On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

Ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies

We develop a model for ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies. This model applies to (i) magnetic materials with both uniaxial and cubic anisotropies, and (ii) magnetic nanoparticles with effective core and surface anisotropies; We numerically compute the resonance frequency as a function of the field and the resonance field as a function of the direction of the applied field for an arbitrary ratio of cubic-to-uniaxial anisotropy. We also provide some approximate analytical expressions in the case of weak cubic anisotropy. We propose a method that uses these expressions for estimating the uniaxial and cubic anisotropy constants, and for determining the relative orientation of the cubic anisotropy axes with respect to the crystal principle axes. This method is applicable to the analysis of experimental data of resonance type measurements for which we give a worked example of an iron thin film with mixed anisotropy.     

Calculation of High Frequency Complex Permeability of Carbonyl Iron Flakes in a Nomagnetic Matrix

The carbonyl iron flakes are fabricated by high-energy ball milling. The effective permeability is measured and calculated for the composite consisting of flakes embedded in a nonmagnetic matrix. The magnetic flakes with a shape anisotropy and random spatial distribution of normal direction are considered to calculate the complex permeability of magnetic flake materials. Its analytical model is derived from the Landau-Lifshitz-Gilbert equation and Bruggeman ＇s effective medium theory. The calculated results agree well with the experiment.     

Synthesis and investigation of precipitated ensembles of magnetic nanoparticles with controlled easy axis orientation

Two samples with immobilized magnetic nanoparticles are synthesized and investigated. The first sample has randomly oriented easy axes of magnetic anisotropy; the second sample has preferentially aligned easy axes, produced via the precipitation of a colloid of ferromagnetic particles in the presence of a magnetic field. It is shown that the precipitation of an aqueous suspension of nanoparticles in the presence of a magnetic field greatly changes the anisotropy of a sample, compared to one prepared by precipitation without a magnetic field. The second sample exhibits a preferential direction of the easy axes of magnetic anisotropy that coincides with the direction of the external magnetic field applied in the drying process of sample preparation.     

Effect of thermal annealing on the magnetic anisotropy of GaMnAs ferromagnetic semiconductor

We have systematically investigated the influence of annealing on the magnetic anisotropy properties of GaMnAs film using an epilayer with a Mn concentration of 6.2%. The GaMnAs epilayer was grown by molecular beam epitaxy and the planar Hall effect measurement was used to monitor the magnetic anisotropy of the film. We found significant annealing-induced changes in the magnetic anisotropy properties of the GaMnAs film that depended on the annealing conditions. For example, the cubic anisotropy that gave a four-fold symmetry of magnetic easy axes decreased while the uniaxial anisotropy that gave a two-fold symmetry of magnetic easy axes increases in the samples annealed temperature below 300 °C. In particular, the uniaxial anisotropy along the [010] direction in as-grown GaMnAs film changed to the [100] direction by rotating by 90° after the sample was annealed at 300 °C for 3 h. This investigation thus indicates that the magnitude and the direction of the magnetic anisotropy in the GaMnAs film can be effectively controlled by choosing an appropriate annealing time and temperature.     

红条毛肤石鳖齿舌牙齿内纳米磁性矿物质的磁各向异性研究

SQUID和磁转矩测量表明红条毛肤石鳖齿舌牙齿内纳米磁性矿物质具有明显的磁各向异性,从能量角度对SQUID和磁转矩曲线的分析发现,这些材料具有明显的单晶单轴特性,对于磁各向异性,起作用的主要是磁晶各向异性。磁化过程中,长条片状纳米磁性矿物质中包含的小纳米晶粒磁畴磁矩转向外磁场方向,直到与外磁场方向一致,达到饱和为止,磁化过程中不存在畴壁的移动。     

红条毛肤石鳖齿舌牙齿内纳米磁性矿物质的磁各向异性研究

SQUID和磁转矩测量表明红条毛肤石鳖齿舌牙齿内纳米磁性矿物质具有明显的磁各向异性,从能量角度对SQUID和磁转矩曲线的分析发现,这些材料具有明显的单晶单轴特性,对于磁各向异性,起作用的主要是磁晶各向异性。磁化过程中,长条片状纳米磁性矿物质中包含的小纳米晶粒磁畴磁矩转向外磁场方向,直到与外磁场方向一致,达到饱和为止,磁化过程中不存在畴壁的移动。     

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.     

Origin of magnetic anisotropy of Gd metal

Using first-principles theory, we have calculated the energy of Gd as a function of spin direction, theta, between the c and a axes and found good agreement with experiment for both the total magnetic anisotropy energy and its angular dependence. The calculated low temperature direction of the magnetic moment lies at an angle of 20 degrees to the c axis. The calculated magnetic anisotropy energy of Gd metal is due to a unique mechanism involving a contribution of 7.5 microeV from the classical dipole-dipole interaction between spins plus a contribution of 16 microeV due to the spin-orbit interaction of the conduction electrons. The 4f spin polarizes the conduction electrons via exchange interaction, which transfers the magnetic anisotropy of the conduction electrons to the 4f spin.     

