into components propagating in the instantaneous direction of m (t). Such a highly damped process is suggestive of the noncoherent reversal mode observed in thin films. For H > H , reversal takes place by a modified uniform rotation; H may p pc pc therefore be identified as the threshold field for coherent rotation. The calculated dependence of H on pc a bias field compares favorably with experiment. The 6-dependence, if 6 can be measured independently, should provide a crucial test of the theory. Accepted for the Air Force Stanley J. Wisniewski Lt Colonel, USAF Chief, Lincoln Laboratory Office * This report is based on a thesis of the same title submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics at Harvard University.