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The requirements for imaging magnetic vortices properly by magnetic force microscopy are discussed. Special attention is devoted to the influence of the tip on the sample magnetic configuration. It is shown that one can obtain a quantitative understanding of the experiments using micromagnetic simulations within a general framework for reversible tip-induced perturbations. Finally, preliminary results obtained with specially prepared 'nanowire tips' are presented.

The magnetization dynamics is studied on 3D micromagnetic structures and in the aperiodic time regime. Experiments are compared with various micromagnetic simulations. The model system chosen is a vertical Bloch line inside a bubble garnet epitaxial film. It is shown that the Slonczewski equations describe with remarkable accuracy the experimental phenomena, qualitatively and quantitatively. The damping constant derived from the adjustment of all data is distinctly higher than the value derived from ferromagnetic resonance. Models for this discrepancy are discussed.

The magnetization distribution in the vicinity of a sharp square edge is investigated analytically, in two and three dimensions. The aim of this calculation is to investigate the consequences of the logarithmic divergence of some components of the demagnetizing field at this point, in order to understand better some recent numerical calculations by Rave, Ramstock and Hubert. A definite solution is found, that depends solely on the magnetization direction at the corner point, and displays a mild r 2 In (r) singularity. Possible applications of this solution range from a plug-in box in numerical simulations to analytical micromagnetics of square single domain particles.

The effect of a spin-polarized current crossing a domain wall in a thin and narrow Permalloy™ strip is studied by micromagnetic simulations, supported by a one-dimensional model of wall dynamics. We use the simplest way to incorporate the spin-polarized current effect in the micromagnetic formalism; namely, a local momentum transfer under the assumption that the current polarization is in local equilibrium. We predict current influence on wall velocity and mobility under field. However, in order to reach agreement with recent experiments, more than ten times larger currents would be required within this simplest model. Thus, more elaborate models of spin transfer are needed.

We have studied the process by which the in‐plane magnetization of an ultrathin (4–11 ML) epitaxial iron film reverses under the action of an external magnetic field. Kerr effect measurements reveal a small in‐plane uniaxial anisotropy superimposed on the cubic magnetocrystalline anisotropy which greatly influences the reversal. In addition, we find that depending upon the field orientation, reversal can proceed either via a ‘‘1‐jump’’ mechanism, by the sweeping of 180° domain walls and which gives a classic square hysteresis loop, or by a ‘‘2‐jump’’ mechanism, by the sweeping of 90° domain walls at two distinct applied field strengths—this gives a more unusual hysteresis loop with two irreversible transitions. We have developed a simple phenomenological energy model which explains how so small a uniaxial anisotropy can play so significant a role in the reversal process. The model explains the two reversal mechanisms and predicts with good experimental agreement which should be observed for different appl...

The injection of a Bloch point, along a Neel line residing in a Bloch wall separating two magnetic domains, was monitored by direct line observation and careful control of the lines state. Injection was achieved by pushing selected lines into a region where the surface had been ion-implanted, resulting in a modification of the spins orientation along the line at surface level. The optical observation of lines relies on an anisotropic dark field imaging technique developed earlier. Direct confirmation of the micromagnetic picture of a Bloch point-containing line is obtained.

The magnetization process in microfabricated NiFe wires was observed using a Kerr microscope. Magnetic wires were made from a 20-nm-thick NiFe film by using lift-off techniques. Their width Wand length L were designed as W= 0.5, 1.0 and 2.0 /Lm and L= 50/Lm, respectively. One end of the wire was connected to a square shaped head with a side of 2 W, which is designed to act as a domain wall source. In each wire, necks with different width of 0.2W, 0.6W, and 0.8W were introduced as artificial pinning sites of a domain wall. By using an oil-immersion lens (NA = 1.3) and a Hg lamp, magnetization reversals in very narrow wires, as narrow as 0.5 /Lm, were clearly observed. It is confirmed that domain wall penetration, pinning, depinning, and also the direction of wall motion are controllable using square shaped head and necks with optimized width.

