Search

International audience; Static and dynamic magnetic properties of Zn0.4Fe2.6O4 nanoparticles synthesized by thermal decomposition have been investigated. Two ranges of diameter have been used: small particles (diameter about 6.2 nm) and larger ones (diameter about 22.4 nm). The nanoparticle microstructure has been characterized by transmission electron microscopy. The temperature dependence of the zero-field dynamic permeability for both nanoparticle sizes has been studied, revealing a superparamagnetic state for the small ones. Effects of the nanoparticle size on the dynamic permeability have been studied, and linked to the superparamagnetic state. A dynamic susceptibility model has been found to reproduce the experimental behavior as well as its temperature dependence.

Magnetic properties of highly magnetostrictive amorphous glass-coated microwires are strongly correlated to the presence of a glass coating that introduces a spatially inhomogeneous stress field distribution. We investigate the influence of mechanical stresses on the inclination of magnetic domain walls in magnetic microwires. Magneto-optical Kerr effect imaging is used to compare the tilted orientation of the domain wall shape in as-cast and annealed microwires. Angular dependencies of magnetization loops measured by alternating gradient field magnetometry reveal that the change of domain wall tilting with annealing is related to the decrease of magnetic anisotropy with axial orientation. Finally, micromagnetic simulations are used to show that sufficiently high uniaxial magnetic anisotropy gives rise to the presence of observed charged domain walls with tilted orientation.

The high frequency magnetic susceptibility of glass-coated microwires with effective circumferential anisotropy has been modeled by micromagnetics. In their amorphous and magnetically soft metallic nucleus, the negative magnetostriction induces a continuous and non-uniform vortex-like structure, with an axially magnetized core coupled to a circumferentially magnetized outer shell. The model is a one-dimensional radial micromagnetic model where exchange, magnetoelastic and magnetostatic energies are considered. The microwave permeability under AC (axial and circumferential) fields is found to be expressed as a sum over a set of eigenmodes, each with a characteristic resonance frequency. In the framework of this model, a sum rule on the frequency-dependent permeability is shown to hold. It provides a figure of merit and guidelines for the design of high permeability materials for applications in the microwave range. © 2012 Elsevier B.V.

The microwave permeability of flake-shaped particles is investigated using a shorted microstrip setup. Several characterizations using two distinct field configurations, with and without the presence of a static field, are performed to provide information about the magnetization dynamics of this new material. A first insight is provided through the framework of Kittel's resonance, but additional features are also found and discussed.

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.

The static magnetization profile of glass-coated microwires with effective circular anisotropy is investigated using micromagnetics. In this family of microwires, the ferromagnetic nucleus with an amorphous character presents a magnetic structure composed of an inner region with axial domains and an outer region with circular domains, due to magnetoelastic anisotropy. A one-dimensional micromagnetic model is developed, taking into account both the exchange and magnetoelastic anisotropy energies, and solved quasi analytically. The total energy, magnetization profiles and magnetization curves are investigated as a function of radius and anisotropy constant of the nucleus. This work represents a fundamental study of the magnetization process in these amorphous microwires and provides guidelines for the production of microwires with tailored magnetic properties. En passant, the nucleation problem in an infinite cylinder, introduced by W.F. Brown, is revisited.

We propose a short overview of a few selected issues of magnetism in reduced dimensions, which are the most relevant to set the background for more specialized contributions to the present Special Issue. Magnetic anisotropy in reduced dimensions is discussed, on a theoretical basis, then with experimental reports and views from surface to single-atom anisotropy. Then conventional magnetization states are reviewed, including macrospins, single domains, multidomains, and domain walls in stripes. Dipolar coupling is examined for lateral interactions in arrays, and for interlayer interactions in films and dots. Finally thermally-assisted magnetization reversal and superparamagnetism are presented. For each topic we sought a balance between well established knowledge and recent developments., 13 pages. Part of a Special Issue of the C. R. Physique devoted to spinelectronics (2005)

The nucleation of reversed magnetic domains in Pt/Co/AlO(x) microstructures with perpendicular anisotropy was studied experimentally in the presence of an in-plane magnetic field. For large enough in-plane field, nucleation was observed preferentially at an edge of the sample normal to this field. The position at which nucleation takes place was observed to depend in a chiral way on the initial magnetization and applied field directions. A quantitative explanation of these results is proposed, based on the existence of a sizable Dzyaloshinskii-Moriya interaction in this sample. Another consequence of this interaction is that the energy of domain walls can become negative for in-plane fields smaller than the effective anisotropy field.

