Simulations of magnetic microstructure in thin film elements used for programmable motion of magnetic particles

The results of two-dimensional micromagnetic modeling of magnetization patterns in Permalloy ellipses under the influence of rotating constant-amplitude magnetic fields are discussed. Ellipses of two different lateral sizes have been studied, 0.5 μm×1.5 μm and 1 μm×3 μm. The amplitude of the rotating magnetic field was varied between simulations with the condition that it must be large enough to saturate or nearly saturate the ellipse with the field applied along the long axis of the ellipse. For the smaller ellipse size it is found that the magnetization pattern forms an S state and the direction of the net magnetization lags behind the direction of the applied field. At a critical angle of the rotating magnetic field the direction of the magnetization switches by a large angle to a new S state. Both the critical angle and the angle interval of the switch depend on field amplitude. For this new state, it is instead the applied field direction that lags behind the magnetization direction. The transient magnetization patterns correspond to multi-domain patterns including two vortices, but this state never exists for the equilibrated magnetization patterns. The behavior of the larger ellipse in rotating field is different. With the field applied along the long-axis of the ellipse, the magnetization of the ellipse is nearly saturated with a vortex close to each apex of the ellipse. As the field is rotated, this magnetization pattern remains and the net-magnetization direction lags behind the direction of the field until for a certain angle of the applied field an equilibrium multi-domain state is created. Comparisons are made with corresponding experimental results obtained by performing in-field magnetic force microscopy on Permalloy ellipses.     

Stress response of Barkhausen noise in a tempered C-Mn steel

The dependence of Barkhausen noise on tensile stress is measured in a high strength vanadium microalloyed C-Mn steel after tempering at 200, 400, 500, 600 and 650°C. Simultaneously, the coercive force and two field parameters related to the magnetic reversal curve are recorded for some of the specimens tempered at 500, 600 and 650°C. Tempering causes a maximum in Barkhausen noise vs. stress curve and minima in the field strength vs. stress curves. An increase in the impedimental force due to stress gradients experienced by domain walls is suggested as the cause of the maximum. Stress gradients with short “wavelenghts” are thought to be produced in lath-or plate-like martensitic/bainitic structures. The effect appears in the course of tempering, as recovery processes reduce the dislocation density, and vanishes as recrystallization leads to an almost complete elimination of these dislocations.     

Barkhausen noise and domain structure dynamics in Si-Fe at different points of the magnetization curve

In the present relationship between Barkhausen noise and domain structure evolution along the hysteresis loop in 3% Si–Fe has been investigated. The noise power spectrum has been measured vs. induction during cyclic magnetization of the material at a very low constant rate. The obtained results show that the behavior of the noise power along the magnetization curve can be related to the character of the domain structure rearrangements taking place at different levels of induction. Such a connection is reflected in a relationship between the noise power and the shape of the hysteresis loop. The measured noise power spectra are interpreted through the use of a suitable model. This makes possible to connect the shape of the magnetization curve to the microscopic parameters characterizing the dynamic of the domain wall during a large Barkhausen jump.     

The effect of the strain amplitude changes on the stress amplitude and resistivity of torsionally fatigued copper

Polycrystalline copper wires were cyclically strained in torsion in liquid nitrogen and the effect of the strain amplitude changes on the stress amplitude and resistivity was followed. It was found that both stress amplitude and resistivity are able to increase or decrease in dependence on the applied plastic strain amplitude. When the strain amplitude was decreased, the reversibility was not complete. By means of intermediate annealing it was found that both the dislocation density and the point-defect concentration follow the changes of the plastic strain amplitude.     

Generation of dislocations introduced by bending stress in a Si wafer

Distribution and morphology for dislocations introduced in (001) Si wafers subjected to bending stress at 800°, 900°, and 1100°C were investigated. For wafers bent around a [110] axis at 900° and 1100°C, straight dislocations appeared along the [110] direction only near the neutral plane, and were absent at the surfaces where bending stress is greatest. However, for wafers bent at 800 °C, such straight dislocations were not formed. Dependence of the dislocation distribution and morphology on heat treatment temperature is explained on the basis of interaction between bending stress and SiO₂ precipitates introduced in bulk. Also, it was found that the straight [110] dislocations remained still near the neutral plane, even when additional reverse bending stress was applied around an axis parallel to the dislocations, but were transfered toward the tensile surface by bending around an axis normal to the dislocation direction.     

