Domain Wall Width Research Articles

Temperature dependence of magnetic exchange stiffness in iron and nickel

This work demonstrates a new technique to derive the magnetic exchange stiffness, A, using a measurement of the Bloch-type 180° domain wall width. Because this method is static and free from external fields, it enables the derivation of A over almost the entire temperature range up to near the Curie temperature, TC, which is difficult for existing techniques. With this technique, the temperature dependence of A for iron and nickel was assessed. Furthermore, after a systematic comparison of existing scaling functions, a promising scaling of A was demonstrated.

Domain walls in antiferromagnets: The effect of Dzyaloshinskii–Moriya interactions

We investigate domain walls in antiferromagnets focusing on the effect of Dzyaloshinskii–Moriya interactions (DMIs). Using spin model simulations and analytical arguments within a continuum theory, we show that Dzyaloshinskii–Moriya interactions affect static as well as dynamic properties of the domain wall. For certain configurations of the DMI vectors, the DMI can either tilt the easy plane of the domain wall, an effect that leads to a reduced domain wall width, or it can favor a certain chirality of the domain wall. Depending on the DMI configuration, the DMI may lead to an increasing or decreasing domain wall velocity. The asymmetry of the domain wall velocity observed in ferromagnets subject to DMI cannot be found in antiferromagnetic systems.

First-principles study of two-dimensional electron and hole gases at the head-to-head and tail-to-tail 180∘ domain walls in PbTiO3 ferroelectric thin films

We study from first-principles the structural and electronic properties of head-to-head (HH) and tail-to-tail (TT) 180$^\circ$ domain walls in isolated free-standing PbTiO$_{3}$ slabs. For sufficiently thick domains ($n$ = 16 unit cells of PbTiO$_{3}$), a transfer of charge from the free surfaces to the domain walls to form localized electron (in the HH) and hole (in the TT) gases in order to screen the bound polarization charges is observed. The electrostatic driving force behind this electronic reconstruction is clearly visible from the perfect match between the smoothed free charge densities and the bound charge distribution, computed from a finite difference of the polarization profile obtained after the relaxation of the lattice degrees of freedom. The domain wall widths, of around six unit cells, are larger than in the conventional 180$^\circ$ neutral configurations. Since no oxygen vacancies, defects or dopant atoms are introduced in our simulations, all the previous physical quantities are the intrinsic limits of the system. Our results support the existence of an extra source of charge at the domains walls to explain the enhancement of the conductivity observed in some domains walls of prototypical, insulating in bulk, perovskite oxides.

Algebraic decay of the nonadiabaticity arising through chiral spin transfer torque in magnetic domain walls with Rashba spin-orbit interaction

Spin transfer torque in a two-dimensional electron gas system without space inversion symmetry was theoretically investigated by solving the Pauli-Schr\"odinger equation for the itinerant electrons inside magnetic domain walls. Due to the presence of the Rashba spin-orbit coupling induced by the broken inversion symmetry, the spin transfer torque is chiral and the nonadiabaticity, which is defined to measure the relative importance of the nonadiabatic fieldlike torque to the adiabatic dampinglike torque, exhibits an inverse power-law decay as the domain wall width is increased. This algebraic decay is much slower than the exponential decay observed for systems without the Rashba spin-orbit coupling, and may find applications in innovative design of spintronic devices utilising magnetic topological textures such as magnetic domain walls and skyrmions.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls.

SummarySpin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Ultrafast dynamics of exchange stiffness in Co/Pt multilayer

The exchange stiffness coefficient, Aex, represents the strength of direct exchange interactions among neighboring spins. Aex is linked to most of the magnetic properties such as skyrmion formation, magnetic vortex, magnetic domain wall width, and exchange length. Hence, the quantification of Aex is essential to understanding fundamental magnetic properties, but little is known for the dynamics of Aex on a sub-picosecond timescale. We report the ultrafast dynamcis of Aex in an ordered magnetic state in Co/Pt ferromagnetic multilayer. Time-resolved magneto-optical Kerr effect and reflectivity measurements were analyzed for various pump fluences. We reveal that the significant dynamical reduction of Aex is responsible for the dramatic increase of remagnetization time for high fluences. The analysis shows that Aex dynamically varies, strongly affecting overall ultrafast demagnetization/remagnetization process. The investigation demonstrates the possibility of Aex engineering in femtosecond timescale and thereby provides a way to design ultrafast spintronic devices.

