Closure Domains Research Articles

Dynamics of domain wall depinning from closure domain structure at the end of bistable glass coated microwire

The study of closure domain structure dynamics at the end of magnetic bistable glass-coated microwire is presented. The method in which critical parameters of the so-called three-level rectangular field pulse are measured is used. It is shown that dependences measured using three-level field pulses cannot be satisfactorily interpreted by the model in which application of a rectangular field pulse causes the release of a single domain wall from a potential well. A new model based on the simplest possible closure domain structures at the microwire end is proposed. In the framework of this model the application of a non-zero first-level field results in changes in domain wall parameters (inertial mass and mobility) which have opposite effects on the prolonging/shortening of critical field pulse width and do not provide satisfactory explanation of experimental observations. Shortening of the path which the wall has to move along to become free can result from the wall lengthening caused by application of the non-zero first-level field. This effect combined with position-independent force acting on the wall can explain the observed behaviour. Modelling of this process is also presented and supports this interpretation.

Controllable Exchange Bias Effect in (Ga, Mn)As/(Ga, Mn)(As, P) Bilayers With Non-Collinear Magnetic Anisotropy

We have investigated the exchange bias (EB) effect occurring in (Ga, Mn)As/(Ga, Mn)(As, P) bilayers, in which the (Ga, Mn)As layer has an in-plane (IP) magnetic anisotropy, and the magnetic anisotropy of the (Ga, Mn)(As, P) layer is out-of-plane (OP). Planar Hall resistance (PHR) measured during magnetization reversal in this system showed a clear shift of the hysteresis loops, indicating the presence of EB in the (Ga, Mn)As layer. The EB significantly depends on the direction of the field used in the field-cooling process. The observed EB occurring in a bilayer in which the constituent layers have orthogonal magnetic anisotropies can be understood in terms of the formation of magnetic closure domains in the (Ga, Mn)(As, P) layer during field cooling. We show that such EB can be effectively controlled by the process of field cooling, suggesting the possibility of memory device applications based on bilayer systems with orthogonal magnetic anisotropy.

Study of bistable behaviour in interacting Fe-based microwires by first order reversal curves

Amorphous ferromagnetic Fe-based microwires (MWs) have a magnetic structure consisting mainly of a single longitudinal domain and small closure domains at both ends. A rectangular hysteresis loop is then observed according to the fast domain wall propagation along the microwire. This type of material is a good physical example of the idea of a magnetic relay hysteron as described in Preisach model of hysteresis. The hysteron was defined as a mathematical operator acting on the field and producing rectangular loops whose superposition gives out the hysteresis loop. The hysteron idealization is frequently used to describe and interpret FORC (First Order Reversal Curve) diagrams by comparison with Preisach plane. The central idea of this work is to study the FORCs of a real physical sample that behaves closely to the ideal hysteron, both isolated and interacting with a twofold aim. On one hand, providing a better understanding of FORC measurements, and, on the other, analyzing the magnetization reversal processes in microwires with rectangular hysteresis loops. While for a single microwire the behaviour is that expected for a hysteron, both in the hysteresis loop and in the FORC diagram, the magnetostatic interaction between two microwires breaks with the ideal behaviour due to the change in the domain wall mobility at the end of the wires.

Controlling domain configuration of the sensing layer for magnetic tunneling junctions by using exchange bias

The control of magnetic domain formation and fluctuations in the sensing layer is important to progress for low noise in magnetic tunnel junction sensors. We studied the effect of exchange bias on the domain structure in micro-patterned Permalloy (Py: Ni80Fe20) sensing layer. We deposited single Py films, and Pt48Mn52/Py films, where the latter showed exchange bias. By controlling the thickness of Py, Pt48Mn52 (15nm)/Py (t=235 nm) showed a small coercivity and exchange bias of 7 Oe. After micro-fabrication into circular pillars 80 µm in diameter, we measured the domain structure by Magneto Optical Kerr Effect (MOKE) microscopy. MOKE images showed that single Py pillars have a simple closure domain, where the domain wall at the center moved with the applied field. The exchange-biased Py pillars exhibited a more complicated structure, but with fixed domains at the center region due to the exchange bias overcoming the magnetostatic energy. The uniform rotation of magnetization at the center of the sample is promising for decreasing the domain hopping magnetic noise.

