Showing papers on "Magnetic domain published in 1991"

A mechanism of magnetic hysteresis in heterogeneous alloys

Abstract: It is suggested that in many ferromagnetic materials there may occur particles distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector. As the field changes continuously, the resolved magnetization may change discontinuously at critical values of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle and on the orientation of easy axes with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magnetocrystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution, along with a less detailed treatment for the general ellipsoidal form.

Observation of two different oscillation periods in the exchange coupling of Fe/Cr/Fe(100).

Abstract: Oscillations of ferromagnetic to antiferromagnetic exchange coupling between two Fe layers separated by a Cr spacer of linearly increasing thickness were investigated by imaging the magnetic domains with scanning electron microscopy with polarization analysis (SEMPA). Up to six oscillations in the coupling with a period of 10\char21{}12 Cr layers were observed, and, in the case of an extremely well ordered Cr interlayer, additional oscillations with a period of 2 Cr layers were observed.

Magnetoresistive sensor based on the spin valve effect

Abstract: A magnetoresistive (MR) sensor comprising a first and a second thin film layer of a magnetic material separated by a thin film layer of a non-magnetic metallic material. The first ferromagnetic layer is magnetically soft. The magnetization direction of the first layer of magnetic material is set substantially perpendicular to the magnetization of the second layer of magnetic material at zero applied field, and the magnetization direction of the second layer of magnetic material is fixed. A current flow is produced through the MR sensor, and the variations in voltage across the MR sensor are sensed due to changes in resistance of the MR sensor produced by rotation of the magnetization in the first layer of magnetic material as a function of the magnetic field being sensed. The variation of the resistance with the angle between the magnetizations of the first and second layers of magnetic material has been defined as the spin valve (SV) effect. It is also shown that, by a suitable direction of the current with respect to the fixed magnetization, the (SV) magnetoresistance can be added constructively to the usual anisotropic magnetoresistance.

Magnetic properties of free cobalt clusters

Abstract: We report in this paper results of Stern-Gerlach experiments for all the systems we have studied to date. Three distinct behaviors are observed. Cobalt exhibits superparamagnetic behavior, with a magnetic moment per atom of 2.29 ± 0.08µ B for N = 115. The rare earths gadolinium and terbium exhibit superparamagnetic behavior for certain clusters, while other clusters exhibit behavior consistent with their moment being locked to the crystal lattice. In both cases, the moments are considerably reduced from the bulk values. The third behavior is no measurable deflection at all, as demonstrated by vanadium, palladium, chromium, and aluminum.

Domain Observations on FeCrFe Layered Structnres. Evidence for a Biquadratic Coupling Effect

Abstract: The recently discovered oscillating exchange effect in iron–chromium multilayers can best be studied on an epitaxial iron sandwich with a wedge shaped chromium interlayer. Domain patterns are analyzed as well as magnetization curves on such samples using magnetooptical techniques. Unusual domains are found in zones around the transitions between ferromagnetic and antiferromagnetic exchange. Also the magnetization curves for larger chromium thickness show some peculiar features. The interpretation of these patterns invokes coupling between the iron layers which favours a right angle between the magnetization directions in both layers. Such a non-collinear interaction can be derived phenomenologi-cally from a biquadratic coupling as introduced earlier in the analysis of spin structures in oxides. A biquadratic coupling can be understood either as a second order Heisenberg or a second order Dzyaloshinskii interaction. In the course of these investigations domain observations proved to be a useful and sensitive method to detect locally the nature of interactions between ferromagnetic layers. Die kiurzlich entdeckte oszillierende Wechselwirkung in Eisen–Chrom-Vielfachschichten kann am besten an einer epitaxialen Schichtanordnung mit einer keilformigen Chromzwischenschicht studiert werden. Die auf solchen Proben beobachtbaren Domanenstrukturen sowie die Magnetisierungskurven werden mit magnetooptischen Verfahren untersucht. Im Bereich der Ubergange zwischen ferroma-gnetischer und antiferromagnetischer Kopplung werden Zonen ungewohnlicher Muster entdeckt. Auch die Magnetisierungskurven fur grosere Chrom-Schichtdicken zeigten eigentumliche Zuge. Die Beobach-tungen lassen sich erklaren, wenn eine zusatzliche Kopplung der Schichten angenommen wird, die einen rechten Winkel zwischen den Magnetisierungsrichtungen in beiden Schichten begunstigt. Phanomenologisch ergibt sich eine solche nicht-kollineare Kopplung aus der Annahme einer biquadrati-schen Wechselwirkung, wie sie fruher in der Analyse von Spinstrukturen magnetischer Oxide eingefuhrt wurde. Eine biquadratische Kopplung Iast sich entweder als Heisenberg- oder Dzyaioshinskii-Wechselwirkung zweiter Ordnung interpretieren. Domanenbeobachtungen erwiesen sich im Laufe dieser Untersuchung als empfindliche Methode zur Untersuchung des Charakters der Kopplung in Vielfachschichten.

