Domain Wall Width Research Articles

Influence of substrate on interfacial Dzyaloshinskii-Moriya interaction in epitaxial Tm3Fe5O12 films

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) promotes homochiral magnetic structures such as N\'eel-type domain walls (DWs) and skyrmions. iDMI as well as chiral magnetic structures have been demonstrated in metal/garnet heterostructures offering desirable properties for spintronic applications compared to their metallic counterparts. By measuring the motion of DWs as a function of current and in-plane magnetic field, we show that for 6.6 nm thick epitaxial thulium iron garnet films with perpendicular magnetic anisotropy grown on gallium garnet substrates, the iDMI and the DW width depend on the substrate but do not scale linearly with lattice mismatch strain. The largest iDMI was $0.007 \mathrm{mJ} {\mathrm{m}}^{\ensuremath{-}2}$, obtained for three substrates of different compositions. The total anisotropy, however, does increase linearly with lattice parameter, indicating a dominant magnetoelastic anisotropy contribution. The sensitivity of iDMI and anisotropy to substrate composition provides opportunities for engineering homochiral magnetic structures and their dynamics.

Domain-wall magnetoelectric coupling in multiferroic hexagonal YbFeO3 films

Electrical modulation of magnetic states in single-phase multiferroic materials, using domain-wall magnetoelectric (ME) coupling, can be enhanced substantially by controlling the population density of the ferroelectric (FE) domain walls during polarization switching. In this work, we investigate the domain-wall ME coupling in multiferroic h-YbFeO3 thin films, in which the FE domain walls induce clamped antiferromagnetic (AFM) domain walls with reduced magnetization magnitude. Simulation according to the phenomenological theory indicates that the domain-wall ME effect is dramatically enhanced when the separation between the FE domain walls shrinks below the characteristic width of the clamped AFM domain walls during the ferroelectric switching. Experimentally, we show that while the magnetization magnitude remains same for both the positive and the negative saturation polarization states, there is evidence of magnetization reduction at the coercive voltages. These results suggest that the domain-wall ME effect is viable for electrical control of magnetization.

Role of heterophase interfaces on local coercivity mechanisms in the magnetic Al0.3CoFeNi complex concentrated alloy

Microstructural features across different length scales have a profound influence on the coercivity of magnetic alloys. Whereas the role of homophase boundaries on the pinning of magnetic domain walls is well established, the influence of heterophase interfaces on domain wall motion is complex and poorly understood. Here, we use state-of-the-art electron microscopy techniques to show that the magnetization reversal process in an Al0.3CoFeNi magnetic complex concentrated alloy (CCA), which is responsible for its coercivity, changes dramatically from a nucleation-type mechanism in the FCC+L12 state of the CCA, with a domain wall width of 171 nm, to a pinning type mechanism in the microstructure with colonies of FCC/L12 nanorods embedded in a BCC/B2 matrix, with a domain wall width of 35 nm. Our work reveals that heterophase FCC/BCC interfaces have a much stronger effect on coercivity than isostructural chemically ordered/disordered interfaces and provides a powerful guide to the rational design of microstructure to tune magnetic properties in both complex concentrated alloys and conventional magnetic alloys.

К аналитической теории магнитных скирмионов высокого порядка в неоднородном магнитном поле

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q| > 1 due to orbital effects. We describe the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor - chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10 /MgO/Nb.

To an analytical theory of higher-order magnetic skyrmions in nonuniform magnetic fields

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q|>1 due to orbital effects. We developed the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor --- chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10/MgO/Nb. Keywords: magnetic skyrmions, nonuniform magnetic fields.

