Domain Wall Pinning Research Articles

Geometry dependent crossover of Barkhausen statistics in iron thin films

We report the crossover of Barkhausen noise statistics upon a change in the measurement geometry. The behaviour is akin to the angle dependent critical to sub-critical crossover of avalanche statistics as present in avalanche models with random anisotropy directions. The samples studied were 15–25 nm thin films of iron, grown on (001) GaAs by pulsed laser ablation. Use of planar Hall effect as a probe for the magnetic state facilitated this work, which would be impractical to do in a MOKE setup. We compare our data with simulations of a random anisotropy Ising model, and demonstrate striking similarity between experimental and simulated avalanche size distributions. Further, through micromagnetic simulations, we conclude that crystallite misorientations were the origin of domain wall pinning in our system leading to Barkhausen noise.

Microstructure, magnetic properties, thermal stabilities and coercivity mechanisms of Ta doped Nd-Fe-B ribbons

The purpose of this paper is to explore Dy-free Nd-Fe-B magnetic alloys which could be developed into Dy-free permanent magnets operating at high temperatures. Nd13.5Fe80.5-xB6Tax (x = 0.0–1.2) alloys have been fabricated by melt spinning technique. It is found out that the addition of Ta in Nd-Fe-B alloys improves the extrinsic and microstructural properties resulting in better magnetic properties and thermal stability. The thermal stability of the alloys measured in terms of temperature coefficient of coercivity (β) improved from −0.41%/K for Nd13.5Fe80.5B6 to −0.27%/K for Nd13.5Fe79.9B6Ta0.6 in the temperature range 300–400 K. It is demonstrated that Ta acts as refractory element, which refines grains and reduces the volume fraction of the undesirable non-magnetic phases. As a result the magnetic properties (Br, Hcj and (BH)max) of the alloys are enhanced, however the intrinsic properties (Tc, Tsr) remain unchanged. The domain wall pinning, determined to be the dominant coercivity mechanism in the investigated alloys, also strengthened by the addition of Ta. It is concluded that Ta alloying can improve the microstructures, magnetic properties and thermal stability of the designated alloys. This research may shed light on further research and development of Dy-free high temperature resistant rare earth magnets.

Magneto-structural behaviour of Gd doped nanocrystalline Co-Zn ferrites governed by domain wall movement and spin rotations

The rare earth gadolinium (Gd3+) ions doped nanocrystalline cobalt-zinc ferrites chemically formulated as Co0.7Zn0.3GdxFe2-xO4 (x = 0–0.1) were synthetically prepared by sol-gel self-ignition process. The characterization the ferrite samples was performed by powder x-ray diffraction method. The analysis of x-ray diffractograms (XRD) reveals formation of cubic spinel phase without presence of any ambiguity peak. The calculated particle size of the samples varies between 18 nm and 28 nm showing decreasing trend with Gd3+ doping. The distribution of cations analysed from XRD data propose occupancy of tetrahedral (A)-site by Zn2+ and Fe3+ while octahedral [B]-site by Fe3+, Gd3+ and Co2+ ions. The morphology of the ferrites was studied from the SEM images. The nanocrystalline particles arranged in layers with presence of porous structure can be observed in the SEM images. The particles of spherical shape with mean diameter of 27 nm were observed in the TEM image. The confirmation of peaks revealed by XRD data was performed by SAED image of the ferrite. The fringe width of the lattice fringe in HRTEM confirms formation of pure spinel phase in the Gd3+ doped Co-Zn ferrite. The VSM data analysed for measurement of magnetic parameters viz. coercivity, retentivity and saturation magnetization. The compositional variation of magnetization with Gd3+ doping reveals spin canting due to non-collinearity of spins of (A) and [B]-site. The Y-K angles calculated from cation distribution data were increased with Gd3+ doping due to spin canting. The variation of coercivity with Gd3+ doping was in accordance with the variation of anisotropy constant. The frequency variation of real part (μ') and imaginary part (μ") of μ* (complex permeability) were studied as a function of Gd3+ composition and frequency. The permeability was influenced by magnetic and structural parameters. The domain wall movement and spin rotations were responsible for magnetism in the ferrites.

