Stoner-Wohlfarth Coherent Rotation Model Research Articles

A Model to Design Giant Magnetoresistive Sensor

Giant magnetoresistive (GMR) sensor has developed rapidly in automobile, consumer electronics and current sensing areas due to its high sensitivity and low power consumption. In this work, we suggest a method to design GMR sensor based on Stoner-Wohlfarth coherent rotation model. We have investigated the influence of width of GMR sensor to its performance with the model and verified with experiments. And different pinning direction GMR elements are also researched to study Wheatstone bridge structure. The experimental results matched well with the simulation results which proved that the model is efficient in designing GMR sensor.

Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy

We report on the crossover from the thermal to athermal regime of an artificial spin ice formed from a square array of magnetic islands whose lateral size, 30~nm~$\times$~70~nm, is small enough that they are superparamagnetic at room temperature. We used resonant magnetic soft x-ray photon correlation spectroscopy (XPCS) as a method to observe the time-time correlations of the fluctuating magnetic configurations of spin ice during cooling, which are found to slow abruptly as a freezing temperature $T_0 = 178 \pm 5$~K is approached. This slowing is well-described by a Vogel-Fulcher-Tammann law, implying that the frozen state is glassy, with the freezing temperature being commensurate with the strength of magnetostatic interaction energies in the array. The activation temperature, $T_\mathrm{A} = 40 \pm 10$~K, is much less than that expected from a Stoner-Wohlfarth coherent rotation model. Zero-field-cooled/field-cooled magnetometry reveals a freeing up of fluctuations of states within islands above this temperature, caused by variation in the local anisotropy axes at the oxidised edges. This Vogel-Fulcher-Tammann behavior implies that the system enters a glassy state on freezing, which is unexpected for a system with a well-defined ground state.

Magnetoelastic coupling induced magnetic anisotropy in Co2(Fe/Mn)Si thin films

The influence of epitaxial strain on uniaxial magnetic anisotropy of Co$_{2}$FeSi (CFS) and Co$_{2}$MnSi (CMS) Heusler alloy thin films grown on (001) SrTiO$_3$ (STO) and MgO is reported. The in-plane biaxial strain is susceptible to tune by varying the thickness of the films on STO, while on MgO the films show in-plane easy axis for magnetization (\overrightarrow{M}) irrespective of their thickness. A variational analysis of magnetic free energy functional within the Stoner-Wohlfarth coherent rotation model with out-of-plane uniaxial anisotropy for the films on STO showed the presence of magnetoelastic anisotropy with magnetostriction constant $\approx$ (12.22$\pm$0.07)$\times 10^{-6}$ and (2.02$\pm$0.06)$\times 10^{-6}$, in addition to intrinsic magnetocrystalline anisotropy $\approx$ -1.72$\times 10^{6}$ erg/cm$^{3}$ and -3.94$\times 10^{6}$ erg/cm$^{3}$ for CFS and CMS, respectively. The single-domain phase diagram reveals a gradual transition from in-plane to out-of-plane orientation of magnetization with the decreasing film thickness. A maximum canting angle of 41.5$^{\circ}$ with respect to film plane is predicted for the magnetization of the thinnest (12 nm) CFS film on STO. The distinct behaviour of \overrightarrow{M} in the films with lower thickness on STO is attributed to strain-induced tetragonal distortion.

On the free layer reversal mechanism of FeMn-biasedspin-valves with parallel anisotropy

Transmission electron microscopy has been used to investigate the `free' layer reversal mechanism of a range of FeMn-biased spin-valves with parallel anisotropy. Fresnel imaging enabled three modes of reversal to be directly observed for different in-plane applied field orientations and interlayer coupling strengths. Low-angle diffraction has provided some quantitative information on the level of dispersion involved in the reversals. Comparison with a modified Stoner-Wohlfarth coherent rotation model is made and magnetic modelling of the free layer energy variation as a function of magnetization orientation is presented. This has helped provide a deeper understanding of the observed discrepancies between the model and experimental data. Finally, a qualitative description of the observed domain processes is given in relation to the free layer energy for the corresponding experimental conditions.

Magnetization rotation in spin-valve multilayers

The magnetic hysteresis associated with the magnetization reversal of the free layer in a spin valve is analysed. A model is proposed which assumes a single-domain behavior of the free layer, and a fixed magnetization of the pinned layer. The model is then developed in the framework of the Stoner—Wohlfarth coherent rotation model, where geometrical solutions are obtained by the astroid method. According to the strength of the interlayer exchange coupling, the applied field direction and the anisotropy arrangement of the magnetic layers, a general classification of the hysteresis loops is proposed. Quantitative comparisons with experiments on spin valves (e.g. NiFe/Cu/NiFe/FeMn) are shown.

Incoherent rotation in barium ferrite thin film recording media

The angular dependence of the remanent magnetic properties of uniaxially in-plane oriented barium ferrite films were found to deviate significantly from the Stoner-Wohlfarth (SW) coherent rotation model. The in-plane torque and the rotational hysteresis were studied in both aligned and randomly oriented films. They were found to be different from that calculated from the SW coherent rotation model, and suggested incoherent rotation of magnetization during the switching process. Incoherent rotation was found to be dependent on grain size and intergranular interactions.