Oxygen transport at a ferroelastic domain wall in CaTiO3

The formation and migration of charged oxygen vacancies at a ${90}^{\ensuremath{\circ}}(100)[001]$ domain wall in orthorhombic ${\mathrm{CaTiO}}_{3}$ were studied by means of atomistic simulation techniques. The segregation-energy profiles of an oxygen vacancy across the wall were revealed through careful discrimination to display hyperbolic secant forms, with a domain-wall width consistent with that obtained from a tilt-angle analysis. Equilibrium distributions of oxygen vacancies across the ferroelastic domain wall in a nominally undoped (weakly acceptor-doped) sample were calculated self-consistently (assuming a sech segregation-energy profile) for various temperatures. The calculations indicate a positively charged domain wall, arising from high vacancy concentrations, compensated by negative space-charge layers, in which vacancies are depleted. The activation barriers for oxygen-vacancy migration along the domain wall, determined from nudged-elastic-band calculations, revealed that the long-range diffusion of oxygen vacancies along the wall is neither strongly enhanced nor strongly hindered.

Domain walls in fractional media.

Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states in the form of domain walls (DWs) in the two-component system of immiscible fields. Numerical study of the underlying system of fractional nonlinear Schrödinger equationsdemonstrates the existence and stability of DWs at all values of the respective Lévy index (α<2), which determines the fractional diffraction, and at all values of the XPM/SPM ratio β in the two-component system above the immiscibility threshold. The same conclusion is obtained for DWs in the system which includes the linear coupling, alongside the XPM interaction between the immiscible components. Analytical results are produced for the scaling of the DW's width. The DW solutions are essentially simplified in the special case of β=3, as well as close to the immiscibility threshold. In addition to symmetric DWs, asymmetric ones are constructed too, in the system with unequal diffraction coefficients and/or different Lévy indices of the two components.

Dynamics of chiral domain walls under applied current in cylindrical magnetic nanowires

The dynamics of two types of chiral magnetic domain walls in magnetic cylindrical nanowires under spin-polarized current are investigated by means of micromagnetic simulations. We show that Bloch point domain walls with chirality identical to that of the Oersted field can propagate without dynamical instabilities with velocities ∼300 m/s. The domain wall width is shown to widen at larger current densities limiting the velocity increase. For domain walls with opposite chirality, we observed a new pinning mechanism created by the action of the Oersted field, limiting their propagation distance even after chirality switching. Vortex–antivortex domain walls transform into Bloch point domain walls, and after that they can unexpectedly propagate either along or against the direction of the current. Our findings demonstrate that domain wall dynamics under current in cylindrical magnetic nanowires can result in a plethora of different behaviors that will have important implications for future 3D spintronic devices.

Unveiling the anisotropic fractal magnetic domain structure in bulk crystals of antiskyrmion host (Fe,Ni,Pd)3P by small-angle neutron scattering

Intermetallic Pd-doped (Fe,Ni)3P, which crystallizes in a non-centrosymmetric tetragonal structure with S 4 symmetry, has recently been discovered to host magnetic antiskyrmions, antivortex-like topological spin textures. In this material, uniaxial magnetic anisotropy and dipolar interactions play a significant role, giving rise to finely branched magnetic domain patterns near the surface of bulk crystals, as revealed by a previous magnetic force microscopy (MFM) measurement. However, small-angle neutron scattering (SANS) is a more suitable method for characterizing bulk properties and fractal structures on the mesoscopic length scale. In this study, using SANS and MFM, the magnetic domain structure in bulk single crystals of (Fe0.63Ni0.30Pd0.07)3P is quantitatively investigated. The SANS results demonstrate that the magnetic domain structure exhibits anisotropic fractal character on length scales down to the width of the magnetic domain walls. The fractal features are gradually lost in magnetic fields, and different field dependencies are observed at 300 and 2 K due to a temperature-dependent anisotropy. This study quantifies the fractality of the highly anisotropic magnetic domain structures in an antiskyrmion material, and highlights the versatility of SANS for the study of fractal structures in magnetic systems.

