Eel Walls Research Articles

Emergence of Sizeable Interfacial Dzyaloshinskii-Moriya Interaction at Cobalt/Fullerene Interface

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) originating from a heavy-metal/ferromagnet (FM) interface plays a crucial role in stabilizing chiral spin textures in magnetic multilayers. Recently, graphene based on the low-spin-orbit-coupling (SOC) element carbon ($\mathrm{C}$) has shown a significant iDMI owing to the Rashba SOC when deposited on top of $\mathrm{Co}$. A similar enhanced SOC has been reported earlier for other $\mathrm{C}$ allotropes, namely fullerene (${\text{C}}_{60}$) and carbon nanotubes, and a sizeable DMI can be expected to emerge from them. In this context, we elucidate the magnetization-reversal mechanism, the domain-wall (DW) dynamics, and the strength of the iDMI in a $\mathrm{Pd}(4.0\phantom{\rule{0.2em}{0ex}}\mathrm{nm})/\mathrm{Co}(0.5\phantom{\rule{0.2em}{0ex}}\mathrm{nm})/{\text{C}}_{60}({t}_{{\mathrm{C}}_{60}})/\text{Pd}(2.0\phantom{\rule{0.2em}{0ex}}\mathrm{nm})$ system with varying ${t}_{{\mathrm{C}}_{60}}$. The field-induced DW velocity measured in the creep region shows a DW velocity 2 orders of magnitude higher for a sample with 1.6 nm of ${\text{C}}_{60}$, due to a lower depinning field and spin-dependent hybridization at the $\text{Co}/{\text{C}}_{60}$ interface. Further, DMI measurements performed by use of the asymmetric DW expansion method exhibit a systematic increase in the iDMI from $\ensuremath{-}0.07$ to $\ensuremath{-}0.46\phantom{\rule{0.2em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$ with an increase in ${t}_{{\mathrm{C}}_{60}}$. Such an enhanced iDMI turns an achiral Bloch wall into a chiral N\'eel wall. The emergence of a finite DMI (${D}_{\mathrm{Co}/{\mathrm{C}}_{60}}\ensuremath{\sim}\ensuremath{-}0.11\phantom{\rule{0.2em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$) from the $\text{Co}/{\text{C}}_{60}$ interface is particularly encouraging for the use of $\mathrm{C}$-based materials in chiral-DW-based device applications.

Fast, semianalytical approach to obtain the stray magnetic field above a magnetic skyrmion

We present a fast, matrix-based semianalytical method to calculate the stray magnetic field and its derivative above spin textures with cylindrical symmetry. A magnetostatic Green's function approach is used to obtain accurate fields and magnetic forces, which are confirmed using micromagnetic simulations. The developed method can be used to quickly analyze and fit experimental measurements of the stray magnetic field (measured, for example, via nitrogen vacancies in diamond) or magnetic forces (measured via magnetic force microscopy) above a thin film or patterned element. Calculations for magnetic skyrmions show that these techniques have the potential to distinguish between Bloch and N\'eel walls for skyrmions in single-layer as well as in multilayer thin films where the wall structure evolves with depth.

Switching between Magnetic Bloch and Néel Domain Walls with Anisotropy Modulations.

It has been shown previously that the presence of a Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films stabilizes Néel type domain walls. We demonstrate, using micromagnetic simulations and analytical modeling, that the presence of a uniaxial in plane magnetic anisotropy can also lead to the formation of Néel walls in the absence of a Dzyaloshinskii-Moriya interaction. It is possible to abruptly switch between Bloch and Néel walls via a small modulation of the in plane, but also the perpendicular, magnetic anisotropy. This opens up a route toward electric field control of the domain wall type with small applied voltages through electric field controlled anisotropies.

Magnetic domain wall dynamics in the precessional regime: Influence of the Dzyaloshinskii-Moriya interaction

The domain wall dynamics driven by an out of plane magnetic field was measured for a series of magnetic trilayers with different strengths of the interfacial Dzyaloshinskii-Moriya interaction (DMI). The features of the field-driven domain wall velocity curves strongly depend on the amplitude of the HD field stabilising chiral N\'eel walls. The measured Walker velocity, which in systems with large DMI is maintained after the Walker field giving rise to a velocity plateau up to the Slonczewski field HS, can be easily related to the DMI strength. Yet, when the DMI field HD and the domain wall demagnetising field HDW have comparable values, a careful analysis needs to be done in order to evaluate the impact of the DMI on the domain wall velocity. By means of a one-dimensional model and 2D simulations, we successfully extend this method to explain experimental results to cases where HD and HDW are comparable.

