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Dipole interaction makes average energy barrier of magnetic fine particles for thermal relaxation reduced while the corresponding blocking temperature distribution is a function of both dipolar interaction strength and particle size distribution of the system. Flatness and fast drop-off of the λ-shape behavior of the field-cooled and zero-field-cooled magnetization varies with both dipolar intereaction strength and field level applied.

We investigated the characteristics of the magnetic switching of the single-domain particles (SDP) and studied its variation as a function of the field orientation, sweep rate, textural distribution and thermal relaxation effects. Our analysis is based on the non-interacting bi-state model using the probabilistic approach. The hysteresis loops measured at high sweep rates are much wider and the corresponding coercivities Hc much larger than those taken at slower sweep rates. An increase in the field-angle orientation from the easy axis reduces the Hc field, while decreasing the sweep rate flattens the trend of the variation of the curve until a very large angle is reached. The thermal factor KV/kBT, on the other hand, plays essentially the same role as the sweep rate does to the Hc values: the larger the value of KV/kBT, the larger the value of Hc. The transition energy barrier is roughly equal to ≈ 25kBT if the field sweep period is 1 h, in agreement with the usual concept of the blocking temperature. However, this concept is subject to dispute if the sweep period is comparatively faster or slower. The variation of the reversible transverse susceptibility (RTS) with respect to the field orientation and thermal relaxation has also been systematically investigated. The cusps or trenches of the RTS due to thermal relaxation were shown to be substantially shaved or filled, while the corresponding Hc values were shifted and reduced. The RTS of the SDPs may exhibit one, two or three prominent cusps at high values of KV/kBT depending upon the configuration and texture or randomness of the system given. The height of the cusp also varies with the field-orientation angles, and the corresponding switching-field distribution becomes broadened and decreases with the values of KV/kBT.

When the deep gap field exceeds the onset of the saturation field the fringe-field becomes nonvanishing and retains a plateau value at large distances from the gap corner. The plateau values increase with increasing deep gap field and decrease with the head dimensions; correspondingly, the charge density on the pole surface also increases. The permeability and volume charge distribution near the pole tip corner at large deep gap fields is a sensitive function of the depth below the pole surface and of the extent of the gap saturation. As a result, the divergence of the magnetization in the region immediately below and a fraction of the gap length further below change signs drastically so that the bordering regions are oppositely charged. >

We investigated the effect of thermal relaxation on reversible transverse susceptibility (RTS), χ, of single domain Stoner–Wohlfarth particles. We studied such an effect as a function of the orientation β of the easy axis with respect to the drive field (the z axis) within a non‐interacting bi‐state model. At β=00 one prominent cusp occurs for both χt1 and χt2 along the direction perpendicular to the drive field at H≂HC

Field angles and sweep rate dependence of coercivity of the Stoner–Wohlfarth (S‐W) particles are studied based on the decay‐rate model. An analytic expression of the hysteresis loops based on the model is obtained as a function of applied field for various frequencies at various field angles with respect to the easy axis. Variation of the coercivities versus the sweep rate (measurement frequency), field angles, anisotropy constant, activation volume, and the combination thereof, and the distribution of easy axis, etc., have been obtained. Comparison with the thermal‐equilibrium and S‐W hysteresis loops are made. Coercivities of such a system generally increase with increasing sweep rate, anisotropy constant and activation volume, etc., hence decreases with increasing sweeping period. As a function of the field angles, the coercivity curve turns flat with increasing field angles and sweeping period.