Steady one-dimensional domain wall motion in biaxial ferromagnets: Mapping of the Landau-Lifshitz equation to the sine-Gordon equation

Motivated by the difference between the dynamics of magnetization textures in ferromagnets and antiferromagnets, the Landau-Lifshitz equation of motion is explored. A typical one-dimensional domain wall in a bulk ferromagnet with biaxial magnetic anisotropy is considered. In the framework of Walker-type of solutions of steady-state ferromagnetic domain wall motion, the reduction of the non-linear Landau-Lifshitz equation to a Lorentz-invariant sine-Gordon equation typical for antiferromagnets is formally possible for velocities lower than a critical velocity of the topological soliton. The velocity dependence of the domain wall energy and the domain wall width are expressed in the relativistic-like form in the limit of large ratio of the easy-plane/easy-axis anisotropy constants. It is shown that the mapping of the Landau-Lifshitz equation of motion to the sine-Gordon equation can be performed only by going beyond the steady-motion Walker-type of solutions.

Ultralow-loss domain wall motion driven by a magnetocrystalline anisotropy gradient in an antiferromagnetic nanowire

Searching for new methods controlling antiferromagnetic (AFM) domain wall is one of the most important issues for AFM spintronic device operation. In this work, we study theoretically the domain wall motion of an AFM nanowire, driven by the axial anisotropy gradient generated by external electric field, allowing the electro control of AFM domain wall motion in the merit of ultra-low energy loss. The domain wall velocity depending on the anisotropy gradient magnitude and intrinsic material properties is simulated based on the Landau-Lifshitz-Gilbert equation and also deduced using the energy dissipation theorem. It is found that the domain wall moves at a nearly constant velocity for small gradient, and accelerates for large gradient due to the enlarged domain wall width. The domain wall mobility is independent of lattice dimension and types of domain wall, while it is enhanced by the Dzyaloshinskii-Moriya interaction. In addition, the physical mechanism for much faster AFM wall dynamics than ferromagnetic wall dynamics is qualitatively explained. This work unveils a promising strategy for controlling the AFM domain walls, benefiting to future AFM spintronic applications.

Regeneration of perpendicular exchange-biased state in high temperature regime in Pt/Co/Au/Cr2O3/Pt stacked films

Exchange bias (EB) has been a hot research topic since its discovery in the 1950s. In this paper, we present the peculiar temperature dependence of perpendicular EB in Pt/Co/Au/Cr2O3/Pt stacked films: the regeneration of the EB in the high temperature regime. Three temperature-dependent states are identified: (1) low temperature exchange-biased state, (2) middle temperature coercivity-enhanced state, and (3) high temperature regenerated exchange-biased state. At the boundary of these states, both EB field (HEB) and coercivity (HC) abruptly switch with the relationship HEB = ΔHC. The low temperature disappearance of EB can be interpreted based on the classical Meiklejohn–Bean exchange anisotropy model. A more complex temperature dependence of the interfacial spin alignment and magnetic domain wall width in the Cr2O3 layer is involved in the high temperature regeneration of EB.

Temperature dependence of exchange stiffness in an off-stoichiometric Ni2MnIn Heusler alloy

Ferromagnetic exchange stiffness is a key to describe the robustness of a ferromagnetic interaction. Because the experimental determination of the exchange stiffness constant $A$ continues to be elusive, especially at elevated temperatures, micromagnetic insights on the impact of thermal fluctuations on the ferromagnetic spin order have remained less tractable. In this study, the temperature dependence of $A$ is experimentally determined for a $\mathrm{N}{\mathrm{i}}_{2}\mathrm{M}{\mathrm{n}}_{0.8}\mathrm{I}{\mathrm{n}}_{1.2}$ single crystal by measuring the ${180}^{\ensuremath{\circ}}$ domain-wall width using off-axis electron holography and magnetocrystalline anisotropy. The theoretically expected power-law scaling with magnetization for $A$ is shown to be applicable only in the low-temperature region (approximately half of the Curie temperature), and $A$ starts to follow the power law with a significantly larger scaling exponent in the higher-temperature region. The decremental trends in the domain-wall width and the exchange length at elevated temperature seem to be attributed to this temperature dependence of $A$.