We employ a scanning nitrogen-vacancy-center microscope to perform stray field imaging of bubble magnetic domains in a perpendicularly magnetized Pt/Co/AlOx trilayer with 6 A of Co. The stray field created by the domain walls is quantitatively mapped with few-nanometer spatial resolution, with a probe-sample distance of about 100 nm. As an example of application, we show that it should be possible to determine the Bloch or Neel nature of the domain walls, which is of crucial importance to the understanding of current-controlled domain wall motion.

The present manuscript represents the third part of a series of studies about a continuous micromagnetic model for amorphous microwires with non-uniform magnetic structure (Torrejon et al., J. Magn. Magn. Mater. 323 (2011) 283; Torrejon et al., J. Magn. Magn. Mater. 333 (2013) 144). Here we compare the predictions of this model with experiments, and show the validity of this approach when a uniform magnetic structure in the microwire cannot be considered. The analyzed microwires exhibit ultrasoft magnetic behaviour and negative magnetostriction, with a non-uniform magnetic structure composed of an axially magnetized inner core exchange-coupled with a circumferentially magnetized outer shell. The static properties were obtained by magnetometry. The high frequency response, axial permeability, was measured from a conventional single coil permeameter connected to a network analyzer. The microwave response is strongly affected by skin effect, which therefore needs to be taken into account for comparison with theory. The validity of the continuous model is proved through the experimental dependence of the permeability on axial static field. Finally, the efficient dynamic magnetization is evaluated from the imaginary component of permeability. © 2014 Elsevier B.V.

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.

Micromagnetic simulations have been performed in order to obtain deeper insight into the domain structures within multilayer films, as they are expected to differ from those of single films. These 2D calculations have been done in the case of multilayers exhibiting a moderate perpendicular anisotropy, with no indirect exchange coupling between the magnetic layers, where a “weak stripe" domain structure develops. First, these results are compared quantitatively to the very detailed experimental data available in the literature on the (Co/Au)N system. More generally, the nucleation of a stripe pattern in multilayers is discussed as a function of the magnetic parameters and the number of magnetic layers in the stack. Compared to a single film, two main differences appear in the equilibrium domain period and the magnetization profiles. The physical origin of these effects is discussed.

We propose a geometrical method to explore the problem of coherent magnetization rotation, for an arbitrary anisotropy and in three dimensions. This method is a nontrivial generalization of the astroid construction which is well known in two dimensions. Specific features to the three-dimensional (3D) problem are highlighted. In order to establish a connection with the thermal and quantum theories of magnetization relaxation, the local curvatures of the potential are also evaluated geometrically. As an application of the method to a real 3D problem, the determination of the effective anisotropy constants from 3D switching field measurements is discussed and first results shown.

Magnetic force microscopy (MFM) is being used to image [Co/Cu].N and pure Co nanowires with diameters in the 80-90 nm range. Symmetry considerations as well as a close inspection of defects in the magnetic sequence allow for detailed conclusions to be reached. Although necessarily resting on a highest likelihood basis, the latter are substantiated by a simple model excluding altogether perturbations of the: magnetization distribution within tip or sample. Crystallographic features are revealed indirectly as well as finely spaced antiferromagnetic type magnetic sequences. It is believed that the present observations reveal for the first time the coexistence of axially and transversally magnetized segments within a given nanowire. Lastly, it is shown from an instrumental point of view that topographic and magnetic imaging are intimately interwoven. (C) 1998 Elsevier Science B.V. All rights reserved.

The problem of the determination of the orientation of a (classical) magnetic moment submitted to an applied field in the presence of an arbitrary anisotropy energy function is investigated theoretically, in two dimensions. The framework is the geometrical method introduced by Slonczewski. After rederiving Slonczewski's results in general terms (i.e. not only in the uniaxial case), extensions and additional properties of the geometric solution are described. An orientation of the critical curve is proposed, a geometrical evaluation of the energy demonstrated, the determination of the anisotropy function by means of switching field angular measurements is discussed and finally, the critical curves are completely characterized. This geometrical solution has several applications. First, it visualizes directly the dependence of the particle switching field on field orientation. Second, it gives simple analytical formulae for the energy barrier close to switching. This quantity is relevant in the study of the reversal of single-domain particles.

