Domain size and structure in exchange coupled [Co/Pt]/NiO/[Co/Pt] multilayers

We investigate the competing effects of interlayer exchange coupling and magnetostatic coupling in the magnetic heterostructure ([Co/Pt]/NiO/[Co/Pt]) with perpendicular magnetic anisotropy (PMA). This particular heterostructure is unique among coupled materials with PMA in directly exhibiting both ferromagnetic and antiferromagnetic coupling, oscillating between the two as a function of spacer layer thickness. By systematically tuning the coupling interactions via a wedge-shaped NiO spacer layer, we explore the energetics that dictate magnetic domain formation using high resolution magnetic force microscopy coupled with the magneto-optical Kerr effect. This technique probes the microscopic and macroscopic magnetic behavior as a continuous function of thickness and the interlayer exchange coupling, including the regions where interlayer coupling goes through zero. We see significant changes in domain structure based on the sign of coupling, and also show that magnetic domain size is directly related to the magnitude of the interlayer exchange coupling energy, which generally dominates over the magnetostatic interactions. When magnetostatic interactions become comparable to the interlayer exchange coupling, a delicate interplay between the differing energy contributions is apparent and energy scales are extracted. The results are of intense interest to the magnetic recording industry and also illustrate a relatively new avenue of undiscovered physics, primarily dealing with the delicate balance of energies in the formation of magnetic domains for coupled systems with PMA, defining limits on domain size as well as the interplay between roughness, domains and magnetic coupling.     

Domain formation in films of magnetic nanoparticles with a random distribution of anisotropy axes

A theoretical model describing the magnetization distribution in a system of closely packed ferromagnetic grains with a random distribution of easy magnetization axes is constructed. It is demonstrated that, in this system, the domain structure with domains characterized by a random distribution of magnetization axes is formed even if the magnetostatic energy is negligible and can be ignored. The domain size increases linearly with an increase in the ratio of the exchange energy of the interaction between grains to the anisotropy energy of a single grain. The inclusion of the magnetostatic energy only insignificantly changes the domain size but leads to the formation of a vortex magnetization distribution inside the domains. The behavior of the system is numerically simulated by the Monte Carlo method. The results of the simulation confirm the conclusions drawn from the theoretical model.     

Disordered domain structures and domain boundaries in thin magnetic films

The behavior of a disordered domain structure and domain boundaries with a change in temperature and magnetic field has been studied. The concept of magnetostatic pressure is used to explain the experimental results. It is shown that “the memory effect” and stability interval of a domain structure with a change in temperature or magnetic field depends on the degree of domain structure disorder and the domain boundary energy.     

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

Direct imaging of asymmetric magnetization reversal in exchange-biased Fe/MnPd bilayers by x-ray photoemission electron microscopy

X-ray photoemission electron microscopy is used to probe the remnant magnetic domain structure in high quality, single-crystalline, exchange-biased Fe/MnPd bilayers. It is found that the induced unidirectional anisotropy strongly affects the overall magnetic domain structure. Real space images of the ferromagnetic domains provide direct evidence for an asymmetric magnetization reversal process after saturation along the ferromagnetic hard direction. The magnetization reversal occurs by moment rotation for decreasing fields while it proceeds by domain nucleation and growth for increasing fields. The observed domains are consistent with the crystallography of the bilayers and favor a configuration that minimizes the overall magnetostatic energy of the ferromagnetic layer.     

Magnetization of the ferromagnetic-superconductor structures

The magnetization of a structure consisting of a thin superconducting film lying on a thin ferromagnetic substrate with uniaxial anisotropy is considered. It is shown that if a ferromagnet is in a multidomain state, then due to the presence of a superconducting film, the period of its domain structures decreases, which is caused by the increase of the magnetostatic energy of the system owing to Meissner currents. In a certain range of the constant of uniaxial anisotropy, under the action of a superconducting film, a domain structure may transform from a strip structure to the structure with closure domains. It is found that due to the nonuniform magnetic field of a multidomain ferromagnet, Abrikosov vortices may exist in a thin film only at certain parameters of the magnetic field.     

Analysis of checkerboard pattern in ultrathin magnetic films

We discuss the magnetostatic energy of checkerboard domain structures in ultrathin magnetic films (of a few monolayer thickness) and in an atomic monolayer using simple magnetostatic considerations where the easy direction of magnetization is perpendicular to the film. The checkerboard domain size, D, the domain-wall width, ω, the ratio f of the uniaxial surface anisotropy, K_s, to the dipolar energy and the binding energy, (BE), have been calculated numerically with the variational parameter δ and the number of atomic layers, n_l, as parameters.     

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.     

