Domain Wall Velocity Research Articles

Magneto‐Ionics in Annealed W/CoFeB/HfO2 Thin Films

AbstractThe magneto‐ionic modulation of the Dzyaloshinskii–Moriya interaction (DMI) and the perpendicular magnetic anisotropy (PMA), in W/CoFeB/HfO2 stacks annealed at different temperatures and for varying annealing times, are presented in this work. A large modulation of PMA and DMI is observed in the systems annealed at 390 and 350 °C, whereas no response to voltage is observed in the as‐grown samples. A strong DMI is only observed in the samples annealed at 390 °C for 1 h, while PMA is present for all annealing times at temperatures of 390 and 350 °C. Magnetic properties including domain wall velocity improve drastically with increasing the annealing temperature and time, while the magneto‐ionic reversibility is increasingly compromised. The changes in PMA and DMI induced by the gate voltages in the samples annealed at 390 °C are permanent, while partial reversibility is only observed for the samples annealed at 350 °C for short times. This dependence of reversibility on post‐grown annealing has been associated to the influence of crystallization on ion mobility. These results show that a compromise between the enhancement of the magnetic properties and the magneto‐ionic performance could be needed in systems requiring annealing to develop PMA and DMI.

Domain wall velocity asymmetries driven by saturation magnetization gradients without a Dzyaloshinskii-Moriya interaction

The discovery of asymmetric domain wall velocities in magnetic alloys and multilayers without a heavy metal underlayer has given rise to claims of a large Dzyaloshinskii-Moriya interaction (DMI) driven by compositional non-uniformities. However, these non-uniformities also give rise to vertically non-uniform magnetic properties which can influence the dynamic properties of domain walls. In this work, we use micromagnetic simulations to show that vertical modulation of the saturation magnetization can give rise to asymmetric domain wall velocities for field and current driven motion, closely resembling the presence of a DMI. For field driven motion, by comparing the velocity asymmetries for varying saturation magnetization gradients, film thicknesses, and average saturation magnetization, we show that the magnitude of effective symmetry breaking field resulting from the non-uniformity can be comparable to those resulting from DMI. These effects scale with thickness and degree of modulation, mirroring recent results in single layer materials. However, the scaling of domain velocity asymmetries is largely suppressed for SOT driven domain dynamics. Therefore, great care needs to be taken when evaluating DMI in non-uniform systems.

Analysis of Barkhausen pulse shapes in lithium niobate single crystals

We present a Barkhausen pulse (BP) shape fitting method that allows extracting the domain wall velocities during a given fast domain shape transformation after merging during switching in lithium niobate. Two scenarios of hexagonal domain merging were distinguished: for domains with comparable sizes, and for large and small domains. The fitting was based on the knowledge about domain wall types and delay time of the external circuit. The derived expressions were successfully used for fitting the shapes of experimentally obtained BPs. Proposed fitting allowed extracting the velocities of fast and superrfast domain walls with high accuracy.

Domain Wall Automotion in Three-Dimensional Magnetic Helical Interconnectors.

The fundamental limits currently faced by traditional computing devices necessitate the exploration of ways to store, compute, and transmit information going beyond the current CMOS-based technologies. Here, we propose a three-dimensional (3D) magnetic interconnector that exploits geometry-driven automotion of domain walls (DWs), for the transfer of magnetic information between functional magnetic planes. By combining state-of-the-art 3D nanoprinting and standard physical vapor deposition, we prototype 3D helical DW conduits. We observe the automotion of DWs by imaging their magnetic state under different field sequences using X-ray microscopy, observing a robust unidirectional motion of DWs from the bottom to the top of the spirals. From experiments and micromagnetic simulations, we determine that the large thickness gradients present in the structure are the main mechanism for 3D DW automotion. We obtain direct evidence of how this tailorable magnetic energy gradient is imprinted in the devices, and how it competes with pinning effects that are due to local changes in the energy landscape. Our work also predicts how this effect could lead to high DW velocities, reaching the Walker limit during automotion. This work demonstrates a possible mechanism for efficient transfer of magnetic information in three dimensions.

Nanosecond ultralow power spin orbit torque magnetization switching driven by BiSb topological insulator

Topological insulators (TIs) are promising for spin–orbit torque (SOT) switching thanks to their giant spin Hall angle. SOT switching using TIs has been studied so far in the thermal activation regime by direct currents or relatively long pulse currents (≥10 ns). In this work, we studied SOT magnetization switching of (Pt/Co) multilayers with strong perpendicular magnetic anisotropy by the BiSb topological insulator in both thermal activation and fast switching regime with pulse width down to 1 ns. We reveal that the zero-Kelvin threshold switching current density Jth0BiSb is 2.5 × 106 and 4.1 × 106 A/cm2 for the thermal activation regime and fast switching regime in a 800 nm-wide Hall bar device via domain wall depining. From time-resolved measurements using 1 ns pulses, we find that the domain wall velocity is 430–470 m/s at JBiSb = 1.6 × 107–1.7 × 107 A/cm2. Our work demonstrates the potential of the BiSb thin film for ultralow power and fast operation of SOT-based spintronic devices.