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.

We study the modification of micromagnetic configurations in nanostructures, due to the Dzyaloshinskii-Moriya interaction (DMI) that appear at the interface of an ultrathin film. We show that this interaction leads to new micromagnetic boundary conditions that bend the magnetization at the edges. We explore several cases of ultrathin film nanostructures that allow analytical calculations (1D systems, domain walls, cycloids and skyrmions), compare with fully numerical calculations, and show that a good physical understanding of this new type of micromagnetics can be reached. We particularly focus on skyrmions confined in circular nanodots and show that edges allow for the isolation of single skyrmions for a large range of the DMI parameter., Comment: Author adress: Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR 8502, F-91405 Orsay Cedex, France

Despite decades of advances in magnetic imaging, obtaining direct, quantitative information with nanometre scale spatial resolution remains an outstanding challenge. Recently, a technique has emerged that employs a single nitrogen-vacancy defect in diamond as an atomic-size magnetometer, which promises significant advances. However, the effectiveness of the technique when applied to magnetic nanostructures remains to be demonstrated. Here we use a scanning nitrogen-vacancy magnetometer to image a magnetic vortex, which is one of the most iconic objects of nanomagnetism, owing to the small size (~10 nm) of the vortex core. We report three-dimensional, vectorial and quantitative measurements of the stray magnetic field emitted by a vortex in a ferromagnetic square dot, including the detection of the vortex core. We find excellent agreement with micromagnetic simulations, both for regular vortex structures and for higher-order magnetization states. These experiments establish scanning nitrogen-vacancy magnetometry as a practical and unique tool for fundamental studies in nanomagnetism. Obtaining quantitative information on nanoscale magnetic structures is a challenge. Here, the authors apply scanning probe magnetometry based on a single nitrogen-vacancy defect in diamond to quantitatively map the stray magnetic field emitted by a vortex state in a ferromagnetic dot.

The $f$-sum rule for the magnetic permeability, derived previously for an assembly of isolated macrospins, is generalized for an arbitrary nonuniform three-dimensional magnetization texture, in which the magnetizations at different points are coupled by exchange and magnetostatic interactions. The sum value depends only on the magnetic texture at rest. It has no direct contribution from the exchange energy, but depends on the anisotropy, applied field, and demagnetizing energies. The derived formula is tested against numerical calculations for several complex and very different magnetization structures. This generalized sum rule should be useful for experiments, numerical simulations, and metrology.

We carried out measurements of domain wall (DW) velocities driven by magnetic-field pulses in symmetric Pt/Co/Pt and asymmetric Pt/Co/AlOx, Pt/Co/GdOx and Pt/Co/Gd trilayers with ultrathin Co layers and perpendicular magnetic anisotropy. The maximum observed velocity is much larger in the asymmetric samples, where the interfacial Dzyaloshinskii-Moriya interaction (DMI) stabilises chiral Neel walls. In quantitative agreement with analytical models, in all samples the maximum observed DW speed scales as , where D is the strength of the DMI and the spontaneous magnetisation. In Pt/Co/Gd, where the anti-parallel coupling between the magnetic moments of Gd and Co leads to a decrease of the total magnetisation, very large DW speeds (up to 700 m/s) are obtained.

A method combining the nudged elastic band method with finite element micromagnetics is used to calculate minimum energy paths, global minima, metastable states and, most importantly, saddle points between energy minima. We study configurational anisotropy effects in thin permalloy elements, e.g., 5 nm thick squares. For squares with the size of 15–200 nm the ground states are so-called “leaf” states with the average magnetization along one of the diagonals. However a second state (“buckle”) becomes stable with the average magnetization along one edge at sizes larger than ∼80 nm. The superposition of the four easy axes leads to a combination of four and eightfold anisotropy. At ∼200 nm size both states have about the same energy so that the overall picture becomes that of an effective eightfold anisotropy.

