Transverse Domain Wall Research Articles

Manipulating the magnetization direction of transverse domain walls in Permalloy/Ir strips using nanosecond current pulses

Using magnetic force microscopy and micromagnetic simulations, we studied the effect of Oersted magnetic fields on transverse magnetic domain walls in Fe20Ni80/Ir bilayer nanostrips. Applying nanosecond current pulses with a current density of around 2×1012A/m2, the magnetization direction of a transverse domain wall in the Fe20Ni80-layer could be switched reversibly and reproducibly. This suggests that in bi- and trilayer strips the Oersted field stabilizes the transverse wall magnetization direction during current-induced domain wall motion and prevents domain wall transformations.

Fast current-induced motion of a transverse domain wall induced by interfacial Dzyaloshinskii–Moriya interaction

Based on a theoretical study, we show that the interfacial Dzyaloshinskii–Moriya interaction results in very efficient current-induced manipulation of a transverse domain wall in magnetic nanowires. The efficient domain wall motion is caused by combined effects of the domain wall distortion induced by the interfacial Dzyaloshinskii–Moriya interaction and the damping-like spin–orbit spin transfer torque. We find that with reasonable parameters, the domain wall velocity reaches a few hundreds m/s at the current density of 107 A/cm2, which has never been achieved before. Our result will be beneficial for low-power operation of domain wall devices.

Logic and memory concepts for all-magnetic computing based on transverse domain walls

We introduce a non-volatile digital logic and memory concept in which the binary data is stored in the transverse magnetic domain walls present in in-plane magnetized nanowires with sufficiently small cross sectional dimensions. We assign the digital bit to the two possible orientations of the transverse domain wall. Numerical proofs-of-concept are presented for a NOT-, AND- and OR-gate, a FAN-out as well as a reading and writing device. Contrary to the chirality based vortex domain wall logic gates introduced in Omari and Hayward (2014 Phys. Rev. Appl. 2 044001), the presented concepts remain applicable when miniaturized and are driven by electrical currents, making the technology compatible with the in-plane racetrack memory concept. The individual devices can be easily combined to logic networks working with clock speeds that scale linearly with decreasing design dimensions. This opens opportunities to an all-magnetic computing technology where the digital data is stored and processed under the same magnetic representation.

Magnetization mechanisms in ordered arrays of polycrystalline Fe100−xCox nanowires

Magnetization reversal processes and coercivity mechanisms in polycrystalline Fe100−xCox nanowire arrays, resulting from an AC electrodeposition process, are investigated. The array coercivity is described on the basis of polarization reversal mechanisms operating in individual wires, under the effect of inter-wire dipolar interactions described by a mean field approximation. For individual wires, a reversal mechanism involving the nucleation and further expansion of domain-wall like spin configuration is considered. The wires have a mean grain size larger than both the nanowire diameter and the exchange length, so localized and non-cooperative nucleation modes are considered. As the Co content increases, the alloy saturation polarization gradually decreases, but the coercive field and the relative remanence of the arrays increase, indicating that they are not controlled by the shape anisotropy in all the composition range. The coercive field dependence on the angle between the applied field and the wire long axis is not well described by reversal mechanisms involving nucleation and further displacement of neither vortex nor transverse ideal domain walls. On the contrary, the angular dependence of the coercive field observed at room temperature is well predicted by a model considering nucleation of inverse domains by localized curling, in regions smaller than the grain size, exhibiting quite small aspect ratios as compared to those of the entire nanowire. In arrays with higher Co contents, a transition from an initial (small angle) localized curling nucleation mechanism to another one, involving localized coherent rotation is observed at about π/4.

3D versus 2D domain wall interaction in ideal and rough nanowires

The interaction between transverse magnetic domain walls (TDWs) in planar (2D) and cylindrical (3D) nanowires is examined using micromagnetic simulations. We show that in perfect and surface deformed wires the free TDWs behave differently, as the 3D TDWs combine into metastable states with average lifetimes of 300ns depending on roughness, while the 2D TDWs do not due to 2D shape anisotropy. When the 2D and 3D TDWs are pinned at artificial constrictions, they behave similarly as they interact mainly through the dipolar field. This magnetostatic interaction is well described by the point charge model with multipole expansion. In surface deformed wires with artificial constrictions, the interaction becomes more complex as the depinning field decreases and dynamical pinning can lead to local resonances. This can strongly influence the control of TDWs in DW-based devices.