Coexistence of Bloch and Néel walls in a collinear antiferromagnet

We resolve the domain-wall structure of the model antiferromagnet $\text{Cr}_2\text{O}_3$ using nanoscale scanning diamond magnetometry and second-harmonic-generation microscopy. We find that the 180$^\circ$ domain walls are predominantly Bloch-like, and can co-exist with N\'eel walls in crystals with significant in-plane anisotropy. In the latter case, N\'eel walls that run perpendicular to a magnetic easy axis acquire a well-defined chirality. We further report quantitative measurement of the domain-wall width and surface magnetization. Our results provide fundamental input and an experimental methodology for the understanding of domain walls in pure, intrinsic antiferromagnets, which is relevant to achieve electrical control of domain-wall motion in antiferromagnetic compounds.

Theoretical study of current-induced domain wall motion in magnetic nanotubes with azimuthal domains

We report a theoretical overview of the magnetic domain wall behavior under an electric current in infinitely-long nanotubes with azimuthal magnetization, combining the $1$D analytic model and micromagnetic simulations. We highlight effects that, besides spin-transfer torques already largely understood in flat strips, arise specifically in the tubular geometry: the \OErsted field and curvature-induced magnetic anisotropy resulting both from exchange and material growth. Depending on both the geometry of the tube and the strength of the azimuthal anisotropy, Bloch or N\'eel walls arise at rest, resulting in two regimes of motion largely dominated by either spin-transfer torques or the \OErsted field. We determine the Walker breakdown current in all cases, and highlight the most suitable parameters to achieve high domain wall speed.

In-plane Néel wall chirality and orientation of interfacial Dzyaloshinskii-Moriya vector in magnetic films

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is of great interest as it can stabilize chiral spin structures in thin films. Experiments verifying the orientation of the interfacial DMI vector remain rare, in part due to the difficulty of separating vector components of DMI. In this study, Fe/Ni bilayers and Co/Ni multilayers were deposited epitaxially onto Cu(001) and Pt(111) substrates, respectively. By tailoring the effective anisotropy, spin reorientation transitions (SRTs) are employed to probe the orientation of the DMI vector by measuring the spin structure of domain walls on both sides of the SRTs. The interfacial DMI is found to be sufficiently strong to stabilize chiral N\'eel walls in the out-of-plane magnetized regimes, while achiral N\'eel walls are observed in the in-plane magnetized regimes. These findings experimentally confirm that the out-of-plane component of the DMI vector is insignificant in these fcc(001) and fcc(111) oriented interfaces, even in the presence of atomic steps.

Magnetic Chirality Controlled by the Interlayer Exchange Interaction.

Chiral magnetism, wherein there is a preferred sense of rotation of the magnetization, determines the chiral nature of magnetic textures such as skyrmions, domain walls, or spin spirals. Current research focuses on identifying and controlling the interactions that define the magnetic chirality in thin film multilayers. The influence of the interfacial Dzyaloshinskii-Moriya interaction (IDMI) and, recently, the dipolar interactions have been reported. Here, we experimentally demonstrate that an indirect interlayer exchange interaction can be used as an additional tool to effectively manipulate the magnetic chirality. We image the chirality of magnetic domain walls in a coupled bilayer system using scanning electron microscopy with polarization analysis. Upon increasing the interlayer exchange coupling, we induce a transition of the magnetic chirality from clockwise rotating Néel walls to degenerate Bloch-Néel domain walls and we confirm our findings with micromagnetic simulations. In multilayered systems relevant for skyrmion research, a uniform magnetic chirality across the magnetic layers is often desired. Additional simulations show that this can be achieved for reduced IDMI values (up to 30%) when exploiting the interlayer exchange interaction. This work opens up new ways to control and tailor the magnetic chirality by the interlayer exchange interaction.