Static properties and current-induced dynamics of pinned90∘magnetic domain walls under applied fields: An analytic approach

Magnetic domain walls are pinned strongly by abrupt changes in magnetic anisotropy. When driven into oscillation by a spin-polarized current, locally pinned domain walls can be exploited as tunable sources of short-wavelength spin waves. Here, we develop an analytical framework and discrete Heisenberg model to describe the static and dynamic properties of pinned domain walls with a head-to-tail magnetic structure. We focus on magnetic domain walls that are pinned by 90$^\circ$ rotations of uniaxial magnetic anisotropy. Our model captures the domain wall response to a spin-transfer torque that is exerted by an electric current. Model predictions of the domain wall resonance frequency and its evolution with magnetic anisotropy strength and external magnetic field are compared to micromagnetic simulations.

Pinning of domain walls in thin ferromagnetic films

We present a quantitative investigation of magnetic domain wall pinning in thin magnets with perpendicular anisotropy. A self-consistent description exploiting the universal features of the depinning and thermally activated sub-threshold creep regimes observed in the field driven domain wall velocity, is used to determine the effective pinning parameters controlling the domain wall dynamics: the effective height of pinning barriers, the depinning threshold, and the velocity at depinning. Within this framework, the analysis of results published in the literature allows for a quantitative comparison of pinning properties for a set of magnetic materials in a wide temperature range. On the basis of scaling arguments, the microscopic parameters controlling the pinning: the correlation length of pinning, the collectively pinned domain wall length (Larkin length) and the strength of pinning disorder, are estimated from the effective pinning and the micromagnetic parameters. The analysis of thermal effects reveals a crossover between different pinning length scales and strengths at low reduced temperature.

The Influence of Loop Geometry on the Asymmetric Pinning of Domain Walls in Films with Uniaxial Anisotropy

The asymmetric pinning of a vortex-domain wall in regions with enhanced values of saturation magnetization and the anisotropy constant (defects) has been studied by a three-dimensional micromagnetic simulation at different geometric parameters of these regions. The dependences of the geometry of shifted hysteresis loops on a spacing between two defects and their size in a 100-nm-wide uniaxial magnetic film have been obtained.

Reprint of Prospect for HRE-free high coercivity Nd-Fe-B permanent magnets

Recent state-of-the-art microstructure investigations on Nd-Fe-B sintered magnets have revealed that the Nd2Fe14B grains in conventional sintered magnets are exchange-coupled through ferromagnetic grain boundary phase and the coercivity is governed by domain wall pinning, while exchange-decoupled sintered magnets can be processed by tuning the chemical composition to a slightly Nd-rich and B-lean one with Ga-doping. The coercivity of exchange-decoupled magnets is governed by the nucleation mechanism, giving rise to higher coercivity. Based on recent studies on microstructure-coercivity relationships of various Nd-Fe-B magnets, prospect of HRE-free high coercivity and high remanence magnets is discussed.

Temperature dependent magnetization and coercivity in morphotropic phase boundary involved ferromagnetic Tb1-xGdxFe2 system

Morphotropic phase boundary (MPB) refers to a transition region separating two ferromagnetic phases having different crystallographic symmetries in a ferromagnetic system. In the present study, magnetization and coercivity of the MPB involved ferromagnetic Tb1-xGdxFe2 system have been measured at selected temperatures between 5 and 300 K. The saturation magnetization MS of the Tb1-xGdxFe2 system varies with Gd concentration exhibiting minimum value at MPB composition x = 0.9 at all temperatures. Calculated magnetic moments of rare earth (RE) elements are lower than those of their corresponding free ions, which can be attributed to the crystal field effect (CFE). The magnetic anisotropy K decreases with increasing Gd concentration and anisotropy compensation has been observed at an MPB composition with x = 0.9. The coercivity HC of the Tb1-xGdxFe2 system was found to decrease with increasing the Gd concentration. Furthermore, HC exhibits a large value at low temperature and decays exponentially with increasing temperature. The observed temperature dependence of the HC can be explained by domain wall pinning, as a high K of rare earth elements (RE) at low temperatures causes a prominent pinning effect at 5 K. Our results shed light on magnetization, magnetic anisotropy and coercivity mechanisms in MPB involved ferromagnetic systems and provides an effective way to design novel functional materials.