A domain wall with head-on magnetizations, with the domain wall normal parallel to the direction of magnetizations, is a charged wall. A charged wall is unstable, which becomes metastable if a zigzag wall is formed to minimize its energy. When information is stored in thin-film magnetic recording media by means of the application of a recording head field, it induces magnetization reversal of head-on domains. The charged zigzag walls in uniaxial ferromagnetic thin films have been observed in several magnetic media such as Co, Gd-Co, and many others. In this paper we propose and derive an analytic expression based on the Neel tail transition model to deal with the minimum energy surface configuration in the media. We take into account: (1) the surface energy of the wall spine proper; (2) the changes in the crystalline anisotropy and exchange energy in the Neel tail transition region; (3) the self-demagnetization energy in the Neel tail transition region due to the in-plane magnetization rotation; and (4) the long-range magnetostatic interaction energy between magnetic charges on different zigzag wall spine segments. The minimum energy configuration as a function of the wall spine width, the Neel tail transition width and the zigzag angle has been evaluated numerically. The results of calculations are compared with the experimental data for Co and Gd-Co films and are found to be in satisfactory agreement.

Nonlinearity and critical behavior in domain wall (DW) dynamics are analyzed using a newly derived generalized domain wall dynamic equation. The DW motion in a steady state, oscillatory state, precessional instability and the corresponding critical parameters are described and discussed.

Comprehensive analysis of the influence of a weak in‐plane field on the dynamics of a planar domain wall in a uniaxial ferromagnet with a small quality factor has been carried out. The peculiarities of the domain‐wall movement in both subcritical Hz

We study the ground state of magnetization orientation inside domains on both sides of a domain wall. In a uniaxial ferromagnet, the orientation becomes asymmetric with respect to the normal to domain‐wall plane when a magnetic field is applied. As a result, the Kondorsky switching‐field distribution function is modified when the magnetization distribution across the wall proper becomes asymmetric and the wall is charged. The variation of the domain‐wall structure, wall‐shape function, and wall‐energy density function γ versus the magnitude and orientation of the external field is examined and discussed. The extra energy associated with the charged wall is expected to enhance domain‐wall relaxation, generating wiggles in thin‐film head readout waveforms.

Gap-nulls appear in the reproducing spectrum in any symmetric inductive head. This poses severe limitations to the application of inductive heads in high density reading processes. However, based on the equivalence of the current thin film sheet to a Karlqvist head in generating magnetic fields and the principle of linear superposition, stacked current thin film sheets, discrete or continuous, can both effectively smooth out the gap-nulls in their respective spectral response curves up to very large k-values. These types of reading heads can be either an asymmetric stack of thin film sheets flushing with one side or a continuoous bulk current film head in a trapezoidal cross section, and are capable of resolving a bit density of 50 Mbpi without producing any gap-nulls.

Blocking temperature, energy barrier, and reversal field variation of interacting fine magnetic particles display similar characteristics as a function of the bonding angle and interparticle distance in the context of the dipole interaction. The energy barrier and reversal field exhibit local maxima at the bonding angles β=0° and π/2 and a global minimum at β≃60°. Thus, the sample average of these quantities is found to reduce with decreasing interparticle distance, in agreement with the latest experimental data. For a system with easy-axis misorientation, magnetization reversal will traverse along the direction in which the misorientation angle and bonding angle have the same sign.

Energy barrier height and coercivity variation of a pair of interacting particles has been studied as a function of the bonding angle β for 0°⩽β⩽π/2 and applied field using the fixed step Monte Carlo simulation approach supplemented by the perturbation method. Coercivity Hc(β) of the system has local maxima at β=0 and π/2, and a global minimum at β≃65°, and remains depressed compared to the noninteracting case for β⩽30° at any temperature. The barrier height behaves similarly. Due to the random nature of distribution dipole interaction, on average, leads naturally to a reduction in coercivity and energy barrier height in comparison with the noninteracting case.

Switching behavior and noise patterns due to an oblique misorientation of the easy axis of a system of noninteracting single domain particles (SDPs) has been investigated. Curvilinear nature of the head field as observed by the particle in the media has been taken into account using Monte Carlo simulation. For a heterogeneous media with a given set of half width of physical parameters in the distribution, one with an oblique misorientation angle near /spl phi//spl sime/15/sup 0/, appears to cause less fluctuation noise spikes and good readout signal. Media with a broad oblique misorientation distribution leads to a correspondingly broad transition width, rough switching curve and noisy signal output.

