Straight Domain Wall Research Articles

Unique vortex and stripe domain structures in PbTiO 3 epitaxial nanodots

The domain structures of PbTiO 3 epitaxial nanodots under the influences of depolarization fields and mismatch strains have been studied using three dimensional phase field simulations. The single-vortex structure and mixed domain configuration, which consisted of zigzag stripe domain and closure dipole flux near the interfaces, were found to be effective in annihilating the depolarization fields in the isotropically tensile and compressive ferroelectric nanodots, respectively. These domain structures were produced by the combined effect of electrostatic and mismatch elastic energies. The width of stripe domain was found to be related to the volume percentage of polarization dipoles along the z-axis, which varied remarkably with the change of compressive mismatch strain. In the case of nanodots under anisotropic mismatch strains, double-vortex domain patterns and stripe domains with nearly straight domain walls were formed. Moreover, the domain structures with electrostatic energy neglected were also studied.

Nanomechanical torque magnetometry of permalloy cantilevers

There is mounting interest in bridging the fields of nanomechanics and nanomagnetism. Metallic nanocantilevers, which are magnetic throughout their volume, were fabricated using permalloy in order to detect domain switching along the cantilever length through mechanical deflection driven by magnetic torque. A finite element model describing the interaction of the magnetization of the cantilever with an external driving field is discussed, and illustrated for the simple example of magnetization reversal via propagation of a straight domain wall. The interferometrically obtained cantilever deflection through the magnetic actuation of the fundamental mode exhibits magnetic hysteresis. The experimental results are also compared to the finite element mechanical transformation of the output from a Landau–Lifshitz–Gilbert based micromagnetic simulation of the hysteresis.

Enhanced soft magnetic properties and magnetocaloric effect in B substituted amorphous Fe–Zr alloy ribbons

Abstract Magnetic properties and magnetocaloric effect in amorphous Fe 89− x B x Zr 11 ( x = 0–10) alloys prepared by melt spinning technique have been investigated. The crystallization temperature, Curie temperature ( T C ), and room temperature saturation magnetization ( M S ) of the alloys increase almost linearly with B addition. Coercivity decreases from 13 Oe to 0.015 Oe with the addition of 5 at.% B and then increases to 0.063 Oe for the alloy with 10 at.% B. Low temperature thermomagnetization curves of Fe 89 Zr 11 alloy show a bifurcation between field-cooled and zero-field-cooled curves below 35 K. No such bifurcation was observed in the alloys containing B. High temperature thermomagnetic curves indicate an amorphous-to-crystalline transition above 800 K corresponding to the precipitation of α-Fe phase. These studies reveal that addition of B not only enhances the crystallization temperature, but also decreases the degree of competition between ferromagnetic and antiferromagnetic interactions and there by enhances the soft magnetic nature of the alloys. Magnetic domain structure shows large-sized domains with smooth and relatively straight domain walls for the Fe 84 B 5 Zr 11 alloy. The magnetic domain structure analysis is used to understand the origin of the ultralow coercivity in these alloys. Due to the enhanced soft magnetic properties of these alloys and the possibility of tuning T C and M S by B addition, change in magnetic entropy (Δ S M ) was also investigated. Δ S M showed enhancement from 1.3 J/(kg-K) for the Fe 89 Zr 11 alloy to 1.73 J/(kg-K) for the Fe 79 B 10 Zr 11 alloy for a field change of 0–18 kOe.

Control of lateral domain spreading in congruent lithium niobate by selective proton exchange

Proton exchange was observed to increase the poling voltage for congruent lithium niobate. Patterned proton exchange was then used to control domain nucleation and inhibit broadening of reversed domains. Periodically proton exchanged samples were used to form domain gratings by electric field poling just using planar electrodes and without need for poling current control. The reversed domain gratings had a duty cycle faithfully reproducing that of the proton exchanged pattern with straight domain walls parallel to the x face, thus demonstrating that high-fidelity reversed domain patterning is possible to obtain by a relatively simple process.

