Remanence due to wall magnetization and counterintuitive magnetometry data in 200-nm films of Ni

200-nm-thick Ni films in an epitaxial Cu/Ni/Cu/Si(001) structure are expected to have an in-plane effective magnetic anisotropy. However, the in-plane remanence is only 42%, and magnetic force microscopy domain images suggest perpendicular magnetization. Quantitative magnetic force microscopy analysis can resolve the inconsistencies and show that (i) the films have perpendicular domains capped by closure domains with magnetization canted at 51 degrees from the film normal, (ii) the magnetization in the Bloch domain walls between the perpendicular domains accounts for the low in-plane remanence, and (iii) the perpendicular magnetization process requires a short-range domain wall motion prior to wall-magnetization rotation and is nonhysteretic, whereas the in-plane magnetization requires long-range motion before domain-magnetization rotation and is hysteretic.     

Domain and wall structures in films with helical magnetization profile

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.     

Magnetostatic energy and stripe domain structure in a ferromagnetic plate of finite width with in-plane anisotropy

The magnetostatic energy and domain structure (DS) in a long ferromagnetic plate of a finite width with in-plane anisotropy are calculated for the case of the domain magnetization vectors lying in the plane of the plate. The situation where the DS period is much shorter than the width but is considerably larger than the thickness of the plate is analyzed in detail. The equilibrium DS period and the width ratio of two adjacent domains are determined as functions of an external magnetic field parallel to the plane of the plate by minimizing the energy. The DS period is found to be proportional to the plate width and the domain wall energy and inversely proportional to the squared saturation magnetization. While the width of the favorable domains (with the magnetization parallel to the field) grows with increasing field, the unfavorable domains, rather than disappearing completely, form relatively narrow transition regions between the favorable domains, i.e., 360° domain walls.     

A study of the stripe domain phase at the spin reorientation transition of two-dimensional magnetic system

Stripe domain phase in a two-dimensional magnetic system was studied using model calculation and Monte-Carlo simulation in the spin reorientation transition (SRT) region. We find that near the SRT point the stripe domains evolve into a static spin wave structure with a fractional in-plane magnetization along the stripe direction and a fractional out-of-plane magnetization in a sinusoidal form. With increase in the uniaxial perpendicular anisotropy, both the wavelength and the height of the static spin wave increase slowly until the saturation of the wave height, after which the stripe width increases exponentially with the magnetic anisotropy. Our theoretical result is in good agreement with experimental observations.     

Current induced domain wall motion in GaMnAs close to the Curie temperature

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 D?ring 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.     

Thickness dependence of magnetic anisotropic properties of FeCoNd films

The magnetic FeCoNd films with thickness (t) from 50 to 166 nm were fabricated by RF magnetron co-sputtering at ambient condition. The amorphous structures of all of the films were investigated by X-ray diffraction and transmission electron microscopy. A spin reorientation transition from in-plane single domain state to out-of-plane stripe domain state was observed as a function of t. When t is below a critical thickness, magnetic moments lie in the film plane corresponding to in-plane single domain state because of the strong demagnetization energy. However, when t is increased, out-of-plane stripe domain structure was developed due to a dominated perpendicular magnetic anisotropy. Scanning electron microscopy data indicate that the perpendicular anisotropy, which is responsible for the formation of stripe domains, may result from the shape effect of the columnar growth of the FeCo grains.     

Stripe domain statics in garnet films

Magnetic garnet films grown epitaxially on nonmagnetic garnet substrates exhibit a growth or stress-induced uniaxial anisotropy in addition to the cubic magnetocrystalline anisotropy associated with their crystal symmetry. When the uniaxial anisotropy is dominant over the cubic, such films exhibit stripe or bubble domain structures; even a small cubic anisotropy component can have a decisive effect on the behavior of the domains in applied fields. We report an experimental study of the quadistatic behavior of domains in fields applied to a (111) film in the film plane along (11$\text{2}$) and ($\text{1}$10). The experimental results are interpreted by a new theory that gives good agreement with the observed behavior, and yields an accurate measurement of the cubic and uniaxial anisotropy constants.The main qualitative features of the results are: In a ($\text{1}$10) field, the walls are Neél walls perpendicular to the field. In a (11$\text{2}$) field the walls are Bloch walls parallel to the field, the domain magnetization in adjacent stripes is not symmetrical about the film plane, and adjacent stripes are not of equal width; the domain period first shrinks and then expands with increasing field; and even though the applied field has no component perpendicular to the film plane, the film develops a net perpendicular magnetic moment.     