Analysis of film strain and stress in a film-substrate cantilever system

The bending problem of a magnetic film-nonmagnetic substrate cantilever system is studied by using the principle of energy minimization. Emphasis is placed on the analysis of geometrical and physical parameter dependence of the neutral plane, internal film stress and strain of the cantilever system, and then the influence of such a parameter on the bending characteristic is presented. The results indicate, owing to the anisotropic expanding feature of the magnetostriction, that the neutral plane is generally anisotropic, and moves downwards rapidly with the increasing thickness ratio. Meanwhile, the bounding rigidity of substrate on the film will decrease with the increasing thickness ratio, and thus release the film stress, i.e., it decreases, but the film strain increases. The effect of Poisson’s ratio of the materials on the film strain, the stress and the neutral plane in the direction transverse to the magnetization is prominent. For the strain and the stress in the magnetization, however, the role of Poisson’s ratio is inconspicuous. This property is due to the initiative elongating (or contracting) feature of the magnetic film along its magnetization. Supported by the National Natural Science Foundation of China (Grant No. 10762001), the Key Project of the Chinese Ministry of Education (Grant No. 206024), and the Program for New Century Excellent Talents in University of China (Grant No. NCET-2005-0272)     

Domain structure of silicon iron single crystals

The model of a new domain structure arising after the magnetization of silicon iron single crystals in planes of the (110) type at an angle of 0°<Θ<-55° to the axis of easy magnetization is considered. Using this model the angular dependence of the domain-structure characteristics is established; it agrees closely with direct observations. On magnetizing a single crystal in the angular range 55° <Θ≤ 90° to the easy axis, layers with a uniform resultant magnetization parallel to the [001] direction are formed.     

Die Temperaturabhängigkeit des magnetischen Barkhausen-Effekts. II

The size distribution of Barkhausen discontinuities was measured during “thermal idealisation” of a hard drawn nickel specimen. Thermal idealisation means the magnetization by increasing temperature in a constant magnetic field. The sensitivity of the apparatus covered a range of magnetic moment between 1.3 and 17.3·10^?6 e.m.u. The results are in good agreement with investigations ofGerlach andTemesváry on the irreversible part of thermal idealisation. The average volume of Barkhausen discontinuities of the measured size was found to be nearly independent of temperature in a range from ?150 to+200°C, while above 200°C the volume increases markedly with temperature. By means of the average Barkhausen volume the temperature dependence ofNéels thermal fluctuation field was calculated. The results are in good agreement with those ofPescetti andBarbier on the temperature dependence of magnetic after effect.     

Optimization of MO Bragg diffraction of guided optical waves by MSW in YIG films by using inclined magnetic bias field

We describe a new scheme of noncollinear interaction geometry for magneto-optical (MO) Bragg cells based on inelastic scattering of guided optical wave beams by magnetostatic waves in yttrium–iron–garnet (YIG) films. A great increase of the diffracted light intensity was obtained when using an inclined magnetization of the film, in the case when static in-plane magnetization component is directed along the light propagation direction. It is shown that the diffraction efficiency can be increased more than two times, at a specific value of the angle (≈35°) between the saturation magnetization vector and the normal to the film surface. The effect can be explained through a four-wave model of the diffraction process, which can take place in optical waveguides with MO gyrotropy. The results obtained by a simple analytical solution of the diffraction problem are found to be in good qualitative agreement with the experimental observations.     

铁磁/反铁磁双层薄膜中应力各向异性研究

采用铁磁共振方法,研究了铁磁/反铁磁双层薄膜中交换各向异性和应力各向异性对其物理性质的影响.结果表明,单向各向异性来源于界面交换作用,应力各向异性对材料的磁化难易程度有较大影响.当外磁场方向与应力场方向平行时,应力场的存在将促进该方向的磁化.反之,应力场将会阻碍该方向的磁化.     

Acoustic excitation of nuclear spin waves in the easy-plane antiferromagnetic material KMnF3