Atomic-scale spin-wave polarizer based on a sharp antiferromagnetic domain wall

We theoretically study the scattering of spin waves from a sharp domain wall in an antiferromagnetic spin chain. While the continuum model for an antiferromagnetic material yields the well-known result that spin waves can pass through a wide domain wall with no reflection, here we show that, based on the discrete spin Hamiltonian, spin waves are generally reflected by a domain wall with a reflection coefficient that increases as the domain-wall width decreases. Remarkably, we find that, in the interesting case of an atomically sharp domain wall, the reflection of spin waves exhibits strong dependence on the state of circular polarization of the spin waves, leading to mainly reflection for one polarization while permitting partial transmission for the other, thus realizing an atomic-scale spin-wave polarizer. The polarization of the transmitted spin wave depends on the orientation of the spin in the sharp domain wall, which can be controlled by an external field or spin torque. Our utilization of a sharp antiferromagnetic domain wall as an atomic-scale spin-wave polarizer leads us to envision that ultra-small magnetic solitons such as domain walls and skyrmions may enable realizations of atomic-scale spin-wave scatterers with useful functionalities.

A mechanically strong and ductile soft magnet with extremely low coercivity

Soft magnetic materials (SMMs) serve in electrical applications and sustainable energy supply, allowing magnetic flux variation in response to changes in applied magnetic field, at low energy loss1. The electrification of transport, households and manufacturing leads to an increase in energy consumption owing to hysteresis losses2. Therefore, minimizing coercivity, which scales these losses, is crucial3. Yet meeting this target alone is not enough: SMMs in electrical engines must withstand severe mechanical loads; that is, the alloys need high strength and ductility4. This is a fundamental design challenge, as most methods that enhance strength introduce stress fields that can pin magnetic domains, thus increasing coercivity and hysteresis losses5. Here we introduce an approach to overcome this dilemma. We have designed a Fe–Co–Ni–Ta–Al multicomponent alloy (MCA) with ferromagnetic matrix and paramagnetic coherent nanoparticles (about 91 nm in size and around 55% volume fraction). They impede dislocation motion, enhancing strength and ductility. Their small size, low coherency stress and small magnetostatic energy create an interaction volume below the magnetic domain wall width, leading to minimal domain wall pinning, thus maintaining the soft magnetic properties. The alloy has a tensile strength of 1,336 MPa at 54% tensile elongation, extremely low coercivity of 78 A m−1 (less than 1 Oe), moderate saturation magnetization of 100 A m2 kg−1 and high electrical resistivity of 103 μΩ cm.

Nanoscale Antiferromagnetic Domain Imaging using Full-Field Resonant X-ray Magnetic Diffraction Microscopy.

The physical properties of magnetic materials frequently depend not only on the microscopic spin and electronic structures, but also on the structures of mesoscopic length scales that emerge, for instance, from domain formations, or chemical and/or electronic phase separations. However, experimental access to such mesoscopic structures is currently limited, especially for antiferromagnets with net zero magnetization. Here, full-field microscopy and resonant magnetic X-ray diffraction are combined to visualize antiferromagnetic (AF) domains of the spin-orbit Mott insulator Sr2 IrO4 with area over ≈0.1 mm2 and with spatial resolution as high as ≈150nm. With the unprecedented wide field of views and high spatial resolution, an intertwining of two AF domains on a length comparable to the measured average AF domain wall width of 545nm is revealed. This mesoscopic structure comprises a substantial portion of the sample surface, and thus can result in a macroscopic response unexpected from its microscopic magnetic structure. In particular, the symmetry analysis presented in this work shows that the inversion symmetry, which is preserved by the microscopic AF order, becomes ill-defined at the mesoscopic length scale. This result underscores the importance of this novel technique for a thorough understanding of the physical properties of antiferromagnets.

Magnetic domain walls of the van der Waals material Fe3GeTe2

Among two-dimensional materials, Fe3GeTe2 has come to occupy a very important place owing to its ferromagnetic nature with one of the highest Curie temperatures among known van der Waals materials and the potential for hosting skyrmions. In this combined experimental and theoretical work, we investigate the magnetic bubble domains as well as the microscopic domain wall profile using spin-polarized scanning tunneling microscopy in combination with atomistic spin-dynamics simulations performed with parameters from density functional theory calculations. We find a weak magneto-electric effect influencing the domain wall width by the electric field in the tunneling junction and determine the critical magnetic field for the collapse of the bubble domains. Our findings shed light on the origins of complex magnetism that Fe3GeTe2 exhibits.