Domain Wall Collision-Induced Spin Waves

A series of micromagnetic simulations are conducted whereby two transverse domain walls are injected into a straight magnetic nanowire under an applied field. It is found that, based on the relative orientation of the domain walls, the two may annihilate, resulting in the generation of an intense spin-wave burst. Since the applied magnetic fields for these simulations are smaller than the Walker breakdown field, these results present an extremely low-energy means of generating and controlling spin waves for engineering applications.

Tailoring the nucleation of domain walls along multi-segmented cylindrical nanoelements

The magnetization reversal of three-segment cylindrical nanoelements comprising alternating nanowire and nanotube sections is investigated by means of Monte Carlo simulations. Such nanoelements may feature a three-state behaviour with an intermediate plateau in the hysteresis curve due to a metastable pinning of the domain walls (DWs) at the wire-tube interfaces. It turns out that vortex as well as transverse DWs contribute to the magnetization reversal. By varying the geometric parameters, the sequence, or the material of the elements the nucleation location of DWs, as well as their nucleation field, can be tailored. Especially interesting is the novel possibility to drive DWs coherently in the same or in opposite directions by changing the geometry of the hybrid nanoelement. This important feature provides additional flexibility to the construction of logical devices based on DW movement. Another prominent outcome is that DWs can be nucleated near the centre of the element and then traverse to the outer tips of the cylindrical structure when the applied field is increased, which also opens the possibility to use these three-segment nanoelements for the field-induced delivery of DWs as substitutes for large nucleation pads.

Role of spin diffusion in current-induced domain wall motion for disordered ferromagnets

Current-induced spin transfer torque and magnetization dynamics in the presence of spin diffusion in disordered magnetic textures is studied theoretically. We demonstrate using tight-binding calculations that weak, spin-conserving impurity scattering dramatically enhances the nonadiabaticity. To further explore this mechanism, a phenomenological drift-diffusion model for incoherent spin transport is investigated. We show that incoherent spin diffusion indeed produces an additional spatially dependent torque of the form $\ensuremath{\sim}{\ensuremath{\nabla}}^{2}[\mathbf{m}\ifmmode\times\else\texttimes\fi{}(\mathbf{u}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\nabla})\mathbf{m}]+\ensuremath{\xi}{\ensuremath{\nabla}}^{2}[(\mathbf{u}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\nabla})\mathbf{m}]$, where $\mathbf{m}$ is the local magnetization direction, $\mathbf{u}$ is the direction of injected current, and $\ensuremath{\xi}$ is a parameter characterizing the spin dynamics (precession, dephasing, and spin-flip). This torque, which scales as the inverse square of the domain wall width, only weakly enhances the longitudinal velocity of a transverse domain wall but significantly enhances the transverse velocity of vortex walls. The spatial-dependent spin transfer torque uncovered in this study is expected to have significant impact on the current-driven motion of abrupt two-dimensional textures such as vortices, skyrmions, and merons.

Coupled domain wall oscillations in magnetic cylindrical nanowires

We report on transverse domain wall (DW) dynamics in two closely spaced cylindrical nanowires. The magnetostatically coupled DWs are shown to undergo an intrinsic oscillatory motion along the nanowire length in addition to their default rotational motion. In the absence of external forces, the amplitude of the DW oscillation is governed by the change in the frequency of the DW rotation. It is possible to sustain the DW oscillations by applying spin-polarized current to the nanowires to balance the repulsive magnetostatic coupling. The current density required to sustain the DW oscillation is found to be in the order of 105 A/cm2. Morover, our analysis of the oscillation reveals that the DWs in cylindrical nanowires possess a finite mass.