Science and Technology of Nanostructured Magnetic Materials

Abstract: Thin Films, Surfaces and Interfaces -- Electronic Structure and Magnetism of Metal Surfaces, Overlayers and Interfaces -- Growth and Magnetic Properties of Metastable Structures -- Spin-Resolved Photoemission -- Correlation of Crystalline and Electronic Structure in Epitaxial FCC-Cobalt Monolayers on Cu(100) -- Hybrid Ferromagnetic/Semiconductor Structures -- Mossbauer Studies of Ultrathin Magnetic Films of Fe/Ag(100) -- Spin-Dependence of Absorbed and Reflected Current on Fe(110) -- MBE Growth of Metal/Semiconductor Interfaces -- Surface and Interface Magnetism -- Ferromagnetic Resonance Studies of BCC Epitaxial Ultrathin Fe(001)/Cu(001) Bilayers and Fe(001)/Cu(001)/Fe(001) Trilayers -- Laser Ablation Deposition of Metallic Thin Films -- Exchange Coupled Films for Magneto-Optic Applications -- Temperature Dependence of Micromagnetic Domain Structure in Cobalt Films -- Hyperfine Interaction Techniques Applied to the Study of Surfaces and Interfaces -- Surface Magnetostriction -- Multilayers -- Magnetic Rare Earth Artificial Metallic Superlattices -- X-Ray Characterization of Magnetic Multilayers and Superlattices -- The Characterization of Interface Roughness and Other Defects in Multilayers by X-Ray Scattering -- Magnetism of Nanostructured Rare Earth Multilayers -- FMR Studies of Metallic Magnetic Thin Films in Layered Structures -- Compositionally Modulated Magnetic Multilayers: Temperature- and Modulation-Dependent Properties -- Structural and Magnetic Properties of Epitaxial Co/Pd Superlattices -- First-Principles Calculation of the Magnetocrystalline Anisotropy Energy of ConPdm Multilayers -- Structural and Magnetic Studies in Co-Pt Multilayers -- Magnetic Properties of Hexagonal Fe/Ru Superlattices With Short Periodicity -- Magnetic Studies of Fe-Si Compositionally Modulated Thin Films -- Mossbauer Spectroscopy of the Fe/Ni Interface -- Analysis of Amorphous Dysprosium-Transition Metal Nanoscale Magnetic Multilayers -- Transport Properties of Thin Metallic Films and Multilayers -- Domain Walls, Magnetic Domains And Techniques For Their Observation -- Micromagnetics of Longitudinal Recording Media -- MO-Recording: The Switching Process and Its Relation to the Magnetic Properties of Thin Films -- Micromagnetic Computations of Magnetization Configurations -- Domain Walls and Wall Structure -- Domain Wall Multiplication in Amorphous Ferromagnetic Alloys -- Electron Microscope Methods for Imaging Internal Magnetic Fields at High Spatial Resolution -- Scanning Tunneling Microscopy and Force Microscopy Applied to Magnetic Materials -- Special Session on Spin-Polarized Vacuum Tunneling -- Magnetic Imaging Via Scanning Electron Microscopy with Polarization Analysis -- Atomic Scale Probe into High-Tc Superconductors Using Scanning Tunnelling Microscopy -- Magnetic Anisotropy and Random Magnets -- Magnetic Anisotropy -- Random Anisotropy in Magnetic Materials -- Perpendicular and In-Plane Anisotropy in Amorphous Tb-Fe -- Magnetostriction in Amorphous Ferromagnets -- Anderson Localization in 3-Dimensional Amorphous Alloys: Evolution with the Content of Magnetic Ions -- On the Law of Approach to Saturation in the Series of Amorphous Alloys a-Dyxd1?xNi -- Magnetoresistance of Amorphous U1?xSbx Films -- Absence of Temperature-Driven First-Order Phase Transitions in Systems with Random Bonds -- Magnetic Semiconductors and Intermetallic Compounds -- Magnetic Behavior of Diluted Magnetic Semiconductors -- Intermetallic Compounds and Crystal Field Interactions -- Crystal-Field and Exchange Interactions in Hard Magnetic Materials -- First Order Magnetization Processes -- Structure and Properties of Novel Ternary Fe-Rich Rare-Earth Carbides -- Fine Particles -- Granular Solids -- Ultrafine Magnetic Particles -- Magnetic Nanometer Systems and Mossbauer Spectroscopy -- Some Topics in Fine Particle Magnetism -- Mossbauer Studies of Fine Fe-Based Particles -- Mossbauer Studies of Fine Particles of Fe-Cr-B -- Chemical Preparation of Amorphous Fe-Cr-B Particles -- Composition and Structure of Fe-Ni-B Alloy Particles Prepared by Chemical Reduction with NaBH4 -- Quantum Effects in Ultrafine Nd-Fe-B Particles -- Magnetization Reversal in Clusters of Magnetic Particles -- Electric and Magnetic Properties of Small Systems -- Existence of Frequency Cut-Off in the Spin Wave Spectrum of Small Magnetic Particles -- Magnetic Hysteresis and Permanent Magnets -- Mechanically Alloyed Permanent Magnets -- Melt-Spun Magnets -- Solid NdFeB Magnets Made by Gas Atomization and Extrusion -- The Role of Microstructure in Permanent Magnets -- Lorentz Microscopy Studies in Permanent Magnets -- Coercivity in Hard Magnetic Materials -- Micromagnetism and Magnetization Processes in Modern Magnetic Materials -- Micromagnetic Approach to Magnetic Hysteresis -- Magnetic Hysteresis in Disordered Magnets -- Coercivity of Nanostructured Materials -- Magnetic Hysteresis of CoPt Films -- Technology and Applications of Permanent Magnets -- Author Index.