Magnetic domain structures and magnetotransport properties in Co-Ag granular thin films

The magnetic microstructures and magnetotransport properties in granular Co_xAg_1-x films with 17%≤x≤62% were studied. Magnetic force microscopy (MFM) observations showed the presence of magnetic stripe domains in as-deposited samples with x≥45% and the evolution of the magnetic domain patterns to in-plane domains with annealing. A perpendicular magnetic anisotropy as high as about 8×10⁵ ergs/cc for as-deposited Co₆₂Ag₃₈ and about 6×10⁵ ergs/cc for as-deposited Co₄₅Ag₅₅ was observed by magnetization and torque measurements. With increasing annealing temperature, the perpendicular magnetic anisotropy became negative. The origin of the perpendicular magnetic anisotropy may be attributed to a rhombohedral distortion of the cubic cell due to residual substrate-film stresses. The magnetic stripe domains are the consequence of the interplay of the indirect or direct exchange, perpendicular magnetic anisotropy and dipolar interactions. Finally, magnetoresistance (MR) curves displayed training behaviours and different shapes when measured with different configurations (parallel, transverse and perpendicular). It is proposed that the existence and the evolution of the magnetic domain structures strongly affect the magnetotransport properties due to the extra contribution of the electron scattering at the domain walls. Furthermore, an anisotropic MR also contributes to the overall MR curves. Received: 2 March 2000 / Accepted: 28 March 2000 / Published online: 23 May 2001     

Magneto-optic study of the behavior of magnetic domains walls in ferrimagnetic garnet films placed over samples with in-plane magnetization

Magneto-optic (MO) imaging is based on Faraday rotation of a linearly polarized incident light beam illuminating a sensitive MO layer placed in close contact to the sample. For in-plane magnetized layers of Lu_3−xBi_x Fe_5−yGa_yO₁₂ ferrimagnetic garnet films, zig-zag domain formation occurs whenever the sample stray parallel field component changes sign. In this work we study the behavior of zig-zag domain walls that appear when the garnet is placed over samples with in-plane magnetization like audio tapes recorded with different signals. We describe the zig-zag walls considering the anisotropy, exchange and magnetostatic energies in the Neel tails and the contribution of an applied magnetic field. Using different recorded signals we have been able to control the gradient of stray parallel field component on the garnet, changing the distance between domains and the size of zig-zag walls. We could even avoid the appearance of these zig-zag domain walls and obtain closed domains structures. We also study the behavior of the domain walls when an external magnetic field is applied parallel to the sample.     

Deroughening of domain wall pairs by dipolar repulsion

As a magnetic domain wall propagates under small fields through a random potential, it roughens as a result of weak collective pinning, known as creep. Using Kerr microscopy, we report experimental evidence of a surprising deroughening of wall pairs in the creep regime, in a 0.5 nm thick Co layer with perpendicular anisotropy. A bound state is found in cases where two rough domains nucleated far away from one another and first growing under the action of a magnetic field eventually do not merge. The two domains remain separated by a strip of unreversed magnetization, characterized by flat edges and stabilized by dipolar fields. A creep theory that includes dipolar interactions between domains successfully accounts for (i) the domain wall deroughening as the width of the strip decreases and (ii) the quasistatic and dynamic field dependence of the strip width s.     

Kinetics of magnetization reversal in a thin La<Subscript>0.7</Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> manganite film

The kinetics of magnetization reversal of a thin LSMO film has been studied for the first time. It is shown that the magnetic domain structure critically depends on the conditions of structure formation. In the demagnetized state (after zero-field cooling from T _c ), a maze-like domain microstructure with perpendicular magnetization is formed in the film. However, after field cooling and/or saturating magnetization by a field of arbitrary orientation, the [110] direction of spontaneous magnetization in the film plane is stabilized; this pattern corresponds to macrodomains with in-plane magnetization. Further film magnetization reversal (both quasi-static and pulsed) from this state is implemented via nucleation and motion of 180° “head-to-head” domain walls. Upon pulse magnetization reversal, the walls “jump” at a distance proportional to the applied field strength and then undergo thermally activated drift. All dynamic characterisitcs critically depend on the temperature when the latter varies around the room temperature.     

