K. J. Harte

Theory of Magnetization Ripple in Ferromagnetic Films

In a polycrystalline ferromagnetic film, the magnetization direction is not uniform but exhibits small wave‐like fluctuations known as magnetization ripple. In this paper, a general theory of ripple is developed, extending previous treatments by the present author, Hoffmann, and others. The theory is applicable to almost any magnetic film without gross domain structure, containing randomly oriented local anisotropies arising from inhomogeneities on any scale and of any physical origin. The magnetization direction is assumed to fluctuate in the plane of the film only. In addition to local anisotropy fields, the theory includes the effects of magnetostatic and exchange interactions, and a uniform field that consists of uniform uniaxial anisotropy and external fields. Nonlinear magnetostatic and uniform fields, which in previous treatments have been either neglected or treated as small perturbations, are taken fully into account through third‐order torque terms. The ripple spectrum is derived, and from it a ...

Noncoherent Switching in Permalloy Films

High resolution Bitter pattern studies of the domain structure of permalloy films, with uniaxial anisotropy Hk and under the influence of applied fields in the film plane, are reported, and from these studies are inferred some aspects of noncoherent flux reversal processes. The threshold field for irreversible domain propagation across the film is measured for a variety of films differing in thickness (150 to 1100 A), rate of deposition (30 to 1100 A/min), substrate temperature (100 to 350°C), and composition (80 to 83.5% Ni), as a function of the angle α between the reversing field and the easy axis, after saturating along the opposite easy direction. For α<αc, where αc depends on thickness and preparation variables and varies from 0° to about 60°, reversal takes place by parallel wall displacement, with a wall coercive force Hw characteristic of the film. Two principal structural features have been identified as affecting Hw: Nonmagnetic inclusions, and local easy axes in the film plane normal to the ma...

Measured Relaxation Times for the Uniaxial‐Anisotropy Spectrum in Nonmagnetostrictive Permalloy Films

The relaxation time τ for realignment of an atomic anisotropy by 90° has been measured for a number of fast processes (τ<103 sec) occurring in nonmagnetostrictive Permalloy films. The method of measurement utilizes the magnetoresistance effect and is described in detail elsewhere. For films deposited between 23° and 200°C at 10−6 to 10−5 Torr and measured at the same temperature and pressure, three distinct processes plus two probable ones have been found, which together account for about one‐quarter of the total anisotropy. The activation energy Q and period factor τ0 which determine the relaxation time τ=τ0 exp (Q/kT) have been determined for each of these processes.

Spin‐Wave Effects in Magnetic‐Film Switching

The nonlinear reaction of dispersion‐induced spin waves on the uniform mode m0 has been calculated for a thin film undergoing rapid rotational magnetization reversal. It is found that if m0 rotates faster than longitudinal spin waves can relax, the magnetization goes through a transient state of high magnetostatic energy. If the pulse switching field Hp is less than a critical field Hpc, the uniform mode becomes locked at some point in the reversal process; rotational switching cannot proceed until initially longitudinal spin waves have relaxed into components propagating in the instantaneous direction of m0, a highly damped process suggestive of the intermediate‐speed reversal mode observed in thin films. The dependence of Hpc on a dc bias field has been verified experimentally; the dispersion dependence should provide a crucial test of the theory.

Theory of Large‐Angle Ripple in Magnetic Films

A theory of planar fluctuations of the direction of magnetization in a thin film which takes into consideration the nonlinear longitudinal magnetostatic force is outlined, and the resultant ripple is compared with that predicted by linear theories. The longitudinal magnetostatic force arises from the change along the direction of mean magnetization m0 of the component of magnetization M(r) parallel to m0; it leads to a torque that varies as the cube of the ripple amplitude. As a result of this torque, the linear theory breaks down for dispersion δ≳δ1, where δ is the rms angular deviation of M from m0 and δ1 is typically only 1° or 2° for a 1000 A Permalloy film in zero field and varies as L−½, where 2L is the film thickness. With the inclusion of this force the range of validity of the theory has been extended to δ≲20°. A number of interesting effects have been found, including (1) an effective field in the direction of m0 (and proportional to δ4 for δ>δ1) acting on ripple components with wavelengths grea...

Domain Wall Profiles in Magnetic Films

An inversion procedure for determining a domain wall profile from the associated Lorentz‐microscopy electron‐density distribution is discussed. This procedure is verified by application to computer‐simulated electron‐density distributions derived from assumed wall profiles. The experimental realization of the inversion procedure is demonstrated for high‐resolution Lorentz micrographs of films ranging in thickness from 100 to 500 A; unreliable profiles were obtained for thicker films. The importance of correcting for the effects of nonmagnetically scattered electrons is emphasized; these effects increase with increasing sample thickness and defocussing distance. The experimental domain wall profiles exhibit first a rapid, then a slow increase of wall angle with distance from the wall center. Wall widths derived from these profiles are consistent with theoretical predictions if corrections are made for nonmagnetic scattering; if such corrections are not made, the large widths reported by other authors are o...

Excitation of Uniaxial‐Anisotropy Relaxation Processes in Magnetic Films by a Rotating Magnetic Anneal

In hard‐axis annealing studies of Permalloy films, which have revealed a number of discrete uniaxial‐anisotropy relaxation processes, all processes are annealed simultaneously, making interpretation difficult and ambiguous. In this paper a new method is reported, in which individual processes are excited by a rotating magnetic anneal. Simple physical considerations show that the easy axes of only those processes with relaxation rates comparable to the annealing frequency will lag the annealing field when that field coincides with the easy axis. A theory based on discrete atomic processes predicts Debye peaks for the easy‐axis lag angle vs annealing frequency; relaxation rates are determined from the location of these peaks. By varying temperature, activation energies and pre‐exponential factors are obtained. The method of detection employs second‐harmonic magnetoresistance in a configuration which is insensitive to magnetization dispersion. The measurement is made automatically in ∼0.2 sec twice every cyc...

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

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...

Flux Reversal by Noncoherent Rotation in Magnetic Films

A model of magnetization reversal in thin ferromagnetic films is proposed. The model is based on a small angular dispersion (∼3°) in the film plane of the axis of planar anisotropy. The dynamical effects of this dispersion are important when the switching field (Hs) is of the order of the anisotropy field, fall off rapidly with increasing Hs, and include a two- to threefold increase in the switching coefficient for bias field large enough to insure unidirectional rotation. In addition, it is shown that the transverse flux reaches its maximum before the longitudinal flux is one-half switched. These results are in reasonable agreement with experiment.