Domain walls, magnetization, and magnetoelectric effect in bismuth ferrite films

The specific features of the antiferromagnetic domain structure, magnetization, and polarization induced by an inhomogeneous micromagnetic distribution in films of bismuth ferrite multiferroics have been investigated. It has been shown that the magnetic domain structure correlates with the ferroelectric domain structure, and the character of the rotation of the antiferromagnetic vector depends on the type of ferroelectric domain walls. An asymmetry in the distribution of the antiferromagnetic vector has been observed for the cases of 109° and 71° ferroelectric domain walls. It has been demonstrated that there are differences in the distributions of the polarization and magnetization in bismuth ferrite films with ferroelectric domains separated by 109° and 71° walls. The basic mechanisms responsible for the magnetization in domain walls in multiferroics have been considered.     

Domain walls in magnetic multilayers with a biquadratic exchange

The structure of domain walls in magnetic multilayers is investigated taking into account the uniaxial anisotropy and biquadratic exchange between the layers. Analytical solutions are derived for different types of domain wall structures. The majority of the solutions obtained have no analogs in conventional magnetic materials. The thickness and the energy density per unit area are calculated for the domain walls under investigation. The range of parameters that correspond to more energetically favorable structures of domain walls is established.     

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.     

Domain structure of GaN/SiC-based materials for semiconductor lasers

The domain structure of GaN/SiC hexagonal semiconductor films has been studied using small-angle X-ray scattering in order to determine possible domain configurations in a GaN/SiC film that can influence the properties of the laser on its basis. Data on specific features of the samples, such as geometrical properties of clusters and the distances in superstructures (layers, superlattices), respectively, have been obtained by the processing of the small-angle X-ray scattering spectra according to Porod’s and Bragg’s models. A model of regular network of domain walls in GaN/SiC film has been proposed. The hypothesis on the formation of filamentary structures near the film-substrate interface has been confirmed.     

Depletion layers and domain walls in semiconducting ferroelectric thin films

Commonly used ferroelectric perovskites are also wide-band-gap semiconductors. In such materials, the polarization and the space-charge distribution are intimately coupled, and this Letter studies them simultaneously with no a priori ansatz on either. In particular, we study the structure of domain walls and the depletion layers that form at the metal-ferroelectric interfaces. We find the coupling between polarization and space charges leads to the formation of charge double layers at the 90 degrees domain walls, which, like the depletion layers, are also decorated by defects like oxygen vacancies. In contrast, the 180 degrees domain walls do not interact with the defects or space charges. Implications of these results to domain switching and fatigue in ferroelectric devices are discussed.     

Experimental investigation of the magnetic structure of domain walls in thin ferromagnetic films

The structure of domain walls in thin magnetic films has been studied by the Lorentz method using electron microscopy. The possible existence of the coinciding and opposite directions of rotation of the magnetization vector in Néel domain walls has been proved experimentally. The domain walls separating 90° domains have been found in single-crystal magnetic films. These walls consist of domains with a considerably smaller area than 90° domains.     

“Switching” phase transition of the nanodomain state of the frustrated ferromagnet-antiferromagnet system

The phenomenon of switching of the domain walls generated by frustrations in a two-layer ferromagnet-antiferromagnet nanostructure has been studied theoretically taking into account the energy of the uniaxial anisotropy beyond the exchange approximation. This phenomenon manifests itself in the fact that, as the magnetic field increases, the ferromagnetic layer divided into nanodomains by domain walls perpendicular to the layer plane becomes single-domain, and the antiferromagnetic layer that is uniform in weak fields is divided into 180° domains by the domain walls perpendicular to the layer. The phase diagram of the two-layer nanostructure has been constructed in the variables “the magnetic field-the characteristic distance between atomic step edges at the interface between the layers.”     

Evolution of domain structure and formation of charged domain walls during polarization reversal in lithium niobate single crystals modified by vacuum annealing

The evolution of the domain structure during polarization reversal has been investigated in plates of lithium niobate with spatially inhomogeneous electrical conductivity produced by vacuum annealing. The formation of charged domain walls in the crystal bulk has been studied. Revealed features of the domain growth in the bulk have been attributed to the formation of nanodomains under the pyroelectric field and inhomogeneous spatial distribution of the electric field. Creation of the charged domain walls with controlled parameters is of great interest for domain walls engineering.     

