Domain formation in films of magnetic nanoparticles with a random distribution of anisotropy axes

A theoretical model describing the magnetization distribution in a system of closely packed ferromagnetic grains with a random distribution of easy magnetization axes is constructed. It is demonstrated that, in this system, the domain structure with domains characterized by a random distribution of magnetization axes is formed even if the magnetostatic energy is negligible and can be ignored. The domain size increases linearly with an increase in the ratio of the exchange energy of the interaction between grains to the anisotropy energy of a single grain. The inclusion of the magnetostatic energy only insignificantly changes the domain size but leads to the formation of a vortex magnetization distribution inside the domains. The behavior of the system is numerically simulated by the Monte Carlo method. The results of the simulation confirm the conclusions drawn from the theoretical model.     

Stray field interaction of stacked amorphous tapes

In this study, magnetic cores made of amorphous rectangular tape layers are investigated. The quality factor Q of the tape material decreases rapidly, however, when stacking at least two tape layers. The hysteresis loop becomes non-linear, and the coercivity increases. These effects are principally independent of the frequency and occur whether tape layers are insulated or not. The Kerr-microscopy was used to monitor local hysteresis loops by varying the distance of two tape layers. The magnetization direction of each magnetic domain is influenced by the anisotropy axis, the external magnetic field and the stray field of magnetic domains of the neighboring tape layers. We found that crossed easy axes (as the extreme case for inclined axes) of congruent domains retain the remagnetization and induce a plateau of the local loop. Summarizing local loops leads to the observed increase of coercivity and non-linearity of the inductively measured loop. A high Q-factor can be preserved if the easy axes of stacked tape layers are identical within the interaction range in the order of mm.     

Asymmetrically shaped hysteresis loop in exchange-biased FeNi/FeMn film

The magnetization reversal of the bilayer polycrystalline FeNi(50 Å)/FeMn(50 Å) film sputtered in a magnetic field has been studied by magnetic and magneto-optical techniques. The external magnetic fields were applied along the easy or hard magnetization axis of the ferromagnetic permalloy layer. The asymmetry of hysteresis loop has been found. Appreciable asymmetry and the exchange bias were observed only in the field applied along the easy axis. The specific features of magnetization reversal were explained within the phenomenological model that involves high-order exchange anisotropy and misalignment of the easy axes of the antiferromagnetic and ferromagnetic layers. It has been shown that the film can exist in one of three equilibrium magnetic states in the field applied along the easy axis. The transitions between these states occur as first-order phase transitions. The observed hysteresis loop asymmetry is related to the existence of the metastable state.     

张应力对铁磁/反铁磁体系交换偏置的影响

 采用能量极小原理及Stoner-Wohlfarth模型,研究了张应力对铁磁/反铁磁双层薄膜交换偏置的影响。在不施加外磁场时,根据体系能量与铁磁层磁化强度方向之间的关系,得到了内禀易轴与内禀难轴的位置。交换各向异性与单轴各向异性之间的竞争使体系存在单稳态与双稳态两种不同的状态,直接决定了交换偏置的角度依赖关系。分析磁化过程发现,外磁场在沿内禀易轴及内禀难轴方向施加时,磁滞回线的一支转换场发生突变,另一支转换场保持不变,最终导致交换偏置场和矫顽场出现阶跃行为。在阶跃点处,体系具有较大的交换偏置场和矫顽场。数值计算表明：张应力的大小与方向对交换偏置均有很大的影响,均可以使体系在单稳态与双稳态之间相互转变并导致角度依赖关系发生显著变化。研究表明,应力可作为一种可行的方法来控制和调节铁磁/反铁磁体系的交换偏置。     

Frustrated multilayer ferromagnet-antiferromagnet structures: Beyond the scope of the exchange approximation (a review)

The frustrations of exchange interaction between ferromagnetic and antiferromagnetic layers, which arise at the uncompensated interface between the layers due to the interface roughness, have been described. The distribution of magnetic order parameters in the vicinity of the interface between the layers has been investigated, and the “layer thickness-roughness” magnetic phase diagram has been obtained in the case of the two-layer ferromagnet-antiferromagnet system and the ferromagnet-antiferromagnet-ferromagnet spin-valve system. An analysis has been performed taking into account the single-ion anisotropy energy, i.e., beyond the scope of the exchange approximation. It has been demonstrated that the number of easy axes in the layer plane, in many respects, determines the existence of an exchange shift of the hysteresis loop of the ferromagnet due to its interaction with the antiferromagnetic substrate.     