Ultrasound damping at T=4.2 K in single crystal easy-plane antiferromagnetic KMnF₃ is studied experimentally as a function of the magnitude and direction of a constant magnetic field H at frequencies of 640–670 MHz, corresponding to the frequencies of nuclear spin waves. Two experimental situations are examined: in the first, the vector H lies in the easy magnetization plane (001), and in the second, H forms an angle with (001). For longitudinal ultrasound waves propagating along the hard magnetization axis [001], it is found that the damping depends resonantly on the magnitude of the field H. In the first case a single damping maximum is observed, and in the second, two damping peaks that are well resolved with respect to the field. The angular dependence of the resonance damping signals on the direction of the constant magnetic field is found to have a 90° periodicity in all cases. The observed effects are explained by resonant ultrasonic excitation of nuclear spin waves. On the basis of an analysis of the magnetoacoustic interaction energy, it is shown that in the first case, nonzero oscillations of the antiferromagnetism vector L occur only in the basal plane, while in the second, oscillations of L occur both in the basal and a vertical plane, which are associated, respectively, with two branches of the nuclear spin waves. It is also shown that the 90° periodicity in the angular dependence of the damping signals is associated with a fourth order [001] axis. Zh. éksp. Teor. Fiz. 112, 1830–1840 (November 1997)     

Anisotropic interface magnetoresistance in Pt/Co/Pt sandwiches

We report on an effect of reduced dimensionality on the magnetotransport in cobalt layers sandwiched by platinum. In a current in-plane geometry it is found that the resistivity depends on the magnetization orientation within the plane perpendicular to the current direction. The resistivity shows a symmetry adapted cos(2) dependence on the angle to the surface normal, with the maximum along the surface normal. The Co thickness dependence of the effect in Pt/Co/Pt sandwiches clearly points out that the mechanism behind this effect originates at the Co/Pt interfaces and is disparate to the texture induced geometrical size effect.     

外应力对铁磁/反铁磁体系交换偏置的影响及阶跃现象

采用能量极小原理及S-W模型研究了外应力对铁磁/反铁磁（FM/AFM）双层薄膜体系交换偏置的影响.不施加外磁场时,根据能量与铁磁层磁化强度方向之间的关系,指出体系存在单稳态和双稳态两种不同的状态,是由交换各向异性与单轴各向异性之间的竞争控制的.体系处于单稳态还是双稳态直接决定着交换偏置的角度依赖关系.分析磁化过程发现,外磁场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,而另一支转换场则保持不变,最终导致交换偏置场和矫顽场出现阶跃行为.数值计算表明,交换偏置场和矫顽场在阶跃点均具有较大的数值 关键词： 单稳态 双稳态 外应力     

Barkhausen effect in magnetic thin films: Experimental noise spectra

In this paper Barkhausen noise spectra are shown that were measured on thin uniaxial 83-17 Ni?Fe films and these spectra were compared with the known magnetic behaviour of these films. On these types of sample the Barkhausen effect had been investigated by Lambeck [1], but their Barkhausen noise spectra have not been investigated so far. The film thicknessd _m in our experiments ranged between 400 and 2400 Å. In this range a change occurs in the dynamics of the magnetization behaviour caused by transitions of the type of domain wall. The results presented here show the very strong dependence of the Barkhausen noise spectra on the type of domain wall. Films with Bloch walls always show a frequency dependence off ^?1.7 in the higher frequency range. Samples in the thickness range where the transition occurs from the Néel wall via the cross-tie wall to the Bloch wall, have exponents between ?1 and ?2. The frequencyf _c above which the measured noise intensity begins to decrease varies very much for the different films. The curve off _c versus film thicknessd _m has the same form as the curve of the domain wall mobilitym versusd _m.     

Angular dependence of the coercivity and remanence of ordered arrays of Co nanowires

The angular dependence of the coercivity and remanence of ordered hexagonal arrays of Co nanowires prepared using anodic aluminum oxide templates was investigated. The experimental evolution of coercivity as a function of the angle, in which the external field is applied, is interpreted considering micromagnetic simulations. Depending on the angle between the axis of the wire and the applied magnetic field direction our results show that the magnetization reversal mode changes from vortex to a transverse domain wall. Besides, we observed that the dipolar interactions cause a reduction in coercive fields, mainly in the direction of easy magnetization of the nanowires. Good agreement between numerical and experimental data is obtained.     

Effect of external stress on discontinuous precipitation in a Cu–2.1 wt % Be alloy

The influence of an applied stress on discontinuous precipitation (DP) in a Cu–2.1 wt % Be alloy aged at 300°C was examined. A compressive stress accelerates the growth of DP cells, which consist of lamellae of the precipitated γ phase and the solute-depleted α phase, but a tensile stress does not essentially change it. The cell growth rates along the loading direction under the compressive and tensile stress are identical to those along the direction perpendicular to the loading direction under the same stress. Both the compressive and tensile stresses have no influence on the incubation time to initiate DP. From measurements of the specimen length change and investigations of the distribution of γ variants in cells in a particular case, specific γ variants among crystallographically equivalent ones are found to be formed, depending on the sense of the applied stress. This result, together with the dependence of the cell growth rate on the sense of the applied stress, can be well understood through the interaction energy between the external stress and the misfit strains of discontinuous γ precipitates.     