Domain wall orientation in magnetic nanowires

Scanning tunneling microscopy reveals that domain walls in ultrathin Fe nanowires are oriented along a certain crystallographic direction, regardless of the orientation of the wires. Monte Carlo simulations on a discrete lattice are in accordance with the experiment if the film relaxation is taken into account. We demonstrate that the wall orientation is determined by the atomic lattice and the resulting strength of an effective exchange interaction. The magnetic anisotropy and the magnetostatic energy play a minor role for the wall orientation in that system.     

Magnetic domain configurations in exchange-coupled NiO/Co bilayer films

The magnetic domain configurations of exchange-coupled NiO/Co bilayers were investigated by magnetic force microscopy. These bilayers exhibit a well-defined uniaxial anisotropy resulting from the deposition at oblique incidence of the NiO layer. Two types of magnetic contrast are identified: (i) bipolar contrast due to 180° Néel walls in the parts of the walls which are parallel to the easy axis of magnetization, and (ii) monopolar contrast in the parts of the walls separating domains with meeting head-on magnetizations. These latter domain walls have a zigzag shape which represents a compromise between a decrease in the local density of magnetostatic energy and an increase in the wall length. The effect of the Co thickness of the shape on the domains is also discussed.     

Domain-wall pinning by local control of anisotropy in Pt/Co/Pt strips

We theoretically and experimentally analyze the pinning of a magnetic domain wall (DW) at engineered anisotropy variations in Pt/Co/Pt strips with perpendicular magnetic anisotropy. An analytical model is derived showing that a step in the anisotropy acts as an energy barrier for the DW. Quantitative measurements are performed showing that the anisotropy can be controlled by focused ion beam irradiation with Ga ions. This tool is used to experimentally study the field-induced switching of nanostrips which are locally irradiated. The boundary of the irradiated area indeed acts as a pinning barrier for the domain wall and the pinning strength increases with the anisotropy difference. Varying the thickness of the Co layer provides an additional way to tune the anisotropy, and it is shown that a thinner Co layer gives a higher starting anisotropy thereby allowing tunable DW pinning in a wider range of fields. Finally, we demonstrate that not only the anisotropy itself, but also the width of the anisotropy barrier can be tuned on the length scale of the domain wall.     

Effect of magnetostatic pressure on the stabilization of a two-phase domain structure in thin garnet ferrite films

The coexistence of two domain phases, namely, a spiral domain and a bubble-domain lattice, is investigated experimentally in thin garnet ferrite films with uniaxial anisotropy. The condition for this coexistence is shown to be the equality of the magnetostatic pressures of the two phases. It is also shown that the possible formation of a spiral domain structure is determined by the magnetostatic pressure.     

Tuning magnetic properties of magnetoelectric BiFeO3-NiFe2O4 nanostructures

Multifunctional thin film nanostructures containing soft magnetic materials such as nickel ferrite are interesting for potential applications in microwave signal processing because of the possibility to shrink the size of device architecture and limit device power consumption. An essential prerequisite to future applications of such a system is a firm understanding of its magnetic properties. We show that nanostructures composed of ferrimagnetic NiFe₂O₄ pillars in a multiferroic BiFeO₃ matrix can be tuned magnetically by altering the aspect ratio of the pillars by depositing films of varying thickness. Magnetic anisotropy is studied using ferromagnetic resonance, which shows that the uniaxial magnetic anisotropy in the growth direction changes sign upon increasing the film thickness. The magnitude of this anisotropy contribution can be explained via a combination of shape and magnetostatic effects, using the object-oriented micromagnetic framework (OOMMF). The key factors determining the magnetic properties of the films are shown to be the aspect ratio of individual pillars and magnetostatic interactions between neighboring pillars.     

Quasiuniform in-plane magnetization state of thin cylindrical dots in a square array and related anisotropy

The energy (magnetostatic, exchange, and Zeeman terms) of a square array of cylindrical submicron dots made of soft ferromagnetic material is calculated analytically and minimized, taking into account the quasiuniformity of dot magnetization. The dependence of the equilibrium energy of the array on the direction of the externally applied magnetic field in the array plane is recovered, exhibiting the fourfold anisotropy. The anisotropy constant is calculated. Its values for different array geometries are in excellent agreement with the recent independent experiments. A new eightfold anisotropy effect is predicted. The theory involves no adjustable parameters.     