Several different soft magnetic materials have been investigated by means of Magnetic Force Microscopy (MFM) using commercial Atomic Force Microscope (Nanoscope III) with slope detection. The observed contrast of basically solenoidal magnetization distributions in nanocrystalline Fe-Permalloy multilayer and single-layer Permalloy thin film elements not only reveals wall locations, and thus the subdivision of the magnetic volume into domains, but also a decomposition into subdomains hitherto undocumented. A strong influence of roughness on the magnetic fine structure is also demonstrated. Additional observations of the classical lancets of Goss texture in bulk Iron confirm the fact that the symmetries of the observed contrast are consistent with those of pendicular component of magnetization within a volume close to the sample surface. >

The magnetization process of micron-sized permalloy elements submitted to in-plane magnetic fields is analyzed by means of magnetic force microscopy (MFM). Depending on the magnetic history of the sample and on the value of the applied field, high remanence domain structures (the so-called S- and C-states) as well as flux closure configurations (Landau and diamond patterns) are observed. Perturbations induced by the MFM tip are found, and the results are discussed with the help of micromagnetic simulations.

We study, by numerical calculations, the static domain wall structures in nanowires with axial magnetization. Then, applying an axial field, the wall dynamics is computed and compared to analytical models. We show that the one-dimensional Bloch wall dynamics, as first described by Walker, is fully realized in such samples.

We study spin-diffusion effects within a continuously variable magnetization distribution, integrating with micromagnetics the diffusive model of Zhang and Li [Phys. Rev. Lett. 93, 127204 (2004)]. Current-driven wall motion is, in the steady velocity regime, shown to be adequately described by an effective nonlocal nonadiabatic parameter. This parameter is found to be 20% larger than its local counterpart for a vortex wall in a NiFe nanostrip and hardly modified for a transverse wall. This may account for the yet unexplained experimental evidence that vortex walls move more easily under current when compared with transverse walls. It is shown that this effective parameter can be derived from the domain wall structure at rest.

Domain wall dynamics produced by spin transfer torques is investigated in (Ga, Mn)As ferromagnetic semiconducting tracks with perpendicular anisotropy, close to the Curie temperature. The domain wall velocities are found to follow a linear flow regime which only slightly varies with temperature. Using the Doring inequality, boundaries of the spin polarization of the current are deduced. A comparison with the predictions of the mean field k⋅p theory leads to an estimation of the carrier density whose value is compatible with results published in the literature. The spin polarization of the current and the magnetization of the magnetic atoms present similar temperature variations. This leads to a weak temperature dependence of the spin drift velocity and thus of the domain wall velocity. A combined study of field- and current-driven motion and deformation of magnetic domains reveals a motion of domain walls in the steady state regime without transition to the precessional regime. The ratio between the non-adiabatic torque β and the Gilbert damping factor α is shown to remain close to unity.

International audience; We have investigated experimentally the field-driven propagation of domain walls (DWs) in perpendicularly magnetized ferromagnetic semiconductor layers. The results were then compared with the historical one-dimensional (1D) DW propagation model widely used in spintronics studies of magnetic nanostructures. Anomalous velocity peaks, not predicted by the 1D model, were observed experimentally. Using micromagnetic simulations we show indeed that, in the particular regime of layer thickness (h) of the order of the exchange length, velocity peaks appear in the precessional regime, their shape and position shifting with h. Analyses of the simulations show a distinct correlation between the curvature of the DW and the twist of the magnetization vector within it and the velocity peak. Associating a phenomenological description of this twist with a four-coordinate DW propagation model, we show that the velocity peaks result from the torque exerted by the stray field created by the domains on the twisted magnetization. The position of the peaks is well predicted from the DW's first flexural mode frequency and depends strongly on the layer thickness. Comparison of the proposed model with data obtained on GaMnAs and GaMnAsP shows that the anomalies observed close to Walker breakdown are indeed induced by the flexion resonance of the domain wall.

We have observed peculiar magnetization textures in Ni${}_{80}$Pd${}_{20}$ nanostrips using three different imaging techniques: magnetic force microscopy, photoemission electron microscopy under polarized x-ray absorption, and scanning electron microscopy with polarization analysis. The appearance of diamondlike domains with strong lateral charges and of weak-stripe structures reveals the presence of both a transverse and a perpendicular anisotropy in these nanostructures. The anisotropy is seen to reinforce as temperature decreases, as testified by observations performed at 150 K. A thermal stress model with relaxation is proposed to account for these observations. Elastic calculations coupled to micromagnetic simulations support qualitatively this model.

A numerical framework is presented for the solution of the Landau–Lifshitz–Gilbert equation of magnetization motion using a semi-implicit Crank–Nicholson integration scheme. Along with the details of both space and time domain discretizations, we report on the development of a physically based self-consistency criterion that allows for a quantitative measurement of error in dynamic micromagnetic simulations. In essence, this criterion relies in recalculating from actual magnetization motion the imposed phenomenological damping constant. Test calculations were performed with special attention paid to the determination of suitable integration time steps.

