Types Of Domain Walls Research Articles

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.

Hysteresis phenomena in permalloy–niobium bilayer films

Kinetics of magnetization reversal is studied in bilayer permalloy–niobium hybrid nanofilms by means of a magneto-optic visualization technique. The Nb-sublayer is found to affect the width of magnetic domain walls, the type of the walls, the orientation of the walls, and the kinetics of magnetization reversal in permalloy. Moreover, the low temperature magnetization reversal dependence upon the high temperature prehistory is revealed for a permalloy layer with domain walls of Bloch type. The niobium retains the information about a magnetic pattern freezed in permalloy and causes its reproduction during magnetization reversal. The “memory” is intact under magnetic field cycling as well as under a current flow. The effect demonstrates the efficiency of magnetic pinning and opens a new method for reversible variation of electromagnetic properties of hybrid devices.

Ferroelectric Domains in MultiferroicBiFeO3Films under Epitaxial Strains

First-principles calculations are performed to investigate energetic and atomistic characteristics of ferroelectric domains walls (DWs) of BiFeO(3) (BFO) films subject to compressive strain. Significantly lower DW energies than those previously reported, and a different energetic hierarchy between the various DW types, are found for small strains. In all investigated cases (corresponding to ideal angles of 71°, 109°, and 180° formed by the domain polarizations), the DW energy reaches its maximum value for misfit strains that are around the critical strain at which the transition between the R-like and T-like phases occurs in single-domain BFO. Near these strains, several quantities depend strongly on the type of domain wall; such distinct behavior is associated with an elastic difference and a large out-of-plane polarization at the DW in the 180° case. A further increase of the magnitude of the strain leads to (i) a change of hierarchy of the DW energies, (ii) large out-of-plane polarizations inside each up and down domain, and (iii) novel atomic arrangements at the domain walls. Our study can thus initiate a new research direction, namely strain engineering of domain-wall functionalities.

Domain structure and magnetization of the permalloy/niobium bilayers

Domain structure and kinetics of the magnetization reversal in the Py/Nb bilayers grown with lift-off lithography have been studied using visualization by magneto-optical indicator film technique. Various types of domain walls and switching behavior are observed depending both on film and substrate thickness. The observed transformations of the domain structure are in agreement with the model, which takes into account effective surface anisotropy governed by surface roughness, while influence of the misfit-induced elastic strain is found to be negligible.

Effect of magnetic surface anisotropy on domain wall structure in magnetic triaxial films

The influence of the presence of surface anisotropy on the micromagnetic structure of the domain wall in magnetic-triaxial films has been investigated. The investigation method is the numerical minimization of the energy functional of the domain wall used in the two-dimensional model of the distribution of magnetization. Films with different orientations of crystallographic axes with respect to the film surface have been considered. The effect of the surface anisotropy type and surface anisotropy constant K S value on the stability of different types of domain walls has been found.

Real-space imaging of ferroelectric and structural antiphase domains in hexagonal YMnO3

A high-angle annular-dark-field (HAADF) imaging technique was applied to the investigation of domain wall structures in the ferroelectric phase of hexagonal manganites, YMnO3, on an atomic scale. The displacements of the Y3+ ions along the [001] direction can be clearly visualized. The ferroelectric dipole moments are revealed to be caused by the opposite and unequal displacements of Y3+ ions. Two types of domain walls should be identified in the ferroelectric domain structures. One is charged longitudinal domain walls with head-to-head or tail-to-tail configurations and the other is non-charged transverse domain walls with head-to-tail configurations. In addition, the ferroelectric and the structural antiphase domains in YMnO3 change into fragmentary domains because of substitution of Ti4+ for Mn3+, and ferroelectric nanodomains with sizes of 10–20 nm are found in the x = 0.30 compound.

Simulation of three-dimensional micromagnetic structures in magnetically uniaxial films with in-plane anisotropy. Dynamics and structural reconstructions

Transition processes in nonequilibrium micromagnetic structures that represent regions of various types of asymmetrical vortex domain walls with closely spaced transition structural elements, including vertical Bloch lines (VBLs), singular points, and clusters consisting of VBLs and singular points, have been studied by the method of threedimensional nume rical simulation of the magnetization behavior. The realization of vari� ous scenarios of dynamic behavior, including the annihilation of transition elements accompanied by the liber� ation of energy and the initiation of wave processes, has been shown to be possible. The simulation was per� formed for the case of magnetically uniaxial ferromagnetic films with an easy axis parallel to their surface with exact allowance for the inhomogeneous exchange, magnetoanisotropic, and magnetostatic interactions.