Direct observation of magnetization reversal in thin Nd2Fe14B film

By utilizing a sharp magnetic needle made of a sintered Nd2Fe14B permanent magnet, we were able to produce a strong magnetic field of up to approximately 560kA∕m in a transmission electron microscope and succeeded in observing the magnetization reversal in a thin film of sintered Nd2Fe14B by in situ Lorentz microscopy. The increase in the magnetic field induced by the magnetic needle led to a pair of straight magnetic domain walls forming abruptly from the grain boundary. The successive nucleation in the neighboring grain started at the grain boundary adjacent to the magnetic domain wall formed first. Eventually, the magnetic domain walls in the neighboring grains connected and moved continuously and finally disappeared.

Ferroelectric domain structures in SrBi2Nb2O9 epitaxial thin films: Electron microscopy and phase-field simulations

Ferroelectric domain structures of (001)SrBi2Nb2O9 epitaxial films, investigated using both transmission electron microscopy and phase-field simulations, are reported. Experiment and numerical simulation both reveal that the domain structures consist of irregularly shaped domains with curved domain walls. It is shown that the elastic contribution to domain structures can be neglected in SrBi2Nb2O9 due to its small ferroelastic distortion, less than 0.0018%. Two-beam dark-field imaging using reflections unique to domains of each of the two 90° polarization axes reveal the domain structure. Phase-field simulation is based on the elastic and electrostatic solutions obtained for thin films under different mechanical and electric boundary conditions. The effects of ferroelastic distortion and dielectric constant on ferroelectric domains are systematically analyzed. It is demonstrated that electrostatic interactions which favor straight domain walls are not sufficient to overcome the domain wall energy which favors curved domains in SrBi2Nb2O9.

The corkscrew instability of a Fréedericksz domain wallin a nematic liquid crystal

A liquid crystal with slightly positive dielectric anisotropy isinvestigated in the planar configuration. This system allowsfor competition between electroconvection and the homogeneousFréedericksz transition, leading to a rather complicatedbifurcation scenario. We report measurements of a novel instability leading to the `corkscrew' pattern. This state isclosely connected to the Fréedericksz state as it manifestsitself as a regular modulation along a Fréedericksz domainwall, although its frequency dependence indicates thatelectroconvection must play a crucial role. It can beunderstood in terms of a pitchfork bifurcation from a straightdomain wall. Quantitative characterization is performed in terms ofamplitude, wavelength and relaxation time. Its wavelength is ofthe order of the probe thickness, while its ondulationamplitude is an order of magnitude smaller. The relaxation time is comparable to the one obtained for electroconvection.

On the orientational relief of the intermolecular potential and the structure of domain walls in fullerite C60

A simple planar model for an orientational ordering of threefold molecules on a triangular lattice modeling a close-packed (111) plane of fullerite is considered. The system has 3-sublattice ordered ground state which includes 3 different molecular orientations. There exist 6 kinds of orientational domains, which are related with a permutation or a mirror symmetry. Interdomain walls are found to be rather narrow. The model molecules have two-well orientational potential profiles, which are slightly effected by a presence of a straight domain wall. The reason is a stronger correlation between neighbor molecules in the triangular lattice versus the square lattice previously considered. A considerable reduction (up to one order) of the orientational interwell potential barrier is found in the core regions of essentially two-dimensional potential defects, such as a three-domain boundary or a kink in the domain wall. For ultimately uncorrelated nearest neighbors the height of the interwell barrier can be reduced even by a factor of 102.

Magneto-optical observation of the latchup effect in CMOS ICs induced by uniform and local irradiation

A new application of garnet films with high Faraday rotation—the first direct observation of latchup effect in serially produced complementary metal-oxide-semiconductor integrated circuits (CMOS ICs)—is reported. The visualization method based on the formation of straight domain walls inside magneto-optical films along electrical current path in ICs is used. The influence of spatially uniform or focused laser irradiation on the latchup configuration and thresholds is discussed.

Magnetic domains and anisotropy in ultrathin Au/Co/Au wedges deposited on sapphire substrates

Ultrathin cobalt wedges Au/Co( d<3 nm)/Au(1 1 1)/Mo/Al 2O 3, grown by MBE, were investigated by using the polar Kerr effect. The magnetic anisotropy constants were determined in a wide thickness range. With increasing cobalt thickness d a second order phase transition occurred from an easy magnetization axis through an easy cone into an easy plane state. A straight domain wall geometry, observed for small d, complicates while increasing d. A spontaneous demagnetization below the reorientation region was deduced.