Unusual magnetoelectric memory and polarization reversal in the kagome staircase compound Ni3V2O8

We study the electric polarization of the kagome staircase $\mathrm{N}{\mathrm{i}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ in magnetic fields up to 30 T and report a magnetoelectric memory effect controlled by bias electric fields. The explored ferroelectric phase in $19--24\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ is electrically controlled, whereas the ferroelectric phase in $2--11\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ exhibits unusual memory effects. We determine a characteristic critical magnetic field ${\mathbit{H}}_{3}=11\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, below which strong memory exists and the polarization is frozen even in opposite bias fields. But when magnetic fields exceed ${\mathbit{H}}_{3}$, the frozen polarization is released and polarization reversal appears by tuning bias electric fields. We ascribe these phenomena to the pinning-depinning mechanism: nucleation and the accompanying pinning of chiral domain walls cooperatively induce the frozen behavior; the polarization reversal results from the depinning through the ferroelectrtic-to-paraelectric phase transition in high magnetic fields. Our experimental results reveal that the first-order phase transition plays an important role in these unusual memory effects.

Effects of Superaging and Percolation Crossover on the Nonequilibrium Critical Behavior of the Two-Dimensional Disordered Ising Model

A Monte Carlo study of the specific features of the nonequilibrium critical behavior has been performed for the two-dimensional “pure” and structurally disordered Ising models in the course of their evolution from the low-temperature initial state at spin concentrations p = 1.0, 0.9, and 0.8. It is shown for the first time that the pinning of domain walls by structural defects leads to the anomalously strong slowing down in the evolution of the autocorrelation function characterized by the superaging effect with exponents μ = 6.25(5) and μ = 6.75(5) for the model with the spin concentrations p = 0.9 and 0.8, respectively. The pure model exhibits the conventional aging with the exponent μ = 1. It is found that the superaging effects in structurally disordered systems lead to vanishing of the limiting fluctuation−dissipation ratio X∞, whereas X∞ = 0.751(24) for the pure model.

Distinct stochasticities between ferromagnetic domain-wall motions driven by magnetic field and electric current

We report the experimental observation of distinct stochasticities between domain-wall motions driven by either a magnetic field or an electric current. In Pt/Co/Ta trilayer films, the arrival time of the current-induced domain-wall motion has a much broader dispersion compared to that of the field-induced motion. Images of the magneto-optical Kerr effect microscope reveal that the current-induced motion experiences significantly stronger domain-wall pinning, contrary to the field-induced domain-wall motion, even though both types of motion take place in the same area of the film. Consequently, the former exhibits stepwise propagation in time, whereas the behavior of the latter is smooth and monotonic. A simple analytic model based on depinning statistics is proposed to explain the relationship between the wide dispersion and the strong pinning mechanisms in current-induced domain-wall motion.

Thermal contact through a two-temperature kinetic Ising chain

We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different temperatures and kinetic parameters on alternating sites. The inhomogeneity of the kinetic parameter is a novelty with respect to the model of Racz and Zia (1994 Phys. Rev. E 49 139), and we exhibit its influence upon the stationary non equilibrium values of the two-spin correlations at any distance. By mapping to the dynamics of spin domain walls and using free fermion techniques, we determine the scaled generating function for the cumulants of the exchanged heat amounts per unit of time in the long time limit.

Simulations of submonolayer Xe on Pt(111): The case for a chaotic low temperature phase.

Molecular dynamics simulations are reported for the structural and thermodynamic properties of submonolayer xenon adsorbed on the (111) surface of platinum for temperatures up to the (apparently incipient) triple point and beyond. While the motion of the atoms in the surface plane is treated with a standard two-dimensional molecular dynamics simulation, the model takes into consideration the thermal excitation of quantum states associated with surface-normal dynamics in an attempt to describe the apparent smoothing of the corrugation with increasing temperature. We examine the importance of this thermal smoothing to the relative stability of several observed and proposed low-temperature structures. Structure factor calculations are compared to experimental results in an attempt to determine the low temperature structure of this system. These calculations provide strong evidence that, at very low temperatures, the domain wall structure of a xenon monolayer adsorbed on a Pt(111) substrate possesses a chaotic-like nature, exhibiting long-lived meta-stable states with pinned domain walls, these walls having narrow widths and irregular shapes. This result is contrary to the standard wisdom regarding this system, namely, that the very low temperature phase of this system is a striped incommensurate phase. We present the case for further experimental investigation of this and similar systems as possible examples of chaotic low temperature phases in two dimensions.

