Closure Domains Research Articles

Three-Dimensional Study of the Vector Potential of Magnetic Structures

The vector potential is central to a number of areas of condensed matter physics, such as superconductivity and magnetism. We have used a combination of electron wave phase reconstruction and electron tomographic reconstruction to experimentally measure and visualize the three-dimensional vector potential in and around a magnetic Permalloy structure. The method can probe the vector potential of the patterned structures with a resolution of about 13nm. A transmission electron microscope operated in the Lorentz mode is used to record four tomographic tilt series. Measurements for a square Permalloy structure with an internal closure domain configuration are presented.

Micromagnetic study of magnetic domains in platelets with perpendicular uniaxial anisotropy

This paper studies the domain configurations in platelets with perpendicular uniaxial anisotropy. Due to the large sample dimensions, one typically relies on the domain theory to describe the domain patterns. The growing computer resources make it however possible to perform full micromagnetic simulations on the domain scale. We compare the domain configurations obtained from micromagnetic simulations with those predicted by different domain theory models for a varying anisotropy strength Ku. It is found that the Landau structure is valid for small Ku, while the open Landau–Kittel structure only poorly describes the closure domains for higher Ku. The model proposed by Hubert, enabling closure domains with a tilted magnetization angle is the most accurate.

Ab initiostudy of ferroelectric closure domains in ultrathinPbTiO3films

Ab initio density-functional theory calculations within the local density approximation were conducted to elucidate whether critical thickness for ferroelectricity intrinsically exists in free-standing polydomain ${\text{PbTiO}}_{3}$ ultrathin films, where there was no screening effect of electrodes. The ferroelectric polydomain state was found to be energetically favorable over the paraelectric state even in the thinnest film one unit-cell thick, indicating no intrinsic critical thickness existed. The ferroelectric distortions in the film were stabilized by the formation of ferromagneticlike closure domains, because the surface charge, which caused a depolarizing field, was sufficiently screened by the in-plane aligned polarization at the surface. Further analysis of the covalent Pb-O bonding structure, which plays a central role in determining ferroelectricity in ${\text{PbTiO}}_{3}$, revealed that the closure domain structure consists of the $180\ifmmode^\circ\else\textdegree\fi{}$ as well as $90\ifmmode^\circ\else\textdegree\fi{}$ domain walls.

Magnetic domain structure and damping capacity of Fe-13Cr-2.5Mo alloy

The magnetic domain structure and damping capacity of Fe-13Cr-2.5Mo (wt. %) alloy have been investigated in this paper. Dynamic mechanical analyzer (DMA) was used to test the damping behavior. Bitter technique was used to observe the magnetic domain structures. The results show that the furnace cooled alloy exhibits significantly higher damping capacity than air cooled alloy. The cooling rate has great effects on morphology of magnetic domain structure. For furnace cooled alloy there are many ‘tree pattern’ domain structures, which contain relatively large volume fraction of 90° magnetic domain walls and favor the damping behavior. However, no ‘tree pattern’ structure exists in air cooled alloy and there are mainly closure and spike domains. The 90° domain walls in spike domain are almost nonexistent and the volume fraction of 90° domain walls in closure domain is small. In addition, the mobility of these both domain structures is relatively poor. Therefore, this alloy exhibits a worse damping behavior.

Transverse Field-Induced Nucleation Pad Switching Modes During Domain Wall Injection

We have used magnetic transmission soft X-ray microscopy (M-TXM) to image in-field magnetization configurations of patterned Ni80Fe20 domain wall ?nucleation pads? with attached planar nanowires. Comparison with micromagnetic simulations suggests that the evolution of magnetic domains in rectangular injection pads depends on the relative orientation of closure domains in the remanent state. The magnetization reversal pathway is altered by the inclusion of transverse magnetic fields. These different modes explain previous results of domain wall injection into nanowires.

Effect of the thickness of Fe-3% Si crystals on the dynamics of the domain structure and magnetic losses in rotating magnetic fields

The effect of the thickness of Fe-3% Si crystals with an easy axis deviated by an angle β = 2.5° from the surface plane on the dynamics of their domain structure and magnetic losses has been studied in rotating magnetic fields. It has been established that the role of the closure domain structure in the magnetization reversal of samples decreases continuously with decreasing crystal thickness down to the thickness d = 0.10 mm, whereas the contribution of the displacements of 180o domain walls of the stripe domain structure to the change in the magnetization of the samples increases. A number of specific features of their behavior in thin samples have been revealed, such as the presence of a strong inhomogeneity of the velocities of displacement of the 180° domain walls of the stripe domain structure and the absence of a refinement of this structure up to Bm = 1.8 T. The data on the dynamics of the domain structure are used for an analysis of the variation of magnetic losses of samples in rotating magnetic fields.

