Curling Mode Research Articles

Occurrence of large perpendicular magnetic anisotropy in bilayered films with nanometer-thick TbFeCo and Al layers

For Tb-Fe-Co(MO)/Al bilayered films, dependence of perpendicular magnetic anisotropy constant Ku⊥ on MO layer thickness tMO of 3–300 nm and Al layer thickness tAl of 5 and 100 nm has been investigated. For either tAl, easy magnetization direction was normal to film plane at tMO above 4 nm. Ku⊥ of films with tAl of 5 nm increased drastically with increasing tMO for tMO<10 nm and then assumed a constant value of 4×106 erg/cm3 which is two times larger than that with tAl of 100 nm. This difference in Ku⊥ between them may be attributed to stress induced anisotropy. Estimation of rotational hysteresis loss Wr and its integral R suggests that the mechanism of magnetization reversal may be attributed to incoherent curling mode.

Coercivity and nucleation field of hollow ferromagnetic particles

Calculations of nucleation fields and critical radii of three possible magnetization reversal modes for an infinite ferromagnetic hollow cylinder with exchange and uniaxial anisotropy are made using Brown's equation. It shows that the curling mode is the favored mode for large radius and the nucleation fields for curling and buckling modes decrease for increasing outer radius and the ratio of inner to outer radius. The transition between these modes is very sensitive to the ratio of inner to outer radius.

Investigation of magnetization reversal mechanism in nanometer-thick Tb-Fe-Co films with Al overlayer

Magnetic anisotropy energy and magnetization reversal mechanism were investigated in the glass/Tb-Fe-Co(MO)/Al films with the MO layer thickness t/sub MO/ 3 to 10 nm. As t/sub MO/ decreases, an easy magnetization direction changed from perpendicular to parallel to a film plane at t/sub MO/ of about 4 nm. Measurements of rotational hysteresis loss suggested that the magnetization reversal in the films seems to be an incoherent curling mode.

A Fast Micromagnetic Simulation Using Magnetic Potentials

A fast simulation program was constructed that solves the Landau-Lifshitz-Gilbert equation and in which the demagnetizing field is derived from magnetic potentials within the magnetic material. The Poisson and Laplace equations are solved iteratively to obtain the potentials. The initial values for iteration are predicted by using the values at previous time steps. The process of magnetization switching of a square prism in the curling mode is simulated to demonstrate the capability of the program and the validity of its results. The derived program was found to have a computational speed some 20 times faster than that of a similar program based on conventional calculations of the demagnetizing field when the computing region consists of 30×30 cells.

Magnetization curling in elongated heterostructure particles.

A rigorous micromagnetic study of nucleation by use of the magnetization curling mode in an elongated particle with heterostructure is presented. We categorize the heterostructure particles into three different types depending on their growth conditions and internal structures. The coercivity of the heterostructure particles critically depends on the relative magnetic parameters of the composite materials. The physical origins of the enhanced coercivity for the three types of heterostructure particles are quite different. The initial slope of the enhanced coercivity of surface-coated particles results from the shell crystalline anisotropy, while the saturation level depends on the interfacial coupling, shell crystalline anisotropy, and shell surface anisotropy. The main contribution to the enhancement of the coercivity of surface-modified particles is the surface anisotropy of the adsorbed layer at the particle surface. The homogeneity of the doped materials within the volume-modified particles affects their coercivity and the saturation level of the coercivity is always higher than that of the other two types. Agreement between theory and experiment is reasonably good.

Interfacial effects on curling mode for a coated particle

A rigorous micromagnetic study for the nucleation by the magnetization curling mode in acicular coated particles is presented. The calculated nucleation field increases with shell thickness and saturates within observable thickness. It is found that the shell uniaxial anisotropy determines the initial slope, and that the saturation level depends on both the interfacial coupling and shell anisotropy. The shell surface anisotropy will further increase the nucleation field. A very good fitting of experimental data can be obtained by this method. >

Spherical center for nucleation by curling in a bulk ferromagnet

The process of nucleation of magnetization reversal in bulk materials by the magnetization curling mode is investigated by a numerical integration of an approximate differential equation. This computation shows that limiting the curling to a spherical shell does not lead to a saddle point, and that the energy which has to be overcome for reversing the magnetization by the curling mode is larger than that required for the previous, tilting mode. Therefore, the latter is left as the only practical nucleation center in bulk materials.