Based on specific examples, we examine the consequence of spin-polarized current injection into confined model micromagnetic configurations, namely a high remanence state known as the S state and a low, though nonzero, remanence state called the Leaf state. Magnetization dynamics is solved in the space and time domain owing to the Landau–Lifshitz–Gilbert equation. It is shown that, within model bounds, the S state is not propitious to fast switching under the sole influence of a polarized current, even if disregarding the current induced field, whereas Leaf state switching characteristics become extremely complex as soon as due account is made for the latter.

Magnetization dynamics is discussed from two distinct viewpoints. Considering first magnetization motion to occur in unison, expressions are provided for the damped precession frequency and characteristic damping time either exactly or asymptotically. These quantities condition the necessary resolution in the time domain. An extension of Stoner and Wohlfarth’s reversal model to the dynamic regime closes the first section. The existence of “ballistic” trajectories is demonstrated. The second section deals with the combined space and time domains. Characteristic lengths are derived which prescribe the ultimate space resolution to be achieved in magnetic microscopy. Numerical simulations help in clearly delineating the differences between the dynamical behaviors of homogeneous and inhomogeneous magnetization distributions. The relevance of global precessional versus Bloch wall motion for fast switching characteristics is emphasized.

We use a micromagnetic approach to calculate the magnetization distribution in a ferromagnetic thin film in the presence of an interface anisotropy competing with the shape anisotropy. The parameters of the calculation are the magnitude of the magnetization, the exchange constant, the interface anisotropy and the film thickness. We find that the magnetization is non-uniform (twisted) in a parameter range that we determine. We calculate the effect of the twist on the magnetization curves. We discuss the importance of taking into account the magnetization twist for the interpretation of the magnetic properties.

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.

Current-induced magnetic domain wall motion has been investigated in microtracks made from a ferromagnetic semiconductor (Ga,Mn)As thin film with perpendicular anisotropy. In order to reveal the nature of this motion, small fields were additionally applied. The results demonstrate that, when driven by a low current density, the domain walls move under weak fields in a steady-state regime, ruling out models based on spin precession of the domain wall magnetization. The interpretation of these results requires a nonadiabatic contribution in the spin transfer, whose value is estimated and compared to recent theoretical calculations. This highlights the role of spin-orbit interaction in the carrier band on spin-transfer torque in continuous magnetic structures.

The static and dynamic magnetic properties of samples consisting of two soft magnetic layers with in-plane easy axes at right angles are studied by micromagnetics and experiments. A one-dimensional micromagnetic model is developed, and solved quasianalytically for statics and dynamics. In particular, it is shown that the magnetic permeability arises from a set of eigenmodes, each with a macrospin (or gyromagnetic) response, that are excited differently depending on ac field orientation. Experiments (magnetization curves, permeability under field and in several directions) on cobalt-based amorphous alloy bilayers are well reproduced by the model with a single set of parameters. Such samples are therefore model one-dimensional nonuniform magnetic systems, simple yet with a rich behavior, for statics and dynamics.

The recent observation of a magnetization‐gradient‐related birefringence in ferromagnetic materials is reviewed. A new phenomenological description using an isotropic dielectric material law in which the dielectric tensor is a linear function of the components of the propagation vector of the light wave and of the symmetric part of the magnetization gradient tensor is proposed. The symmetry of this interaction is derived in terms of space and time inversion invariance requirements, adding information from perpendicular incidence experiments. The dielectric law contains only one material parameter and displays additional unexpected symmetries. It is compatible with all observations for the perpendicular incidence, in‐plane magnetization case. Its predictions for the case of oblique incidence and a gradient in the polar component of magnetization are found not to be in contradiction with experiments when precautions are taken to avoid asymmetric diffraction due to the polar Kerr effect.

Spin-polarized current in a ferromagnet is known to lead to the instability of the uniformly magnetized state. In this paper, it is demonstrated by micromagnetic simulations that, in films or wide wires, the above instability is followed by the formation of magnetic vortices. Subsequent magnetization dynamics is also studied in terms of vortices, which includes pair dynamics and pair annihilation. Using a simple analytical model that considers the vortices as points, the dynamics of two interacting vortices under the current is classified according to their vorticity and polarity. This explains well the essential features of the simulation results.