It is proposed that the main source of contrast of vertical Bloch lines (VBLs) in bubble garnets, when viewed by means of anisotropic dark field optical imaging, is a microdeformation of the wall plane at line location. The motive force for wall tilting is the compensation of the monopolar σ charges borne by VBLs. The tilted wall section acts as a phase object and allows for the formation of line images with well‐defined symmetries and independent of the incident‐beam polarization. All these features agree fully with experimental evidence. An approximate model of the wall deformation is presented and shown to be consistent for a given thickness and material parameters with the results of an ab initio numerical computation of the 3D structure of a VBL. The implications of the microdeformation model in terms of line observability are analyzed and compared with experimental data.

The radial motion of magnetic bubbles submitted to expanding bias field pulses is studied by means of laser stroboscopy in a thin moderately damped garnet film. A bubble instability associated to a velocity breakdown appears periodically as the pulse amplitude increases. This experiment is performed on χ bubbles carrying no vertical Bloch lines (VBL's). The probability of state conversion is studied as a function of the pulse amplitude for the two initial chiralities and χ + and χ - . In both cases four transitions associated to chirality changes are observed. If the pulse amplitude is close to the transition threshold VBL's can be nucleated so that the final bubble state is σ. Comparison of the two experiments shows that the critical amplitudes for bubble instability and chirality change are the same, the nucleation of VBL's being responsible for the bubble instability. A one dimensional model is presented that predicts the maximum average azimuthal angle ψ. A heuristic approach of the bifurcation associated to a chirality change is presented. The results are in good agreement with the experimental data and are compared to the horizontal Bloch line (HBL) model and the Walker model of wall motion.

The technique for optical microscopy, [polarized anisotropic dark‐field observation (PADO)], of vertical Neel lines (also called vertical Bloch lines) existing inside the Bloch walls separating magnetic domains in thin epitaxial films of ferrimagnetic garnets (bubble garnets) is studied and applied here. Results of experiments investigating the role of the polarization of light impose severe constraints on the theoretical models. The picture emerging from them excludes a contrast due to light diffracted by the usual magneto‐optical effects inside the wall. By varying the angle of incidence of the anisotropic dark‐field illuminating beam, line contrast inversions can be obtained. It is shown that the sample’s thickness, when well above the wavelength of light, is responsible for that fact. Moreover, to reproduce all line contrast reversals, an effective height which is smaller than the sample’s thickness has to be considered for the line structure. A tempting conclusion from this study may be that lines ar...

As magnetic devices become smaller and faster, it is becoming increasingly important to understand the dynamics of magnetic domains on small spatial and temporal scales. In their Perspective, Miltat and Thiaville highlight the report by Acremann et al., whose magnetooptical microscope combines state of the art space and time resolution, thus allowing the precessional motion of magnetic domains to be studied directly. The dynamics they observe are complex, indicating that in both the space and time domains, neither the magnetization nor the applied field should be viewed as uniform.

First, the number of irreducible wall configurations is derived, both for an odd and an even number of magnetic layers. Second, the comparison of simulated wall structures in stacks made of three and four magnetic layers serves as an illustration of the interplay between flux–closure mechanisms and interlayer exchange interactions. Flux closure is shown either to compete or accommodate with ferromagnetic-type interlayer exchange interactions owing to its short- or long-range character. Last, an equivalent single layer behavior is shown to develop with an increasing number of magnetic layers, magnetic layer thickness, and interlayer (ferromagnetic-type) exchange parameter.

Magnetic and magnetostrictive hysteresis loops of TbCo/CoFe multilayers under field applied along the hard magnetization axis are studied using vectorial magnetization measurements, optical deflectometry and magneto optical Kerr microscopy. Even a very small angle misalignment between hard axis and magnetic field direction is shown to drastically change the shape of magnetization and magnetostrictive torsion hysteresis loops. Two kinds of magnetic domains are revealed during the magnetization: big regions with opposite rotation of spontaneous magnetization vector and spontaneous magnetic domains which appear in a narrow field interval and provide an inversion of this rotation. We show that the details of the hysteresis loops of our exchange-coupled films can be described using the classical model of homogeneous magnetization rotation of single uniaxial films and the configuration of observed domains. The understanding of these features is crucial for applications (for MEMS or microactuators) which benefit from the greatly enhanced sensitivity near the point of magnetic saturation at the transverse applied field., 10 pages, 11 figures

Magnetic force microscopy is a scanning technique, derived from atomic force microscopy, that maps the magnetic interaction between a sample and a magnetic tip. It is simple to use (most microscopes operate in ambient conditions) and provides images with a resolution down to 20 nm in best cases. The images do not, however, correspond directly to the sample magnetization, because of the long range of magnetic forces, their complex sources, as well as the potentially perturbing effect of tip-sample interaction. The emphasis of this chapter is on contrast modeling, especially in nanostructures.