The dependence of the magnetization azimuthal angle on the coordinate normal to the pinned domain wall has been obtained for the one-dimensional wall model. For an external magnetic field normal to the anisotropy axis, consideration of the coordinate dependence of the magnetization azimuthal angle leads to a decrease in the domain wall energy. The dependence of the domain wall energy on the transverse field is obtained and compared with previous results when the azimuthal angle was assumed to be constant.

The Landau-Lifshitz equation with the relaxation terms introduced by Bar'yakhtar is discussed. These relaxation terms take into account the spatial dispersion of the relaxation caused by the exchange interaction and correct symmetry properties of the well known relativistic part of the relaxation term in the Landau-Lifshitz equation. The Slonczewski type equation obtained on the basis of this new equation for the dynamics of the magnetic moment are presented. Some concrete results for the characteristic parameters of the domain wall motion are also given.

Simultaneous variation of the magnetization angles (ϑ, ϕ) across the DW proper and the DW energy variation versus the transverse magnetic field h t has been studied for the pinned domain wall. When the ψ H angle of the magnetic field is π/2 the DW will undergo the phase transition to a homogeneous state at a relatively small field of h t = 0.225.

Analysis of the characteristic dependency of the switching field distribution of a system of noninteracting single domain particles was conducted based on the bi-state, nonequilibrium probabilistic approach. The analysis was carried out as a function of applied field orientations, transition energy barrier variation, and in combination with a given distribution of the particle size and anisotropy constant, under the influence of thermal relaxation. The concept of the blocking temperature that the energy barrier being approximately equal to /spl sim/25 k/sub B/T was shown to be invalid unless the period of the field sweep is /spl sim/1 h.

The pinned domain‐wall (DW) structure is investigated using a perturbational approach in terms of the inverse quality factor 1/Q and the ratio of H∥/Hk (H∥ being the component magnetic field parallel to the anisotropy axis, Hk being the anisotropy field). The parallel component field gives rise to asymmetric boundary conditions which asymmetrize the DW structure. Dependence of the DW energy, static DW structure, and width on the orientation and the strength of the magnetic field has been evaluated and the corresponding Kondorsky function obtained.

Generalized domain wall dynamic equations have been derived. The influence of the external magnetic field normal to the anisotropy axis on the critical parameters of the domain wall motion has been studied and illustrated.

The response of a system to an infinitesimal perturbation becomes singular if the system changes its degree of metastability, i.e., if it has an inflection point. This theory is used to calculate the reversible transverse susceptibility χt of a single domain particle executing a major hysteresis loop under the influence of a field H(t) applied at an angle β to the easy axis. Thermal relaxation is taken into account and the response of the nonequilibrium system to the infinitesimal field h(t)=h sin ωt, h⊥H, is found. The resultant χt is studied as a function of β, temperature, and of the frequency Ω of the biasing field H.

Generalized domain wall dynamic equations in an infinite medium with the quality factor Q > 1 in the presence of the in-plane field is derived, Characteristic varaiation of the Walker critical field and critical velocity with the in-plane field, among other factors, are discussed.

Fluctuation in the magnetization transition for a given distribution of the physical parameters of the particle and orientation of the easy axis of a system of thermally activated noninteracting single-domain particles under a pulsed recording-head field has been analyzed. Our analysis takes into account the vector nature of the head field as observed by the particle in the media. Under the same head, the layer of the media closer to the head gap exhibits much lower noise than the layer farther from the head gap.

Depending on the textural distribution of easy axes of the particles there could exhibit one, two or three prominent cusps in the curves for the reversible transverse susceptibility at high KV / k B T . Experimentally, the number of cusps detected at low KV / k B T may be one less since the cusp at H c is fairly sensitive to thermal relaxation.

Analysis of the fringing field anomaly and the surface charge distribution of the ferrite head pole tip at and off the saturation field has been carried out using 2D finite element analysis (FEA). Dimensional dependence of the anomaly and distribution is discussed.