Magnetic domain structure and exchange coupling in epitaxial Fe/FeRh([formula omitted]) and NiFe/FeRh([formula omitted]) bilayers

Magnetic domain structure related to a coercivity mechanism in Fe/FeRh(001) exchange coupled ferromagnet/antiferromagnet bilayers was studied as a function of Fe layer thickness, tFe, by magnetic force microscopy (MFM). Magnetooptic magnetometry revealed coercive fields reaching a value of 250 Oe at tFe=5 nm and decreasing down to 80 Oe at tFe=20 nm. In as-grown specimens with tFe>20 nm, the MFM images show micron-scale magnetic domains with rather straight domain walls parallel or perpendicular to [110] crystallographic direction of the Fe film. For tFe<20 nm, fine and random magnetic patterns composed of small elements with a lateral size of 200–300 nm are observed. For tFe<4 nm these elements are separated. With increasing tFe they start to gather and form complicated elongated island objects. Mechanism to form such very small elements in the Fe layer is thought to be the fine magnetic structure of the underlying FeRh–Ir layer, i.e. to the excessive magnetic charges at terrace edges and screw dislocations or to a related domain structure of the antiferromagnetic layer.

Kerr microscopy of small synthetic Ti‐rich titanomagnetite grains

Magnetic domain structure observations have been carried out on small synthetic Ti‐rich titanomagnetite (TM) grains (ulvöspinel content 50%–70%) employing the magneto‐optical Kerr effect (MOKE). On randomly oriented grains simple domain structures with planar domains or complex domain structures with curved domains and reverse spike domains have been observed. In addition to the description of the domain pattern, a qualitative determination of the magnetization direction within the domains is presented. Planes with a magnetization parallel to the surface show broad domains with nearly straight domain walls while planes with a magnetization normal to the surface show narrow domains and more complex patterns. With the help of the observed domain patterns on the randomly oriented grains and the knowledge about the magnetization direction within the domains a three‐dimensional (3‐D) domain structure model for Ti‐rich TM is proposed. These Ti‐rich titanomagnetites have only one easy direction of the magnetization and show a real unaxial character, although the magnetic mineral is cubic.By analysing the domain structure of more than a hundred TM particles in a range of size between 1.7 and 20 microns the transition from the single‐domain (SD) to the multidomain (MD) state is determined. The fit of the data in this study gives a critical SD size of ≈ 1.1 µm for Ti‐rich TM.

Theory for the magnetic phase diagram of thin films: Role of domain formation.

The magnetic phase diagram of a thin film is determined at T=0. The exchange coupling, the magnetic dipole coupling, as well as the second- and fourth-order lattice anisotropies are taken into account. The long-range dipole coupling causes an instability of the uniform magnetization with perpendicular orientation and leads to a domain phase. Four different phases, in particular stripe domain structures with perpendicular and canted orientations of the domain magnetization, are found to be stable. The parameter region near the magnetic reorientation is studied in greater detail. It is shown that the higher-order lattice anisotropies may induce a continuous reorientation from a perpendicular to an in-plane magnetization, also for a domain phase. By carrying out lattice sums we conclude that a periodic array of straight domain walls should be stable against spatial dislocations. Our results suggest that the domain phases may alter the nature of the phase transitions at finite temperatures in thin films. Rather than phase transitions with critical phenomena a simple rotation of the magnetization might occur.

Domain wall structures in an ordered Si/Fe(110) surface alloy

During the annealing process of an Fe96.5Si3.5(100)/(110) bicrystal, silicon and impurity carbon segregate to the surface. The structures formed by the segregands on the (110) surface have been studied by STM (geometry) and AES (chemical information). Silicon substitutes iron surface atoms and forms a two-dimensional alloy, whereas carbon occupies hollow sites in the first monolayer, leading to a distortion of the substrate lattice. The structures are based on a c(1 × 3)Si θ = 1/3 ordered surface alloy. Additional silicon as well as the co-segregating impurity carbon are inserted into this structure by formation of domain walls. If the density of these nearly straight and parallel domain walls becomes high enough, commensurate domain wall structures with c(1 × n) supercells can be observed.

T-Jz model on the Cayley tree and the square lattice.