It is shown that, in spite of the introduction of an adaptive meshing along the normal to the wall plane, the micromagnetic calculation of 2D symmetrical Neel walls in ultra-thin films still requires a large number of mesh points before reaching numerical stability, in opposition to the 1D case. >

By combining a finite element tip model and numerical simulations of the tip–sample interaction, it is shown that magnetic force microscopy images of patterned soft elements may be quantitatively compared to experiments, even when performed at low lift heights, while preserving physically realistic tip characteristics. The analysis framework relies on variational principles. Assuming magnetically hard tips, the model is both exact and numerically more accurate than hitherto achieved., Partial support from the SUBMAGDEV Training and Mobility of Researchers European Program is gratefully acknowledged.

The wall state stability of magnetic bubbles in ferrimagnetic as-grown garnet films suitable for Bloch line memory applications is investigated in order to predict the stability of vertical Bloch line pairs. In the experiment (1, 0) and (0, 2) bubbles are subjected to fast bias pulses (15-ns width) and to an in-plane field. It is found that the winding line pair present in a (0, 2) bubble can be annihilated, resulting in a (1, 0) final state. On the other hand, a (1, 0) bubble can be switched into a (0, 2) bubble with different experimental conditions. These nonconservative switching processes are in most cases irreversible. However, the switching probability never reaches 100%. An interpretation of the annihilation mechanism is given, and the consequences for devices are discussed. >

Experimental data on features of the contrast of vertical Bloch lines obtained in a polarized anisotropic dark field are examined. The possibility that a wall deformation is the cause of the line contrast is considered. Two types of wall deformation are proposed: a displacement (over a height smaller than the thickness) and a tilt. >

We have calculated temperature-dependent switching curves using the stochastic Landau–Lifshizt–Gilbert equation for a macrospin with a uniaxial anisotropy. As in experimental results, we obtained curves that shrink with increasing temperature. We find that an Arrhenius law for the relaxation time τ corresponds well to calculations, thus allowing for a determination of the attempt frequency. The results are also found to compare favorably with Coffey's formulae for τ in the low and high damping limit.

These lecture notes aim at introducing the main concepts underlying magnetic domain and wall physics. Emphasis is laid on soft magnetic materials, i.e. materials which, in the bulk state, are essentially magnetically isotropic, although most of the phenomenology remains general. Besides, magnetization dynamics and its consequences on domain wall state transformations are not treated in this chapter. The text is divided into nine sections. Section 2 depicts the various energy terms to be considered within the micromagnetic approach which treats the magnetization as a continuous Maxwell field whereas energy minimization in the general case is treated in Section 5, leading to the basic static equilibrium equations governing the distribution of magnetization inside a magnetic body. The question of the motive force behind decomposition into domains and domain geometry is addressed in Sections 4, 6 and 7. The former briefly pinpoints the magnetostatic energy reduction stemming from a decomposition of the magnetized volume into domains. The latter describes in detail the domain configuration to be expected from anisotropy-free soft magnetic elements with a basically two-dimensional in-plane magnetization distribution, and offers several illustrations of the elegant geometrical construction due to Van den Berg. It also provides an introduction to quasi-singular magnetization distributions in soft ferromagnets. Section 6, devoted to the nucleation of stripe domains, provides one example of the use of the general equilibrium equations in the vicinity of saturation. The rather involved issue of domain wall structures is considered in Sections 8, 9 and 10. A comprehensive treatment of one-dimensional wall structures expected to occur in bulk materials will be found in the first of these three sections, whereas the second is concerned with those specific domain wall structures to be found at intermediate thicknesses and in the half-space. Wall sub-structures, namely lines, are briefly alluded to. Section 10 is also devoted to the fast growing field of magnetic artificial structures with dipolar and exchange inter-layer interactions. Lastly, intrinsic coercivity mechanisms are described in Sections 3 and 11, starting with Stoner-Wohlfarth hysteresis in thin films and ending with some manifestations of the more intricate topological hysteresis, i.e. those hysteretic phenomena associated with noncontinuous transformations of the magnetization distribution.