The dynamics and relaxation of magnetization M(r,t) is usually described phenomenologically by the Landau–Lifshitz (LL) equation with relaxation term M=−γ[M×F]+R, where γ is the gyromagnetic ratio (γ≳0), F is the effective field, and R describes the relaxation of the magnetization toward its equilibrium value. It is already well known that the relaxation term of either the LL or Gilbert form does not give a correct description of the dependence of spin‐wave damping on the wave vector at small wave vectors for the models of an isotropic and easy plane ferromagnet. The correct behavior of the spin wave damping may be obtained by taking into account the spatial dispersion of the relaxation caused by the exchange interaction and correct symmetry structure of the relativistic part of the relaxation term which now has to be represented as a sum of the exchange and relativistic parts by R=Rex+Rτ. A review of the recent results on the relaxation obtained in the frames of the LL equation with the relaxation term s...

Domain wall motion under the influences of weak in-plane fields applied along arbitrary directions in an infinite medium with uniaxial anisotropy has been considered. Typically, the azimuthal angle of the magnetization vector along with the domain wall central plane exhibits transient, stationary and oscillatory behavior. The azimuthal angle displays a terrace-like structure at the critical field when subject to a weak perturbation field along the domain wall normal direction. As a result, the domain wall cants out its magnetization vector out of the wall plane and stays in that configuration as it continues to translate onward like a hybrid of Bloch-Néel wall in a quasi-static manner without precession. The in-plane field along the wall normal has limited effect on the domain wall upper bound velocity, while the field parallel to the domain wall can substantially increase it. At a higher drive field, the magnetization (φ) precesses nonuniformly with time and results in nonuniform, anharmonic oscillatory behavior for domain wall motion. Also, as domain wall picks up its velocity, it contracts to reduce its surface demagnetization energy and at the same time interchanges between Bloch type and Néel type in an oscillatory manner.

An exact conformal mapping calculation is carried out, which maps the entire upper edge of an idealized ring head and a symmetric thin-film head in the complex z plane to the real axis of the complex t plane, and uses the slotted-plane approximation to obtain the inverse mapping function t(z). The latter is used to calculate not only the head fields of a given geometry, but also the kernal function to evaluate the total demagnetization field of the interaction head-media system including the media self-demagnetization and the image field induced on the head poles. The total demagnetization field contours for a single-bit arctangent transition and a dibit biquadratic transition corresponding to various head configurations have been obtained and their physical meaning elaborated on. >

The authors present a detailed analysis of capillarity effect in the presence of surface diffusivity variation and use this as a basis to describe evolution of the surface profiles generated by the electromigration-induced surface and grain boundary (GB) diffusion in a bicrystal film. Thermal GB grooving is asymmetric in the presence of diffusivity variation across the GB, but the extent of asymmetry is rather significant, less than 0.14% from the symmetric case, but up to 60% in diffusivity variation considered. Surface profiles of the electromigration-induced surface and GB diffusion for the samples with and without prior heat treatments have been carefully analysed and compared. The surface morphological changes can be understood in terms of the combined action of the following effects: (i) Dynamic balance between the surface tension and the GB tension incorporation with surface diffusivity variation across the GB generates further disparity in the profile changes. The effect lasts as long as the sample is under power stressing. (ii) The non-vanishing surface flux divergence with the GB acting either as a sink or source of the flux contributes dominantly to the GB disfiguration. (iii) Four additional transient terms originating from the capillarity effect aggravate the surface profile changes in the early stage of electromigration, causing surface undulation and so on, but gradually, the effect is overshadowed. Electromigration damages are mainly dictated by a quantity M which in turn is determined by the interplay between the GB flux and the surface diffusivity variation. With a negative M the profile starts with a sharp cusp which in time turns obtuse, then the minimum moves downstream into the grain. When M is positive, the GB profiles change rapidly with a small increase in M and in power stressing time. The profiles contract and protrude like a mound, and quickly rise above the x axis. Beyond this point, the shape of the surface morphology becomes relatively unchanged. Furthermore, when two or more GB diffusions are activated simultaneously, the superpositional effect of the GB fluxes may lead to trapezoidal growth and/or faceted voids, among other types of profiles. Finally, the problems with respect to further quantification of the quantity M are briefly discussed.