Hysteresis, microstructure, and magneto‐optical recording in Co/Pt and Co/Pd multilayers

Abstract: The factors that influence the coercive field Hc and the shape of the magnetic hysteresis loop for Co/Pt multilayers (MLs), applied as a magneto‐optical (MO) recording medium, have been investigated. The hysteresis loop of MLs, made by evaporation of Kr sputtering, became more rectangular when the total film thickness was reduced, i.e., the saturation field Hs decreased and the nucleation field Hn increased. Hs was calculated using a stripe domain model and Hn was modeled assuming that nucleation took place at a field that destabilized small vestigial magnetic domains. Both models assumed that domain walls can move in the ML film and the agreement with experiment was good. However, these models could not explain the hysteresis loops for the MLs deposited on a thick Pt base layer or made at high sputter gas pressure. These MLs showed a more particulate microstructure and the hysteresis loop was sheared, consistent with magnetic reversal by uniform rotation rather than domain‐wall motion. From thermomagneti...

Magnetic properties and microstructures of the Nd‐Fe‐B magnet powder produced by hydrogen treatment

Abstract: The hydrogen treatment of the Nd‐Fe‐B alloy ingots was found to produce magnet powders with good magnetic properties. Typical magnetic properties of these powders are as follows; 4πIs = 9.5 kG, Br = 7.7 kG, iHc = 9.4 kOe, and (BH)max = 12.2 MGOe. Microstructural studies of these powders showed that they are made of fine crystalline grains of ∼0.3 μm diameter and that these crystalline grains in the individual magnet powder are not necessarily enclosed with boundary phase(s), which is quite different from previously known Nd‐Fe‐B magnets, i.e., the sintered magnet (the nucleation type magnet) or the amorphous ribbon magnet (the pinning type magnet). It is also noted that the size of these crystalline grains is comparable to that of the single magnetic domain of the tetragonal Nd2Fe14B intermetallic compound and the coercive force of these powders appears to be related to their fine crystalline grain size.

Quantum dynamics and tunneling of domain walls in ferromagnetic insulators.

Abstract: It is shown how large domain walls, containing \ensuremath{\ge}${10}^{10}$ spins, can behave as quantum objects at low temperatures. They move quantum diffusively, and exhibit macroscopic tunneling from defect pinning centers. The dissipation is calculated and shown to be very small; it does not involve the usual Caldeira-Leggett environmental couplings. The theory can also be used to treat smaller single-domain-wall behavior.