Reorientation,multidomain states and domain walls in diluted magnetic semiconductors

The competition between surface/interface and intrinsic anisotropies yields a number of specific reorientation effects and strongly influences magnetization processes in diluted magnetic semiconductors as (Ga,Mn)As and (In,Mn)As. We develop a phenomenological theory to describe reorientation transitions and the accompanying multidomain states applicable to layers of these magnetic semiconductors. It is shown that the magnetic phase diagrams of such systems include a region of four-phase domain structure with four adjoining areas of two-phase domains as well as several regions with coexisting metastable states. We demonstrate that the parameters of isolated domain walls in (Ga,Mn)As nanolayers are extremely sensitive to applied magnetic field and can vary in a broad range. This can be used in microdevices of magnetic semiconductors with pinned domain walls. For (Ga,Mn)As epilayers with perpendicular anisotropy the geometrical parameters of domains have been calculated.     

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     

Ferroelastic domain structure of (CH3)4N CdCl3 (TMCC) crystal

The ferroelastic domain structure and the phase boundaries of TMCC have been studied in the temperature range 114-90 K by direct observation under polarised light. By applying an external, compressive and unidirectional mechanical stress the ferroelastic character of the domain structure has been confirmed. The orientation of the domain walls and phase boundaries are analysed. To characterise quantitatively the observed domain wall distribution the classical symmetry approach, based on the criterion of spontaneous strain compatibility, has to be extended to allow small rotations of the domain walls with respect to their ideal orientation. The observed switching process among the different domains can be understood as a mechanism that minimises the elastic energy. Received 21 July 2000     

Effect of magnetoelectrical interactions on the multiferroic domain walls

The antiferromagnetic domain structure of a multiferroic has been investigated in the presence of a ferroelectric domain structure. It has been demonstrated that an inhomogeneous magnetoelectric (flexomagnetoelectric) interaction leads to pinning of antiferromagnetic domain walls at the walls of the ferroelectric domains and to a change in the structure of antiferromagnetic domain walls.     

Diffraction of light from a stripe domain structure with tilted domain walls

The intensity and polarization parameters of light waves diffracted from a stripe domain structure with tilted domain walls and the magnetic moment in domains oriented parallel to the walls are determined in the approximation of thin layers and linear magnetooptical coupling.     

Conversions of free wall clusters in soft magnetic layers

The theory of free clusters in thin soft magnetic layers has been further developed by investigating their conversions. A wall cluster is a collection of domain walls (considered to be infinitely thin surfaces over which the magnetization abruptly changes its direction) that have one intersection line, the so-called cluster knot, in common. The cluster knot of a free wall cluster does not coincide with any of the bounding edges of the magnetic geometry. The domain structure is considered as a concatenation of wall clusters, in which already existing clusters initiate the development of new ones, which subsequently provide for an extension in the domain structure. Only reversible changes in the domain structure are considered. In this context, the fact that the creation line is the orthogonal trajectory to a continuous magnetization field plays a crucial role in the creation of (sub)clusters. This takes place without having to overcome a threshold formed by the domain-wall energy. Concave and convex subclusters are defined in order to facilitate the analysis of the creation of new (sub)clusters. It is shown, among other things, that a concave subcluster consists of an even number of uniform domains. The part that these types of subclusters play in free-cluster conversions is demonstrated. Bifurcation of clusters has been considered in detail, and the boundaries of the sectors, in which the intermediate domain wall between both clusters has to be situated, are given. The theoretical findings are supported by experimental evidence.     