The time‐dependent temperature distribution of a thin‐film stripe has been solved rigorously using two successive Laplace transforms on both time and coordinate. For a good conducting stripe with a δ‐shaped crack it is shown that the temperature distribution can be very adequately described by the steady‐state solution provided only that the time scale involved is of the order of 10−3 sec or longer. No localized hot spot is possible, for whatever reasons, for a good conductor. However, if heat generation outpaces heat conduction, as would be the case for a poor conductor, a localized temperature becomes quite realizable. Finally, if stripe cracking is developed via grain‐boundary grooving processes somewhere along the stripe, in particular near the anode, void formation there is simply a natural consequence of the temperature‐grandient effect.

The surface morphological changes at the grain boundary (GB) is characterized by a surface flux discontinuity quantity M’ which is compounded by the capillarity‐induced surface diffusion and the electromigration‐induced surface and GB diffusion in polycrystalline films. The quantity M’ has to do with the surface diffusivity and the so‐called threshold current density across the GB in connection with the pertinent physical parameters in the GB concerned. Qualitative plots of the GB profiles by treating M’ as a parameter show very good conformity with experimental observations. The circumstances surrounding the existence and nonexistence of the threshold current density in relation to the surface diffusivity variation across the GB and the mobile concentration gradient of the diffusion species in the GB are discussed for pure system and light alloy system. Their relation to the GB segregation and the second phase formation is pointed out.

Mullins' thermal grooving analysis has been extended to cases where there is a ridge or notch. Annealing may blunt the ridge and shallow the notch under appropriate conditions. A quantity M which is held to be responsible for non-vanishing flux divergence, i.e. ∇· J ≠ 0, in thin film metallization in electromigration has been positively identified. Since the quantity M will never vanish unless the film is a single crystal, electromigration is expected to be operative at all current levels. The grain boundary grooving of the electromigration origin is shown to dominate the failure processes and the changes in surface morphology.

Remanent magnetisation for randomly distributed cubic particles, with the first order anisotropy constant K1 > and 0, and Mr = 0.866Ms for K1 < 0, as expected.

The capillarity‐induced surface mass transport has been extended to cases where there is a notch and/or a ridge on a bicrystal system. Changes in the surface morphology caused by capillarity‐induced and electromigration‐induced surface diffusions and grain boundary diffusions have been analyzed. Thermal grooving is shown to develop only when the initial slope of a notch on the crystal surface is less than γb/2γs (γb and γs are, respectively, the grain boundary and the surface Gibbs free energy) or when the initial surface contains a ridge at the grain boundary. The slope of the grooving profile is invariant with time but its depth develops as the one fourth power of time. Surface fluxes due to the electromigration origin change the morphology in an asymmetric manner, biased in the direction of the electron flow. When combined with fluxes from grain boundary diffusion, severe mass depletion and accumulation can occur, giving rise to characteristic electromigration damage of open circuit failures. Finally, ...

The exact head field and image field are used to study the recording behaviors of ring and thin film head. We find that: (1) for ring head, the readback voltage is smaller than that from using Karlqvist's head approximation. (2) For thin film head, the image field in writing process cannot be neglected.

A mathematical analysis of the variation of resistance and the electric line of force over a greion in a conducting strupe with a geometrical defect is carried out based on the Christoffel‐Schwarz transformation. The overall resistance of the sripe with a bump‐type defect may turn out to be less than that of homogeneous stripe of the same physical length despite the added resistance due to the current crowding. Possible implications of this effect are pointed out. The electromigration flux divergence at the edige of a void or a cracking is substantially greater than that at the edge of the bump‐type defect. This is in line with the notion that stripe cracking or a faceted void in its embryonic stage first nucleated at the grain‐boundary triple points.