Understanding Dense Active Nematics from Microscopic Models

We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to "arch" solutions forming a globally polar, smecticlike arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.

Theory of the Interfacial Dzyaloshinskii-Moriya Interaction in Rashba Antiferromagnets.

In antiferromagnetic (AFM) thin films, broken inversion symmetry or coupling to adjacent heavy metals can induce Dzyaloshinskii-Moriya (DM) interactions. Knowledge of the DM parameters is essential for understanding and designing exotic spin structures, such as hedgehog Skyrmions and chiral Néel walls, which are attractive for use in novel information storage technologies. We introduce a framework for computing the DM interaction in two-dimensional Rashba antiferromagnets. Unlike in Rashba ferromagnets, the DM interaction is not suppressed even at low temperatures. The material parameters control both the strength and the sign of the interfacial DM interaction. Our results suggest a route toward controlling the DM interaction in AFM materials by means of doping and electric fields.

Domain-width model for perpendicularly magnetized systems with Dzyaloshinskii-Moriya interaction

The influence of the Dzyaloshinskii-Moriya interaction (DMI) on stripe domains in perpendicularly magnetized thin ferromagnetic films is theoretically and experimentally investigated. We develop a domain spacing model describing the dependence of the stripe domain width on the magnetic properties of the sample. By including the magnetostatic energy of the domain walls the model correctly describes the transition from Bloch to N\'eel walls with increasing DMI constant. An approach to determine the magnitude of the DMI constant by fitting the stripe domain width as a function of the effective perpendicular anisotropy of wedge-shaped samples is developed and applied to several ultrathin multilayer samples based on Ni/Fe/Cu(001). The magnitude of the DMI constant arising from Fe/Ni and Ni/Fe interfaces is $0.3\ifmmode\pm\else\textpm\fi{}0.14$ meV/atom, indicating that the domain walls are in a pure chiral N\'eel state. Furthermore, phase diagrams of the skyrmionic bubble domain phase are recorded for two samples with different DMI constants, and by scaling the magnetic field a universal phase diagram for perpendicularly magnetized systems is obtained.

Achiral tilted domain walls in perpendicularly magnetized nanowires

Perpendicularly magnetized nanowires exhibit distinct domain wall types depending on the geometry. Wide wires contain Bloch walls, narrow wires N\'eel walls. Here, the transition region is investigated by direct imaging of the wall structure using high-resolution spin-polarized scanning electron microscopy. An achiral intermediate wall type is discovered that is unpredicted by established theoretical models. With the help of micromagnetic simulations, the formation of this novel wall type is explained.

Domain walls in finite-width nanowires with interfacial Dzyaloshinskii-Moriya interaction

It is widely known that the interfacial Dzyaloshinskii-Moriya interaction (DMI) may stabilize N\'eel walls rather than Bloch walls in magnetic thin films. When the DMI is weak, it results in a ``tilted'' Bloch wall. However, for most applications, domain walls are in nanowires rather than thin films. Here we present a semianalytic two-parameter calculation for the static domain wall in a nanowire of finite width and thickness, with DMI. The DMI strength that is needed to force a N\'eel wall is smaller in nanowires than in films due to demagnetizing energy. Even nanowires that are hundreds of nanometers wide may have different domain wall solutions than thin films and so their finite size must be considered. The impact of this result on current experiments is briefly discussed. We extend the model to show that applying a weak magnetic field allows the domain wall type to be tuned.

Interacting tails of asymmetric domain walls: Theory and experiments

In this paper, we address the structure and interaction of neighboring asymmetric N\'eel and Bloch walls in soft ferromagnetic films. First, we review a recent reduced model for the structure of parallel systems of asymmetric walls with potentially interacting tails and provide a derivation via the method of matched asymptotic expansions, starting from the micromagnetic-torque equation. Then, we report on experimentally observed domain-wall transitions under a varying hard-axis field in ${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$ films. Upon the wall transition, the average hard-axis magnetization in the domains increases significantly, by an amount that depends on the width of the domains. For films of moderate thickness, the hard-axis magnetization jump that the theory predicts excellently agrees with the experimental data. Hence, we conclude that interacting tails of neighboring asymmetric N\'eel walls cause the observed additional rotation of the magnetization towards large hard-axis fields.

