Domain Wall Velocity Research Articles

Modeling magnetic domain-wall evolution in trilayers with structural inversion asymmetry

The one-dimensional motion of magnetic domain walls in a thin ferromagnetic nanostrip sandwiched between a heavy metal and a metal oxide is investigated analytically in the framework of the extended Landau–Lifshitz–Gilbert equation. The trilayer system under investigation exhibits structural inversion asymmetry and exploits the combined effects of spin-transfer-torque and spin-orbit-torque to optimize the domain-wall propagation along the nanostrip. Through the traveling-wave formalism, an explicit expression for the key features involved in both steady and precessional regimes is provided, with a particular emphasis on the role played by the two spin-orbit-torque contributions, Rashba and Spin-Hall. In particular, it is shown how the domain-wall velocity and mobility, the direction of propagation, the depinning threshold and the Walker breakdown can be controlled via a suitable combination of Rashba and Spin-Hall coefficients. A comparison between analytical results and numerical data extracted from literature is also addressed revealing a qualitative agreement between them. Additional information on spin-orbit-torque-driven DW dynamics is extracted from such an analysis and, in particular, a linear dependence between the spin-Hall angle and the azimuthal angle is outlined as a possible mechanism responsible for the reversal of propagation direction.

Highly Asymmetric Chiral Domain-Wall Velocities in Y-Shaped Junctions.

Recent developments in spin-orbit torques allow for highly efficient current-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy. Here, we show that chiral DWs can be driven into nonequilibrium states that can persist over tens of nanoseconds in Y-shaped magnetic nanowire junctions that have an input and two symmetric outputs. A single DW that is injected into the input splits and travels at very different velocities in the two output branches until it reaches its steady-state velocity. We find that this is due to the disparity between the fast temporal evolution of the spin current derived spin-orbit torque and a much-slower temporal evolution of the DMI-derived torque. Changing the DW polarity inverts the velocity asymmetry in the two output branches, a property that we use to demonstrate the sorting of domains.

SAW assisted domain wall motion in Co/Pt multilayers

The motion of domain walls in thin ferromagnetic films is of both fundamental and technological interest. In particular, the ability to use drivers other than magnetic fields to control the positions of domain walls could be exciting for memory applications. Here, we show that high frequency dynamic strain produced by surface acoustic waves is an efficient driver of magnetic domain walls in ferromagnetic films with perpendicular anisotropy. A standing surface acoustic wave of resonant frequency 96.6 MHz increases the domain wall velocities in thin films of [Co/Pt]n by an order of magnitude compared to magnetic fields alone. This effect is highly resonant, effectively ruling out thermal effects, and the velocity shows distinct variations in the domain wall velocity at the nodes and antinodes of the standing wave. The data indicate that standing strain waves can drive the domain wall motion from the creep to the flow regime as the amplitude increases. Hence, strain waves could provide an alternative route to rapid domain wall motion.

Controlling chiral domain walls in antiferromagnets using spin-wave helicity

In antiferromagnets, the Dzyaloshinskii-Moriya interaction lifts the degeneracy of left- and right-circularly polarized spin waves. This relativistic coupling increases the efficiency of spin-wave-induced domain-wall motion and leads to higher drift velocities. We demonstrate that, in biaxial antiferromagnets, the spin-wave helicity controls both the direction and the magnitude of the magnonic force on chiral domain walls. In this case it is shown that the domain-wall velocity is an order of magnitude faster in the presence of the Dzyaloshinskii-Moriya interaction. In uniaxial antiferromagnets, by contrast, the magnonic force is always propulsive, but its strength is still helicity dependent.

Speeding up nanomagnetic logic by DMI enhanced Pt/Co/Ir films

We investigated a new type of multilayer film for Nanomagnetic Logic with perpendicular anisotropy (pNML) enhanced by the Dzyaloshinskii-Moriya interaction (DMI). The DMI effect provides an additional energy term and widens the design space for pNML film optimization. In this work we added an Ir layer between Co and Pt to our standard pNML multilayer (ML) film stack - [Co/Pt]x4. Multilayer stacks of films with and w/o Ir were sputtered and patterned to nanowires of 400 nm width by means of focused ion beam lithography (FIB). For comparability of the films they were tuned to show identical anisotropy for multilayer stacks with and w/o Ir. The field-driven domain wall (DW) velocity in the nanowires was measured by using wide-field MOKE microscopy. We found a strong impact of Ir on the DW velocity being up to 2 times higher compared to the standard [Co/Pt]x4 ML films. Moreover, the maximum velocity is reached at much lower magnetic field, which is beneficial for pNML operation. These results pave the way for pNML with higher clocking rates and at the same time allow a further reduce power consumption.

