Domain Wall Kinetics Research Articles

Persistent dynamic magnetic state in artificial honeycomb spin ice

Topological magnetic charges, arising due to the non-vanishing magnetic flux on spin ice vertices, serve as the origin of magnetic monopoles that traverse the underlying lattice effortlessly. Unlike spin ice materials of atomic origin, the dynamic state in artificial honeycomb spin ice is conventionally described in terms of finite size domain wall kinetics that require magnetic field or current application. Contrary to this common understanding, here we show that a thermally tunable artificial permalloy honeycomb lattice exhibits a perpetual dynamic state due to self-propelled magnetic charge defect relaxation in the absence of any external tuning agent. Quantitative investigation of magnetic charge defect dynamics using neutron spin echo spectroscopy reveals sub-ns relaxation times that are comparable to the relaxation of monopoles in bulk spin ices. Most importantly, the kinetic process remains unabated at low temperature where thermal fluctuation is negligible. This suggests that dynamic phenomena in honeycomb spin ice are mediated by quasi-particle type entities, also confirmed by dynamic Monte-Carlo simulations that replicate the kinetic behavior. Our research unveils a macroscopic magnetic particle that shares many known traits of quantum particles, namely magnetic monopole and magnon.

A phase-field model for ferroelectrics with general kinetics, Part I: Model formulation

When subjected to electro-mechanical loading, ferroelectrics see their polarization evolve through the nucleation and evolution of domains. Existing mesoscale phase-field models for ferroelectrics are typically based on a gradient-descent law for the evolution of the order parameter. While this implicitly assumes that domain walls evolve with linear kinetics, experiments instead indicate that domain wall kinetics is nonlinear. This, in turn, is an important feature for the modeling of rate-dependent effects in polarization switching. We propose a new multiple-phase-field model for ferroelectrics, which permits domain wall motion with nonlinear kinetics, with applications in other solid–solid phase transformation problems. By means of analytical traveling wave solutions, we characterize the interfacial properties (energy and width) and the interface kinetics of straight domain walls, as furnished by the general kinetics model, and compare them to those of the classical Allen–Cahn model. We show that the proposed model propagates domain walls with arbitrarily chosen nonlinear kinetic relations, which can be tuned to differ for the different types of domain walls in accordance with experimental evidence.

Magnetic indicators for evaluating plastic strains in electrical steel: Toward non-destructive assessment of the magnetic losses

Electric steel is widely used for magnetic conversion of electrical energy such as in electric motors and power transformers. Electric steel sheets are cut using mechanical methods (such as punching) during manufacturing. These methods induce local plastic strains, which lead to overall degradation in magnetic performance.Plasticity and magnetic losses are physically related in electrical steel. It is impossible to measure the magnetic losses on the production line using standard methods. Non-destructive testing (NDT) based on magnetization mechanisms is a promising alternative, giving access to local plastic strains and indirectly to local magnetic losses.In this study, a setup was designed to stimulate the magnetization mechanisms separately while maintaining the same experimental conditions. The magnetization processes related to the domain wall kinetics were revealed to be more correlated to plastic strain. The magnetic incremental permeability hysteresis area and maximal value, and the coercivity associated with Barkhausen noise were found to be the best plastic strain indicators. Additional tests in an NDT context confirmed the correlations, the equal applicability of the proposed indicators, and their viability in predicting static hysteresis loss.

Kinetics of ferroelectric switching in poled barium titanate ceramics: Effects of electrical cycling rate

Our understanding of the rate-dependent electro-mechanical response of ferroelectric ceramics is incomplete – primarily due to limited experimental data characterizing the material behavior at high rates (or short time scales). Therefore, we experimentally study the effect of cycling rate on polarization switching in poled barium titanate (BaTiO3) ceramics across five orders of magnitude in cycling rate. Mechanical strain data as a function of the applied electric field were collected across three orders of magnitude. We quantify the rate-dependent coercive field, remanent and peak polarization, apparent permittivity and apparent piezoelectric coefficient, and actuation strain. Results reveal a reduction in polarizability of the material with increasing rate and a strong asymmetry in the electromechanical hystereses, which comes with differences in the rate dependence when loading parallel vs. anti-parallel to the direction of poling. Supported by a simple model and ex-situ piezoresponse force microscopy, we conclude that rate effects arise from the mobility of 90∘ domain walls and the competition between nucleation and growth of domains. The asymmetric hysteresis highlights the importance of point charge and dipole defects, which affect the domain wall kinetics and hence the rate effects of polarization switching through the competing time scales of space charge migration, dipole reorientation, and domain wall activity.

