H. Neal Bertram

Micromagnetic studies of thin metallic films (invited)

A computer simulation model has been developed to conduct micromagnetic studies of thin magnetic films. Thin‐film media are modeled as a planar hexagonal array of hexagonally shaped grains. Each grain is a single domain particle whose magnetization reverses by coherent rotation. The computation utilizes coupled gyromagnetic dynamic equations with phenomenological Landau–Lifshitz damping. In particular, the effects of particle interactions are investigated. The effect of media microstructure on magnetic hysteresis is examined as well as the effect of intergranular exchange coupling. The difference between planar and completely random orientation of the crystalline anisotropy axes is discussed. Recorded transitions are simulated by allowing a pair of perfect transitions to relax. With no intergranular exchange coupling, the transitions show profound irregularity and zig‐zag structure. Intergranular exchange coupling produces more uniform transitions with increased zig‐zag structure amplitude. For a closely ...

Magnetization processes in ferromagnetic cubes

A cubic discretization procedure of the micromagnetic energy functional is used to carry out numerical studies of the magnetization process in ferromagnetic cubes. Equilibrium magnetization configurations and their switching behavior are calculated for particle sizes in the range from 100 to 550 A. In the model calculations the particles are assumed to have uniaxial crystalline anisotropy with an anisotropy constant of 18 500 erg/cm3, a saturation magnetization of 370 emu/cm3, and an exchange constant of 10−6 erg/cm. For particle sizes smaller than 520 A the remanent state has a flowerlike magnetization configuration. Beyond 520 A this state is replaced by a vortex structure about the easy axis. For particles smaller than 450 A switching occurs by approximately uniform rotation of the flower state. The switching fields are larger than the corresponding Stoner–Wohlfarth value. Beyond 450 A the application of an external field leads to the formation of a vortex configuration. The switching of the vortex con...

Magnetization reversal in CoCr perpendicular thin films

Computer simulation has been utilized to study magnetization reversal processes in CoCr perpendicular films. The model is based on the columnar structure of the film. Each column is considered to be a single crystal with perpendicular uniaxial crystalline anisotropy. The model assumes that each column is always uniformly magnetized even during its magnetization reversal. The gyromagnetic equation of motion with phenomenological Landau–Lifshitz damping is utilized to describe the magnetization rotation of this coupled system. The study focuses on the collective magnetization reversal modes of the particles due to magnetostatic interactions and intergranular exchange coupling. Low nucleation fields occur which are characterized by a planar chain nucleation mode. This yields coercivities equal to or less than the crystalline anisotropy field 2K/M. It is argued that, due to this collective process, the uniform rotation reversal mechanism for the individual particles in the film is energetically more favorable...

Fundamental Magnetization Processes in Thin-Film Recording Media

Publisher Summary This chapter discusses the magnetic hysteresis, reversal processes, and domain patterns in hard magnetic materials utilized as thin-film recording media. It also presents the results of numerical simulations that exhibit some of the complexities of the magnetic recording technology. In numerical simulations of magnetization patterns and reversal processes in hard as well as soft magnetic materials, the ability to model accurately has been limited by current computational power. The inherent difficulty inaccurate modeling of magnetic systems is the incorporation of the long-range magnetostatic fields. Any reasonable numerical spatial or temporal discretization requires significant computer storage and speed. The simulations exhibit a fascinating interplay between physics and complexity. For example, in a typical in-plane isotropic film, nucleation of magnetization reversal occurs by vortex formation. The expansion of reversed regions during hysteresis is achieved through vortex motion. The vortices are better defined if the magnetostatic interaction strength is large relative to the grain anisotropy; they are larger and more distantly separated if the intergranular exchange coupling is large. Strongly interacting assemblies of magnetic grains exhibit self-organized behavior.