Exchange bias in ferromagnetic bilayers with orthogonal anisotropies: the case of GaMnAsP/GaMnAs combination

We report the observation of exchange bias in a ferromagnetic Ga0.94Mn0.06As0.77P0.23/ Ga0.94Mn0.06As bilayer, in which the easy axis in one layer is oriented out-of-plane, and in the other in-plane. Magnetization reversal in this system is explored using planar Hall effect (PHE) measurements under various initial conditions and with various field-cooling orientations. Our results show that the two magnetic layers are ferromagnetically exchange-coupled, and that such coupling results in pronounced exchange-bias-like shifts of magnetic hysteresis loops during reversal of in-plane magnetization. The presence of exchange bias in this system can be understood on the basis of magnetic closure domains formed in the layer with the out-of-plane easy axis.

Thermo-electro-mechanical phase-field modeling of paraelectric to ferroelectric transitions

Ferroelectric materials are widely used in engineering and science applications due to their large nonlinear thermo-electro-mechanical coupling. This paper develops and studies a phase-field model to describe paraelectric to ferroelectric phase transitions and the giant electrocaloric effect, a large adiabatic temperature change with the application of an electric field. Spatially inhomogeneous temperature distributions, latent heat due to phase changes, and heat conduction are included in the model. The model is derived from fundamental balances of force, charge, micro-force, and energy. The second law of thermodynamics further constrains the constitutive behaviors derived from a phenomenological free energy function for the material. The finite element method is applied to solve the governing equations for a selected set of boundary value problems. First, the motion of a paraelectric/ferroelectric phase boundary controlled by the application and removal of heat is simulated. Then, a model electrocaloric cooling device based on a multilayer ferroelectric capacitor is simulated through a full thermodynamic refrigeration cycle. The model geometry and boundary conditions are chosen to match realistic device configurations. The device is driven through a cycle with two adiabatic and two constant electric field legs, and compared with the analytically computed ideal bulk electrocaloric cooling cycle. Several inefficiencies arise in the device, including incomplete transformation, entropy loss due to phase boundary motion, and high energy zones with large stresses and closure domains at the electrode tip.

The magnetic domain rotation in the magnetostriction process of Fe-Ga alloy

The domain rotation process during magnetostriction in Fe-Ga rolled sheet has been clarified. The magnetic domain pattern variation with magnetic field of rolling surface was observed by magneto-optic Kerr Microscopy in-situ. According to the sample information and magnetostriction, different magnetic domain structures were constructed for different magnetization stage. In the demagnetized state, the magnetic domain structure of Fe-Ga rolled sheet was closure domain with lancet domain as supplementary domain, and when the magnetic field is larger than 8.3 kA/m the magnetic domains is lancet domains, which well explains the domain rotation process at the stage of slow magnetostriction growth. Using an equivalent stress, the magnetostriction of Fe-Ga polycrystal was simulated by an energy-based domain rotation model. The result fits well with the measured magnetostriction in rapid growth stage and saturation stage. These two models work as a complement to each other and clearly show the domain rotation process during magnetostriction.

The Study of Closure Domain Structure Dynamics in Bistable Microwires Using the Technique of Three-Level Field Pulses

The process of release of a single domain wall from the closure domain structure at the microwire ends and the process of nucleation of the reversed domain in regions far from the microwire ends were studied using the technique that consists in determining the critical parameters of the rectangular magnetic field pulse (magnitude— $H_{\mathrm {pc}}$ and length— $\tau _{c}$ ) needed for free domain wall production. Since these processes can be influenced by the magnitude of the magnetic field before or after the application of the field pulse ( $H_{p}$ , $\tau$ ), we propose a modified experiment in which the so-called three-level pulse is used. The three-level pulse starts from the first level, then continues with the second measuring rectangular pulse ( $H_{p}$ , $\tau$ ), which ends at the third field level. Based on the results obtained in experiments using three-level field pulses, it has been shown that reversed domains are not present in the remanent state in regions far from the microwire ends. Some modification of the theoretical model of a single domain wall trapped in a potential well will be needed for an adequate description of the depinning processes.