Effect of Humidity on the Writing Speed and Domain Wall Dynamics of Ferroelectric Domains

AbstractThe switching dynamics of ferroelectric polarization under electric fields depends on the availability of screening charges in order to stabilize the switched polarization. In ferroelectrics, thin films with exposed surfaces investigated by piezoresponse force microscopy (PFM), the main source of external screening charges is the atmosphere and the water neck, and therefore relative humidity (RH) plays a major role. Here, it is shown how the dynamic writing of domains in BaTiO3 thin films changes by varying scanning speeds in the range of RH between 2.5% and 60%. The measurements reveal that the critical speed for domain writing, which is defined as the highest speed at which electrical writing of a continuous stripe domain is possible, increases non‐monotonically with RH. Additionally, the width of line domains shows a power law dependence on the writing speed, with a growth rate coefficient decreasing with RH. The size of the written domains at a constant speed as well as the creep‐factor μ describing the domain wall kinetics follow the behavior of water adsorption represented by the adsorption isotherm, indicating that the screening mechanism dominating the switching dynamics is the thickness and the structure of adsorbed water structure and its associated dielectric constant and ionic mobility.

Ferroelectric Domain Wall Motion in Freestanding Single-Crystal Complex Oxide Thin Film.

Ferroelectric domain walls in single-crystal complex oxide thin films are found to be orders of magnitude slower when the interfacial bonds with the heteroepitaxial substrate are broken to create a freestanding film. This drastic change in domain wall kinetics does not originate from the alteration of epitaxial strain; rather, it is correlated with the structural ripples at mesoscopic length scale and associated flexoelectric effects induced in the freestanding films. In contrast, the effects of the bond-breaking on the local static ferroelectric properties of both top and bottom layers of the freestanding films, such as domain wall width and spontaneous polarization, are modest and governed by the change in epitaxy-induced compressive strain.

Cobalt-Induced Performance Instabilities of Mn–Zn Ferrite Cores

Stability and reliability of transformers and inductors in power applications strongly depend on the quality of the employed ferrite cores. Given the critical role of cores, Mn–Zn ferrites’ sensitivity to their magnetic history and environmental storage conditions is investigated. To this end, Co-doped and Co-free Mn–Zn ferrites are prepared and primarily characterized in terms of structural, microstructural, and magnetic properties. The produced cores are subjected to endurance tests of technical interest comprising the response to a saturating magnetic bias and longtime storage under elevated temperature or humidity levels. With the exception of the damp heat test, prior imposition of a strong field or thermal aging process are found to induce significant instabilities to the power loss density of the Co-containing Mn–Zn ferrite cores in particular. Depending on the excitation, power loss may notably increase in the low- or high-frequency regime, whereas the effects can be either reversed with time or time independent. The proposed underlying mechanisms are based on the magnetically and thermally induced reorientation of Co2+ cations, which affects magnetocrystalline anisotropy and domain wall kinetics. Studies of different stress tests are supported by analysis of complex permeability spectra and electrical characteristics.

Characterization of domain structure and domain wall kinetics in lead-free Sr2+ doped K0.5Na0.5NbO3 piezoelectric ceramics by piezoresponse force microscopy

ABSTRACTThe domain structure and local polarization reversal were studied in lead-free ceramics (K0.5Na0.5)1-2xSrxNbO3 by various modes of scanning probe microscopy. It was shown that the increase in Sr concentration led to a decrease in both grain and domain sizes. The local polarization reversal study provided important information on the domain wall dynamics in this complicated system. The defect distribution in doped ceramics was proposed as a major factor limiting domain wall mobility and internal bias field decrease together with the increase of the activation field for domain wall motion.

Domain wall kinetics of lithium niobate single crystals near the hexagonal corner

A mesospheric approach based on a simple microscopic 2D Ising model in a hexagonal lattice plane is proposed to explain macroscopic “asymmetric in-out domain wall motion” observation in the (0001) plane of MgO-doped stoichiometric lithium niobate. Under application of an electric field that was higher than the conventional coercive field (Ec) to the ferroelectric crystal, a natural hexagonal domain was obtained with walls that were parallel to the Y-axis of the crystal. When a fraction of the coercive field of around 0.1Ec is applied in the reverse direction, this hexagonal domain is shrunk (moved inward) from the corner site into a shape with a corner angle of around 150° and 15° wall slopes to the Y-axis. A flipped electric field of 0.15Ec is then applied to recover the natural hexagonal shape, and the 150° corner shape changes into a flat wall with 30° slope (moved outward). The differences in corner domain shapes between inward and outward domain motion were analyzed theoretically in terms of corner and wall site energies, which are described using the domain corner angle and wall slope with respect to the crystal Y-axis, respectively. In the inward domain wall motion case, the energy levels of the evolving 150° domain corner and 15° slope walls are most competitive, and could co-exist. In the outward case, the energy levels of corners with angles >180° are highly stable when compared with the possible domain walls; only a flat wall with 30° slope to the Y-axis is possible during outward motion.