Ultrafast magnetic scattering on ferrimagnets enabled by a bright Yb-based soft x-ray source

Development of ultrafast table-top x-ray sources that can map various spin, orbital, and electronic configurations and reordering processes on their natural time and length scales is an essential topic for modern condensed matter physics as well as ultrafast science. In this work, we demonstrate spatiotemporally resolved resonant magnetic scattering (XRMS) to probe the inner-shell 4d electrons of a rare-earth (RE) composite ferrimagnetic system using a bright > 200 e V soft x-ray high harmonic generation (HHG) source, which is relevant for future energy-efficient, high-speed spintronic applications. The XRMS is enabled by direct driving of the HHG process with power-scalable, high-energy Yb laser technology. The optimally phase-matched broadband plateau of the HHG offers a record photon flux ( > 2 × 1 0 9 p h o t o n s / s / 1 % bandwidth) with excellent spatial coherence and covers the entire resonant energy range of RE’s N 4 , 5 edges. We verify the underlying physics of our x-ray generation strategy through the analysis of microscopic and macroscopic processes. Using a CoTb alloy as a prototypical ferrimagnetic system, we retrieve the spin dynamics, and resolve a fast demagnetization time of 500 ± 126 f s , concomitant with an expansion of the domain periodicity, corresponding to a domain wall velocity of ∼ 750 m / s . The results confirm that, far from cross-contamination of low-energy absorption edges in multi-element systems, the highly localized states of 4 d electrons associated with the N 4 , 5 edges can provide high-quality core-level magnetic information on par with what can be obtained at the M edges, which is currently accessible only at large-scale x-ray facilities. The analysis also indicates the rich material-, composition-, and probing-energy-dependent driving mechanism of RE-associated multicomponent systems. Considering the rapid emergence of high-power Yb lasers combined with novel nonlinear compression technology, this work indicates potential for next-generation high-performance soft x-ray HHG-based sources in future extremely photon-hungry applications on the table-top scale, such as probing electronic motion in biologically relevant molecules in their physiological environment (liquid phase), and advanced coherent imaging of nano-engineered devices with 5 ∼ 8 n m resolution.

Domain Wall Acceleration by Ultrafast Field Application: An Ab Initio‐Based Molecular Dynamics Study

Optimizing ferroelectrics for contemporary high‐frequency applications asks for the fundamental understanding of ferroelectric switching and domain wall (DW) motion in ultrafast field pulses while the microscopic understanding of the latter is so far incomplete. To close this gap in knowledge, ab initio‐based molecular dynamics simulations are utilized to analyze the dynamics of 180° DWs in the prototypical ferroelectric material BaTiO3. How ultrafast field application initially excites the dipoles in the system and how they relax to their steady state via transient negative capacitance are discussed. Excitingly, a giant boost of the DW velocity related to the nonequilibrium switching of local dipoles acting as nucleation centers for the wall movement is found. This boost may allow to tune the local ferroelectric switching rate by the shape of an applied field pulse.

Enhanced current-induced domain wall motion by tuning the cubic in-plane magnetic anisotropy

The influence of cubic in-plane magnetic anisotropy on current-induced domain wall (DW) motion was investigated by micromagnetic simulation. DW velocity is enhanced when the nanostripes are placed in an optimized cubic in-plane magnetic anisotropy field that almost exactly compensates the demagnetizing field. An increase is also observed in the walker limit current, which is the linearity loss of the DW velocity as a function of spin current density when the latter exceeds a critical value. The microwave-assisted DW motion that is usually proposed to increase DW velocity is further improved by adding the cubic magnetic anisotropy field on the nanostripes. These effects of enhancing current-induced DW motion are useful for device applications.

Antiferromagnetic domain wall dynamics in magnetoelectric MnTiO3 studied by optical imaging

Domain-wall velocity is one of the key parameters which governs the switching dynamics in antiferromagnets. Antiferromagnetic domain walls in magnetoelectric materials are driven by the joint action of electric and magnetic fields. Here, the authors capture by optical magnetochiral imaging the millisecond dynamics in domain switching in the collinear antiferromagnet MnTiO${}_{3}$. Detailed investigation of the domain-wall motion with varying temperature and external-field strength reveals the thermal effects on the domain-wall mobility.