Control of the magnetization in pre-patterned half-metallic La0.7Sr0.3MnO3 nanostructures

The evolution of the magnetization configurations in highly spin polarized La0.7Sr0.3MnO3 (LSMO) thin film elements (20–60 nm in thickness) as a function of external magnetic field and temperature is studied by direct magnetic imaging using x-ray magnetic circular dichroism photoemission electron microscopy. The sample structuring is done via a pre-patterning process using a Cr mask layer. The LSMO grows amorphous on the Cr layer for the 20 nm thick film but polycrystalline at larger thicknesses. Temperature dependent studies allow for a direct comparison of the properties of the strained and unstrained LSMO regions on a single sample and show that the polycrystalline areas exhibit a higher TC compared to the epitaxial areas. The single crystalline areas are largely magnetically decoupled from the matrix. The magnetic switching between domain states and domain wall spin structures is determined for LSMO ring elements of varying size and thickness. We find that the magnetic field values required to depin domain walls or to nucleate domains increase with decreasing ring width due to the increasing role of shape anisotropy and edge defects. Both transverse and vortex domain walls are stable spin configurations at room temperature and at zero field. In particular, we demonstrate that the desired domain wall type can be selected by applying an appropriate field sequence.

Domain growth kinetics in La0.89Sr0.11MnO3 single crystal studied by piezoresponse force microscopy

Ferroelectric-like nanodomains have been written by applying voltage pulse of different durations to the surface of La0.89Sr0.11MnO3 manganite single crystals and subsequently examined by the piezoresponse force microscope (PFM) technique. The domain wall velocity was then calculated based on conventional PFM procedure. A transition from the non-activated to the activated type domain wall motion has been observed due to the inhomogeneous spatial variation of the tip-induced electric field. The maximum domain size that can develop in a non-activated motion process has been found to be ∼170 nm. The formation of these ferroelectric-like nano domains at room temperature by PFM has been rationalized within phenomenological model based on Landau-Ginzburg formalism. Written domains are sufficiently stable and are attractive for device applications in nonvolatile random-access memories and development of metamaterials.

Influence of transverse fields on domain wall pinning in ferromagnetic nanostripes

We report an experimental study dealing with the influence of in-plane transverse fields on the domain wall (DW) pinning in ferromagnetic nanostripes. We analyzed the pinning probability and depinning fields for several fabrication induced pinning sites. For all measurements reported here, the depinning field decreases with increasing transverse field independently from the actual domain wall type and the shape of the pinning site. The pinning probability decreases with increasing transverse fields for weak pinning sites. Stronger pinning sites can be active for large field ranges and show a complex dependence of the pinning probability on the applied transverse field. The occurrence of different domain wall types as well as the influence of a transverse field on the domain wall dynamics can explain this behavior.

Concepts and steps for the realization of a new domain wall based giant magnetoresistance nanowire device: From the available 24 multiturn counter to a 212 turn counter

Two concepts for new types of a magnetic domain wall (DW) based multiturn counter with true power on functionality are presented. Both counters use several closed loops of magnetic nanowires, each with different numbers of cusps. The turns are counted by the motion of domain walls through the loops, whereas a DW will move through one cusp during 90° external field rotation. Two concepts are introduced: a system based on binary logic, which is easy to integrate in digital electronics, and a system based on coprime numbers, which is useful to count large numbers. We have performed micromagnetic simulations in order to optimize the geometry of the cusp with respect to the operation margin of the device. Experimental verification of the domain wall motion through a giant magnetoresistance stack cusp is given. Furthermore, the read-out scheme for both systems is shown.

Topology of solitary magnetic inhomogeneities in a thin ferromagnetic film

We investigate the influence of demagnetizing fields on the conditions for the appearance of magnetic inhomogeneities of the type of 0-degree domain walls in thin ferromagnetic films and on their structure theoretically. We obtain expressions for demagnetizing fields generated by samples of a given geometry in the thin-film approximation and find the magnetization distributions for non-Bloch-type inhomogeneities and their stability region.

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.

CHIRAL ZERO MODES ON VORTEX-TYPE INTERSECTING HETEROTIC FIVE-BRANES

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8×E8 heterotic string theory to search for localized chiral zero modes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zero modes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zero modes, one of which has opposite chirality to the other two. This agrees with the result previously obtained in the domain-wall type solution, supporting the claim that there exists one net chiral zero mode localized on the heterotic five-brane system.