- Calculations shows that asymmetric ring heads exhibit sharp field gradient for both the H, and H, field components at large inclination and low spacings. These characteristics can be exploited to improve bit density in longitudinal and vertical recording, respectively. Introduction Theoretical and experimental studies of both lon- gitudinal and vertical modes of magnetic recording all supports the idea that magnetic recording is write field limited and not demagnetization limited [I]. Funda- mental limitations to head field gradients give rise to a minimum transition width that is larger than the simple stability-versus-demagnetization limit [2]. For this reason, it is highly desirable to find a magnetic head which has large field gradient in the writing pro- cess, and has a narrow field width in the reproducing process. Asymmetric ring head is a prime candidate equiped with the characteristics whereby high bit den- sity recording can be effectively realized. Head field calculations The essence of an assymmetric ring head is shown in figure 1. Assuming that the relative permeability of the head core is infinite, we may use Schwartz trans- formation to map the upper edge of the recording head in the

We have derived the static spin configurations of the various kinds of bubble domains using the cylindrical coordinate system. The spin deviation from the wall normal and the variation of the wall width and its characteristic length, etc., have been solved and discussed at some length. The present results can be reduced to the corresponding planar wall results at an appropriate limit, with the exception of the stability condition.

A model calculation on the contribution to electropositive impurity diffusion by divacancy processes in f.c.c. noble metals has been carried out. Four different types of divacancy configuration were considered. It is shown that ΔQ 2 v = Q i 2 v − Q o 2 v , the difference in the activation energy between impurity diffusi and its thermal average, ΔQ 2 v av , are generally more negative than ΔQ tv s as calculated by LeClaire. D i 2v D i 1v , the ratio of the impurity diffusion coefficient by the divacancy process to that by the monovacancy process, is found to be in the range of 8.2–16.7% for copper and 27.3–36.7% for silver at 1000°K, both noticeably larger than the corresponding ratio for the self-diffusion coefficients. In addition, the present calculation has shown appreciable improvement in edging closer to the experimental data than the previous calculations.

The contribution of a stripe cracking to its resistance is obtained in a closed form by means of Christoffel-Schwarz transformation. It is shown that the cracked region resistance is a sum of two terms in series: one is the typical resistance term which is linearly proportional to the width and inversely proportional to the cross section of the stripe, the other depends sensitively upon the perpendicular depth of the crack, known as the current crowding resistance. Some numerical results for the crack region resistance are presented. The extra local electric field, its corresponding mass flux and their potential implications to electromigration arc also discussed.

The motion of a 180° domain‐wall in pure yttrium iron garnet has been investigated, using the Winter‐Janak domain‐wall excitation spectrum. In particular, the domain‐wall mobility as a function of temperature has been thoroughly studied. It is shown that the demagnetization energy due to the surface roughness of the sample where the domain‐wall plane crosses the sample surface is the main source of resistance to domain‐wall motion; the two‐body part of the surface roughness causes transitions from a uniform translational domain‐wall magnon mode to a degenerate domain‐wall translational magnon mode, and is the predominant process that leads to the domain‐wall motion relaxation. The four‐body interaction intrinsic process contributes very little even at higher temperatures (about 10% of the two‐body interaction at 300°K, much less at lower temperatures). The two‐body process being considered here is, in some sense, similar to the Sparks‐Loudon‐Kittel calculations in which each pit is assumed to scatter inde...

Bubble statics and dynamics is studied using the micromagnetic method. A wall width expression as a function of Q , spin orientations, and number of BLs is derived. Comparison is made between a bubble and a planar wall in motion. The linear relationship between collapse time vs. applied field at high fields and low fields, the bubble collapse below the collapse field, H c , etc. are discussed.

Fourier coefficients for fing head and pole type head for various configurations and flying heights are evaluated, the corresponding head field distribution obtained and compared. The Write field of the ring head differs considerably from that of the pole types head when measured along the media motion but behaves similarly if measured along its respective image plane.