Thickness induced magnetic anisotropic properties of Tb-Fe-Co thin films

The influence of Tb₂₅Fe₆₁Co₁₄ thin film thicknesses varying from 2 to 300 nm on the structural and magnetic properties has been systematically investigated by using of X-ray diffraction, scanning electron microscopy, transmission electron microscopy, magnetization, and magneto-optic Kerr effect microscopy measurements. Thin film growth mechanism is pursued and controlled by ex-situ X-ray refractometry measurements. X-ray diffraction studies reveal that the Tb₂₅Fe₆₁Co₁₄ films are amorphous regardless of thin films thicknesses. The magnetic properties are found to be strongly related to thickness and preferred orientation. With an increase in film thickness, the easy axis of magnetization is reversed from in-plane to out-of-plane direction. The change in the easy axes direction also affects the remanence, coercivity and magnetic anisotropy values. The cause for the magnetic anisotropy direction change from in-plane to out-of-plane can be related to the preferred orientation of the thin film which depends on the large out-of-plane coercivity and plays an important role in deciding the easy axes direction of the films. According to our results, up to the 100 nm in-plane direction is dominated over the whole system under major Fe-Fe interaction region, after that point, the magnetic anisotropy direction change to the out-of-plane under major Tb-Fe/Tb-Co interaction region and preferred orientation dependent perpendicular magnetic anisotropic properties become more dominated with 2.7 kOe high coercive field values.     

Magnetization reversal processes in layered high-temperature superconductors with ferromagnetic impurities

The self-consistent interaction of a vortex system of a high-temperature superconductor and ferromagnetic impurities, including single impurities and their clusters, has been considered in the model of a layered high-temperature superconductor. For different temperatures and concentrations of ferromagnetic impurities, the magnetization reversal loops have been calculated by the Monte Carlo method taking into account an ensemble of ferromagnetic particles with different orientations of their easy magnetization axes with respect to the direction of an external magnetic field and for different magnetic anisotropy energies. It has been demonstrated that there is a nonlinear interaction of the high-temperature superconductor with ferromagnetic impurities, in which the initially thermodynamically reversible character of the magnetization reversal of the ferromagnetic ensemble can become irreversible. For a periodic lattice of clusters of ferromagnetic impurities, the magnetization curves of the high-temperature superconductor have been calculated for different sizes and configurations of the clusters. It has been revealed that, when extended defects are oriented parallel to the direction of the entrance of vortices in the sample, the length of the defects does not affect the remanent magnetization. It has been shown that the inclusion of the interaction between the magnetic moments inside the impurity cluster leads to a decrease in the magnetization reversal loop, the coercivity, and, accordingly, the energy loss due to magnetization reversal.     

Domain and wall structures in films with helical magnetization profile

We study soft magnetic bilayers having orthogonal, in-plane easy axes. The layers are thicker than the Bloch wall width linked to the anisotropy, so that a helical magnetization with a large angle exists across the sample thickness. The magnetic domains structure has been investigated at both sample surfaces, using magneto-optical microscopy. The domain structure is found to be similar to that of double films with biquadratic coupling. Two kinds of domain walls are identified, namely with a 90° and 180° rotation of the average magnetization. The detailed structure and energy of these walls are studied by micromagnetic calculations.     

Effect of noncrystallographic magnetic anisotropy on magnetization reversal in multilayer magnetic films

A study has been carried out of the magnetization of a layered system consisting of two exchange-coupled easy-axis ferromagnetic layers separated by a nonmagnetic spacer and having mutually perpendicular anisotropy axes. It is shown that the magnetization of such a system can undergo stepwise decrease with increasing magnetic field. The field dependence of the magnetization has a bifurcation point. The magnetization orientation can exhibit jumps in excess of 90° depending on the angle of magnetic-field orientation. Fiz. Tverd. Tela (St. Petersburg) 41, 660–664 (April 1999)     

Specific features of the EPR line shape of dimers due to spin-lattice relaxation

The magnetization relaxation in a coupled system of two spins has been shown to induce magnetization transfer between the observed transitions. In the degeneracy region of the transitions, the magnetization transfer becomes most effective and leads to the collapse of the magnetic resonance lines. In the electron paramagnetic resonance (EPR) spectra calculated for a polycrystal, this effect manifests itself in the form of additional peaks in the absorption line. The effect of anisotropy of the g factors of the dimer spins and misalignment of the axes of the g tensor and the interaction tensor on the appearance of additional lines in the EPR spectra has been analyzed.     