Origin and tailoring of the antiferromagnetic domain structure in α-Fe2O3 thin films unraveled by statistical analysis of dichroic spectromicroscopy (x-ray photoemission electron microscopy) images

The magnetic microstructure and domain wall distribution of antiferromagnetic α-Fe2O3 epitaxial layers is determined by statistical image analyses. Using dichroic spectromicroscopy images, we demonstrate that the domain structure is statistically invariant with thickness and that the antiferromagnetic domain structure of the thin films is inherited from the ferrimagnetic precursor layer one, even after complete transformation into antiferromagnetic α-Fe2O3. We show that modifying the magnetic domain structure of the precursor layer is a genuine way to tune the magnetic domain structure and domain walls of the antiferromagnetic layers.     

“Unusual” domain walls in multilayer systems: Ferromagnet + layered antiferromagnet

The structure and conditions for the onset of a new type of domain wall in multilayer systems comprising a ferromagnet and a layered antiferromagnet is investigated by numerical simulation. Domain walls occur as the result of frustrations produced by interface roughness, i.e., by the existence of atomic steps on them. The domain walls are investigated both in a ferromagnetic film on a layered antiferromagnetic substrate and in multilayer structures. It is shown that a domain wall broadens with increasing distance from the interface; this trend is attributed to the nontrivial dependence of the wall energy on the thickness of the layer. The structure of the domain walls in multilayer ferromagnet-layered antiferromagnet systems varies dramatically as a function of the energies of interlayer and in-layer exchange interactions between adjacent layers. Zh. éksp. Teor. Fiz. 114, 1817–1826 (November 1998)     

Shape instability in out of equilibrium magnetic domains observed in ultrathin magnetic films with perpendicular anisotropy

The magnetic configurations induced by the growth process in a thin film with perpendicular magnetisation have been observed by magnetic force microscopy (MFM). The FePd thin film has been grown by molecular beam epitaxy. A high uniaxial chemical ordering of the alloy into the tetragonal L1₀ structure induces the development of a large perpendicular anisotropy. As the growth process is performed below the Curie temperature of the FePd alloy, domain nucleation occurs during the growth process. The magnetic configuration has been imaged in the as grown state. As the equilibrium size of the magnetic domains decreases when the thickness of the layer increases, the domains obtained from spontaneous nucleation at the beginning of the growth of the thin film are submitted to very large strains as the layer thickness increases. At low thicknesses (low strains), the domain wall instability gives rise to an undulation of the domain walls. Thereafter, it leads to the formation of well-defined magnetic fingers, thus giving birth to the coexistence of two length scale in the domain structure. A quantitative estimation of the strain leading to the fingering instability is obtained. Last, the implications of these observations on the kinetic of domain wall distortion in ultrathin layers are discussed.     

Relaxation stimulated in the domain structure of a triglycine sulfate crystal by an alternating-current electric field

The relaxation of the domain structure in a triglycine sulfate crystal from a nonequilibrium state induced by an alternating-current electric field has been investigated. The distributions of the activation energy of the processes under consideration and the energy of interaction of domain walls with defects over the exciting fields have been obtained.     

Two-dimensional micromagnetic simulation of domain structures in films with combined anisotropy

The transformation of the domain structure of micrometer-thick films with variations in the induced uniaxial anisotropy constant with the easy magnetization axis perpendicular to the film surface has been investigated using numerical micromagnetic simulation in the framework of a two-dimensional model of the magnetization distribution. The case where the tetra-axial crystallographic anisotropy exists in the film with uniaxial magnetic anisotropy has been considered. The transformation of the open domain structure into the structure with a magnetic flux closed inside the sample has been investigated in detail, and new types of 109-degree and 90-degree vortex-like domain walls and periodic domain structures have been obtained.     

Magnetic phase diagram of a ferromagnet-antiferromagnet-ferromagnet spin-valve structure with rough interfaces

The thickness-roughness phase diagram of a ferromagnet-antiferromagnet-ferromagnet spinvalve system is studied in the case where the roughness of the interfaces between the layers causes frustration of the exchange interaction between them. It is shown that the inclusion of easy-axis single-ion anisotropy makes the phase diagram significantly more complicated in comparison with that calculated within the exchange approximation. A new type of domain walls (three-layered domain walls) is predicted to arise due to frustrations. It is shown that domain walls in the antiferromagnetic interlayer are switched when the parallel orientation of the magnetization vectors of the ferromagnetic layers changes to the antiparallel one.