Temperature dependence of domain wall creep motion in ferrimagnetic Tb/CoFeB/MgO microwires

In this work, we examine the temperature dependence of magnetic domain wall (DW) creep motion in ferrimagnetic Tb/CoFeB/MgO microwires by using a real-time DW detection method. By measuring the field-dependent DW velocity at various temperatures, the creep-scaling constant and the characteristic velocity were evaluated from the creep-scaling analysis. We found that the DW velocity changed significantly with temperature and was mainly attributed to the variation in the creep-scaling constant than that in the characteristic velocity. Possible mechanisms for the temperature dependence of each parameter are discussed.

Domain wall propagation in Fe-rich magnetic microwires with graded magnetic anisotropy

We observed that stress-annealing of Fe75B9Si12C4 magnetic microwire at variable annealing temperature allows to create graded magnetic anisotropy. We have found that single domain wall (DW) propagation in a media with graded magnetic anisotropy is essentially non-uniform: faster DW propagation is observed in the region with moderate stress-annealing induced magnetic anisotropy. Higher DW velocity in the region with induced magnetic anisotropy is explained by the transverse character of stress-annealing induced magnetic anisotropy which affects the travelling DW in a similar way as application of transversal bias magnetic field. Obtained graded magnetic anisotropy allows engineering the DW dynamics of Fe-rich microwires.

Low pressure drive of the domain wall in Pt/Co/Au/Cr2O3/Pt thin films by the magnetoelectric effect

The magnetoelectric (ME) effect is one of the methods for electrically controlling the magnetization direction. In this study, we investigated the ME-driven domain wall creep and depinning using a Pt/Co/Au/ME-Cr2O3/Pt thin film. The domain switching process is governed by domain wall propagation rather than the nucleation of reversed domains, similar to a pure ferromagnet. The domain wall velocity v increases exponentially with the ME pressure, that is, the simultaneous application of magnetic H and electric E fields. The v–E curve under a constant H can be scaled by the ME pressure with the assistance of the exchange bias. We determined the depinning threshold, pinning energy scale, and depinning velocity based on the model for the magnetic domain wall creep. Compared with the depinning velocity in various other systems, it was suggested that the ME-driven mechanism could yield a fast domain wall velocity utilizing the low pressure.

Structural relaxation in metastable magnetic submicronic wires

Changes triggered by low temperature metastable relaxation annealing in the peculiar magnetic behavior of rapidly solidified submicronic amorphous wires are reported. The overall aim was to understand the effects of the associated stress relief process on magnetization switching and magnetic domain wall propagation in these low dimensional amorphous wires with cylindrical symmetry. The results have shown that, even though the employed relatively low annealing temperatures did not initiate any crystallization, i.e., the amorphous state has been preserved, the consequences in terms of magnetic behavior are significant, with important variations in both magnetic switching field and domain wall velocity values. The observed modifications have been interpreted based on the interplay between the magnetoelastic and magnetostatic anisotropies within the submicronic amorphous wires, as well as on the complex changes in the underlying nonlinear stress distribution generated by the rapid solidification process. The outcomes of this investigation, alongside the general framework for their explanation, have unraveled novel ways of accurately tailoring and controlling the magnetic characteristics of the amorphous submicronic wires for developing new applications in sensors and domain wall logic devices, in which rapid switching and fast domain walls can make an important impact.

Multiple Walker breakdowns in magnetic multilayers

Herein, we report an exotic domain-wall dynamics showing double Walker breakdowns in magnetic multilayer films composed of two magnetic layers. Such multiple Walker breakdowns are attributed to the internal magnetic dipole field, which is antisymmetric on the domain walls of the lower and upper magnetic layers. A micromagnetic simulation shows four phases of the domain-wall dynamics, which result in a phase diagram with the phase boundaries of the double Walker breakdown fields. Such double Walker breakdowns lead to two minima in the variation of the domain-wall velocity, as often observed experimentally.

Direct Visualization of a Domain Wall Pinning by Time-Resolved Microscopy in Amorphous Glass-Coated Microwires

Amorphous glass-coated microwires with positive magnetostriction are composite material with very fast domain wall (DW) propagation that can reach up to 18 km/s. Previously it was shown that such high DW velocity can be explained by the tilted orientation of a DW in static or quasi-static experimental conditions. Here we perform time-resolved observation of a DW in propagation. The shape of a DW is studied via magneto-optical Kerr effect (MOKE) imaging. Time-resolved MOKE microscope operating in the single-shot regime and a static mode is used to ascertain the role of surface pinning on DW velocity fluctuation. It is shown that a tilted DW undergoes complex DW distortions on a local scale.