磁位を利用したマイクロマグネティックスのための高速シミュレーション

A fast simulation program was constructed that solves the Landau-Lifshitz-Gilbert equation and in which the demagnetizing field is derived from magnetic potentials within the magnetic material. The Poisson and Laplace equations are solved iteratively to obtain the potentials. The initial values for iteration are predicted by using the values at previous time steps. The process of magnetization switching of a square prism in the curling mode is simulated to demonstrate the capability of the program and the validity of its results. The derived program was found to have a computational speed some 20 times faster than that of a similar program based on conventional calculations of the demagnetizing field when the computing region consists of 30×30 cells.

Nucleation of magnetization reversal via the curling mode for an infinite cylinder.

For an infinite ferromagnetic cylinder with exchange, uniaxial anisotropy, demagnetizing field, and an external magnetic field applied along its axis, curling-mode solutions to Brown's equation (the static Landau-Lifshitz equation) exist. It is proved that these solutions are unstable, and by analogy to a specific-sized water droplet in a supersaturated vapor for which an unstable equilibrium exists, the solution for a given magnetic field is shown to be the configuration of smallest energy through which magnetization reversal can nucleate in the curling mode.

Magnetization curling in an infinite cylinder with a uniaxial magnetocrystalline anisotropy

The magnetization curling mode for an infinite cylinder with a uniaxial magnetocrystalline anisotropy is considered. The angular dependence of the nucleation field HN and the coercive force Hc are estimated as a function of the radius, the magnetocrystalline anisotropy, and the inclination of the axis to the applied field. It is assumed that only curling and rotation in unison occur, and that the discontinuous jump by the curling mode brings the magnetization to the lower energy state given by Stoner–Wohlfarth. With this assumption, the rotational hysteresis loss Wr and integral Rh are evaluated both for an aligned and for a random assembly of infinite cylinders.

ROTATIONAL HYSTERESIS MEASUREMENTS ON ALUMITE PERPENDICULAR MEDIA

Rotational hysteresis energy loss measurements have been performed to support the analysis of the magnetization processes of Fe- and Co-alumite perpendicular recording media. Two measurement techniques gave comparable results within error limits. The rotational hysteresis integral is severly lowered by the demagnetizing field. Normalizing the integral with the remanent magnetization instead of the saturation magnetization gives for Fe-alumite values indicating the curling mode, which was also proved by other measurement techniques. The half width value D(1/H)50 is introduced in the rotational loss graph. This value is an estimate for the dispersion of anisotropy axes and in our case it its proportional to the diameter of the Fe-needles. The in-plane loss is very low for the Fe-alumite samples, whereas it is high for the Co-alumite. In the well aligned Fe-alumite, rotation around the easy-axis does not give rise to an energy loss because no anisotropy is present in the rotation plane to cause irreversible magenetization jumps. The crystal anisotropy of fcc-Fe is small compared to the shape anisotropy of the particles. The high in-plane loss measured for Co-alumite is thought to originate from the dispersion of hcp-axes in the Co-needles.

Magnetostatics of curling in a finite cylinder

The magnetostatic self energy is calculated for the magnetization curling mode in a finite cylinder, for the model proposed by Ishii and Sato [J. Appl. Phys. 65, 3146 (1989)]. It is shown that slight modifications of that model can eliminate all the cumbersome computations and allow all the integrations to be done analytically.

Analysis of Head to Medium Magnetic Interaction in Perpendicular Magnetic Recording by Finite Element Method Combined with Magnetization Model

A new simulation program has been developed for the analysis of perpendicular magnetic recording. This is the finite element method program which adopts a magnetization curling mode and a statistical method to calculate vectorial magnetizations in a medium. Using this simulation analysis, we could explain quantitatively the effects of the magnetic interaction between a single-pole head and a double-layer medium which were predicted from the experimental results. Furthermore, we were able to analyze a vectorial recording and reproducing mechanism. This new program is a very powerful tool which can more precisely simulate the magnetic recording process.

Magnetization reversal in Ir-doped CrO 2 particles

The possible evolution of the magnetization reversal mode of Ir-doped CrO 2 particles as the Ir content increases is analyzed through rotational hysteresis and H c vs. θ measurements. The reversal mode evolves from the curling mode (undoped particles) to the fanning (low Ir content) and becomes more and more heterogeneous with Ir increasing.