Three-dimensional spin orientation in antiferromagnetic domain walls of NiO studied by x-ray magnetic linear dichroism photoemission electron microscopy

A determination of the three-dimensional spin directions in all types of domain walls (DWs) of antiferromagnetic NiO has been successfully performed by photoemission electron microscopy combined with x-ray magnetic linear dichroism (XMLD), both for $s$- and $p$-polarized light. By comparing the azimuthal angle dependence of the XMLD contrast in the DWs with cluster model calculations which include the crystal symmetry and full-multiplet splitting, we determine the spin structures in the ${001}$ T walls, ${011}$ T walls, 120\ifmmode^\circ\else\textdegree\fi{} S walls, and 180\ifmmode^\circ\else\textdegree\fi{} S walls. In some cases, distinct S walls are not formed between two adjacent S domains, and the spin direction changes gradually over a wide range of the S domain structures. In the S walls, the spin direction is parallel to the magnetic easy ${111}$ plane. These spin configurations arise from the large difference in anisotropy energy between the in-plane and out-of-plane directions. Unexpectedly large widths in the several hundred nanometer range were observed for all the DWs. This also shows that NiO has a small magnetocrystalline anisotropy energy. Together with Monte Carlo simulation results, the qualitative phenomena concerning the wall energies are discussed. We further investigated the difference in wall energy between the ${001}$ T wall and the ${011}$ T wall. From the Monte Carlo simulation and an experimental study of heating effects, it is revealed that the ${001}$ T wall energy is smaller than the ${011}$ T wall energy.

Vortex Domain Walls in Helical Magnets

We show that helical magnets exhibit a nontrivial type of domain wall consisting of a regular array of vortex lines, except for a few distinguished orientations. This result follows from topological consideration and is independent of the microscopic models. We used simple models to calculate the shape and energetics of vortex walls in centrosymmetric and noncentrosymmetric crystals. Vortices are strongly anisotropic, deviating from the conventional Berezinskii-Kosterlitz-Thouless form. The width of the domain walls depend only weakly on the magnetic anisotropy, in contrast to ferromagnets and antiferromagnets. We show that vortex walls can be driven by external currents and in multiferroics also by electric fields.

A simple model for calculating magnetic nanowire domain wall fringing fields

We present a new approach to calculating magnetic fringing fields from head-to-head type domain walls (DWs) in planar magnetic nanowires. In contrast to calculations based on micromagnetically simulated structures the descriptions of the fields are for the most part analytic and thus significantly less time and resource intensive. We begin with an intuitive picture of DWs, which is built upon in a phenomenological manner. The resulting models require no a priori knowledge of the magnetization structure, and facilitate calculation of fringing fields without any free parameters. Comparisons with fields calculated using micromagnetic methods show good quantitative agreement. We demonstrate that parameters key to atomic physics applications can easily be calculated with errors of around 10%. The model we present has greatest accuracy and hence utility for distances roughly greater than the width of the DW under consideration.

Nanoscale diffraction imaging of the high-pressure transition in Fe1−xO

To further understand the long-debated origin of the high-pressure cubic-rhombohedral transition in FeO, we investigated the domain wall structure in Fe0.94O using high-pressure microdiffraction imaging techniques. The results reveal a non-reflection type domain wall structure forming due to the cubic-rhombohedral transition in Fe0.94O, which suggests the transformation could be associated with defects and is unlikely to be ferroelastic in nature.

Dynamics of domain walls in weak ferromagnets with quadratic magnetoelectric interaction

The dynamics of domain walls of the ab type in weak ferromagnets with a quadratic magnetoelectric interaction has been studied in ac magnetic and electric fields. The specific features of the vibrational and drift motions of the domain walls as functions of parameters of the external fields and characteristics of the material have been discussed. The possibility of drift occuring the domain walls in a purely electric field has been predicted.

Remote domain wall chirality measurement via stray field detection

We have calculated magnetostatic fields from transverse and vortex magnetic domain walls in a planar Ni81Fe19 nanowire using micromagnetic simulations. Magnetic fields were calculated either side of the wire in the wire plane. Asymmetries in the stray field from the two types of domain walls can be understood in terms of monopole, dipole and quadrupole contributions. These calculations indicate the required sensitivity of a nearby sensor for domain wall detection or being able to distinguish domain wall character. We demonstrate this by modeling the electrical response of a magnetoresistive multilayer element to a domain wall in a nearby magnetic nanowire.