Stochastic Magnetization Switching in Rapidly Solidified (Co0.94Fe0.06)72.5Si12.5B15 Amorphous Submicronic Wires.

Submicrometric magnetic amorphous wires are good candidates for future development of miniaturized sensors and magnetic logic applications. Here we report the results of an in-depth investigation of magnetization switching in rapidly solidified nearly zero magnetostrictive (Co0.94Fe0.06)72.5Si12.5B15 amorphous samples with diameters of the actual magnetic wires between 300 and 450 nm. All samples were found to be magnetically bistable, displaying characteristic rectangular hysteresis loops. This shows that magnetization reversal occurs through the depinning and subsequent propagation of a magnetic domain wall, whose velocity depends on the applied field and on the sample dimensions. The results of this study reveal stochastic nonlinear dependencies of both the magnetic switching field and the domain wall velocity on the sample diameter. The analysis of the potential causes, which include nonlinear residual stresses, fluctuations in wire dimensions (metal and glass), and competing magnetic anisotropies of different origins, show that a combination of all three factors could lead to the observed stochastic behavior. Calculated values of the switching field, which consider only changes in the wire dimensions, indicate that such influence alone cannot account for the strong nonlinearities. The results are important for the applications of such ultrathin cylindrical magnetic amorphous wires.

Elucidation of the mechanism for maintaining ultrafast domain wall mobility over a wide temperature range

To achieve a 20 Gbps data rate using the upcoming 5G communication standard, it is crucial to recognize a domain wall (DW) velocity (vDW) of 1200 m s−1.

Domain wall motion driven by a wide range of current in coupled soft/hard ferromagnetic nanowires.

Racetrack memory with the advantages of small size and high reading speed is proposed based on current-induced domain wall (DW) motion in a ferromagnetic (FM) nanowire. Walker breakdown that restricts the enhancement of DW velocity in a single FM nanowire can be depressed by inter-wire magnetostatic coupling in a double FM nanowire system. However, this magnetostatic coupling also limits the working current density in a small range. In the present work, based on micromagnetic calculation, we have found that when there is a moderate difference of magnetic anisotropy constant between two FM nanowires, the critical current density for triggering the DW motion can be reduced while that for breaking the inter-wire coupling can be enhanced significantly to a magnitude of 1013 A m−2, which is far above the working current density in current electronic devices. The manipulation of working current density is relevant to the modification of DW structure and inter-wire magnetostatic coupling due to the difference of the anisotropy constants between the two nanowires and paves a way to develop racetrack memory that can work in a wide range of current.

Curved domain walls in the ferromagnetic nanostructures with Rashba and nonlinear dissipative effects

This work reveals an analytical investigation of the curved domain wall motion in ferromagnetic nanostructures in the framework of the extended Landau-Lifshitz-Gilbert equation. To be precise, the study delineates the description of curved domain wall motion in the steady-state dynamic regime for metallic and semiconductor ferromagnets. The study is done under the simultaneous action of the Rashba field and nonlinear dissipative effects described via the viscous-dry friction mechanism. By means of reductive perturbation technique and realistic assumption on the considered parameters, we establish an analytical expression of the steady domain wall velocity that depends on mean curvature of domain wall surfaces, nonlinear dissipation coefficients, Rashba parameter, external magnetic field, and spin-polarized electric current. In particular, it is observed that the domain wall velocity, mobility, threshold, and Walker breakdown can be manipulated by the combined mechanism of the Rashba field and nonlinear dissipation coefficients. Finally, the obtained analytical results are illustrated numerically for the curved domain walls through constant-curvature surfaces under-considered scenarios. The results presented herein are in qualitatively good agreement with the recent observations.

Dzyaloshinskii–Moriya interaction determined from spin wave nonreciprocity and magnetic bubble asymmetry in Pt/Co/Ir/Co/Pt synthetic ferrimagnets

We present analysis of the effect of Dzyaloshinskii–Moriya interaction (DMI) on spin wave nonreciprocity and bubble expansion asymmetry in Pt/Co/Ir/Co/Pt synthetic ferrimagnets with perpendicular magnetic anisotropy. We propose analysis of the DMI by Brillouin light scattering technique (BLS) and Kerr microscopy (MOKE) in the presence of interlayer exchange coupling strongly changing spin wave dispersion law and field dependences of domain wall velocity in comparison with those observed earlier in Ir/Co/Pt structures with a single Co layer. We have determined DMI values of each Co layer from unusually inverted dependence of velocity of the domain wall on in-plane magnetic field. Opposite signs of effective fields and DMI fields in the two Co layers invert field dependence of the domain wall velocity. DMI energy determined from BLS is higher than values, determined by bubble expansion.