Interface biquadratic coupling and magnon scattering in exchange-biased ferromagnetic thin films grown on epitaxial FeF2

The magnetic anisotropy of ferromagnetic (FM) Ni, Co, and Fe polycrystalline thin films grown on antiferromagnetic (AF) FeF(2)(110) epitaxial layers was studied, as a function of temperature, using ferromagnetic resonance. In addition to an in-plane anisotropy in the FM induced by fluctuations in the AF short-range order, a perpendicular (biquadratic) magnetic anisotropy, with an out-of-plane component, was found which increased with decreasing temperature above the AF Neél temperature (T(N) = 78.4 K). This is a surprising result given that the AF's uniaxial anisotropy axis was in the plane of the sample, but is consistent with prior experimental and theoretical work. The resonance linewidth had a strong dependence on the direction of the external magnetic field with respect to in-plane FeF(2) crystallographic directions, consistent with interface magnon scattering due to defect-induced demagnetizing fields. Below T(N), the exchange bias field H(E) measured via FMR for the Ni sample was in good agreement with H(E) determined from magnetization measurements if the perpendicular out-of-plane anisotropy was taken into account. A low field resonance line normally observed at H ≈ 0, associated with domain formation during magnetization in ferromagnets, coincided with the exchange bias field for T < T(N), indicating domain formation with the in-plane FM magnetization perpendicular to the AF easy axis. Thus, biquadratic FM-AF coupling is important at temperatures below and above T(N).     

Observation and theory of strong stripe domains in amorphous sputtered FeB films

Domain structures in thin sputtered amorphous FeB films are studied by means of the longitudinal Kerr effect. In addition to the irregular domain structure characteristic of soft magnetic materials, we observe in certain regions a fine equilibrium domain structure with periodicity of a few micrometers. The Kerr contrast indicates that the magnetization at the surface of the film lies partially along the stripe direction. These characteristics and the behavior in applied fields suggests that the domains are similar to type II “strong stripe domains” observed earlier in permalloy films. Extending an earlier theory by Hara, we use a stray-field-free model with tilted orthorhombic anisotropy to show that there are at least two qualitatively different strong stripe structures: type IIa with surface magnetization perpendicular to the stripes and type IIb with surface magnetization at least partially parallel to the stripes. Type IIb is favored when K_p/K₀<cos 2θ ₀ where K₀ is the anisotropy component with axis tilted by θ₀ out of the film plane, and K_p is an in-plane anisotropy perpendicular to K₀. Strong stripes in amorphous FeB appear to be type IIb while those in permalloy are usually type IIa.     

Altering the superconductor transition temperature by domain-wall arrangements in hybrid ferromagnet-superconductor structures

The [Co/Pt]n/Nb/[Co/Pt]n hybrids with perpendicular magnetic anisotropy reveal enhanced superconductivity with the presence, and the arrangements, of domain walls, where superconductivity persists. An in-plane field can manipulate the domain walls from labyrinth to stripe patterns and drive the hybrids from normal to superconducting. We observe anisotropic superconductivity in hybrids with stripe domains, along which enhanced superconductivity is realized.     

Domain wall creation in nanostructures driven by a spin-polarized current

We report on current-driven magnetization reversal in nanopillars with elements having perpendicular magnetic anisotropy. Whereas only the two uniform magnetization states are available under the action of a magnetic field, we observed current-induced Bloch domain walls in pillars as small as 50 x 100 nm(2). This domain wall state can be further controlled by current to restore the uniform states. The ability to nucleate and manipulate domain walls by a current gives insight into the reversal mechanisms of small nanoelements and provides new prospects for ultrahigh density spintronic devices.     