Lorentz TEM Imaging of Stripe Structures Embedded in a Soft Magnetic Matrix

N\'eel walls in soft magnetic NiFe/NiFeGa hybrid stripe structures surrounded by a NiFe film are investigated by high resolution Lorentz transmission electron microscopic imaging. An anti-parallel orientation of magnetization in 1000 nm wide neighboring unirradiated-irradiated stripes is observed by forming high angle domain walls during magnetization reversal. Upon downscaling the stripe structure size from 1000 nm to 200 nm a transition from a discrete domain pattern to an effective magnetic medium is observed for external magnetic field reversal. This transition is associated with vanishing ability of hosting high angle domain walls between adjacent stripes. The investigation also demonstrated the potentiality of Lorentz microscopy to image periodic stripe structures well under micron length-scale.

Role of nonlinear anisotropic damping in the magnetization dynamics of topological solitons

The consequences of nonlinear anisotropic damping, driven by the presence of Rashba spin-orbit coupling in thin ferromagnetic metals, are examined for the dynamics of topological magnetic solitons such as domain walls, vortices, and skyrmions. The damping is found to affect Bloch and N\'eel walls differently in the steady-state regime below Walker breakdown and leads to a monotonic increase in the wall velocity above this transition for large values of the Rashba coefficient. For vortices and skyrmions, a generalization of the damping tensor within the Thiele formalism is presented. It is found that chiral components of the damping affect vortexlike and hedgehoglike skyrmions in different ways, but the dominant effect is an overall increase in the viscouslike damping.

Measuring and tailoring the Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films

We investigate the Dzyaloshinskii-Moriya interactions (DMIs) in perpendicularly magnetized thin films of Pt/Co/Pt and Pt/Co/Ir/Pt. To study the effective DMI, arising at either side of the ferromagnet, we use a field-driven domain wall creep-based method. The use of only magnetic field removes the possibility of mixing with current-related effects such as spin Hall effect or Rashba field, as well as the complexity arising from lithographic patterning. Inserting an ultrathin layer of Ir at the top Co/Pt interface allows us to access the DMI contribution from the top Co/Pt interface. We show that the insertion of a thin Ir layer leads to reversal of the sign of the effective DMI acting on the sandwiched Co layer, and therefore continuously changes the domain wall structure from the right- to the left-handed N\'eel wall. The use of two DMI-active layers offers an efficient way of DMI tuning and enhancement in thin magnetic films. The comparison with an epitaxial Pt/Co/Pt multilayer sheds more light on the origin of DMI in polycrystalline Pt/Co/Pt films and demonstrates an exquisite sensitivity to the exact details of the atomic structure at the film interfaces.

Electric field induced domain-wall dynamics: Depinning and chirality switching

We theoretically study the equilibrium and dynamic properties of nanoscale magnetic tunnel junctions (MTJs) and magnetic wires, in which an electric field controls the magnetic anisotropy through spin-orbit coupling. By performing micromagnetic simulations, we construct a rich phase diagram and find that, in particular, the equilibrium magnetic textures can be tuned between N\'eel and Bloch domain walls in an elliptical MTJ. Furthermore, we develop a phenomenological model of a quasi-one-dimensional domain wall confined by a parabolic potential and show that, near the N\'eel-to-Bloch-wall transition, a pulsed electric field induces precessional domain-wall motion which can be used to reverse the chirality of a N\'eel wall and even depin it. This domain-wall motion controlled by electric fields, in lieu of applied current, may provide a model for ultralow-power domain-wall memory and logic devices.

Matching domain-wall configuration and spin-orbit torques for efficient domain-wall motion

In our numerical study, we identify the best conditions for efficient domain wall motion by spin-orbit torques originating from the Spin Hall effect or Rashba effect. We demonstrate that the effect depends critically on the domain wall configuration, the current injection scheme and the symmetry of the spin-orbit torque. The best identified configuration corresponds to a N\'eel wall driven by spin Hall Effect in a narrow strip with perpendicular magnetic anisotropy. In this case, the domain wall velocity can be a factor of 10 larger than that for the conventional current-in-plane spin-transfer torque.

Domain wall nanoelectronics

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.