Nanometer scale probe for an atomic force microscope, and method for making the same

Abstract: Methods are described for producing a needle probe tip having prescribed magnetic properties for a scanning magnetic force microscope (MFM) on a substrate positioned in an evacuated environment. A substantially rigid, nanometer-scale needle-like structure is produced by selective decomposition of a volatile organic compound by a highly focussed electron beam. Processing steps are described to obtain prescribed magnetic properties of such a needle probe structure; in particular, the fabrication of a single magnetic domain, with hard or soft magnetic properties at the distal end of the needle structure. Three dimensional probe tips are also achieved. These magnetic sensing probes allow magnetic imaging at the nanometer-scale level.

Stacked structures of passive magnetic bearings

Abstract: The stiffness of magnetic bearings composed of only two permanent magnet rings is limited. To increase this stiffness, stacked structures are used. Conventional stacking is obtained by placement of the magnetizations in opposition. This article presents another type of stacking with rotating magnetization direction (RMD), which improves the stiffness by about a factor of 2 in comparison with the conventional stack.

Magnetic domain patterns observed on synthetic Ti‐rich titanomagnetite as a function of temperature and in states of thermoremanent magnetization

Abstract: The fundamental temperature dependence of magnetic domain structure has been recognized for several decades, but its relationship to thermoremanent magnetization (TRM) has been unexplored. As one step toward investigating this possible link, we have studied Bitter patterns on synthetic Ti-rich titanomagnetite (Al0.1Mg0.1Ti0.6Fe2.2O4; Curie point of approximately 75°C) as a function of temperature in a weak field (0.42 Oe), in states of weak field TRM, and after alternating field demagnetization. Two different types of patterns were studied with the following goals: (1) simple Kittel-like patterns of straight walls were studied in order to gain insight into the nature of TRM domain structures and the various possible mechanisms by which particles acquire weak field TRM; (2) mazelike patterns, which occupy regions of high surface stress, were studied in order to estimate the temperature dependence of magnetostriction constant in this material. Results of experiments to study Kittel-like patterns suggest that two different mechanisms, and two resulting species of domain structure, could account for fundamental differences between multidomain and pseudosingle-domain thermoremanence in titanomagnetite. In accordance with traditional models, typical multidomain TRM results from wall pinning in a particle that contains several domains whose volumes are approximately equal to each other. In contrast, pseudosingle-domain TRM is acquired when denucleation of domains and domain walls yields a domain structure with a large associated “intrinsic” moment. The following observations support these conclusions. In a particle with a Kittel-like pattern, the number of domains varies from one TRM experiment to the next. This variation indicates that a grain can acquire TRM in a range of local energy minimum states, rather than in one particular domain configuration of absolute minimum energy. Many such TRM patterns represent the near-ideal local energy minimum domain states, consisting of several domains of approximately equal widths, usually envisioned in models of multidomain thermoremanence. Observations suggest that a particle can maintain such states during cooling if weakly pinned walls adjust readily to demagnetizing fields generated during the denucleation process. In this case, TRM results from small displacements of pinned walls with respect to a state of minimum magnetostatic energy; several observations suggest that blocking of walls at pinning centers in the classical manner occurs mainly after the final nucleation event as the particle cools toward room temperature from the Curie point. In contrast, we have observed examples in which denucleation leaves behind an anomalously large domain where several approximately uniform domains existed prior to denucleation; several smaller domains survive elsewhere in the particle, virtually unaffected by the transition. Evidently, strong wall-pinning forces sometimes prevent surviving walls from responding to the change of internal field which must accompany the denucleation process. It is observed that denucleation can yield single-domain-like states during TRM acquisition. Thus denucleation, rather than complete failure to nucleate during TRM acquisition, is one mechanism for producing single-domain-like states in particles which ordinarily favor walls. Possibly, such states exist by virtue of strong pinning forces at surface defects, into which denucleating domains and domain walls collapse. Particles with an odd number of approximately uniform domains also are observed in TRM states, and such particles also may carry large intrinsic moments owing to domain imbalance; possibly, such domain configurations result from the final denucleation episode during cooling. Thus these observations indicate a strong link between TRM acquisition mechanisms, magnetic domain transitions, and the accessibility of domain states. We hypothesize that denucleation could account for the most desirable properties of TRM associated with pseudosingle-domain titanomagnetite particles, namely, high intensity and high thermal stability. The second class of patterns, mazelike patterns, was studied to estimate the temperature dependence of domain wall energy and magnetostriction constant from the observed temperature dependence of domain width. The temperature dependence of magnetostriction constant obtained in this manner for AMTM60 is similar to that obtained for magnetite in earlier studies.