Large eddy simulation of turbulent flow over and through a rough permeable bed

This work elucidates the impacts of model construction choices on turbulence characteristics and solution fidelity in the simulation of coupled freestream and porous turbulent flows. A freestream-porewater interface is modeled numerically as a matrix of regularly spaced spheres submerged in a surrounding flow. Simulations are conducted to solve the continuity and momentum equations via Large Eddy Simulation (LES) using the Control Volume Finite Element Method (CVFEM) on an unstructured, surface-conforming mesh, and simulated flow fields are compared with experimental results. Key parameters are identified, allowing for model creation recommendations. A mesh refinement study is performed, and characteristic required mesh sizes in both the bed and the freestream are identified that achieve a good trade-off between accuracy and efficiency. Additionally, it is shown that similar to wall-bounded flows, the computational domain for a coupled freestream and porous flow must be sufficiently large to capture the relevant largest-sized eddies and to avoid the spanwise locking of flow structures; such structures may affect the flow field in the pores as well as in the freestream. Dimensions of 7.5H × 3.5H × H, where H is the freestream height, are found to give satisfactory comparison with experimental results for the cases studied. Finally, it is found that the wall-adapting local eddy-viscosity (WALE) turbulence closure scheme is better able to model the fluid velocity in the problem domain compared with the Smagorinsky model. Failure to select the proper turbulence closure model or domain size leads to a misrepresentation of the turbulent structures. Because of the strong coupling between the porewater flow and the freestream, these modeling errors propagate in both flow regions.

Spin-orbit torque induced dipole skyrmion motion at room temperature

We demonstrate deterministic control of dipole-field-stabilized skyrmions by means of spin-orbit torques arising from heavy transition-metal seed layers. Experiments are performed on amorphous Fe/Gd multilayers that are patterned into wires and exhibit stripe domains and dipole skyrmions at room temperature. We show that while the domain walls and skyrmions are achiral on average due to lack of Dzyaloshinskii-Moriya interactions, the N\'eel-like closure domain walls at each surface are chiral and can couple to spin-orbit torques. The current-induced domain evolutions are reported for different magnetic phases, including disordered stripe domains, coexisting stripes and dipole skyrmions, and a close-packed dipole skyrmion lattice. The magnetic textures exhibit motion under current excitations with a current density $\ensuremath{\sim}{10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{A}/{\mathrm{m}}^{2}$. By comparing the motion resulting from magnetic spin textures in Fe/Gd films with different heavy transition-metal interfaces, we confirm spin currents can be used to manipulate achiral dipole skyrmions via spin-orbit torques. We further show the current-induced response of a dipole skyrmion lattice where skyrmions move in channels between pinned regions.

Magnetic properties and magnetization reversal in Co nanowires with different morphology

In the present study, magnetic properties and demagnetization processes of Co nanowires with various morphologies (ellipsoids, capped cylinders, and cylinders) are investigated by means of Object Oriented Micromagnetic Framework (OOMMF) software package with finite difference micromagnetic simulation. The results show that the aspect ratio, morphology, and dipolar interactions of the nanowires play a key role in determining the switching modes and hence the magnetic properties. For the Co nanowires with the same morphology and diameter, the coercivity increases substantially with increasing aspect ratio of the nanowires due to the increased shape anisotropy when the aspect ratio is less than 3. For a single nanowire with a fixed diameter of 15 nm and a length of 200 nm, the coercivity of ellipsoids of 14.45 kOe is noticeably higher than those of capped cylinders of 12.55 kOe and cylinders of 11.15 kOe, indicating the considerable influence of the morphology on the coercivity of the wires. The magnetization reversal mechanism of a single Co nanowire is mainly described by a nucleation propagation process, which starts at the ends of the nanowires. For the nanowires assembly, the magnetic moment reversal of some nanowires occurs first, and the rest reverse gradually with increasing applied field and ultimately the reversal of the whole assembly is achieved. This process could be theoretically interpreted based on the nucleation of closure domains at the ends of the wires as well as the subsequent depinning and propagation of domain walls. Meanwhile, the squareness of the demagnetization curve and coercivity of the nanowires assembly deteriorate faster than those of the single nanowires due to the dipole interactions.