Dynamics of ferromagnetic domain walls under extreme fields

We report the existence of a new regime for domain wall motion in uniaxial and near-uniaxial ferromagnetic nanowires, characterised by applied magnetic fields sufficiently strong that one of the domains becomes unstable. There appears a new stable solution of the Landau-Lifshitz-Gilbert equation, describing a nonplanar domain wall moving with constant velocity and precessing with constant frequency. Even in the presence of thermal noise, the new solution can propagate for distances on the order of 500 times the field-free domain wall width before fluctuations in the unstable domain become appreciable.

Dynamics of domain-wall motion driven by spin-orbit torque in antiferromagnets

Ultrafast dynamics of antiferromagnetic materials is an appealing feature for novel spintronic devices. Several experiments have shown that both, the static states and the dynamical behavior of the antiferromagnetic order, are strictly related to stabilization of domains and domain wall (DW) motion. Hence for a quantitative understanding of statics and dynamics of multidomain states in antiferromagnetic materials a full micromagnetic framework is necessary. Here, we use this model to study the antiferromagnetic DW motion driven by the spin-orbit torque. The main result is the derivation of analytical expressions for the DW width and velocity that exhibit a very good agreement with the numerical simulations in a wide range of parameters. We also find that a mechanism limiting the maximum applicable current in an antiferromagnetic racetrack memory is the continuous nucleation of the domains from the edge, which is qualitatively different from what is observed in ferromagnetic racetracks.

Magnetostriction in transversely isotropic hexagonal crystals

The simultaneous occurrence of direct and inverse magnetostriction in transversely isotropic hexagonal crystal is theoretically investigated. Particular emphasis is here given to the need of identifying the fourth-order magnetostriction tensor, as it represents the most primitive object from which all related physical quantities of interest in micromagnetism are deduced. For hexagonal crystals, the magnetostriction tensor is expressed in terms of six independent magnetostrictive coefficients whose values are, so far, unknown. Indeed, the existing literature provides just four independent constraints that are extracted from the expression of the differential scalar strain in a given direction. In this work, the two extra conditions required to solve this identification problem are obtained by deducing the explicit functional dependence of the main features characterizing the motion of a magnetic domain wall along the major axis of a thin magnetostrictive nanostrip placed on the top of a thick piezoelectric actuator. The results of our analysis reveal that such two conditions may be associated to the effective anisotropy coefficient and the domain-wall width. To validate our proposal, a comparison with some recent experimental results is also successfully addressed.

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.

Charged domain walls in lithium tantalate with compositional gradients produced by partial VTE process

The morphology of a single charged domain wall, appeared under the action of composition gradients produced by partial VTE procedure by Cherenkov-type second harmonic generation microscopy, was observed in detail. The width of the charged domain wall was estimated as 70 μm. Non-through and through narrow domains, grown from the charged domain wall, were revealed. The maximum length of non-through domains with submicron diameter was about 100 μm. The growth of narrow domains from the charged domain wall was demonstrated and attributed to the action of pyroelectric field. The widening of domains occurred after achieving the polar surface.

General nature of the step-induced frustration at ferromagnetic/antiferromagnetic interfaces: topological origin and quantitative understanding

We present a study of the magnetic configuration due to step-induced magnetic frustration at ferromagnetic/antiferromagnetic (FM/AFM) interfaces. At a substrate monatomic step edge, a 180° domain wall emerges. A physically appealing form for the thickness dependence of the domain wall width is obtained. It follows a universal behaviour in the whole thickness range, from ultrathin film to bulk and in both cases of an AFM domain wall on top of the FM layer and a FM domain wall on top of an AFM substrate. In the ultrathin limit of the capping layer, the domain wall grows linearly with the slope depending only on the ratio of the inter-layer and intra-layer Heisenberg exchange constants, regardless of the presence of magneto-crystalline anisotropy. These findings are in good agreement with previous experimental observations. As the thickness grows beyond the ultrathin regime, the corresponding thickness dependence departs from linearity and tends to its bulk value. The analytical insights are supported by conclusive numerical simulations of two independent varieties, namely, the Monte Carlo method which also includes the growth kinetics and the object oriented micromagnetic framework based micromagnetic simulations. While the quantitative details of the study are naturally dependent on the specific material parameters of the complex magnetic system, the global features of the spin texture in the capping layer are dictated by the topological step-edge defect. The latter in itself is quantifiable by a winding number of