Exchange interactions and giant magnetoresistance in magnetic multilayers

Abstract: Magnetic layer structures consisting of alternating magnetic and non-magnetic layers exhibit new magnetic phenomena with great potential for applications in magnetic storage technology. It is found experimentally that the magnetic moments of neighbouring magnetic layers are spontaneously aligned ferromagnetically or antiferromagnetically depending on the thickness of the intervening nonmagnetic layers. This implies an oscillatory magnetic coupling between the layers mediated by the nonmagnetic spacer layers. The resistance of the structure when a current is passed in the direction parallel to the layers is much higher in the antiferromagnetic configuration than in the ferromagnetic one. The magnetic configuration of the layers, and hence the resistance of the structure, is strongly influenced by an applied magnetic field. This effect, called giant magnetoresistance, can be exploited to read information from a magnetic disc. The purpose of this review is to introduce the reader to magnetic multila...

Spin Polarized Low Energy Electron Microscopy of Surface Magnetic Structure

Abstract: Spin polarized low energy electron microscopy (SPLEEM) has been developed for the high resolution imaging of surface magnetic structure. The existing LEEM ha.s been modified by the incorporation of a. GaAs-type spin polarized electron gun. Large image contrast arises due to the spin-dependent exchange scattering, whifle the st.in-orbit contribution vanishes uniquely for the normal incidence/exit geometry used here. Pixel by pixel image subtraction for incident electron beams of opposite polarization yields precisely the spatially resolved Bragg reflection asymmetry observed in spin polarized low energy electron diffraction. The shallow electron penetration depth arising from the strong coulombic interaction is advantageous for separating surface behavior from the normally overwhelning bulk. Therefore, the use of transversally polarizedI electron beams allows the determination of in-plane surface magnetization directions. Fnrthermore, the parallel illumination and detection of SPLEEM makes it possible to image quickly with a. resolution better than 500 A in the present configuration. A useful and direct. comparison between surface magnetic, structural, and topological features is made possible by the augmentation of the unique imaging capabilities of conventional LEEM with the magnetic sensitivity of SPLEEM. In this manner, the magnetic domain structure of a Co (0001) surface and in-situ grown Co filmns on Mo(110) have been determined.

Hartree-Fock study of the magnetism in the single-band Hubbard model.

Abstract: We study the magnetic phases of the single-band Hubbard model within the self-consistent Hartree-Fock formalism applied to a large supercell. We find that incommensurate spin-density waves gradually deform into domain walls with increasing correlation energy U, in agreement with previous studies. For U/tg8 the domain walls evaporate into separated magnetic polarons. For U/t20, the spin expectation values are collinear. However, we find clear evidence for the importance of the transverse spin components in the large-correlation limit, although the exact ground state cannot be determined. The connection between the resulting band structures and photoabsorption and optical data is discussed.

Domain-wall dynamic transitions in thin films.

Abstract: Two-dimensional domain-wall configurations and dynamics in thin films with the easy axis parallel to the film plane are calculated by using LaBonte-like energy minimization as well as solving the Landau-Lifshitz equation with phenomenological damping. Under a sufficiently small uniform field applied in the easy direction, the effective wall mass and the viscosity coefficient induced from a uniform wall motion are compared with theoretical values. For external fields much greater than the anisotropy field, the wall motion exhibits complex features, including periodic transitions between asymmetric Bloch and N\'eel wall structures and the emergence of multivortices, depending on the film thickness. The latter serves as a precursor to turbulent wall dynamics at even higher external fields. With a varying external field applied in the hard direction and parallel to the film surface, wall structure changes between asymmetric Bloch- and N\'eel-type walls are also seen. An irreversible transition is observed which causes a constricted hard-axis hysteresis loop. Dynamically, this hysteretic transition can be associated with wall creep.