Excess velocity of magnetic domain walls close to the depinning field

Magnetic field driven domain wall velocities in [Co/Ni] based multilayers thin films have been measured using polar magneto-optic Kerr effect microscopy. The low field results are shown to be consistent with the universal creep regime of domain wall motion, characterized by a stretched exponential growth of the velocity with the inverse of the applied field. Approaching the depinning field from below results in an unexpected excess velocity with respect to the creep law. We analyze these results using scaling theory to show that this speeding up of domain wall motion can be interpreted as due to the increase of the size of the deterministic relaxation close to the depinning transition. We propose a phenomenological model which allows to accurately fit the observed excess velocity and to obtain characteristic values for the depinning field $H_d$, the depinning temperature $T_d$, and the characteristic velocity scale $v_0$ for each sample.

AC-current-induced magnetization switching in amorphous microwires

We studied the influence of AC current flowing through microwires, on magnetization dynamics. We used a previously developed Sixtus-Tonks modified setup to evaluate the domain wall (DW) velocity within the microwire. However, instead of a magnetizing solenoid, we used a current flowing through the microwire. We observed that the AC current flowing through the annealed Co-rich microwire leads to remagnetization by fast domain wall propagation. The estimated DW velocity was approximately 4.5 km/s, which is similar to and even higher than that reported for the magnetic-field-driven domain wall propagation in Fe- and Co-rich microwires. We measured the DW velocity under tensile stress, and found that the DW velocity decreases under applied stress. An observed DW propagation induced by the current flowing through the microwire is explained considering the influence of an Oersted magnetic field on the outer domain shell. This field has a circular easy magnetization direction and magnetostatic interaction between the outer circumferentially magnetized shell and the inner axially magnetized core.

The interfacial nature of proximity-induced magnetism and the Dzyaloshinskii-Moriya interaction at the Pt/Co interface

The Dzyaloshinskii-Moriya interaction has been shown to stabilise Nèel domain walls in magnetic thin films, allowing high domain wall velocities driven by spin current effects. The interfacial Dzyaloshinskii-Moriya interaction (IDMI) occurs at the interface between ferromagnetic and heavy metal layers with strong spin-orbit coupling, but details of the interaction remain to be understood and the role of proximity induced magnetism (PIM) in the heavy metal is unknown. Here IDMI and PIM are reported in Pt determined as a function of Au and Ir spacer layers in Pt/Co/Au,Ir/Pt. Both interactions are found to be sensitive to sub-nanometre changes in the spacer thickness, correlating over sub-monolayer spacer thicknesses, but not for thicker spacers where IDMI continues to change even after PIM is lost.

Study of A Phenomenon STT (Spin Transfer Torque) on the Material La0.7Sr0.3MnO3 Shaped Nanowire Using Micromagnetic Simulation

STT (Spin Transfer Torque) can be referred to as a process of manipulation and control of spin current in the field of spintronics. When the material is ferromagnetic nanowire La0.7Sr0.3MnO3injected currents will move the domain wall with accompanying changes of spin currents. In mikromagnetik simulation shows that the application is capable of producing flow velocity or pressure of domain wall in the direction of electron flow. The domain wall pressure generating magnetization changes with increasing current density occurs. To that end, the simulation research was done in order to obtain the effect of the injection of electric current to the magnetization of the material. This phenomenon is simulated by modeling the material into the 3D geometry. The greater the current density is given the domain wall velocity or pressure on the nanowire faster so that the magnetization process is also faster. Changes in the velocity of the fastest domain wall is obtained when the material is injected with a current density as well as M-t get a graph showing oscillation pattern that is denser when the current is increased. Furthermore, the total energy analysis with variations in size diameter of 10 nm, 20 nm and 30 nm. The results show that with increasing diameter, total energy tends to increase. Keywords: spin transfer torque, La0.7Sr0.3MnO3, magnetisation, domain wall, ferromagnetic

Spin-Transfer-Driven Dynamics of Magnetic Vortices and Antivortices in Dots With Crystalline Cubic Anisotropy