Quantifying the nucleation effect of correlated matrix grains in sintered Nd-Fe-B permanent magnets

The long-standing issue-the ferromagnetic coupling of adjacent Nd2Fe14B matrix grains across grain boundaries severely impedes further coercivity enhancement of sintered Nd-Fe-B permanent magnets. However, the quantitative role of the ferromagnetic coupling across grain boundaries on the coercivity degradation of sintered Nd-Fe-B magnets is still not well understood. Here, we quantified the nucleation effect of correlated (ferromagnetically coupled) matrix grains in sintered Nd-Fe-B magnets by integrating electron backscatter diffraction, energy dispersive spectroscopy, atom probe tomography, and high-resolution magnetic force microscopy in conjunction with micromagnetic simulations. We revealed that (1) the de-nucleation effect of correlated matrix grains (αψ) across intergranular grain boundaries is linearly enhanced with the increasing thickness (d) of grain boundaries (αψ = kd + l) and k is reduced with increasing exchange stiffness of these grain boundaries when the d is comparable to the domain wall width of the Nd2Fe14B matrix grains in sintered Nd-Fe-B magnets; (2) The thickness variation of the ferromagnetic grain boundary at the nanoscale is harmful to achieving high intrinsic coercivity of sintered Nd-Fe-B magnets; (3) The nucleation field is reduced if there is a little misalignment between correlated (ferromagnetically coupled) matrix grains. These findings shed light on grain boundary engineering at the nanoscale for enhancing the coercivity of Nd-Fe-B permanent magnets.

Analytical computation of the demagnetizing energy of thin-film domain walls

Due to its non-local nature, calculating the demagnetizing field remains the biggest challenge in understanding domain structures in ferromagnetic materials. Analytical descriptions of demagnetizing effects typically approximate domain walls as uniformly magnetized ellipsoids, neglecting both the smooth rotation of magnetization from one domain to the other and the interaction between the two domains. Here, instead of the demagnetizing field, we compute analytically the demagnetizing energy of a straight domain wall described by the classical $\tanh$ magnetization profile in a thin film with perpendicular magnetic anisotropy. We then use our expression for the demagnetizing energy to derive an improved version of the 1D model of field-driven domain wall motion, resulting in accurate expressions for important properties of the domain wall such as the domain wall width and the Walker breakdown field. We verify the accuracy of our analytical results by micromagnetic simulations.

Engineering of Magnetic Softness and Domain Wall Dynamics of Fe-rich Amorphous Microwires by Stress- induced Magnetic Anisotropy

We observed a remarkable improvement of domain wall (DW) mobility, DW velocity, giant magnetoimpedance (GMI) effect and magnetic softening at appropriate stress-annealing conditions. Beneficial effect of stress-annealing on GMI effect and DW dynamics is associated with the induced transverse magnetic anisotropy. An improvement of the circumferential permeability in the nearly surface area of metallic nucleus is evidenced from observed magnetic softening and remarkable GMI effect rising. We assumed that the outer domain shell with transverse magnetic anisotropy associated to stress-annealing induced transverse magnetic anisotropy affects the travelling DW in a similar way as application of transversal bias magnetic field allowing enhancement the DW velocity. Observed decreasing of the half-width of the EMF peak in stress-annealed microwires can be associated to the decreasing of the characteristic DW width. Consequently, stress annealing enabled us to design the magnetic anisotropy distribution beneficial for optimization of either GMI effect or DW dynamics.

Magnetic properties of isolated skyrmion under the in-plane magnetic field and anisotropy gradient

The basic magnetic properties of isolated skyrmions in thin films are fundamental to understanding the physics of magnetic skyrmions and their applications in potential spintronic devices. Here, we study the static and dynamic magnetic properties of isolated skyrmions under an in-plane magnetic field and a magnetic anisotropy gradient using micromagnetic simulations. The results demonstrate that the rotational symmetry of skyrmions is broken under the in-plane field. The radius and domain wall width of the isolated skyrmion exhibits the dependence of the external stimuli. Furthermore, the skyrmion velocity can be effectively modulated by the anisotropy gradient as well as the in-plane field. An analysis model is also derived. This work may provide guidance for the design of next-generation spintronic devices.