Metamagnetic states in single crystal HoNi<Subscript>2</Subscript>B<Subscript>2</Subscript>C at <Emphasis Type="Italic">T</Emphasis> ≈ 1.9 K: Torque magnetometry study

Metamagnetic transitions in single-crystal rare-earth nickel borocarbide HoNi₂B₂C have been studied at T ≈ 1.9 K with a Quantum Design torque magnetometer. With increasing field, transitions to antiferromagnetic, ferrimagnetic, non-collinear, and saturated paramagnetic states take place. The critical fields of the transitions depend crucially on the angle θ between applied field and the easy axis [110]. Measurements of torque along the c axis have been made while changing the angular direction of the magnetic field (parallel to basal tetragonal ab planes) and with changing field at fixed angle over a wide angular range. Two new phase boundaries in the region of the non-collinear phase have been observed, and the direction of the magnetization in this phase has been precisely determined. At low field the antiferromagnetic phase is observed to be multidomain. In the angular range around the hard axis (?6° ≤ ? ≤ 6°, where ? is the angle between the field and hard axis [100]) the magnetic behavior is found to be “frustrated” with a mixture of phases with different directions of the magnetization.     

Possible weakening of the many-body interactions in the organic quasi-two-dimensional metal α-(BETS)<Subscript>2</Subscript>NH<Subscript>4</Subscript>Hg(SCN)<Subscript>4</Subscript>

The behavior of the de Haas-van Alphen oscillations in the organic quasi-two-dimensional metal α-(BETS)₂NH₄Hg(SCN)₄ is comprehensively studied as a function of the angle between the magnetic-field direction and the normal to the conducting layers in it. The angular dependence of the oscillation amplitude has minima at angles of ±40° and ±62°, which are caused by the spin zero effect. The positions of these minima suggest that the electron-phonon and electron-electron interactions in this metal are significantly weakened.     

Tailoring the magnetic properties of Fe asymmetric nanodots

Asymmetric dots as a function of their geometry have been investigated using three-dimensional (3D) object oriented micromagnetic framework (OOMMF) code. The effect of shape asymmetry of the disk on coercivity and remanence is studied. Angular dependence of the remanence and coercivity is also addressed. Asymmetric dots are found to reverse their magnetization by nucleation and propagation of a vortex, when the field is applied parallel to the direction of asymmetry. However, complex reversal modes appear when the angle at which the external field is applied is varied, leading to a non-monotonic behavior of the coercivity and remanence.     

Principal component analysis of shear strain effects

Shear stresses are always present during quasi-static strain imaging, since tissue slippage occurs along the lateral and elevational directions during an axial deformation. Shear stress components along the axial deformation axes add to the axial deformation while perpendicular components introduce both lateral and elevational rigid motion and deformation artifacts into the estimated axial and lateral strain tensor images. A clear understanding of these artifacts introduced into the normal and shear strain tensor images with shear deformations is essential. In addition, signal processing techniques for improved depiction of the strain distribution is required. In this paper, we evaluate the impact of artifacts introduced due to lateral shear deformations on the normal strain tensors estimated by varying the lateral shear angle during an axial deformation. Shear strains are quantified using the lateral shear angle during the applied deformation. Simulation and experimental validation using uniformly elastic and single inclusion phantoms were performed. Variations in the elastographic signal-to-noise and contrast-to-noise ratios for axial deformations ranging from 0% to 5%, and for lateral deformations ranging from 0 to 5° were evaluated. Our results demonstrate that the first and second principal component strain images provide higher signal-to-noise ratios of 20 dB with simulations and 10 dB under experimental conditions and contrast-to-noise ratio levels that are at least 20 dB higher when compared to the axial and lateral strain tensor images, when only lateral shear deformations are applied. For small axial deformations, the lateral shear deformations significantly reduces strain image quality, however the first principal component provides about a 1–2 dB improvement over the axial strain tensor image. Lateral shear deformations also significantly increase the noise level in the axial and lateral strain tensor images with larger axial deformations. Improved elastographic signal and contrast-to-noise ratios in the first principal component strain image are always obtained for both simulation and experimental data when compared to the corresponding axial strain tensor images in the presence of both axial and lateral shear deformations.