A transmission electron microscope study of N\xe9el skyrmion magnetic textures in multilayer thin film systems with large interfacial chiral interaction

Skyrmions in ultrathin ferromagnetic metal (FM)/heavy metal (HM) multilayer systems produced by conventional sputtering methods have recently generated huge interest due to their applications in the field of spintronics. The sandwich structure with two correctly-chosen heavy metal layers provides an additive interfacial exchange interaction which promotes domain wall or skyrmion spin textures that are Néel in character and with a fixed chirality. Lorentz transmission electron microscopy (TEM) is a high resolution method ideally suited to quantitatively image such chiral magnetic configurations. When allied with physical and chemical TEM analysis of both planar and cross-sectional samples, key length scales such as grain size and the chiral variation of the magnetisation variation have been identified and measured. We present data showing the importance of the grain size (mostly < 10 nm) measured from direct imaging and its potential role in describing observed behaviour of isolated skyrmions (diameter < 100 nm). In the latter the region in which the magnetization rotates is measured to be around 30 nm. Such quantitative information on the multiscale magnetisation variations in the system is key to understanding and exploiting the behaviour of skyrmions for future applications in information storage and logic devices.

Thickness dependent response of domain wall motion in declamped {001} Pb(Zr0·3Ti0.7)O3 thin films

Scaling effects were investigated in tetragonal {001} textured Pb(Zr0·3Ti0.7)O3 thin films doped with 2 mol% Nb over a thickness range of 0.27 μm–1.11 μm. Scaling effects refer to the size-induced degradation of properties at length scales exceeding those associated with the ferroelectric stability limit. The irreversible Rayleigh coefficient was found to be thickness-dependent, indicating suppression of the extrinsic contributions to the relative permittivity for all clamped films. Both defects in the seed layer and substrate clamping contributed to the observed thickness dependence. The influence of the seed layer on dielectric properties was accounted for using a capacitor in series model. After the films were partially declamped from the substrate, the irreversible contributions increased up to 23% in Nb-doped films and became more frequency dependent (by up to 29%). The suppressed frequency dependence in the clamped films was attributed to the pinning of irreversible domain walls active at lower frequencies. Both the seed layer and substrate clamping contributed to the pinning of irreversible domain walls.

Prospect for HRE-free high coercivity Nd-Fe-B permanent magnets

Recent state-of-the-art microstructure investigations on Nd-Fe-B sintered magnets have revealed that the Nd2Fe14B grains in conventional sintered magnets are exchange-coupled through ferromagnetic grain boundary phase and the coercivity is governed by domain wall pinning, while exchange-decoupled sintered magnets can be processed by tuning the chemical composition to a slightly Nd-rich and B-lean one with Ga-doping. The coercivity of exchange-decoupled magnets is governed by the nucleation mechanism, giving rise to higher coercivity. Based on recent studies on microstructure-coercivity relationships of various Nd-Fe-B magnets, prospect of HRE-free high coercivity and high remanence magnets is discussed.

Microstructures, magnetic properties and coercivity mechanisms of Nd-Ce-Fe-B based alloys by Zr substitution

In this paper, the effects of Zr addition on microstructures, magnetic properties, exchange coupling, and coercivity mechanisms of Nd-Ce-Fe-B alloys fabricated by melt-spinning technique are investigated. It is found that the coercivity Hcj is enhanced significantly by Zr substitution in the (Nd0.8Ce0.2)13Fe82-xZrxB5 alloys, while the remanence Jr is reduced slightly. The Hcj increases from 12.2 to 13.7 kOe by adding Zr up to 1.5 at. %, whereas Hcj is decreased with a further increase in Zr content. The larger lattice constants and unit cell volumes of the matrix phase indicate that Zr atoms enter into the hard magnetic phase by substituting Fe sites. The reduction of Tc implies the attenuation of the exchange interaction in the 2:14:1 phase with Zr occupying the Fe sites. The weakened intergranular exchange coupling of the Zr added alloy may be attributed to the formation of a non-magnetic intergranular phase. It is worth noting that the coercivity is dominated by the pinning of domain walls at defect positions even though the nucleation of reversal domains still exists. The synergistic function between the pinning effect and the exchange coupling leads to improved magnetic properties.