Metastable magnetic domain walls in cylindrical nanowires

The stability of the asymmetric domain wall (ATDW) in soft magnetic cylindrical nanowires and nanotubes is investigated using micromagnetic simulations. Our calculated phase diagram shows that for cylindrical permalloy nanowires, the transverse domain wall (TDW) is the ground state for radii below 20 nm whilst the Bloch point wall (BPW) is favoured in thicker wires. The ATDW stabilises only as a metastable state but with energy close to that of the BPW. Characterisation of the DW spin structures reveals that the ATDW has a vortex-like surface spin state, in contrast to the divergent surface spins of the TDW. This results in lowering of surface charge above the critical radius. For both cylindrical nanotubes and nanowires we find that ATDWs only appear to exist as metastable static states and are particularly suppressed in nanotubes due to an increase in magnetostatic energy.

Programmable Logic Operation via Domain Wall Profile Manipulation

In this paper, we propose a prototype domain wall (DW) programmable magnetic logic device that is able to perform the AND and OR logic functions. The device operates by manipulating the information encoded in the internal spin structure of a transverse domain wall (TDW). The input and output bits in this scheme are the transverse profiles of the domain wall. By exploiting the inherent pinning and depinning mechanisms of the TDW within the device structure, the output DW profile can be deterministically controlled. The logical operation can be programmed at run time by the application of a local Oersted field.

Gilbert damping in noncollinear ferromagnets.

The precession and damping of a collinear magnetization displaced from its equilibrium are well described by the Landau-Lifshitz-Gilbert equation. The theoretical and experimental complexity of noncollinear magnetizations is such that it is not known how the damping is modified by the noncollinearity. We use first-principles scattering theory to investigate transverse domain walls (DWs) of the important ferromagnetic alloy Ni80Fe20 and show that the damping depends not only on the magnetization texture but also on the specific dynamic modes of Bloch and Néel DWs in ways that were not theoretically predicted. Even in the highly disordered Ni80Fe20 alloy, the damping is found to be remarkably nonlocal.

Reversal modes in FeCoNi nanowire arrays: Correlation between magnetostatic interactions and nanowires length

FeCoNi nanowire arrays (175 nm in diameter and lengths ranging from 5 to 40 μm) were fabricated into nanopores of hard-anodized aluminum oxide templates using pulsed ac electrodeposition technique. Increasing the length had no considerable effect on the composition and crystalline characteristics of Fe47Co38Ni15 nanowires (NWs). By eliminating the dendrites formed at the bottom of the pores, we report a careful investigation on the effect of magnetostatic interactions on magnetic properties and the effect of nanowire length on reversal modes. Hysteresis loop measurements indicated that increasing the length decreases coercivity and squareness values. On the other hand, first-order reversal curve measurements show a linear correlation between the magnetostatic interactions and length of NWs. Comparing reversal modes of the NWs both experimentally and theoretically using angular dependence of coercivity, we find that when L≤22 μm, a vortex domain wall mode is only occurred. When L>22 μm, a non-monotonic behavior indicates a transition from the vortex to transverse domain wall propagation. As a result, a critical length was found above which the transition between the reversal modes is occurred due the enhanced interactions. The transition angle also shifts toward a lower angle as the length increases. Moreover, with increasing length from 22 to 31 μm, the single domain structure of NWs changes to a pseudo single domain state. A multidomain-like behavior is also found for the longest NWs length.

Angular Dependence of the Coercivity in Electrodeposited Co–Pt Nanostructures With a Tube–Wire Morphology

We have fabricated Co-Pt cylindrical nanostructures comprised of a pair of nanotube and nanowire segments via direct electroplating into anodic alumina (AAO) membranes. The fabrication of such nanostructures is possible due to the penetration of sputtered gold (Au) nanoparticles inside the template, which serve as nucleation spots. The current transient monitored during the deposition process allowed us to distinguish between the nanotube and nanowire formation regime during the electrodeposition. In this paper, we report on the systematic changes in the angular dependence of the coercivity behavior due to the change in the length of the nanowire segment of these nanostructures, while keeping the nanotube segment constant. Considering the range of parameters studied, we found that the tube segment always reverses its magnetization through a vortex domain wall, whereas the nanowire segment reverses its magnetization through a transverse domain wall. Our results are in good agreement with literature. The possibility to alter the magnetization reversal mode in such nanostructures provides an attractive way to control the motion of the magnetic domain walls.