Ferromagnetic resonance study of the effect of elastic stresses on the anisotropy of magnetic films

The distribution of the magnitude and direction of the uniaxial magnetic anisotropy field over the area of permalloy films obtained by thermal evaporation in vacuum was studied using a scanning ferromagnetic resonance spectrometer. The films were deposited on glass substrates subjected to bending stress in the presence of an in-plane static magnetic field. Depending on the character of the elastic-stress distribution over a local spot of a film, the uniaxial anisotropy induced by a magnetic field is either enhanced or completely compensated, which is accompanied by a significant change in the direction of the easy axis of magnetization. The observed effects are in good agreement with phenomenological calculations.     

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.     

Control of magnetic anisotropy in (Ga,Mn)as by lithography-induced strain relaxation

We report control of magnetic anisotropy in epitaxial (Ga,Mn)As by anisotropic strain relaxation in patterned structures. The strain in the structures is characterized using reciprocal space mapping by x-ray techniques. The magnetic anisotropy before patterning of the layer, which shows biaxial easy axes along [100] and [010], is replaced by a hard axis in the direction of large elastic strain relaxation and a uniaxial easy axis in the direction where pseudomorphic conditions are retained.     

Fluctuating spin g-tensor in small metal grains

In the presence of spin-orbit scattering, the splitting of an energy level varepsilon(&mgr;) in a generic small metal grain due to the Zeeman coupling to a magnetic field B--> depends on the direction of B-->, as a result of mesoscopic fluctuations. The anisotropy is described by the eigenvalues g(2)(j) ( j = 1,2,3) of a tensor G, corresponding to the (squares of) g-factors along three principal axes. We consider the statistical distribution of G and find that the anisotropy is enhanced by eigenvalue repulsion between the g(j).     

Magnetic domain and local atomic structures of the Fe<Subscript>0.94</Subscript>Si<Subscript>0.06</Subscript> alloy before and after thermomagnetic treatment in an alternating-current magnetic field

The changes observed in the local atomic structure of an iron alloy with 6 at % Si as a result of thermomagnetic treatment in an alternating-current magnetic field and their correlation with magnetic characteristics, such as the domain structure and magnetic properties, have been investigated using Mössbauer spectroscopy. It has been shown that the destabilization of the domain structure is caused by the destruction of uniaxial magnetic anisotropy in domains due to a disordered distribution of pairs of silicon atoms along the 〈100〉 easy magnetization axes. Annealing and cooling without an external magnetic field and in an alternating-current magnetic field lead to a change in the magnetic texture of single-crystal samples of the siliconiron alloy. When the samples are annealed in an alternating-current magnetic field, the magnitude of this effect depends on the orientation of the magnetic field with respect to the crystallographic axes of the sample.     

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.     

Imry–Ma disordered state induced by impurities of “random local anisotropy” type in the system with <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) symmetry

For the system with the n-component order parameter (O(n)-model), conditions for initiation of the Imry–Ma disordered state resulting from the influence of impurities of the “random local anisotropy” type were discovered. The initiation of such a state was shown to be possible if the distribution of local anisotropy axes directions in the order parameter space is nearly isotropic, and the limiting degree of the distribution anisotropy was found. For a higher anisotropy in the distribution of local axes directions, the long-range order in the system holds true even in the presence of impurities of the given type.     

Critical properties of random anisotropy magnets

The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.     

Ferromagnetic resonance of nonstoichiometric zinc ferrite and cobalt-doped zinc ferrite nanoparticles

Ferromagnetic resonance spectra of zinc ferrite and cobalt doped zinc ferrite nanoparticles, measured at various temperatures, exhibit an invariant point at a given field. This makes it possible to determine the equation relating the resonance field shift to the peak-to-peak linewidth. When particles are frozen in a matrix in a magnetic field, the anisotropy constant of the material can be derived from the angular variation of the resonance field. This procedure is useful to determine the thermal dependence of the anisotropy constant, but is shown to require various freezing temperatures experiments to estimate the accuracy of the deduced anisotropy constant values. It is also shown that the angular dependence of the resonance field is similar for a uniaxial (zinc ferrite) and cubic (zinc ferrite containing 40% cobalt ions) anisotropy. This unexpected result is explained by the weakness of the texturation, leading to a distribution in easy axes directions.     

Magnetization process in holmium: easy axis spin reorientation induced by the magnetostrictive basal plane distortion

We report on the change of the easy axis direction in holmium, from the a to the b axis, under the application of a magnetic field in the basal plane. This spin reorientation is observed by measuring the magnetic torque in Ho(n)/Lu(15) superlattices (n and 15 are the number of atomic planes in the Ho and Lu blocks). We also observe that, at the field H0 and temperature at which the reorientation occurs, both axes are easy directions. Based on the fact that the field H0 depends on n in the same way as the field-induced magnetoelastic distortion does, we propose that this spin reorientation originates from the strong field-induced magnetoelastic deformation within the basal plane. The modulation of the alpha strains with sixfold symmetry originates a 12-fold term in the magnetic anisotropy energy.     

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.