Detection of anisotropy in the reversible transverse susceptibility

A model of reversible transverse susceptibility is proposed. It is based on the Stoner–Wohlfarth coherent rotation model, but with a macroscopic mean field interaction included to represent mutual interaction between particles. Unlike previous predictions, our calculated results show that the determination of the magnetic anisotropy field strength by means of the location of the peak in the transverse susceptibility curve works only in a weakly interacting particle system. For a strongly correlated system, nucleation does not start at the anisotropy field; therefore, it can be concluded that the peak detection method of anisotropy in transverse susceptibility should fail in this system.

Magnetization reversal in Co/Cr multilayer films

Magnetization reversal of Co/Cr multilayer films is studied by utilizing initial magnetization curves, minor loops, isothermal and dc demagnetization remanence curves, and temperature dependence of the loops. Electron microscope observations reveal that the films consist of columnar grains of size from 400 to 800 Å. It is suggested that the magnetization reversal is dominated by rotation of single-domain grains. Numerical calculations are performed based on the Stoner–Wohlfarth coherent rotation model for noninteracting, single-domain particles of uniaxial anisotropy. The calculated results agree qualitatively with the experimental results. To investigate the quantitative differences, magnetic interactions among the grains are measured in terms of deviations from the linear Hankel plot predicted by Wohlfarth.

A mean field Stoner-Wohlfarth hysteresis model

A model of magnetic hysteresis is proposed. It is based on the Stoner-Wohlfarth coherent rotation model, but with a macroscopic mean field interaction (similar to Weiss's molecular field theory), added to represent interaction between domains. Rotation of domain magnetization vectors gives both reversible and irreversible changes in bulk magnetization. A qualitative correlation is obtained between hysteresis curves calculated using this theoretical model and experimentally measured hysteresis curves of a ferrite permanent magnet. >

Magnetic viscosity studies of cobalt-aluminum fine-particle ferromagnets

Magnetic viscosity experiments were performed on Co-25-at.% Al fine-particle ferromagnets aged to peak magnetic hardness in the temperature range 298-573 K, and the results were found to obey the relationship M=A-S/sub 0/ ln t over a time interval of approximately 1 to 10/sup 3/-10/sup 4/ s. Coefficients of magnetic viscosity and susceptibility data are analyzed taking into account corrections for a finite demagnetizing factor, thus allowing the determination of the fundamental viscosity coefficient S/sub nu /=k/sub b/T/ nu M/sub s/, where nu is the activation volume. A linear fit and extrapolation of the temperature dependence of the maximum effective viscosity coefficients gives rise to nonzero intercepts, suggesting that interparticle interactions may influence magnetization reversal. The viscosity data are found to be in general agreement with a previously proposed modified Stoner-Wohlfarth coherent rotation model for predicting the levels of coercivity in these Co-Al alloys. >

Angular Dependence of Coercivity for Barium Ferrite Coated Perpendicular Media

The authors studied the angular dependences of the coercivity H c and remanent coercivity rH c in Ba-ferrite perpendicular-oriented film and other media, to investigate magnetization reversal in Ba-ferrite particles in the media. Comparisons with behaviors predicted by the Stoner-Wohlfarth coherent rotation model indicated that while magnetization reversal in such film shows single-domain behavior, it cannot be regarded as necessarily coherent in nature, although reversals within individual particles may be so.

Theoretical and experimental aspects of coercivity versus particle size for barium ferrite

The Stoner-Wohlfarth coherent rotation model has been extended to particle sizes approaching the superparamagnetic critical size S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> for the case of barium ferrite. It is shown that at particle volumes up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">100 S_{c}</tex> , the coercivity factor will be lower than the Stoner-Wohlfarth factor of 0.48. Experimentally, micro-powders of barium ferrite with variable particle size have been formed using the glass-ceramic process. The particle size was determined with X-ray and electron microscope techniques. Although coercivities in excess of 5000 Oe were measured, the comparison between experiment and theory is not good. This has been attributed to the fact that the particles are poorly crystallized even though formation proceeded by a precipitation and crystal growth process.

Torque and Rotational Hysteresis in fcc Single-Crystal Cobalt Films

The Stoner-Wohlfarth coherent rotation model is extended to the case of biaxial anisotropy. The rotational hysteresis Wr as a function of reduced field h is zero for all values of h except 0.25≤h≤1, and the maximum value of Wr/K=2.38 at h=0.25. The rotational hysteresis integral W equals 1.54. Measurements on fcc single-crystal Co films (−K=4−6×105 ergs/cm3) prepared by epitaxial evaporation onto the (100) face of single-crystal MgO slabs held at 400°C yield results in wide disagreement with the theory. While the expected angular symmetry of the torque is observed, the model does not correctly predict the magnitude of the torque nor the fields at which specific types of angular dependence will be observed. The rotational hysteresis begins in every case before the predicted onset and continues beyond the expected cutoff. The maximum value of Wr/K and W are found to vary from 1.0 to 1.6 and from 2.9 to 1.7, respectively. It is concluded that the magnetization reversal process in single-crystal Co films is not coherent and that, as in the case of polycrystalline films, noncoherent rotations or wall motions must be investigated. This situation in single-element, single-crystal films calls for a reappraisal of the importance of compositional inhomogeneities and local crystalline anisotropy in polycrystalline alloy films.