This paper addresses the question of the significance of micromagnetic simulations applied to ordinary (3D) spins in the 2D physical space in the prediction of hysteretic phenomena. It is shown that a physically simple mechanism accounts for the transition between a winding Neel type surface magnetization distribution into an unwinding state. The associated transition field is expected to prove mesh dependent but remains intrinsic. Inversely, the reversal of the core magnetization of a vortex like configuration involves states which prove mutually inaccessible if preserving the symmetry imposed by the field. The associated transition field thus proves extrinsic and physically meaningless.

Bloch-Line memories are a new class of non-volatile solid-state memories relying on specific domain wall internal structures for data storage. They thus inherently allow for storage capacities in the 256 M-Bit/cm2 range. Critical aspects of their operation are outlined

Two-dimensional wall configurations in exchange coupled bilayers are calculated using numerical micromagnetic simulations. Starting with a 180 degrees domain arrangement in zero field, full saturation is, under hard axis field, only reached for field values large with respect to the anisotropy field, due to the nucleation of 360 degrees walls. Their collapse field is computed versus the magnitude of the interlayer exchange coupling. A novel hysteresis mechanism, specifically for large coupling constants and involving superposed 360 degrees walls, is described. >

Spin-transfer effects on the magnetization motion are investigated in the free layer of a giant magnetoresistance device flooded with spin-polarized electrons, and more specifically microwave excitations in elliptical permalloy elements. The spin torque is found to excite at low current precessional trajectories compatible with the platelet eigenmodes. Then a forced regime is activated that is, characterized by trajectory broadening with increasing current and an almost spatially uniform power density. The effect of temperature on resonance frequencies and linewidth becomes negligible at high current.

Dynamical X-ray diffraction theory in elastically distorted crystals is used to simulate the rocking curves of ion-implanted ferrimagnetic garnet epilayers. It is found that excellent agreement between experimental and simulated rocking curves may be obtained in the case of a standard neon implantation. On the other hand, despite numerous attempts, only a poor fit has been achieved in the case of hydrogen implantation. Peak and sub-peaks broadening suggests that Huang scattering takes place, at least at a precursor level. Finally, the (plastic) strain profiles deduced from the rocking-curve analysis provide a means of computing the elastic strains associated with implantation boundaries, according to the model developed in the first part of this work. Satisfactory agreement between theory and the experimental determination of these strains is obtained by means of plane-wave X-ray imaging.

Two examples of in situ dynamic experiments using synchrotron white beam X-ray topography are described. The first is concerned with the plastic deformation of FeSi single crystals and the second with the recrystallisation of aluminium polycrystalline samples. Only partial but representative results are presented. The main advantages and shortcomings of the technique are discussed.

The structures of Neel (also called Bloch) lines in uniaxial materials with quality factor Q larger than 1 are determined by means of a two-dimensional numerical relaxation method. Lines perpendicular and parallel to the easy magnetization axis, respectively, the horizontal and vertical lines in bubble garnets, are considered. The behaviour vs. Q of the line width, wall contraction at line location and wall buckling in the case of lines parallel to the easy axis are established. The energy of the converged structures is calculated and compared to the energy pertaining to the analytical model excluding or including wall contraction.

Neel (or Bloch) line dynamics has been investigated in garnet epilayers characterized by huge and moderate damping parameters. Direct pressure velocities are found to be in fair agreement with expected values. Velocity saturation is, however, observed in moderately damped material. The gyrotropic coupling to wall motion is shown to produce a variety of line displacement behaviours.

A new technique for observing domain walls and lines in materials with perpendicular anisotropy is presented. It employs laser light in a laser scan microscope and uses anisotropic diffraction by the wall/line magnetic structure. The contrast obtained can be understood simply and a numerical computation shows good agreement with experimental results. Wall configurations with numerous lines may be obtained when nucleating parallel stripes upon reduction to zero of a saturating in‐plane field.