Dense skyrmion crystal stabilized through interfacial exchange coupling: Role of in-plane anisotropy

A Monte Carlo simulated-annealing algorithm was used to study the magnetic state in an in-plane helimagnet layer on triangular lattice that exchange couples to an underlayer with strong out-of-plane anisotropy. In the single helimagnet layer with in-plane anisotropy (K), the formation of labyrinthlike domains with local spin spirals, instead of parallel stripes, is favored, and these domains rapidly transform into dense skyrmion crystals with increasing interfacial exchange coupling (J′), equivalent to a virtual magnetic field, and finally evolve to an out-of-plane uniform state at large enough J′. Moreover, with increasing K, the skyrmion crystal state can vary from regular 6-nearest-neighboring circular skyrmion arrangement to irregular squeezed skyrmions with less than 6 nearest neighbors when the in-plane anisotropy energy is higher than the interfacial exchange energy as the skyrmion number is maximized. Finally, we demonstrated that the antiferromagnetic underlayer cannot induce skyrmions while the chirality inversion can be achieved on top of an out-of-plane magnetization underlayer with 180◦ domain walls, supporting the experimental findings in FeGe thin film. This compelling advantage offers a fertile playground for exploring emergent phenomena that arise from interfacing magnetic skyrmions with additional functionalities.     

Anisotropy of domain wall resistance

The resistive effect of domain walls in FePd films with perpendicular anisotropy was studied experimentally as a function of field and temperature. The films were grown directly on MgO substrates, which induces an unusual virgin magnetic configuration composed of 60 nm wide parallel stripe domains. This allowed us to carry out the first measurements of the anisotropy of domain wall resistivity in the two configurations of current perpendicular and parallel to the walls. At 18 K, we find 8.2% and 1.3% for the domain wall magnetoresistance normalized to the wall width (8 nm) in these two respective configurations. These values are consistent with the predictions of Levy and Zhang.     

Kinetics of magnetization reversal in a heterophase nanomagnet with spatially modulated anisotropy

Magnetization reversal modes in a thin-film NiFeCuMo ferromagnet (FM) with periodically varying in-plane anisotropy are studied by the magneto-optical indicator film (MOIF) technique. The uni-directional anisotropy in FM regions exchange-coupled to a FeMn antiferromagnet (AFM) film in the form of square mesh stripes is alternated by the uniaxial anisotropy in the FM regions inside this mesh. It is shown that the boundaries formed along the edges of these stripes, which separate FM regions with different anisotropy, crucially influence the kinetics of domain-structure transformation in both types of FM regions. It is established that the lateral exchange anisotropy in the ferromagnet, which is determined by the stabilization of the spin distribution in the FM layer along the FM-(FM/AFM) interface, leads to the asymmetry of the magnetization reversal in FM regions bordered with an FM/AFM structure. Anisotropy of the mobility of 180-degree “charged” and “uncharged” domain walls situated, respectively, perpendicular and parallel to the unidirectional anisotropy axis is revealed. The difference observed between the mobilities of charged and uncharged domain walls is attributed to the difference in the spin distribution in these walls with respect to the unidirectional anisotropy axis and is a key factor for the difference between the magnetization reversal kinetics in horizontal and vertical exchange-biased FM stripes. Drastic differences are revealed in the asymmetry of magnetization reversal processes in mutually perpendicular narrow stripes of FM/AFM structures. Possible mechanisms of magnetization reversal in low-dimensional FM-(FM/AFM) heterostructures are discussed with regard to the effect of domain walls localized on the edges of AFM layers.     

Magnetization distribution in magneto-optical medium on patterned substrate

A micromagnetic calculation of magnetization in a ferromagnetic thin film with a perpendicular magnetic anisotropy fabricated on a patterned substrate is carried out. The domain wall energy of pinning of domain walls between up and down magnetized domains is shown to be determined by geometry of substrate. Estimations of regions of stability of two different domain structures in the hexagonal lattice of circle patches are given.     

Influence of induced uniaxial anisotropy on the domain structure and phase transitions of yttrium-iron garnet films

The effect of induced uniaxial anisotropy on the properties and parameters of the domain structure and phase transitions in yttrium-iron garnet (YIG) films is investigated. Based on the measurements and the derived formulas we determine the difference between the magnetization and the uniaxial anisotropy field for each of the films. We have also measured the parameters of the domain structures and phase transitions of the films for the magnetization parallel and perpendicular to the projections of the [111] crystallographic axes onto the plane of the film. We find that films of pure YIG films grown in (111) are characterized by the existence of some critical value of the uniaxial anisotropy field. It is found that for films in which the uniaxial anisotropy field is larger than this critical value and films in which it is less than this critical value, such parameters of the domain structures as the ratio of the width of the domains to the film thickness, the orientation of the magnetization of the domains, the orientation of the domain boundaries, and the magnitudes of the phase transition fields differ substantially. Fiz. Tverd. Tela (St. Petersburg) 41, 2034–2041 (November 1999)