We report on a theoretical study, by an atomic scale micromagnetic model, of the magnetic configurations and magnetization reversal in cobalt circular nanodots (one and two atomic layers thick, up to 10 nm in diameter) with enhanced magnetocrystalline anisotropy at the edge. According to the dot diameter, out-of-plane, twisted, and in-plane configurations are found. The results are first compared to the macrospin model, usually applied to this type of nanoparticles, and then to a continuous micromagnetic model with a sole radial variation of the magnetization. Field induced magnetization switching is also computed. We observe a process close to coherent rotation for nanodot diameters as small as 2 nm, but with a lower switching field as compared to the macrospin model, that may be called quasiuniform rotation. Our results fix the application limits of the macrospin model, which forgets atomic-scale variation of the properties.

This first review introduces the equations of magnetization dynamics, starting from the basic equations of quantum mechanics. The macrospin model is then considered, i.e. a model in which no spatial variation of magnetization is allowed for. General expressions for the frequencies and decrement rates of small magnetization oscillations are established. Within the macrospin model, the different behaviors of magnetization submitted to pulsed fields are investigated for a set of typical parameters. The existence of ballistic trajectories (the “no-ringing case”) is established. The first part ends with a description of magnetization dynamics based on a Lagrangian formalism. The second part deals with nonuniform magnetization distributions. After recalling the relevant equations for the dynamics of these structures, several results of numerical simulations in the case of submicron size rectangular Permalloy platelets are shown and discussed. The relevance of precessional motion for fast switching characteristics is emphasized. The concept of an apparent damping constant, derived from the temporal evolution of average quantities, is introduced. This apparent damping constant is always larger than the microscopic one. A procedure that checks the accuracy of the time integration of the Landau-Lifshitz-Gilbert equation is described, in which the microscopic damping constant is systematically recalculated. Following an initial quasi-coherent rotation of the magnetization, simulation results reveal the development of large amplitude magnetization waves, which bear some analogy to the spin waves that exist in such confined structures.

A magnetic vortex is a curling magnetic structure realized in a ferromagnetic disk, which is a promising candidate of a memory cell for future nonvolatile data storage devices. Thus, understanding of the stability and dynamical behaviour of the magnetic vortex is a major requirement for developing magnetic data storage technology. Since the experimental proof of the existence of a nanometre-scale core with out-of-plane magnetisation in the magnetic vortex, the dynamics of a vortex has been investigated intensively. However, the way to electrically control the core magnetisation, which is a key for constructing a vortex core memory, has been lacking. Here, we demonstrate the electrical switching of the core magnetisation by utilizing the current-driven resonant dynamics of the vortex; the core switching is triggered by a strong dynamic field which is produced locally by a rotational core motion at a high speed of several hundred m/s. Efficient switching of the vortex core without magnetic field application is achieved thanks to resonance. This opens up the potentiality of a simple magnetic disk as a building block for spintronic devices like a memory cell where the bit data is stored as the direction of the nanometre-scale core magnetisation., Comment: 20 pages, 4 figures. Supplementary discussion included. Accepted for publication in Nature Materials

We consider a microscopic model of itinerant electrons coupled via ferromagnetic exchange to a local magnetization whose direction vector n(r,t) varies in space and time. We assume that to first order in the spatial gradient and time derivative of n(r,t) the magnetization distribution function f(p,r,t) of itinerant electrons has the Ansatz form: f(p,r,t)=f_{parallel}(p)n(r,t)+ f_{1 r}(p) n ^ nabla_{r} n+f_{2 r}(p) nabla_{r} n+ f_{1 t}(p) n ^ partial_t n+f_{2 t}(p) partial_t n. Using then the Landau-Sillin equations of motion approach we derive explicit forms for the components f_{parallel}(p), f_{1 r}(p), f_{2 r}(p), f_{1 t}(p) and f_{2 t}(p) in "equilibrum" and in out of equilibrum situations for: (i) no scattering by impurities, (ii) spin conserving scattering and (iii) spin non-conserving scattering. The back action on the localized electron magnetization from the out of equilibrum part of the two components f_{1 r}, f_{2 r} constitutes the two spin transfer torque terms., Comment: Revised version accepted for publication, 12 pages, one figure

Domains were imaged by magnetic force microscopy (MFM) on materials where the domain size exceeds the sample thickness by three orders of magnitude. Selected samples are a magnetooptical medium and ultrathin cobalt films, all with perpendicular magnetization. A strong domain contrast is observed in both cases. This fact is confronted to the usual theory of MFM image formation, in which the stray field from one body (tip or sample) is sensed by the other, without altering of the magnetization distributions. It is shown that the domain contrast in such extreme conditions cannot be explained with that theory. On the contrary, Abraham and McDonald’s model, which considers the response of the sample to the tip field, is quantitatively compared to experiment. It is shown to provide a good qualitative description of the results, but not a quantitative one, because of oversimplification.

