Spin-Wave Locking of the Uniform Rotational Switching Mode in Magnetic Films

Abstract

The threshold field for high‐speed, uniform rotational switching in magnetic films is experimentally found to be higher than predicted by single‐domain theory.^1,2 This discrepancy, which leads to the appearance of an intermediate‐speed switching process, can be explained by a spin‐wave locking model, which is here reviewed and extended. The underlying physical mechanism is the conversion of longitudinal spin‐wave modes to transverse modes via the rotation of the uniform mode. A transient state of high magnetostatic energy is thereby created, and if the resultant spin‐wave reaction torque becomes greater than the uniform torque, the uniform mode locks. Two limiting cases are discussed. In the first, the spin‐wave relaxation time is assumed to be greater than the uniform‐mode switching time.³ It is the initial spin‐wave state which acquires a transverse component, and locking can occur at any time up to the minimum in the uniform torque. In the second case, the relaxation time is assumed to be much less than the switching time.⁴ The initial spin‐wave modes remain in equilibrium with respect to the uniform mode and grow in amplitude until they are prevented from reorienting by local instabilities induced by the component of the longitudinal magnetostatic force antiparallel to the magnetization,⁵ which becomes large near the minimum of the uniform torque. Then. conversion to transverse modes occurs as before, with locking of the uniform mode taking place near the torque minimum. From calculations based on an initial dispersion‐induced ripple state, the ``universal'' relation T_u (0) = 0.122 K_uα is derived for both cases and over a wide range of experimental situtions, where T_u (0) is the threshold starting torque for uniform rotation, K_u is the uniaxial anisotropy energy, and α is the rms hard‐axis fallback angle^6,7 (in degrees). Experimental results of Telesnin et al.⁸ appear to verify the above law. Finally, an experiment is proposed to distinguish between the slow‐ and fast‐relaxation models.