Micrometric non-contact position magnetoimpedance sensor

In this work a sensitive micrometric non-contact position sensor based on the Giant MagnetoImpedance effect (GMI) is analyzed. A nearly zero magnetostrictive CoFeSiBCr wire was employed as sensor nucleus. The sensing principle is based on the changes in the high frequency electric impedance, Z, of the soft magnetic element as a function of the relative position of a permanent magnet generating a non-uniform magnetic field along the wirés axis. The sensor sensitivity is analyzed in terms of the magnetic field gradient and wire’s length. The comparison between the sensing response of a single wire element and a long wire (12 cm in length) with different voltage contacts along its axis is performed. Higher micrometric sensitivities are achieved in wires with a certain critical length. A slight enhancement of the sensor sensitivity is found under the single wire configuration below the critical wire length. These results are interpreted as the contribution of the characteristic closure domain structure at the sample ends in these soft magnetic wires. Finally, the application of the sensor for the detection of the daily micrometric trunk shrinkage variations in a lemon tree is presented. The results indicate that this type of magnetic sensors can be easily implemented in the agricultural sector, providing a low cost and sensitive detection technique regarding water monitoring purposes.

Effect of Al content on magnetic domains of {1 0 0} grains in electrical steels

Magnetic domains of {100} grains in electrical steels with 1.85 ≤ Al ≤ 6.54 wt% were observed by magneto-optic Kerr microscopy. The characteristics and motion of magnetic domains were correlated with hysteresis loss, anomalous loss and permeability. As Al contents increased, domain wall energy decreased, so the magnetic domain size of {100} grains decreased. In steel with Al 6.54 wt%, 90° domain walls appeared, so the complexity of domain structures increased. Addition of Al caused increase in hysteresis loss. Anomalous loss decreased until Al 4.68 wt%, then saturated, despite high resistivity and small domain size. External magnetizing force H→ required to induce maximum permeability µmax increased drastically at Al 6.54 wt%. These changes of magnetic properties may be caused by pinning of 90° walls during magnetization. As domain size decreased to form closure domains, the complexity of reorganization of magnetic domains increased, and they were interrupted by pinning 90° walls.

Natural and experimental fluorine substitution in biotite: Implications for fluid-rock thermochronometry and application to the Seridó Belt, northeastern Brazil

Abstract We modeled non-steady-state, fluid-assisted diffusion in a sheet plane, infinite cylinder and finite thin cylinder using analytical solutions of the diffusion equation and the experimental diffusivity of F-in-biotite. Diffusion experiments on natural biotite in the presence of hydrofluoric acid at 0.4 GPa and 650, 700, and 750 °C produced diffusive influx perpendicular to the c-axis. EPMA mapping and profiling allow us to define the following Arrhenius expression of F diffusion in biotite: D = 7.04 m 2 s × 10 − 4 × exp − 221 kJ mol RT − 1 The results yield the discrimination of a high-T homogenization domain where cooling paths continuously reequilibrate F-in-biotite, an intermediate-T zonation domain where cooling paths record F-in-biotite diffusion profiles and a low-T closure domain where F-in-biotite remains unchanged. The zonation domain significantly expands with increasing cooling rates and decreasing diffusion time. We systematically analyzed F-in-biotite with electron microprobe in samples collected along representative cross-sections within the Serido Belt, northeastern Brazil. Its metasedimentary units reached upper amphibolite grade metamorphic conditions, with constant F-in-biotite (F ≈ 0.33 wt.%) in grains from mica schist and paragneiss. The Ti-in-biotite geothermometer yielded nearly constant temperatures around 623 °C. The F-in-biotite regional background values remain unchanged at the contact with the major Ediacaran F-rich Acari pluton. It indicates the absence of magmatic fluid influx into the host rocks and is evidence for a fluid-absent nature of melts. By contrast, the F-in-biotite of the metric mica schist enclaves within dykes and sills of Cambrian pegmatitic granites was reequilibrated by interaction with exsolved fluids. The Ti-in-biotite geothermometer indicates temperatures around 642 °C, and our model suggests 100 kyr as a minimal duration for fluid-rock interaction. The preservation of intra-grain F-in-biotite homogeneity requires fluid flux cessation before cooling or fluid-present cooling rates below 100 °C Myr−1. Higher cooling rates would generate F-in-biotite intra-grain zonation. At the contact with the pegmatitic granites, the metasedimentary rocks show meter-scale F-in-biotite gradients due to thermal profiles setting the fluid (fH2O/fHF) gradient. The preservation of such gradients is related to a relatively fast fluid flux episode compared to the overall duration of the elevated thermal profile. The absence of intra-grain zonation indicates that F-in-biotite re-equilibration was fast relative to that of the fluid flux duration. We found intra-grain F-in-biotite zonation within an orthogneiss sample from the Paleoproterozoic Caico complex basement nearby the metasedimentary belt and intruded plutons. The fit of the natural profile by modeled profiles for cooling rates below 10 °C Myr−1, obtained from available Serido Belt U-Pb and 40Ar/39Ar ages, indicates that the orthogneiss cooled from 475 °C. It suggests the existence of a thermal gradient as the inner part of the belt cooled from 623 °C.