Nanoscale magnetic configurations of supported Fe nanoparticle assemblies studied by scanning electron microscopy with spin analysis

Microscopic magnetic behavior of supported nanoparticles is strongly correlated with their functionalities, especially in data storage and biological applications, but still needs to be clarified. We studied nanoscale magnetic configurations of Fe nanoparticle assemblies using scanning electron microscopy with polarization analysis. The flux closure domain configurations and the reduced magnetic correlation length $(\ensuremath{\sim}250\text{ }\text{nm})$, relative to the conventional thin films, are determined. Quantitative analysis indicates the magnetic interaction energy to be 80--99 meV, close to the magnetic dipolar coupling energy. These direct observations evidence the aforereported simulations and will be valuable for fabricating magnetic nanoparticle assemblies with the desired magnetic properties.

The influence of the geometry of micro-patterned thin films on the effective permeability and resonance frequency by domains development

For the application in high-frequency micromagnetic devices, the permeability and resonance frequency of ferromagnetic components is of high interest. It is dominantly influenced by different factors, the external field and direction and the domain distribution, shape and orientation. By the use of micromagnetic simulation, the domain pattern in films was determined and the effective permeability was calculated. The results of the calculations were compared with the domain shape of patterned microstructures of thin FeCoTaN-films, which were deposited onto oxidised silicon substrates by reactive r.f.-magnetron sputtering by employing 6-in Fe 37Co 46Ta 17 targets. To achieve a high-frequency suitability, the films have to be annealed in a static magnetic field of 50 mT between 400 and 500 °C, which are typical temperatures used in CMOS processes, to induce an in-plane uniaxial anisotropy needed for the high-frequency performance. Magnetic softness was obtained by producing amorphous or nanocrystalline films, and additionally, by aspiring low magnetocrystalline anisotropies for, e.g., certain Fe/Co fractions. The unpatterned films with a lateral dimension of 5×5 mm 2 were measured in a strip line permeameter in a frequency range up to 5 GHz and exhibited ferromagnetic resonance frequencies between 2 and 2.5 GHz within a low-loss permeability spectrum (low width of imaginary part of permeability). For possible integrations in passive microelectronic components the films were patterned to a few tenths of micrometers by near ultra-violet lithography and plasma beam etching, and then consequently annealed to obtain the static and dynamic magnetic properties. To influence the amount of closure domains, designs were conceived to influence the domain formation by creating additional internal boundaries. As a result, the ferromagnetic resonance frequency and the effective permeability are strongly driven by internal and external boundaries.

Calixarene-stabilised cobalt nanoparticle rings: Self-assembly and collective magnetic properties

Calixarenes can be used to promote the self-assembly of thermoremanent cobalt nanoparticles into bracelet-like rings below 100 nm in diameter. These kinetically stable assemblies are regulated by the equilibrium between enthalpic gain (dipole–dipole and long-range van der Waals interactions) and entropic loss, analogous to the thermodynamic balance of forces governing supramolecular self-assembly. Examination of the Co nanoparticle rings by electron holography (an electron microscopy technique for imaging in-plane magnetic induction) reveals the existence of chiral flux closure (FC) domains at room temperature, comprising a ‘racemic’ mixture of clockwise and anticlockwise states. Furthermore, these FC polarisations can be reversed by applying out-of-plane magnetic pulses (H z ) in alternating directions. This switching behaviour has no known analogy at the macroscopic level, and may represent a uniquely nanoscale phenomenon.

Development of MFM with Magnetic Fields Applied by Orthogonal Electromagnets and its Applications to Analysis of Magnetic Domain Structures

We developed a magnetic force microscope (MFM) where magnetic fields were applied by orthogonal electromagnets. This equipment can be used to observe magnetic domains by specifying an arbitrary angle while applying an external magnetic field of 5 kOe or less. A dot and a rectangular thin film made of permalloy were measured with this equipment. The chirality of the vortex state in the permalloy dot could be determined by using this apparatus. Furthermore, the shape of the closure domain changed every time the direction of the magnetic field was changed by 45 degrees. These results are discussed in detail together with the micromagnetics simulations.