Presentation de deux modeles elastiques, decrivant le phenomene du titre, qui relient les densites de defauts, les dislocations infinitesimales et les defauts ponctuels dans l'approximation du continu

X-ray section topographs of Dijkstra & Martius [Rev. Mod. Phys. (1953), 25, 146–150] magnetic domains in silicon–iron (2.4 wt. % Si) were simulated by means of a Fourier-transform numerical resolution of the Takagi–Taupin equations which describe X-ray propagation in distorted crystals. Two types of incident wave were used: a plane wave limited by a narrow slit at the entrance of the crystal, and a cylindrical wave centred at a distance of 10 to 50 cm from the crystal along the incident-beam direction. The agreement with experiments made by Schlenker & Kleman [J. Phys. C: Solid State Phys. (1971), 32 (Suppl.), 256–257] is good in the case of reflexions such as Co Kα11\bar 10 or Mo Kα1 1\bar 10, for which the magnetostrictive distortion field due to the junction of magnetic domains may be neglected, and only the discontinuity of the magnetostrictive distortion across a domain wall is taken into account in the computation. For the reflexion Mo Kα1 2\bar 20 the simulation does not exhibit the experimental contrast observed at the location of the 180° walls. A fair agreement with the experiment is, however, observed regarding the other features of the topograph.

White beam or transmission Laue X-ray topography is a now widely used imaging technique, especially in association with synchrotron sources. Several images may be recorded simultaneously, potentially allowing for direct defect characterization. Owing, however, to projection conditions, these images suffer from rather large geometrical distortions. This paper presents a general treatment of the projective properties of Laue topographs. Specific results applicable to a simple but frequently utilized specimen-detector geometry are also given. An example serves to demonstrate the usefulness of such calculations in the interpretation of experimental results.

White beam synchrotron X-ray topography has been used to conduct in situ studies of the influence of applied elastic tensile stress on magnetic domain configurations in Fe 3.5 wt.% Si single crystals. Specimens of [011] tensile axis, and either (100) or (011) surface orientation were utilized. Tensile stress was applied using a specially designed miniature tensile stage. In specimens of (011) surface the characteristic Dijkstra and Martius type I structure is induced upon application of stress, eventually to be replaced by the type II structure. The transition is understandable in terms of stress-induced anisotropy. On the other hand, in specimens of (100) surface, the initial structure, which essentially consists of 90° walls perpendicular to the tensile axis, changes to one which mainly consists of (010) and (001) 180° walls. Both structures have approximately equal volumes magnetized along [001] and [010]. This suggests that the transition is not driven by induced anisotropy. Alternative explanations are discussed. Changes in domain configurations around inclusions are also discussed.

The dynamics of vertical Bloch lines (VBL) in the Bloch walls of bubble garnet films are studied experimentally. A direct optical observation technique reveals VBL position. Static and pulsed in-plane as well as bias fields are used. The coercive properties of the sample give rise to complicated experimental behaviour in which zero VBL displacement coexists with erratic and 'regular' VBL displacement. The results are discussed qualitatively. >

A tensile stage measuring about 50 mm*100 mm has been constructed to fit onto the goniometer of a Lang or other camera for X-ray topography. It is designed primarily for specimens of relatively strong metals with gauge dimensions 10 mm*5 mm*0.1 mm. Loads up to 300 N can be applied and measured using a cantilever beam and capacitance transducer; a similar transducer could be used to measure strain. The design incorporates precision linear bearings to minimize specimen bending and a topograph taken using an Fe-Si alloy specimen is shown.

Magnetization inhomogeneities are observed by optical means in the walls of domains in bubble garnet films with perpendicular magnetization. Specific illumination conditions (scanned laser light, angular selection, dark field imaging) allowed for this achievement. Experiments using known wall states, static in-plane field and pulsed bias field indicate that the magnetic origin of these structures can be assigned to vertical Bloch lines (Neel segments in Bloch walls). A magnetooptical explanation of the observed contrasts is outlined. >

The net displacements of Neel lines belonging to unwinding or winding line pairs, resulting from the application of pulsed direct or gyrotropic forces, is investigated. It is found that pairs, whether winding or unwinding, shrink faster than they expand under the action of direct forces; under the action of gyrotropic forces, winding pairs exhibit a peculiar behavior; and a static field parallel to the easy axis has a considerable influence on line displacements, especially under the action of gyrotropic forces. Samples utilized in the present study are thick (TbY)/sub 3/(FeAl)/sub 5/O/sub 12/ garnet epilayers grown on