Energy barriers for thermal reversal of interacting single domain particles

An analytic solution to the energy barriers of two interacting single domain particles is presented. Identical volumes and uniaxial anisotropies are assumed with easy axes parallel to an external magnetic field. The locations and heights of the system energy barriers are analytically determined when the line joining the two particles is either parallel or perpendicular to the easy axes and the external field. The lowest energy barriers are saddle points of the energy surface and correspond to reversal modes under thermal agitation. When dipole coupling is not strong, the mode of thermal switching is asymmetric fanning or asymmetric coherent rotation, depending upon the bond angle, rather than symmetric fanning or coherent rotation that occurs at the nucleation field. An effective volume that describes the cooperative effect is calculated and good agreement with the numerical results using the Fokker–Planck equation is obtained. The energy barriers can be used to calculate the superparamagnetic relaxation ...

Phenomenology of δM curves and magnetic interactions

Abstract The δM curve is defined as a normalized difference of the two principal remanent curves: the isothermal remanent curve Mr and the dc demagnetization curve Md. In general non-zero δM arises from complicated interaction phenomena in magnetic material. Recent application has been to systems of interacting particulate assemblies and polycrystalline thin films. In this paper, a simple phenomenological model is introduced to characterize magnetic interactions. The net magnetic field includes the external field, plus a mean field as well as a second-order interaction field representing fluctuations. With this model, the δM curve and relative properties of media can be easily fitted to experimental data. Excellent agreement with experiment for tape as well as single- and double-layer thin film media is found.

Reversal mechanisms and domain structures in thin‐film recording media (invited)

Magnetization reversal in longitudinal and perpendicular thin films is studied via computer simulation. Collective micromagnetic processes and the formation of magnetization patterns driven by magnetostatic interactions and intergranular exchange coupling is analyzed. In longitudinal thin films, it is found that a reversal starts by formation of magnetization vortices. The collective formation of vortices yields elongated reverse regions along the direction of the applied field. Intergranular exchange coupling enhances these magnetization structures and results in large‐size domains. Reversal of a typical perpendicular film (CoCr) consists of discrete nucleation processes. Each individual process is characterized by a planar chain nucleation mode. These collective micromagnetic processes cause film magnetic properties to be significantly different from those of a simple assembly of noninteracting grains. Medium noise in perpendicular films occurs mainly away from transitions in distinct contrast to longit...

Self-organized behavior in thin-film recording media

Magnetization domain structures in thin metallic films utilized as recording media are modeled by a cellular automation on a two‐dimensional triangular lattice. This alternative approach permits significantly large arrays (≳ 106 grains) to be investigated as compared to an exact calculation (≊ 5 × 103 grains). Thus a study of the statistical distribution of the domain sizes and their power spectra can be made. Magnetostatic interactions and intergranular exchange coupling are included in a simple manner so that collective behavior is incorporated. It is found that away from the saturation remanent state, the distribution of the size of the avalanches (or the number of sites reversed in a single reversal sequence) follows a power‐law behavior: D(S) = AS−α where S is the avalanche size and α varies in the vicinity of 1 depending on the interaction strength. The reversal field keeps the system marginally stable. It is found that the reproduce noise power varies as the derivative of the M‐H loop.

Ferromagnetic switching in elongated γ‐Fe2O3 particles

Results of numerical micromagnetic calculations of the switching process in elongated γ‐Fe2O3 particles are reported. The particles are represented by square rectangular prisms of aspect ratio 3:1 and 5:1, respectively. The crystalline anisotropy is cubic with K1=−4.6×104 erg/cm3 and with the [110] direction in the long particle axis. The application of a reverse field leads to formation of vortices at the ends of the particle. As the reverse field is increased in magnitude the vortices expand from the ends of the particle inwards. Equilibrium and transient magnetization states are computed as a function of particle size. The resulting dependence of the switching field on the particle size and on the angle of the applied field is similar to what has been suggested by experimental evidence.

Microwave assisted magnetization reversal in composite media

Magnetic reversal in exchange-coupled composite elements under microwave fields is characterized by several unique properties including reduced reversal fields, microwave fields, microwave resonant frequencies, and reduced sensitivity to anisotropy distributions as compared to homogeneous elements. We find that reversal can occur in uniform and nonuniform regimes. The uniform regime is characterized by coherent spin precession enhancement by the microwave field. In the nonuniform regime domain walls in the soft layer mediate reversal and under linearly polarized microwave fields, can lead to a formation of localized reversal/nonreversal areas in the “applied field-frequency” phase plane.