Candidates for the ground state of the anisotropic t-${\mathit{J}}_{\mathit{z}}$ model at low hole doping are studied within two related lattices: the Cayley tree and the square lattice. The Cayley tree allows for the evaluation of the single hole as well as the hole-pair ground states to arbitrary precision. Threshold values for the formation of bound hole pairs appear to be similar for both lattices. We show that the main contributions to the binding of a hole pair on the Cayley tree comes from the excess number of frustrated bonds (``spinons''). Considering systems with a larger number of holes, we establish high stability of configurations with holes forming straight domain walls between nonequivalent antiferromagnetic domains. In particular, for the Cayley tree we find that domain-wall-like configurations have lower energy than separate hole pairs. For the square lattice, however, there exists at low but finite doping a parameter interval 0.18J/t0.56 where, in the ground state, holes are paired.

Single Bloch wall dynamics in amorphous ribbons: A comparison between experimental and theoretical results

A numerical approach is introduced to study the motion of a single bowed domain wall in an isotropic ferromagnetic lamination under general conditions of time dependence of the exciting magnetic field. A large set of numerical results concerning the behavior of Bloch walls in a magnetostrictive amorphous ribbon (Allied Signal Metglas 2605 SC), submitted to a sinusoidal field of varying amplitude and frequency is reported and discussed. The results are compared with the ones reported in the literature and obtained through different methods of calculation. The present approach allows one to get valuable information on the effect of wall bowing on the magnetic permeability, the so-called magnetic skin effect and the critical field which corresponds to a domain-wall instability resulting in wall multiplication. The peculiar behavior of the phase shift between wall oscillations at the lamination surface and within the lamination bulk appears to be very sensitive to the value of the wall’s surface energy density σw, at least within an appropriate frequency domain, thereby suggesting a reliable method of measuring this quantity. Actual measurements performed on a Metglas 2605 SC ribbon by using a Kerr-effect optical technique are reported and compared with the theoretical predictions. When a tensile stress of about 500 MPa is applied to this highly magnetostrictive material to provide a regular pattern of straight domain walls aligned along the ribbon axis, a value of σw=1.7×10−3 J/m2 is found. This value is consistent with the one calculated from the magnetostriction and the exchange energy coefficient of Metglas 2605 SC, which is between 1.4×10−3 and 1.8×10−3 J/m2. Measurements of the behavior of the wall oscillation amplitude as a function of the field intensity are also reported and discussed.

Experimenting with Bloch points in bubble garnets

The properties of vertical Néel lines containing one Bloch point (BP) are investigated experimentally. Lines contained in a single straight domain wall are observed by means of a direct optical technique, and the effect of a BP on its dynamic behaviour measured. The displacement of the BP proves to be relatively easy when compared to expectations.

Investigation of CoNiCr thin films deposited on

This paper reports on Co{sub 62.5} Ni{sub 30}Cr{sub 7.5} thin films that were sputtered onto (100) and (110) Cr single crystals as well as polycrystalline Cr TEM folls. VSM measurements have revealed the existence of an anisotropy in the in-plane coercivity. This stems from the development of a crystallographic texture in the plane of the film. TEM investigations have found the presence of crystallographic variants in the direction of the hcp c-axis in the CoNiCr films deposited on (100) and (110) Cr surfaces. Lorentz microscopy studies have found relatively straight domain walls which lie parallel to the specific crystallographic directions. The direction of magnetization within each domain is along the c-axis.

Bloch Line Propagation in Straight Domain Walls

Bloch Line Propagation in Straight Domain Walls

Domain structure and ambiguities in the dipole direction

A self-consistent mathematical formulation of the magnetization distribution in ideal soft-magnitude media, which is based on the constitutive equation previously derived from micromagnetic principles by the author, is presented. We confine ourselves to two-dimensional solenoidal distributions in thin-film objects. In particular, we focus on the magnetization distribution in elliptical objects, and Lagrange's method is used to solve the boundary-value problem. A function of the fourth degree in the magnetization direction results that gives rise to more than one real root for each location. We make a systematic inventory of the meaning of the various roots and construct magnetization distributions that satisfy the boundary conditions. We prove that the requirement of continuity of the magnetization distributions leads to the conclusion that the magnetization direction is multiple-valued in some regions and that the domain structure is required to prevent these ambiguities from occurring. We demonstrate both theoretically and experimentally that the simplest domain structure in an ellipse is formed by a simple, straight domain wall along the longitudinal symmetry axis of the ellipse.