High Sensitivity Spin Valve Sensors With AF Coupled Flux Guides

Giant magnetoresistive (GMR) sensors can have their field sensitivity enhanced by many fold if located in the gap of two magnetically soft flux-guides (FG). In this paper, we present spin valve (SV) sensors, with saturation fields of less than 3 Oe and high linearity characterized by coercive forces of less than 0.5 Oe. FG require magnetically soft thin films with thicknesses in the range of 100-500 nm . In previous work, we prepared single-layer (SL) films of amorphous Co 90.7(Zr-Nb)9.3 that exhibited stripe domains (SD) when patterned into FG, causing Barkhausen noise and complete lost of linearity in the SV sensors response. In this article, single layer films of an amorphous alloy of Co88.4Zr3.3Nb8.3 , patterned into flux guides, do not exhibit SD but well-behaved closure domains. Nevertheless, these induce hysteresis in the sensors response, characterized by a coercive force of 0.7 Oe. This hypothesis is corroborated by focused beam magneto-optic Kerr effect (MOKE) magnetometry, performed in the poles region the CZN FG. By contrast, FG integrating instead multilayer (ML) thin films consisting of ferromagnetic layers of permalloy weakly anti-ferromagnetically (AF) coupled through Ru interlayers cause a strong reduction of hysteresis in the SV sensors response. The sensors in the gap of AF coupled (NiFe/Ru)xn FG, exhibit saturation fields of about 2 Oe and coercive forces of 0.3 Oe, despite the fact that the isolated sensors exhibit coercive forces of 2 Oe.

Effects of internal stress on remanence intensity jumps across the Verwey transition for multi-domain magnetite

The magnetic properties of magnetite (Fe 3O 4) are strongly dependent on the internal stress related to stress-controlled regions and to closure domains associated with defects. The contribution of internal stress to the low-temperature magnetic properties of magnetite was tested using annealed and unannealed multi-domain (MD) magnetites. During low-temperature cooling, a room temperature-induced saturation isothermal remanent magnetization (SIRM) increased abruptly at the Verwey transition ( T v ∼ 122 K). In particular, the absolute intensity jump ( δ VJ, defined as the jump in SIRM at T v upon cooling) resulted from the high-coercivity fraction of MD grains. We observe that annealing significantly reduces internal stress and thus decreases the average microcoercivity. Comparison of the alternating field (AF) demagnetization spectra of δ VJ both for annealed and unannealed magnetites directly links δ VJ to the internal stress. It is likely that removal of the closure domain associated with stress-controlled regions was dominant when the peak AF was less than the average micromagnetic coercivity 〈 h c〉, resulting in a net increase of δ VJ with increasing AF. However, when the AF exceeded the 〈 h c〉 threshold, δ VJ decreased because the stress-controlled regions were demagnetized. Such observations could therefore be useful for estimating the 〈 h c〉 of MD magnetite.

Heat transfer in vacuum packaged microelectromechanical system devices

This study analyzes heat transfer effects inside vacuum packaged microelectromechanical system (MEMS) devices. A packaged device is simplified as four plates forming a square cavity, the bottom plate represents a hot chip, while the other three plates are maintained at room temperature. For a highly rarefied free molecular internal gas flow scenario, the corresponding detailed density and temperature fields are analytically determined with a proposed speculation. This speculation indicates that for a steady free molecular gas flow inside a convex closure domain formed by walls maintained at different temperatures: (1) the velocity distribution functions for those molecules diffusely reflected at different walls and traveling away from them are Maxwellian with different number densities; (2) for each distribution, niTi is a constant, where ni is the number density for the group of reflected molecules, and Ti is the temperature for the ith plate. For a near continuum flow scenario, the governing energy equation degenerates to Laplace’s equation with several temperature-jump wall boundary conditions. This study also includes discussions and comparisons among analytical results, simulation results from the direct simulation Monte Carlo method, and results by solving the Navier–Stokes equations with proper wall boundary conditions. The approach used in this study is generally applicable to study internal flows and heat transfer effects in other vacuum packaged MEMS devices with different shapes.

Micro-Brillouin Light Scattering Spectroscopy of Magnetic Nanostructures

We describe a new technique, micro-Brillouin light scattering spectroscopy, for investigation of spin wave dynamics in magnetic nanostructures. The technique offers advantages for studies of small magnetic squares with closure domain structure and magnetic nanoelements similar to those used in magnetic random access memory. The technique is particularly effective in two-dimensional mapping of spin waves excited by a single nanocontact due to the spin torque transfer effect.

Soft X-ray resonant magnetic scattering of magnetic nanostructures

Soft X-ray resonant magnetic scattering offers a unique element-, site- and valence-specific probe to study magnetic structures on the nanoscopic length scale. This new technique, which combines X-ray scattering with X-ray magnetic circular and linear dichroism, is ideally suited to investigate magnetic superlattices and magnetic domain structures. The theoretical analysis of the polarization dependence to determine the vector magnetization profile is presented. This is illustrated with examples studying the closure domains in self-organising magnetic domain structures, the magnetic order in patterned samples, and the local configuration of magnetic nano-objects using coherent X-rays. To cite this article: G. van der Laan, C. R. Physique 9 (2008).