Defect-driven flexochemical coupling in thin ferroelectric films

Using Landau-Ginzburg-Devonshire theory, we considered the impact of the flexoelectro-chemical coupling on the size effects inpolar properties and phase transitions of thin ferroelectric films with a layer of elastic defects. We investigated a typical case, when defects fill a thin layer below the top film surface with a constant concentration creating an additional gradient of elastic fields. The defective surface of the film is not covered with an electrode, but instead with an ultra-thin layer of ambient screening charges, characterized by a surface screening length. This geometry is typical for the scanning probe piezoelectric force microscopy. Obtained results revealed an unexpectedly strong effect of the joint action of Vegard stresses and flexoelectric effect (shortly flexo-chemical coupling) on the ferroelectric transition temperature, distribution of the spontaneous polarization and elastic fields, domain wall structure and period in thin PbTiO3 films containing a layer of elastic defects. A nontrivial result is the ferroelectricity persisting at film thicknesses below 4 nm, temperatures lower than 350 K and relatively high surface screening length (~0.1 nm). The origin of this phenomenon is the re-building of the domain structure in the film (namely the cross-over from c-domain stripes to a-type closure domains) when its thickness decreases below 4 nm, conditioned by the flexoelectric coupling and facilitated by negative Vegard effect. For positive Vegard effect, thicker films exhibit the appearance of pronounced maxima on the thickness dependence of the transition temperature, whose position and height can be controlled by the defect type and concentration. The revealed features may have important implications for miniaturization of ferroelectric-based devices.

The magnetic structure and palaeomagnetic recording fidelity of sub-micron greigite (Fe3S4)

We present the results of a finite-element micromagnetic model of 30nm to 300nm greigite (Fe3S4) grains with a variety of equant morphologies. This grain size range covers the magnetic single-domain (SD) to pseudo single-domain (PSD) transition, and possibly also the PSD to multi-domain (MD) transition. The SD–PSD threshold d0 is determined to be 50nm≤d0≤56nm depending on grain shape. The nudged elastic-band method was used to determine the room temperature energy barriers between stable states and thus the blocking volumes. It is found that, in the absence of interparticle magnetostatic interactions, the magnetisation of equant SD greigite is not stable on a geological scale and only PSD grains ≥70nm can be expected to carry a stable magnetisation over billion-year timescales, i.e., all non-interacting SD particles are essentially superparamagnetic. We further identify a mechanism for the PSD to multi-domain (MD) transition, which is of a continuous nature from PSD nucleation up to 300nm, when structures typical of MD behaviour like closure domains begin to form.