Magnetic properties of fine crystalline Fe–P–C–Cu–X alloys

Abstract: The crystallization process and magnetic properties of Fe–P–C–Cu–Ge–Si amorphous alloys were investigated. After annealing above the crystallization temperature, the bcc Fe particles, with nanoscale grain size, precipitated in the amorphous alloy for a wide P concentration range. The volume ratio of the bcc Fe phase to amorphous was about 30%. The mixed phase of these alloys shows a drastic decrease of coercive force (Hc) and particle diameter (d) as P concentration increases. The lowest Hc was obtained for Fe78P16C2Cu0.5Ge3Si0.5, and Hc and d were 1.8 A/m and 16 nm, respectively. Observation by in situ Lorentz scanning electron microscopy (SEM) revealed that the width of magnetic domains were 0.01 or 0.1 mm and the domain walls with smaller bcc Fe particles moved in a weaker magnetic field than those with larger ones. So the low Hc is attributed to the decrease of magnetocrystalline anisotropy caused by fine structures. The core loss of fine crystalline Fe–P–C–Cu–Si–Mo alloy, W14/50, was 0.22 W/kg after ...

Anisotropy pinning of domain walls in a soft amorphous magnetic material

Abstract: Ribbons were annealed in the demagnetized state with one wall along the ribbon middle. This wall becomes pinned during the heat treatment. Reentrant reversal occurs when reverse domains are nucleated at the ribbon edge with a threshold field larger than the demagnetizing field; this wall does not annihilate when it meets the pinned wall but leaves a line of reverse domains stabilized by ripple in the anisotropy. These domains permit a regular smooth reversal for the demagnetization process until the ribbon returns to the pinned configuration. The regular loop appears when the ribbon has been completely saturated by a large field. Mobile walls are nucleated on both sides of the pinned wall so that the ribbon does not return to the pinned configuration. Reversal now follows the usual demagnetization curve over the entire cycle. Kerr magnetooptical domain and domain wall observations are used in this investigation. All of the possible wall structures predicted by the model of asymmetric flux closed Bloch walls were identified. >

Problems of loss separation for crystalline and consolidated amorphous soft magnetic materials

Abstract: Losses were measured as a function of magnetization frequency f/sub d/ for two advanced soft magnetic alloys: laser-scribed 0.23-mm HI-B steel ZDKH (designated HB) and consolidated amorphous Powercore (designated PC). Although domain observations on HB yielded distinct domain refinements due to the laser treatment, anomalous losses W/sub a/ still proved to be higher than the classical ones. A further refinement resulted from increasing f/sub d/. Thus, anomalous eddy current losses were reduced while hysteresis losses were increased. As a consequence, it is suggested to separate W/sub a/ into an eddy current component and a hysteresis component, which arises in addition to the classical hysteresis loss. With increasing f/sub d/, especially wide domains were refined. Results of loss measurements performed at high f after demagnetization with low f/sub d/ indicated similar bar-type domain structures in HB and PC, the domain widths of the latter exceeding those of HB, however, by one order of magnitude. A Kerr-effect scanning technique confirmed the existence of an inner bar-type domain structure with domain widths of some millimeters. >

Using multipoles decreases computation time for magnetostatic self-energy

Abstract: The calculation of the magnetostatic self-energy and field is the most computationally intensive aspect of micromagnetics simulations. The computation time is proportional to N/sup 2/, where N is the number of cells in the discretized problem. The authors have implemented an algorithm that uses multipole expansions of the field integrals for cells suitably far from the field evaluation point. The computation time is asymptotically proportional to N log N. This implementation is demonstrated by computing the micromagnetic structure of domain walls in both thin and thick ferromagnetic films. >

Computation of electron diffraction patterns in Lorentz electron microscopy of thin magnetic films

Abstract: Lorentz electron microscopy is a powerful tool for high‐resolution studies of magnetic structure in thin films.1–3 The physical mechanism that underlies all known modes of Lorentz microscopy is the interaction between the propagating electron wave and the magnetic vector potential field. For a given electron trajectory the interaction, commonly known as the Aharonov–Bohm effect, results in a phase delay directly proportional to the path integral of the vector potential.4 Lorentz microscopy is therefore a branch of phase‐contrast microscopy whose various modes (e.g., Fresnel, Foucault, differential phase contrast, small‐angle diffraction, electron interference, and holography) simply represent different designs for capturing the information contained in the phase of the beam after passage through the sample. This paper introduces a general technique for computing the phase imparted to the electron beam by a two‐dimensional pattern of magnetization. The vector potential field for a thin film with arbitrary ...