Effects of magnetic field on shape evolution of Fe–Co particles in a Cu matrix

The effects of magnetic field on the shape evolution of ferromagnetic fcc Fe–Co particles in Cu–0.83 at.% Fe–1.37 at.% Co alloy single crystals were examined using magnetic anisotropy measurements. The Cu–Fe–Co single crystals were aged at 993 K for 2 h to 24 h under a magnetic field of 10 T parallel to either the [001] or [011] direction. The magnetic anisotropy was examined by measuring magnetic torque around the (100) plane. It was found that the fcc Fe–Co particles are elongated in the direction parallel to the magnetic field. Furthermore, the elongation along [001] is more remarkable than that along [011]. The results are explained quantitatively by considering the minimization of the sum of the interface energy, elastic strain energy and magnetostatic energy of spheroidal particles.     

Layer-resolved microscopy of magnetic domains in multi-layered systems

Photoelectron emission microscopy in connection with magnetic circular dichroism in soft X-ray absorption can be used for the microscopic imaging of magnetic domains in layered thin film structures consisting of several magnetic layers. Due to the element-selectivity of the method, the different magnetic layers in such a structure can be imaged separately, provided that they contain different elements. This has been applied for the investigation of Co/Cu/Ni trilayers, epitaxially grown on Cu (001). The magnetic coupling between the Co and Ni layers can be directly visualized from comparing layer-resolved magnetic domain images of both layers. As a consequence of the competition between the anisotropy energies of the two magnetic layers and the magnetic coupling energy, spin-reorientation transitions between collinear and non-collinear magnetic configurations are observed. Apart from this globally observable magnetic interlayer coupling a micromagnetic coupling mechanism is also evident from the layer-resolved domain images. It is caused by magnetostatic interaction of local stray fields from domain walls. Received: 22 August 2002 / Accepted: 2 October 2002 / Published online: 5 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-345/5511-223, E-mail: kuch@mpi-halle.de     

On features of magnetization self-organization in 1D stochastic ferromagnetic systems

The magnetic structure of a polycrystalline nanowire at the weak or missing magnetostatic interaction exhibits the special self-organization of magnetization. As is known, the magnetization structure forming in a random crystallographic anisotropy field has a characteristic length range, which involves tens and hundreds of crystallites. This leads to the occurrence of stochastic domains. The induced uniform anisotropy of magnetostatic nature or the texture co-directed with the crystallite anisotropy axes masks the picture of stochastic domains. Nevertheless, as we show, the information on stochastic domains remains in the magnetization structure. The experimental techniques for obtaining information on the magnetic properties of stochastic domains are proposed.     

Uniaxial magnetic anisotropy in nanostructured Co/Cu(001): from surface ripples to nanowires

We have investigated the correlation between morphology and magnetic anisotropy in nanostructured Co films on Cu(001). The formation of nanoscale ripples by ion erosion is found to deeply affect the magnetic properties of the Co film. A surface-type uniaxial magnetic anisotropy with easy axis parallel to the ripples is observed. The origin of the magnetic anisotropy has been identified with the modification of thermodynamic-step distribution induced by ripple formation. At higher ion doses, when Co ripples detach and crystalline nanowires form, a strong enhancement of the magnetic anisotropy due to magnetostatic contributions is observed.     

Behavior of domain structure in a Co/Ag superlattice with dispersion of magnetic anisotropy

It is found that the magnetization reversal of an array of superthin Co films coupled by the ferromagnetic exchange interaction through the Ag layers may result in a domain structure of an unexpected new type. Due to the incoherent different-sense spin rotation upon lowering the field perpendicular to the easy axis, the specific macrodomains first form in a sample. They are separated not by the Neél domain wall but by a wide transition region containing high-density microdomains of sizes correlating with the grain sizes in the films. Further magnetization reversal proceeds through the formation of standard domain walls in the macrodomain in a magnetostatic field at the plate edge and through their shifting toward the transition region. These processes are explained with taking into account the character of the revealed magnetic anisotropy dispersion.     

Nonlinear reconfiguration of vortexlike domain walls in magnetically uniaxial films under the action of an external field normal to the easy magnetic axis

The effect of external magnetic field H normal to the anisotropy axis on the energy and configuration of vortexlike asymmetric magnetic walls in a magnetically uniaxial film with an easy magnetic axis parallel to its surface is studied. The investigation is based on minimizing the energy functional of the film with due regard to exchange energy, magnetic anisotropy energy, magnetostatic energy, and Zeeman energy. The range of H below the anisotropy field is found where the asymmetric Néel wall is stable, unlike the case H = 0, when the asymmetric Bloch wall is stable. It is shown that an asymmetric Bloch wall becomes absolutely unstable and reconfigures into an asymmetric Néel wall at some critical values of H = H _⊥. The dependences of critical field H _⊥ on the film thickness and saturation induction at different values of the anisotropy field are determined: field H _⊥ depends on the thickness nonlinearly and on the saturation induction nonmonotonically.