Application of the Point-Like Contact Model: Resistance Oscillations of the Domain Wall in Magnetic Nanowires and Junctions Due to Mean Free Path Effects

This work is focused on determining the electrical resistance, which is induced by single domain wall (DW) in magnetic nanowire (NW) with a negligible defect. The provided model covers a wide range of NW diameters. The obtained result demonstrates a few-order rapid reduction of the DW resistance accompanied by its possible deviations versus the diameter growth ranging from 1.2[Formula: see text]nm to 15.2[Formula: see text]nm. The origin of these deviations, which are also identified as oscillations, is referred to the nonuniform electron scattering on the DW due to the intermixing electron scattering conditions: ballistic for one spin channel and quasi-ballistic for other one with opposite spin direction. It may happen when the DW width by value is approximately in between two lengths: a mean free path (MFP) with the spin down and spin up. The indirect evidence of this finding also comes from the fact that homogeneous NWs show the most valuable DW resistance oscillations by magnitude rather than segmented magnetic NWs. In addition to the approach, where DW width is constant, the other reasonable model is used when the DW can be constrained for some conditions. The same results are valid for magnetic junctions with DW. Finally, resistance simulation in the diffusive range, when a diameter of the NW (or point-like junction) is larger than any of spin-resolved MFP of electrons, successfully follows experimental data for the single and double DW resistances available in literature.

Spin transfer torque bias (STTB) due to domain wall resistance in an infinitely long ferromagnetic nanowire

The shift of a magnetization loop along the magnetic field axis for a ferromagnetic (FM)/anti-ferromagnetic (AFM) system when it is cooled through Néel temperature of AFM layer is called exchange anisotropy or exchange bias. Here, using micromagnetic simulations we propose that spin transfer torque (STT) mechanism would indeed be helpful in realizing the shift of the magnetization loop along magnetic field axis through domain wall (DW) resistance for an infinitely long FM nanowire without having AFM layer, which we call as spin transfer torque bias (STTB). Essentially, STTB is realized on both positive and negative magnetic field axes by varying the angle between spin polarized current and Zeeman field from 0° to 180° respectively and the origin is attributed to helical motion of the DW. However, we do not see STTB at 90° due to coherent rotation of domain. We also ascertain that STTB is also a function of magnetic anisotropy, current density, polarization strength and non-adiabatic STT term. Variation in STTB for different FM systems such as Fe2CoSi, Ni80Fe20 and Fe is attributed to a change in DW width. We believe that present results would lead to a new dimension in the field of spintronics.

Ultra-thin interfacial domain wall less than 1 nm based on TbxCo100−x/Cu/[Co/Pt]2 heterostructures for multi-level magnetic pillar memory

We propose a new pillar type of multi-level memory with TbxCo100−x/Cu/[Co/Pt]2 heterostructures to achieve high storage density and controllable domain wall position in-memory applications. The structure consists of amorphous ferrimagnetic Tb–Co alloy films and ferromagnetic Co/Pt multilayers separated by less than one monolayer of Cu. Here, we observe that the interfacial domain wall energy density can be controlled by changing the interlayer thickness of Cu and Tb–Co composition. We also observe two competing mechanisms, one leading to an increase and the other to a decrease, corresponding to the effect of Tb content on saturation magnetization and coercivity of heterostructures. Theoretical and experimental results show that by tuning the Tb–Co composition, we were able to decrease domain wall (DW) width and precisely control the DW position of the multilayer structure. The interfacial domain wall width is significantly decreased to less than 1 nm compared to other reports. Moreover, controlling the DW position and width offers a novel multi-level magnetic memory with high performance compared to conventional memory applications.