Coercivity mechanism of rare-earth free MnBi hard magnetic alloys

In this work, we present and discuss results concerning the hard magnetic behavior of rare earth-free MnBi alloys obtained by suction casting technique. The physics of coercivity for these type of alloys is based on the nucleation process of reverse domains, which in turn is determined by the alloy microstructure features such as phase distribution, morphology, grain size and in particular, defects, which are characteristic ofreal materials. The microstructure of the as-cast alloy presented here comprises the formation of the Low Temperature Intermetallic Phase (LTIP)-MnBi, interspersed within Bi- and Mn-rich areas. A considerable intrinsic coercivity field of 238 kA/m together with a saturation magnetization of 0.04 T were observed. The nucleation controlled mechanism of this alloy was described in terms of the Kronm¨uller equation, which incorporates the detrimental effect of microstructure defects through fitting parameters associated to reduced intrinsic magnetic properties at grain size boundaries, interfaces and local demagnetizing fields. A notorious switching of coercivity mechanism associated with domain wall pinning was found to be produced upon annealing of the alloy at 583 K for 24 hrs, yielding a drastic reduction of coercivity (down to 16 kA/m). The key microstructural feature determining the switching of coercivity mechanism is the formation/suppression of Bi-rich areas, which promotes the nucleation and growth of LTIP.

The anhysteretic polarisation of ferroelectrics

Measurement and calculation of anhysteretic curves is a well-established method in the field of magnetic materials and is applied to ferroelectric materials here. The anhysteretic curve is linked to a stable equilibrium state in the domain structure, and ignores dissipative effects related to mechanisms such as domain wall pinning. In this study, an experimental method for characterising the anhysteretic behaviour of ferroelectrics is presented, which is subsequently used to determine the anhysteretic polarisation response of polycrystalline barium titanate and a doped lead zirconate titanate composition at room temperature. Various external parameters, such as electric field, stress, and temperature, can significantly affect ferroelectric behaviour. Ferroelectric hysteresis curves can assess the importance of such effects but cannot distinguish their contribution on the different intrinsic and extrinsic mechanisms involved in ferroelectric behaviour. In this work, the influence of compressive stress on the anhysteretic polarisation is measured and discussed. The comparison of the polarization loop to the anhysteretic curve under compressive stress elucidates the effects on the stable equilibrium domain configuration and dynamic effects associated to dissipation.

Coercivity enhancement of hot-deformed Nd–Fe–B magnets with Pr–Cu alloy addition

Effects of low-melting Pr–Cu alloy addition on the microstructure and magnetic properties of the hot-deformation Nd–Fe–B magnets were investigated. A small amount of Pr–Cu addition enhances the coercivity of the hot-deformation Nd–Fe–B magnets obviously. The coercivity of the hot-deformation Nd–Fe–B magnets with 4.0 wt% Pr85Cu15 addition increases to 1271 kA·m−1, 75.69% higher than that of Pr–Cu-free magnet (723 kA·m−1), and then decreases with 5 wt% Pr85Cu15 addition. It is observed that there a uniform RE-rich phase is formed wrapping the Nd2Fe14B main phase in the sample with 4.0% Pr85Cu15 addition by scanning electron microscopy (SEM), which promotes the coercivity. The angular dependence of coercivity for the hot-deformation Nd–Fe–B magnets indicates that the coercivity mechanism is nucleation combined with domain wall pinning. The domain wall pinning is weakened, while the nucleation is enhanced after Pr–Cu addition. The remanence, intrinsic coercivity, and maximum magnetic energy product of the original Nd–Fe–B magnet are 1.45 T, 723 kA·m−1, and 419.8 kJ·m−3, respectively, and those of the sample with 4.0% Pr85Cu15 alloy addition are 1.30 T, 1271 kA·m−1, and 330.0 kJ·m−3, respectively.