We study the magnetization dynamics of a vortex- or antivortex-containing nanodot driven by an out-of-plane polarized electric current within micromagnetic simulations. The dot is an ultra-thin structure created using a material with strong crystalline cubic anisotropy. It is in-plane ordered with an effective fourfold anisotropy. In the case of the antivortex, we consider astroid-shaped dots, while in the case of the vortex, the circular dots and the astroid-shaped ones. Unlike in the soft-magnetic dots, the vortex (antivortex) textures in thin layers with sufficiently strong fourfold anisotropy consist of four closure domains independent of the dot shape. The magnetization in the domain walls (DWs) deviates from the dot plane under the action of the out-of-plane polarized electric current normal to the dot, which drives the DW propagation—a rotation of the texture around the vortex (antivortex) center. The DW velocity is dependent on the distance from the vortex (antivortex) core; thus, the DWs deform under the current creating a fourfold spiral shape. For sufficiently hard cubic magnets, we find a regime of the oscillatory dynamics of the dot [a cyclic switching between the spiral state and the closure-domain vortex (antivortex) state]. For softer magnets, we consider a spin-transfer-driven fast magnetization reversal of the vortex state mediated by the creation of the spiral state.

Oscillatory behavior of the domain wall dynamics in a curved cylindrical magnetic nanowire

Understanding the domain wall dynamics is an important issue in modern magnetism. Here we present results of domain wall displacement in curved cylindrical nanowires at a constant magnetic field. We show that the average velocity of a transverse domain wall increases with curvature. Contrary to what it is observed in stripes, in a curved wire the transverse domain wall oscillates along and rotates around the nanowire with the same frequency. These results open the possibility of new oscillation-based applications.

Electric field controlled domain wall dynamics and magnetic easy axis switching in liquid gated CoFeB/MgO films

We present reversible electric (E) field driven switching of the magnetic easy axis in CoFeB/MgO/HfO2 heterostructures from perpendicular to in-plane using an ionic liquid gate. The modification of magnetic anisotropy reaches 0.108 mJ/m2 in a gate voltage range between −3 V and 3.5 V with an efficiency of 82 fJ (V m)–1. The influence of the E-field induced anisotropy changes on domain nucleation and propagation of magnetic domain walls has also been studied in the perpendicular anisotropy state. A significant modulation of the domain wall velocity is observed in both the creep and depinning regimes of domain wall motion consistent with the E-field induced anisotropy variation. In addition, we demonstrate voltage controlled magnetization switching under a constant magnetic field and voltage control of domain wall pinning.

Annealing effect on current-driven domain wall motion in Pt/[Co/Ni] wire

The annealing effect on the efficiency of current-driven domain wall motion governed by the spin Hall effect in perpendicularly magnetized Pt/[Co/Ni] wires is investigated experimentally. Important physical parameters, such as the Dzyaloshinskii-Moriya Interaction (DMI), spin Hall angle, and perpendicular anisotropy field strength, for the domain wall motion are all characterized at each annealing temperature. It is found that annealing of wires at temperatures over 120 ºC causes significant reduction of the domain wall velocity. Energy dispersive X-ray spectroscopy analysis shows pronounced Co diffusion across the Pt/Co interface resulted from annealing at relatively high temperatures. The combined modeling study shows that the reduction of DMI caused by annealing is mostly responsible for the domain wall velocity reduction due to annealing.

Role of RKKY torque on domain wall motion in synthetic antiferromagnetic nanowires with opposite spin Hall angles

We experimentally show the effect of enhanced spin-orbit and RKKY induced torques on the current-induced motion of a pair of domain walls (DWs), which are coupled antiferromagnetically in synthetic antiferromagnetic (SAF) nanowires. The torque from the spin Hall effect (SHE) rotates the Néel DWs pair into the transverse direction, which is due to the fact that heavy metals of opposite spin Hall angles are deposited at the top and the bottom ferromagnetic interfaces. The rotation of both DWs in non-collinear fashion largely perturbs the antiferromagnetic coupling, which in turn stimulates an enhanced interlayer RKKY exchange torque that improved the DW velocity. The interplay between the SHE-induced torque and the RKKY exchange torque is validated via micromagnetic simulations. In addition, the DW velocity can be further improved by increasing the RKKY exchange strength.