Resolving the spin polarization and magnetic domain wall width of (Nd,Dy)2Fe14B with spin-polarized scanning tunneling microscopy

The electronic structure and the domain wall width of industrial (Nd,Dy)2Fe14B hard magnets were investigated using low-temperature, spin-polarized scanning tunneling microscopy (STM) in ultra-high vacuum. In a first step, atomically clean and flat surfaces were prepared. The flat terraces were separated by monatomic steps. Surface termination was identified as the Fe c layer from atomically resolved STM imaging. The electronic density of states and its spin polarization agree well with ab initio predictions of the Fe c layer. High-resolution spin-polarized STM images allowed to finally resolve the domain wall width w of only 3.2 ± 0.4 nm.

Detailed examination of domain wall types, their widths and critical diameters in cylindrical magnetic nanowires

Understanding and mastering the magnetic properties of domain walls in cylindrical nanowires is a fundamental pillar for developing novel 3D information technologies. For this purpose, a good comprehension of domain wall (DW) dynamical properties, which are strongly dependent on its type and size, is needed. In this work, by means of micromagnetic simulations, we focus on the accurate determination of DW types (transverse, vortex-antivortex, and the Bloch point) and DW widths and present a state diagram as a function of the diameter and the nanowire material. Using different initial states and trajectories we find a large region of metastability where the Bloch-point domain wall co-exists with either transverse or a more energetical vortex-antivortex one. We determine the domain wall width and its dependence on the nanowire diameter either for the transverse or the vortex-antivortex domain wall showing that it is always larger than the nanowire diameter. We also find simple expressions for the DW widths and the critical diameter for the transition between different DW types which agree well with direct simulations. Our results are useful for the experimental design of cylindrical nanowires for multiple applications.

Strong-coupling corrections to hard domain walls in superfluid He3−B

Domain walls in superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}B$ have gained renewed interest in light of experimental progress on confining helium in nanofabricated geometries. Here, we study the effect of strong-coupling corrections on domain wall width and interfacial tension by determining self-consistent solutions to spatially-dependent Ginzburg-Landau equations. We find that the formation of domain walls is generally energetically favored in strong coupling over weak coupling. Calculations were performed over a wide range of temperatures and pressures, showing decreasing interface energy with increasing temperature and pressure. This has implications for the observability of such domain walls in $^{3}\mathrm{He}\text{\ensuremath{-}}B$, which are of both fundamental interest and form the basis for spatially-modulated pair-density wave states, when stabilized by strong confinement.

Computation of magnetization, exchange stiffness, anisotropy, and susceptibilities in large-scale systems using GPU-accelerated atomistic parallel Monte Carlo algorithms

Monte Carlo algorithms are frequently used in atomistic simulations, including for computation of magnetic parameter temperature dependences in multiscale simulations. Even though parallelization strategies for Monte Carlo simulations of lattice spin models are known, its application to computation of magnetic parameter temperature dependences is lacking in the literature. Here we show how, not only the unconstrained algorithm, but also the constrained atomistic Monte Carlo algorithm, can be parallelized for any spin–lattice crystal structure. Compared to the serial algorithms, the parallel Monte Carlo algorithms are typically over 200 times faster, allowing computations in systems with over 10 million atomistic spins on a single graphical processing unit with relative ease. Implementation and testing of the algorithms was carried out in large-scale systems, where finite-size effects are reduced, by accurately computing temperature dependences of magnetization, uniaxial and cubic anisotropies, exchange stiffness, and susceptibilities. In particular for the exchange stiffness the Bloch domain wall method was used with a large cross-sectional area, which allows accurate computation of the domain wall width up to the Curie temperature. The exchange stiffness for a simple cubic lattice closely follows an mk scaling at low temperatures, with k < 2 dependent on the anisotropy strength. However, close to the Curie temperature the scaling exponent tends to k = 2. Furthermore, the implemented algorithms are applied to the computation of magnetization temperature dependence in granular thin films with over 15 million spins, as a function of average grain size and film thickness. We show the average Curie temperature in such systems may be obtained from a weighted Bloch series fit, which is useful for analysis of experimental results in granular thin films.