Domain Walls in Nanostripes of Cubic-Anisotropy Ferromagnetic Materials

We discuss the structure of the domain walls (DWs) in ferromagnetic nanostripes formed of cubic-anisotropy materials. Within certain approximations, such stationary textures are described by soliton solutions to the sine-Gordon equation in 2-D that is obtained with a constraint on the Landau-Lifshitz equation. Preferable stable and metastable types of the DWs (transverse DWs, vortex DWs, and others) are established with dependence on the stripe width and thickness using the micromagnetic simulations for a set of the so-called spintronic materials, which are of the current interest with regard to controlling the DW state. The simulated DW textures are classified on the basis of the stationary multisoliton states of the sine-Gordon model in 2-D.

Micromagnetic Modeling on Current-Induced Multiple Domain-Wall Motion in Permalloy Nanotubes

We performed micromagnetic modeling on moving multiple data bits (2-64 bits) in permalloy (Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> ) cylindrical nanotubes (PCNTs) and numerically investigated the domain-wall movement, which relies on the applied current, the Gilbert damping factor α, and radii ratio β. It was found that current-driven multiple transverse domain walls (TDWs) motion in nanotubes with an outer diameter below 25 nm and β > 0.33 was characteristic of an exceptional massless mobility. We observed that the velocity of TDWs confined in nanotubes, which was in proportion to the applied current, depended mainly on the sizes of the tubes, and α, but was independent of the number of TDWs. The obtained results offer a way to design the magnetization structures for the DW-based devices by controlling the nanotube geometric and material parameters.

Domain Wall Pinning by Antiferromagnets in Magnetic Nanowires

The use of antiferromagnets to pin domain walls in ferromagnetic nanowires was investigated using simulations. Pinning was effective for both in-plane and perpendicularly magnetized nanowires with transverse, Néel and Bloch domain walls. Domain walls could be depinned using external applied fields or electric currents and a pulsed current mode could be used to shift domain walls from one pinning site to the next.

Domain-Wall-Assisted Switching of Chains of Coupled Nanomagnets

We experimentally demonstrate that the stray field of a propagating transverse domain wall can switch chains of coupled nanomagnets (nanomagnet wires) to a magnetically ordered, low energy ground state. We fabricated nanomagnet wires consisting of 6 and 20 nanomagnets that were placed adjacent to a domain-wall conductor. Magnetic force microscope images clearly show the nanomagnet wire switching from an initial metastable state to an ordered ground state. This can be exploited for controlled order of nanomagnet switching and for energy-efficient clocking of nanomagnet logic devices. Reference structures were fabricated and characterized to prove our assumptions.

Direct observation of domain wall evolution at a bifurcation in magnetic network structures

We report on the magnetization dynamics at a bifurcation in a dual-branch magnetic network structure. When a transverse domain wall (DW) propagates through the network, interaction with an edge defect at the bifurcation leads to the transformation of the DW from transverse to vortex. The topological charge is conserved as the DW moves through the bifurcation, and this charge conservation is intrinsically linked to a −1/2 topological defect in the system. Magnetic force microscopy (MFM) imaging enables the direct observation of defect displacement during DW transformation, which induces a selective switching in the branch of the network structure.

Dynamic interaction between domain walls and nanowire vertices

The dynamic behavior of magnetic domain walls incident upon a $\mathsf{Y}$-shaped junction between three nanowires is explored. Details in the micromagnetic structure of the domain wall and the local spin texture at a vertex result in a complex interaction which ultimately determines the propagation direction of the domain wall following the vertex. This interaction has been explored through both magneto-optical Kerr effect experiments and micromagnetic simulations on single-vertex structures. Differences in the micromagnetic structure of incident domain walls in the dynamic regime have a significant influence on the interaction. We observe an oscillatory path selection with increasing domain wall propagation distance preceding the vertex. Our analysis shows that this behavior originates from cyclic reversals of the transverse domain wall chirality due to Walker breakdown processes.