Material Developments and Domain Wall-Based Nanosecond-Scale Switching Process in Perpendicularly Magnetized STT-MRAM Cells

We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities.

Spatially and time-resolved magnetization dynamics driven by spin-orbit torques.

Current-induced spin-orbit torques are one of the most effective ways to manipulate the magnetization in spintronic devices, and hold promise for fast switching applications in non-volatile memory and logic units. Here, we report the direct observation of spin-orbit-torque-driven magnetization dynamics in Pt/Co/AlOx dots during current pulse injection. Time-resolved X-ray images with 25 nm spatial and 100 ps temporal resolution reveal that switching is achieved within the duration of a subnanosecond current pulse by the fast nucleation of an inverted domain at the edge of the dot and propagation of a tilted domain wall across the dot. The nucleation point is deterministic and alternates between the four dot quadrants depending on the sign of the magnetization, current and external field. Our measurements reveal how the magnetic symmetry is broken by the concerted action of the damping-like and field-like spin-orbit torques and the Dzyaloshinskii-Moriya interaction, and show that reproducible switching events can be obtained for over 1012 reversal cycles.

Simultaneous control of the Dzyaloshinskii-Moriya interaction and magnetic anisotropy in nanomagnetic trilayers.

Magneto-optical Kerr effect (MOKE) microscopy measurements of magnetic bubble domains demonstrate that Ar^{+} irradiation around 100eV can tune the Dzyaloshinskii-Moriya interaction (DMI) in Pt/Co/Pt trilayers. Varying the irradiation energy and dose changes the DMI sign and magnitude separately from the magnetic anisotropy, allowing tuning of the DMI while holding the coercive field constant. This simultaneous control emphasizes the different physical origins of these effects. To accurately measure the DMI, we propose and apply a physical model for a poorly understood peak in domain wall velocity at zero in-plane field. The ability to tune the DMI with the spatial resolution of the Ar^{+} irradiation enables new fundamental investigations and technological applications of chiral nanomagnetics.

Fast switching and signature of efficient domain wall motion driven by spin-orbit torques in a perpendicular anisotropy magnetic insulator/Pt bilayer

We report fast and efficient current-induced switching of a perpendicular anisotropy magnetic insulator thulium iron garnet by using spin-orbit torques (SOT) from the Pt overlayer. We first show that, with quasi-DC (10 ms) current pulses, SOT-induced switching can be achieved with an external field as low as 2 Oe, making TmIG an outstanding candidate to realize efficient switching in heterostructures that produce moderate stray fields without requiring an external field. We then demonstrate deterministic switching with fast current pulses (≤20 ns) with an amplitude of ∼1012 A/m2, similar to all-metallic structures. We reveal that, in the presence of an initially nucleated domain, the critical switching current is reduced by up to a factor of five with respect to the fully saturated initial state, implying efficient current-driven domain wall motion in this system. Based on measurements with 2 ns-long pulses, we estimate the domain wall velocity of the order of ∼400 m/s per j = 1012 A/m2.

Combined effect of magnetic field and charge current on antiferromagnetic domain-wall dynamics

We theoretically examine a cross effect of magnetic field and charge current on antiferromagnetic domain wall dynamics. Since antiferromagnetic materials are largely insensitive to external magnetic fields in general, charge current has been shown recently as an alternative and efficient way to manipulate antiferromagnets. We find a new role of the magnetic field in the antiferromagnetic dynamics that appears when it is combined with charge current, demonstrating a domain wall motion in the presence of both field and current. We show that a spatially-varying magnetic field can shift the current-driven domain-wall velocity, depending on the domain-wall structure and the direction of the field-gradient. Our result suggests a novel concept of field-control of current-driven antiferromagnetic dynamics.

Current-induced magnetic domain wall motion in Pt/Co/Pd and Pd/Co/Pt structures with opposite sign of Dzyaloshinskii-Moriya interaction

The authors have investigated magnetic domain wall (DW) motion induced by electrical current in the perpendicularly magnetized Pt/Co/Pd and Pd/Co/Pt structures. In these systems, owing to the spin-orbit torque (SOT) and the interfacial Dzyaloshinskii-Moriya interaction (DMI), the DW moves in the current flowing direction. On the other hand, the threshold current density, DW velocity and magnitude of the DMI were found to be different between them even though the same combination of the materials are used. This results suggest that the SOT induced DW motion is significantly influenced by the stack sequence of the film.