Domain structures and the influence of current on domains and domain walls in highly spin-polarizedCrO2wire elements

We present a detailed study of the equilibrium magnetization configurations and their response to injected current pulses in microstructured $\mathrm{Cr}{\mathrm{O}}_{2}$ wire elements. Using magnetic force microscopy, we determine that the magnetic domain structure of $\mathrm{Cr}{\mathrm{O}}_{2}$ wires strongly depends on the wire geometry, in particular, on the wire width and the wire orientation with respect to the magnetocrystalline anisotropy axes. Depending on the wire geometry and the orientation of the initialization magnetic field used, single domain or closure domain configurations have been observed. The domain widths depend on the wire width and are very well reproduced by analytical calculations, as well as by micromagnetic simulations. Currents of up to $5.1\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{m}}^{2}$ were injected into the $\mathrm{Cr}{\mathrm{O}}_{2}$ wires at room temperature and found to alter their magnetic domain configuration. Temperature-dependent resistance measurements during the current pulse injection reveal the importance of Joule heating, which can raise the sample temperature above the Curie temperature of $\mathrm{Cr}{\mathrm{O}}_{2}$ for pulses injected at room temperature. Low-temperature magnetoresistance measurements reveal a strong reduction in the domain wall depinning field even for injected current densities as low as ${10}^{10}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{m}}^{2}$.

Analysis of steplike change of impedance for thin-film giant magnetoimpedance element with inclined stripe magnetic domain based on magnetic energy

The phenomenon of steplike impedance change for thin-film giant magnetoimpedance (GMI) element was reported. The steplike change happens simultaneously with the appearance or the disappearance of stripe magnetic domain. This phenomenon is obtained for amorphous Co85Nb12Zr3 soft magnetic thin film in a rectangle shape with an in-plane uniaxial easy axis in the direction nearly 60° against the short-side axis of the element. The steplike change of impedance appears in a certain magnitude of external magnetic field. A high-sensitive magnetic field sensor can be realized by applying this phenomenon. In this study, a mechanism of the appearance or the disappearance of inclined stripe magnetic domain is discussed based on an analysis of magnetic domain energy, for the purpose of applying to a high-sensitivity magnetic field sensor. We assume these extremely different magnetic domains as (I) stripe domain with closure domain and (II) single domain, based on experimentally observed domain structures. The result of analysis shows that the magnetic energy of these two phases intersects each other in a certain external magnetic field, which means that the basis of steplike GMI of thin-film element is revealed as a structural change of magnetic domain based on magnetic energy.

Advantages of CNT–MFM probes in observation of domain walls of soft magnetic materials

The advantage of the CoFe-coated carbon nanotube (CNT) probes in a magnetic force microscope (MFM) is verified on in-plane magnetized soft magnetic materials. CoFe-coated CNT, standard and low-moment MFM probes were used to observe closure domains in square and rectangular Permalloy elements. The perturbative effect of the CNT–MFM probe was far less than that of a standard MFM probe. Domain walls were clearly observed as a pair of dark and bright lines which was in agreement with the micromagnetic simulations. The vortex core was also clearly observed using the CNT–MFM probes.

Domain-wall dynamics in glass-coated magnetic microwires

Glass-coated magnetic microwires with positive magnetostriction show peculiar domain structure that consists mostly of one large domain with magnetization-oriented axially. It was shown that small closure domains appear at the end of the microwire in order to decrease the stray fields. As a result of such domain structure, the magnetization reversal in axial direction runs through the depinning of one of such closure domains and subsequent propagation of the corresponding domain wall. Quite unusual domain-wall (DW) dynamics of the DW propagation predicted previously from the theory has been found in such amorphous microwires. In this paper, we are dealing with the DW dynamics of glass-coated microwires with small positive magnetostriction. The DW damping coming from the structural relaxation dominates at low temperatures as a result of the decrease of the mobility of the structural atomic-level defects. Negative critical propagation field points to the possible DW propagation without applied magnetic field. Probable explanation could be in terms of the effective mass of the DW.

A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries

Ferroelectric perovskites are used in various transducer, memory and optical applications due to their attractive properties. In these applications, the ferroelectric materials often have complex geometries and electrode arrangements, and are subjected to domain switching. Therefore, it is important to understand the domain pattern that forms in these geometries. However, models of domain evolution often make assumptions like periodicity and complete shielding which make them unrealistic for these applications. In this paper, we develop a phase-field approach that can study domain patterns and domain evolution in complex geometries with no a priori assumption on geometry, electrode arrangement, and dielectric properties. The key idea is a boundary element method to resolve the electrostatic fields. We illustrate the method by examining the closure domains that form at a free surface and domain switching under cyclic electric field in a device with interdigitated electrodes.