Analysis of perpendicular magnetic recording mechanism by finite element analysis combined with medium magnetization model

A new program for simulating magnetic write and read processes was developed, incorporating into the finite element method a model of curling mode magnetization in the perpendicular magnetic recording medium. That is, the curling mode was adopted as describing the mechanism of magnetization reversal in the fine crystal grains comprising the Co-Cr recording layer, and the magnetization vector is computed stochastically, with the dispersion in the easy axis of magnetization and the anisotropy field represented by a probability density function. Such finite element analysis simulations incorporating a magnetization model are capable of addressing complex magnetization processes within the recording medium. This method takes into account magnetic interactions between head and medium which depend on saturation in the head and medium soft magnetic layer and on the strength of magnetization in the medium, effects not accounted for by the scalar potential method; it also incorporates magnetization by rotation, which cannot be included in ordinary finite element analysis. As a result, this approach enables highly accurate, quantitative computer simulations of magnetic read and write processes which take into account not only such magnetic properties of the recording medium as the Co-Cr layer coercivity and saturation magnetization, but magnetic properties of the head and the medium backing layer as well, such as permeabilities and saturation flux densities.

Modeling of elongated fine ferromagnetic particles

This paper presents some results of a numerical micromagnetic calculation for ferromagnetic fine particles. Two basic shapes are discussed: elongated parallelopipeds and parallelopipeds with pointed ends. The variation of coercivity, switching field, and reversal modes with particle size, orientation, and material parameters are discussed. Equilibrium magnetization structures suggest that particles may have remanent states that are substantially nonuniform. The flipping mode, in which the magnetization reversal starts from the longitudinal ends of the particles, is found to be the energetically favorable switching mechanism. Small particles are switched by the quasi-coherent flipping mode, while large particles are reversed by the quasi-curling flipping mode. The angular dependence of the coercive and switching fields for three particle sizes is found to agree qualitatively with classical results, but both fields are quantitatively smaller. The nucleation field is compared with the Stoner–Wohlfarth model as well as with the curling mode, and is found to be about half of their value.

Magnetization curling in a finite cylinder

In order to see the variation of the magnetization state in a finite cylinder, it is assumed that the magnetization changes its direction by the magnetization curling mode in which θ is given by θ=λ(z/L)2+ν, where θ is the deviation of the magnetization in the cylinder from the z axis which is the axis of the cylinder, L is half of the cylinder length, and λ and ν are the coefficients which specify the magnetization state. Finding λ and ν which minimize the total energy ε of the cylinder, we obtain the hysteresis loops and the coercive force. The coercive force obtained in this work agrees well with the experimental results for a cylinder 2.5 μm long and a diameter from about 50 to about 130 nm. It is also found that the configurations can be stable in which the magnetizations are not along the z axis, and the hysteresis loops are not rectangular, even though an applied field is along the z axis.

アルミニウム円管端末の球面状口広げ成形中に生じるカーリング現象

The curling behavior in aluminun was investigated to clarify the condition for curling during the tube end spherical flaring. The influence of die radius R, lubricant, ratio of the tube wall thickness to diameter t0/d0, work hardening exponent n and forming speed V on the condition for curling was investigated in the aluminum tubes. It was found that the curling took place when the apparent die angle α' at the initial contact point of a tubular specimen to the hemispherical die was larger than the critical die angle αS with the conical die. Furthermore, the multi- and single-stage methods to prevent the curling in the case of the conical die were proposed and experimentally examined. The curling mode was prevented under the proposed preventing condition. Thus, these results suggested that the curling mechanism in the hemispherical die was similar to that in the conical die.

Preparation and magnetic properties of anodic oxide magnetic films

AbstractThe M‐H curve, coercive force and magnetic anisotropy of magnetic anodic oxide films containing electro‐deposited iron particles in pores were measured for the various pore diameters between 150 and 1200 Å, packing densities between 0.13 ‐ 0.48 and film thicknesses between 0.08 and 1.3 μm. As a result, it was found that the coercive force perpendicular to the film surface depends only on the pore diameter when the length of the iron particle is 15 times larger than its diameter, and that it decreases in inverse proportion to the square of the pore diameter when the pore diameter is larger than 350 Å. This indicates that the mechanism of magnetization reversal in these films follows the curling mode. The coercive force parallel to the film surface is affected by the shape of the initially deposited iron particles. The magnetic anisotropy depends strongly on the packing density of the iron particles. When the packing density is less than 0.32, the direction perpendicular to the film surface is the direction of easy magnetization. When the packing density is higher than 0.32, the direction parallel to the film surface is the direction of easy magnetization.

磁化モデルを組み込んだ有限要素法による単磁極ヘッド・二層媒体間磁気的相互作用の解析

A new simulation program has been developed for the analysis of perpendicular magnetic recording. This is the finite element method program which adopts a magnetization curling mode and a statistical method to calculate vectorial magnetizations in a medium. Using this simulation analysis, we could explain quantitatively the effects of the magnetic interaction between a single-pole head and a doublelayer medium which were predicted from the experimental results. Furthermore, we were able to analyze a vectorial recording and reproducing mechanism. This new program is a very powerful tool which can more precisely simulate the magnetic recording process.