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 domain wall motion by spin polarized current injection has been studied. The critical current for instability of uniform magnetization is investigated by micromagnetic computer simulation.

We performed magnetic-field-induced experiments on micron-sized patterned Co70.4Fe4.6Si15B10 square thin-film elements with in-plane magnetic anisotropy by magneto-optical scanning near-field optical microscopy (MO-SNOM) with a spatial resolution better than 200nm. Markedly different local hysteresis loops (LHLs) were measured on selected positions in one element. Some LHLs presented an unusual shape intrinsic of local magnetic-field-induced process. Comparison of the MO-SNOM imaging results with high-resolution far-field Kerr microscopy has confirmed the local character of the MO-SNOM measurements. This has also helped us to understand the unusual LHLs shapes as related to the field-induced rearrangement of the domain structure within the square element during the magnetization process. The magnetic structure in small field is well described by two overlapping four-domain flux-closure configurations that are well modeled by micromagnetic calculations.

Magnetization dynamics is discussed from two distinct viewpoints. Considering first magnetization motion to occur in unison, expressions are provided for the damped precession frequency and characteristic damping time either exactly or asymptotically. These quantities condition the necessary resolution in the time domain. An extension of Stoner and Wohlfarth’s reversal model to the dynamic regime closes the first section. The existence of “ballistic” trajectories is demonstrated. The second section deals with the combined space and time domains. Characteristic lengths are derived which prescribe the ultimate space resolution to be achieved in magnetic microscopy. Numerical simulations help in clearly delineating the differences between the dynamical behaviors of homogeneous and inhomogeneous magnetization distributions. The relevance of global precessional versus Bloch wall motion for fast switching characteristics is emphasized.

International audience; The first three-dimensional switching field measurements of an individual nanometer-sized magnetic particle are presented. The angular dependence of the switching field can be described by the model of uniform rotation of magnetization. However, the anisotropy function proposed by Stoner and Wohlfarth appears to be simplistic. In order to reproduce the measured switching fields, one has to take into account higher order anisotropy terms. These terms are very important to understand dynamical magnetization reversal properties in the classical and the quantum regimes.

A low-frequency resonance (sub-GHz) is observed in microwave permeability spectra of anisotropic flake-shaped ferromagnetic particle composites. The resonance frequency of this peak increases linearly with the saturation magnetization of flakes, their aspect ratio, and the amplitude of a perpendicular static magnetic field. In addition, this resonance becomes extinct for a perpendicular RF exciting magnetic field. These experimental features are reproduced by an analytical model of vortex dynamics which militates in favor of an assignment of this low-frequency signal as an embedded vortex translation mode within a multidomain magnetic structure.

Anisotropic-dark-field optical imaging is shown to reveal the presence of horizontal Bloch lines (HBL's) in the moving walls of bubble garnets. It relies on the deformation of the wall shape under dynamic conditions due to the presence of a HBL. The wall tilt is detected because it affects the intensity of the wall images much in the same way as localized wall tilts reveal the location of vertical Bloch lines (VBL's) in static conditions. Quantitative time-resolved measurements of wall intensity are presented and shown to compare very favorably with numerical computations. These use a simplified spin dynamics equation (Slonczewski's equations) describing the wall position and wall-core magnetization in-plane angle, as a function of position across the thickness, and time. Dynamic reversals of VBL's contrast have also been observed. The fact that they occur for one half of the possible configurations is puzzling. They are tentatively explained on the basis of a dynamically induced charge distribution at VBL location, which arises from a wall wave developing around the moving VBL.

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][1] highlight the report by [ Acremann et al .][2], 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. [1]: http://www.sciencemag.org/cgi/content/full/290/5491/466 [2]: http://www.sciencemag.org/cgi/content/short/290/5491/492