Spin-Transfer-Driven Dynamics of Magnetic Vortices and Antivortices in Dots With Crystalline Cubic Anisotropy

We study the magnetization dynamics of a vortex- or antivortex-containing nanodot driven by an out-of-plane polarized electric current within micromagnetic simulations. The dot is an ultra-thin structure created using a material with strong crystalline cubic anisotropy. It is in-plane ordered with an effective fourfold anisotropy. In the case of the antivortex, we consider astroid-shaped dots, while in the case of the vortex, the circular dots and the astroid-shaped ones. Unlike in the soft-magnetic dots, the vortex (antivortex) textures in thin layers with sufficiently strong fourfold anisotropy consist of four closure domains independent of the dot shape. The magnetization in the domain walls (DWs) deviates from the dot plane under the action of the out-of-plane polarized electric current normal to the dot, which drives the DW propagation—a rotation of the texture around the vortex (antivortex) center. The DW velocity is dependent on the distance from the vortex (antivortex) core; thus, the DWs deform under the current creating a fourfold spiral shape. For sufficiently hard cubic magnets, we find a regime of the oscillatory dynamics of the dot [a cyclic switching between the spiral state and the closure-domain vortex (antivortex) state]. For softer magnets, we consider a spin-transfer-driven fast magnetization reversal of the vortex state mediated by the creation of the spiral state.

Magnetization dynamics of weak stripe domains in Fe–N thin films: a multi-technique complementary approach

The resonant eigenmodes of an α′-FeN thin film characterized by weak stripe domains are investigated by Brillouin light scattering and broadband ferromagnetic resonance experiments, assisted by micromagnetic simulations. The spectrum of the dynamic eigenmodes in the presence of the weak stripes is very rich and two different families of modes can be selectively detected using different techniques or different experimental configurations. Attention is paid to the evolution of the mode frequencies and spatial profiles under the application of an external magnetic field, of variable intensity, in the direction parallel or transverse to the stripes. The different evolution of the modes with the external magnetic field is accompanied by a distinctive spatial localization in specific regions, such as the closure domains at the surface of the stripes and the bulk domains localized in the inner part of the stripes. The complementarity of BLS and FMR techniques, based on different selection rules, is found to be a fruitful tool for the study of the wealth of localized magnetic excitations generally found in nanostructures.

Dual-cantilever magnetometer for study of magnetic interactions between patterned permalloy microstructures

We have designed and implemented a dual-cantilever magnetometer, in which the coupling magnetic forces between the two cantilevers can be switched on/off by an external magnetic field. The coupling is realized by a pair of ferromagnetic ellipses, located on the cantilevers. One of the ellipses is “narrow” – it bears only a single domain magnetic state independently of the applied external field. The other one is “wide”, and can be either in single- or closure-domain states depending on the applied field. In such configuration, the interacting force between the cantilevers can be attractive (both ellipses are in single domain state conforming to the external field), repulsive (both are in single domain states, but the narrow ellipse is in a meta-stable state, with magnetization opposite to the field) or switched off (when the closure domain state appears in the wide ellipse). We found that the coupling between the ellipses directly corresponds to the phase shift of the vibrating cantilevers. In this manner, the cantilever phase detection can be used to read out the magnetic state of the ellipses, which depends on the applied magnetic field. Moreover, we study how the magnetic state of the wide ellipse influences the flipping field of the narrow ellipse. Our observations are supported by micromagnetic simulations and by additional magnetic force microscopy experiments. We also discuss sensitivity and potential application of the magnetometer in future experiments.

Tuning the polar states of ferroelectric films via surface charges and flexoelectricity

Using the self-consistent Landau-Ginzburg-Devonshire approach we simulate and analyze the spontaneous formation of the domain structure in thin ferroelectric films covered with the surface screening charge represented by the Bardeen-type surface states. Hence we consider the competition between the screening and the domain formation as alternative ways to reduce the electrostatic energy and reveal unusual peculiarities of distributions of polarization, electric and elastic fields conditioned by the surface screening length and the flexocoupling strength. We have established that the critical thickness of the film and its transition temperature to a paraelectric phase strongly depend on the Bardeen screening length, while the flexocoupling affects the polarization rotation and closure domain structure. Furthermore the flexocoupling induces ribbon-like nano-scale domains in the film depth far from the top open surface, which might be related to the enigmatic polar nanoregions in relaxor ferroelectrics. Thus the joint action of the surface screening (originating from e.g. the adsorption of ambient ions or surface states) and flexocoupling may remarkably modify polar and electromechanical properties of thin ferroelectric films.