Magnetic relaxation in a random system of interacting rodlike nanoparticles

It is shown in the framework of the generalized mean-field approximation taking into account spatial fluctuations of the local magnetic field that the collective effect of dipole interaction in a random 3D system of identical (rodlike) magnetic nanoparticles with parallel easy magnetization axes shifts the relaxation magnetization curves towards shorter times (i.e., accelerates the relaxation process). In addition, the course of this process depends (via the demagnetizing field) on the sample shape. The interaction between nanograins affects the magnetization relaxation of a random 2D system only when the magnetic moments of the grains are perpendicular to the plane of the system.     

易轴取向对Nd2Fe14B/α-Fe双层膜退磁过程影响的微磁学分析

运用一维和三维微磁学模拟探究了易轴与外场存在偏角β情况下Nd₂Fe₁₄B/α-Fe 双层膜的磁矩反转过程, 计算了磁矩反转过程中磁滞回线和磁能积, 并与实验结果进行了对比. 计算结果表明, 在膜面内的易轴偏角β严重影响磁矩反转过程. 当β≠0°时, 磁矩反转过程中无明显成核现象, 随着易轴偏角β的增大, 剩磁显著减小, 磁滞回线方形度变差, 导致磁能积急剧减小. 对于Nd₂Fe₁₄B(10 nm)/α-Fe(8 nm)双层膜, β=10°时, 最大磁能积下降30.3%. 在磁矩反转过程中, 总能量最大时对应的外磁场能随易轴偏角的增大而减小, 交换作用能先增大后减小, 磁晶各向异性能则随着易轴偏角的增大而增大. 软磁相厚度越大, 双层膜的磁能积受易轴偏角影响越大. 在膜面外的易轴偏角对磁矩反转过程也有类似的影响. 关键词： 微磁学模拟 磁晶易轴 磁能积 能量     

Out-of-plane magnetic anisotropy in columnar grown Fe–Ni films

Polycrystalline thin films usually present magnetic anisotropy resulting from a conjunction of textures, residual stresses, surface effects, and magnetic dipole distribution. The shape anisotropy, which is caused by the magnetic dipole distribution, is dominant in most of the cases, and it forces the occurrence of in-plane easy axes for the magnetization. Contrary to this common expectation, we have found predominant out-of-plane easy axes in a series of Fe–Ni thin films produced by DC sputtering. Films with different thicknesses, from 40 to 1000 nm, and different deposition temperatures have been tested and show similar results. These unusual characteristics are results of a particular columnar structure formed during the films growth. The magnetic characterization of the samples has been done by Mössbauer spectroscopy, magnetometry, and ferromagnetic resonance. The unusual anisotropy observed is not believed to be uniform along the film thickness. This interpretation comes from the comparison of the experimental results with hysteresis obtained by micromagnetic simulations. Five distinct configurations for the anisotropies have been simulated for this comparison.     

Monte carlo simulation of magnetization and coercivity of free magnetic clusters

Based on Monte Carlo method, the oscillatory behaviour of the average magnetic moment as a function of the cluster sizes and the temperature dependences of magnetic moment with different sizes have been studied. It is found that the oscillations superimposed on the decreasing moment are associated with not only the geometrical structure effects but also the thermal fluctuation. The hystereses and thermal coercivities for free clusters with zero and finite uniaxial anisotropies have been calculated. The simulated thermal dependence of the coercivity is consistent with the experimental result, but does not fit the T^α law in the whole temperature range. It is evident that an easy magnetization direction and an anisotropy resulting from the spin configurations exist in the free clusters with the pure exchange interaction, which is also proved by the natural angle and energy distribution of clusters. A systematic theoretical analysis is also made to establish the relationship between natural angle and coercivity.     

Temperature dependence of exchange bias and coercivity in ferromagnetic/antiferromagnetic bilayers

A model for the temperature dependence of exchange bias and coercivity in epitaxial ferromagnetic (FM)/ antiferromagnetic (AFM) bilayers is developed. In this model, the interface coupling includes two contributions, the direct coupling and the spin-flop coupling. The temperature dependence arises from the thermal disturbance to the system, involved in the thermal fluctuations of magnetization of AFM grains and the temperature modulation of the relevant magnetic parameters. In addition, the randomness of original orientations of easy axes of AFM grains after field cooling is taken into account. A self-consistent calculation scheme is proposed and numerical treatment is carried out. The results show that the temperature dependence of exchange bias and coercivity is closely related to the sizes of AFM grains and the interface exchange coupling constants. Especially, the exchange bias will have a peak and the blocking temperature will increase if the spin-flop coupling plays a role. On the other hand, the original orientation distribution of easy axes of AFM grains will affect exchange bias and coercivity prominently. The prediction has been well supported by experiments.Received: 12 May 2004, Published online: 31 August 2004PACS: 75.30.Et Exchange and superexchange interactions - 75.50.Ee Antiferromagnetics - 75.30.Gw Magnetic anisotropy     