Domain-wall creep driven by spin torque in nanoscale ferromagnetic cylinders

We have explored the mechanism of spin-torque-driven domain-wall (DW) depinning in cylindrical nanowires of nickel using noise in electrical resistance. We find that the spectral slope of noise is a sensitive probe to the DW kinetics that reveals a creeplike behavior of the DWs at the depinning threshold, and diffusive DW motion at higher spin-torque drive. Different regimes of DW kinetics were characterized by universal kinetic exponents.

A level set approach to domain wall kinetics and domain patterning in elastic ferroelectrics

The level set method is a powerful tool for tracking a moving interface. In ferroelectric materials the boundaries between domains of uniform polarization, referred to as domain walls, are viewed as interfaces. In this work, a variational level set method is used to formulate a model for the behavior of elastic ferroelectrics and more particularly to describe the domain formation and the domain wall kinetics. A regularized version of the sharp-interface theory is introduced by substitution of the singular surfaces with thin transition layers, inserting so inhomogeneities into the energy density function. It is proved that the forces driving domain wall motion are, in fact, inhomogeneity forces. With this description, the level set method becomes an appropriate framework to insert and exploit material forces. The proposed model may interpret typical microstructures in 2-D elastic ferroelectrics with tetragonal crystal symmetry. Comparisons with phase-field models and experiments show good agreement.

On the effect of thermal history on magnetic properties of CuFe 2−2 xAl xCr xO 4 system

The effect of thermal history on the structural and magnetic properties of the quenched and slow-cooled powdered samples of the spinel system CuAl x Cr x Fe 2−2 x O 4 for compositions with x=0.2, 0.4, 0.6 and 0.8 has been investigated by means of XRD, high field (6 T) magnetization, low field dc magnetization, ac susceptibility and Mössbauer spectroscopy. The results have been explained on the basis of random canting of spins model and domain wall kinetics.

Domain walls in crystals with incommensurate phase

Abstract Domain walls in crystals with preceding incommensurate phases are discussed. The factors which stabilize the incommensurate phases with decreasing temperatures, prior to the commensurate phase, affect the spatial variation of the order parameters in the commensurate phase. In the type-II incommensurate phase like in NaNO2, the spatial variation of order parameters shows the “overshoot” and the “oscillation” in approaching the equilibrium values in the domains. In the type-I incommensurate phases like in K2SeO4, the Lifshitz invariant makes the feature of domain walls different according to how two domains are disposed. The domain wall kinetics will be briefly mentioned for the type-II case, using a lattice model.

Domain-wall kinetics and tunneling-induced instabilities in superlattices.

We report on time-resolved studies of electric-field domains in weakly coupled GaAs quantum-well structures. Photoluminescence and photocurrent experiments probe the motion of charged domain walls triggered by steplike changes in the illumination. Results reveal complex oscillations with frequencies in the range 4--8 MHz. These findings are discussed in terms of a discrete drift model relying on negative-differential conductance due to resonant tunneling. Calculations give a global phase diagram and time behavior consistent with experiments.

Some problems in domain wall kinetics

A few examples of space-time complexity in condensed matter physics are discussed in terms of domain walls which are inherent in nonlinear field equations governing the system. First we propose a coarse-grained kinetic description for systems of flat parallel domain walls (kinks and antikinks). Next we sketch our recent works on two-dimensional pattern evolution in incommensurate modulated systems of chiral as well as non-chiral types.

Domain wall kinetics in soft ferromagnetic metallic glasses

Domain wall kinetics are studied in glassy iron-base wire and iron-nickel–base ribbon. These materials exhibit high wall mobilities. The wire is examined in a single-wall regime below the nucleation field. Here reversal takes place by propagation of a domain wall of 2.5-cm axial length along the wire. The mobility normal to the wall is 270 cm/sec Oe. In the case of glassy iron-nickel–base ribbon the number of walls taking part in reversal is measured to be two. Using this number, the wall mobility is 1700 cm/sec Oe. The viscosity limiting the wall mobility is partitioned into a (calculated) eddy-current contribution and a spin-relaxation contribution. The latter constitutes about 40% of the total viscosity in the wire and about 50% in the ribbon samples. Gilbert damping constants for these samples, 0.44 (wire) and 0.19 (ribbon), are small compared with similarly obtained values for comparable polycrystalline alloys.