Magnetostriction domain structure in a periodic system of magnetoelastic and elastic nonmagnetic layers

The spectrum of magnetoelastic waves in a periodic structure of alternating ferromagnetic and nonmagnetic layers was studied. In the case of ferromagnetic layers with easy magnetization axes parallel to the layer surfaces, an orientational phase transition induced by an external tangential magnetic field H_e was considered. The formation of an inhomogeneous phase with a spatially modulated order parameter, which is caused by the magnetization being coupled through magnetostriction to lattice strains near the interfaces separating the magnetoelastic from elastic media, is predicted. It is shown that at a certain critical field in excess of the orientational phase transition field in the system without magnetostriction, a magnetoelastic wave propagating in a direction parallel to the in-plane magnetization vector M becomes unstable at finite values of the wave vector and condenses into a magnetostriction domain structure. A phase diagram in the (L, T, H_e) coordinates is constructed, and the regions of existence of thermodynamically equilibrium collinear, canted, and domain phases are established (L and T are the thicknesses of the ferromagnetic and nonmagnetic layers, respectively).     

Growth-induced perpendicular anisotropy of grains in Co-Al-O nanogranular ferromagnetic films

This paper reports on the results of the magnetostatic measurements for Co-Al-O nanogranular films over a wide range of concentrations of the ferromagnetic component x. It has been revealed that grains in the films are characterized by the growth-induced anisotropy with easy axes directed perpendicular to the film plane. The maximum field of the single-grain perpendicular anisotropy reaches ∼2.5 kOe for samples in the vicinity of the percolation threshold (x ≈ 61 at % Co). It has been established that the characteristic features of the superparamagnetic behavior of an ensemble of oriented Stoner-Wohlfarth particles are retained for the sample with x ≈ 61 at % Co in the presence of the demagnetization field associated with the net magnetization of the film. The influence of the demagnetization field of the film on the shape of the magnetization reversal curves, the coercivity, and the blocking temperature has been investigated and simulated. The results of the simulation are consistent with the experimental data.     

Large magnetic anisotropy in single crystal us

It is shown for ferromagnetic US that an extremely large anisotropy restrains magnetic moments to 〈111〉 easy axes, resulting in a near cos θ angular dependence of the magnetization away from the 〈111〉 axes. This is further confirmed by torque measurements, which in addition show large hysteresis effects upon rotation through the hard axes. It is illustrated through torque and magnetization measurements that a near stable domain configuration can be established by field rotation through decreasing angular amplitude around a hard 〈001〉 direction. The anisotropy constant K₁(T) is estimated by computing the small angle through which the magnetization deviates from the 〈111〉 axes when a field is applied along the [001] direction.     

Remanence Characteristic of Nanostructure of Hard／Soft Magnetic Multilayered Systems

The relation between microscopic properties (e.e.,layer thickness,easy axis orientation) and the macroscopic magnetic properties such as remanent magnetization of the ferromagnetic multilayer system is investigated based on a simple micromagnet approach.We concentrate on a multilayer design with periodic boundary condition,where alternating soft/hard layers build a nanostructured multilayer.For any easy axis direction in the soft and hard layers a simple explicit expression of remanence of the system has been derived analytically.We find that the remanence clearly depends on the thickness of the soft magnetic layer and is nearly independent of the thickness of hard magnetic layer.On the other hand,the remanence increases upon reducing the angle enclosed by the saturation magnetization and the easy axis directions of soft magnetic layer.However,it is unsensitive to the easy axis direction of hard magnetic layer,but there exists a maximum remanence for a certain easy axis direction of hard magnetic layer.     

Replica behavior in direct overwritable exchange-coupled magneto-optical multilayer system

The process of direct overwriting by light intensity modulation has been simulated for an exchange-coupled multilayer film without an initializing magnetization. Using the mean-field theory, the temperature dependence of the interlayer wall energy has been calculated for a magnetic triple layer, and the effect of interlayer exchange coupling on magnetization reversals has been investigated. The simulation has shown that replica can be easily realized by the arrangement of the Curie and compensation temperatures of the magnetic layers. A new mechanism of achieving replication from the initializing to the writing layers in the writing process is described in terms of subnetwork moments with high laser power.