Domain Wall Velocity Research Articles

Tuning the perpendicular magnetic anisotropy, spin Hall switching current density, and domain wall velocity by submonolayer insertion in Ta/CoFeB/MgO heterostructures

By submonolayer insertion of Au, Pt, or Pd into Ta/CoFeB/MgO/Ta heterostructures, we tune the perpendicular magnetic anisotropy and the coercive field of the ferromagnetic layer. We demonstrate that this has a major influence on the spin Hall switching current density and its dependence on the external magnetic field. Despite a rather small effective spin Hall angle of θSH≈−0.07, we obtain switching current densities as low as 2×1010 A/m2 with a 2 Å Au interlayer. We find that the Dzyaloshinskii-Moriya interaction parameter D is reduced with Au or Pd interlayers, and the perpendicular anisotropy field is reduced by an order of magnitude with the Pd interlayer. The dependence of the switching current density on the current pulse width is quantitatively explained with a domain wall nucleation and propagation model. Interface engineering is thus found to be a suitable route to tailor the current-induced magnetization switching properties of magnetic heterostructures.

Dispersive Stiffness of Dzyaloshinskii Domain Walls.

It is well documented that subjecting perpendicular magnetic films that exhibit the interfacial Dzyaloshinskii-Moriya interaction to an in-plane magnetic field results in a domain wall (DW) energy σ, which is highly anisotropic with respect to the orientation of the DW in the film plane Θ. We demonstrate that this anisotropy has a profound impact on the elastic response of the DW as characterized by the surface stiffness σ[over ˜](Θ)=σ(Θ)+σ^{''}(Θ) and evaluate its dependence on the length scale of deformation. The influence of stiffness on DW mobility in the creep regime is assessed, with analytic and numerical calculations showing trends in σ[over ˜] that better represent experimental measurements of domain wall velocity in magnetic thin films compared to σ alone. Our treatment provides experimental support for theoretical models of the mobility of anisotropic elastic manifolds and makes progress toward a more complete understanding of magnetic domain wall creep.

Inversion of the domain wall propagation in synthetic ferrimagnets

We report on magnetic domain wall velocity measurements in a synthetic ferrimagnet made of two perpendicular ferromagnetic layers antiferromagnetically exchange coupled. In this system, two types of transitions may be observed: one from a parallel alignment to an antiparallel alignment of the magnetization of the two layers and the other between the two possible antiparallel alignments. Those transitions are shown to be dominated by domain wall propagation. The domain wall velocity as a function of the applied magnetic field pulse amplitude has been measured. Two remarkable features are observed: first, a drastic breakdown of the domain wall velocity and then an inversion of the domain propagation direction are observed when the field pulses reach values comparable to the exchange field between the two layers. This unexpected behavior can be understood qualitatively using a simple model taking into account the competition between interlayer exchange coupling and the external driving field.

Dynamics of ferroelectric 180° domain walls at engineered pinning centers

The interaction between domain walls and pinning centers in ferroelectrics is of great interest from both fundamental and practical points of view. In this work, we show that, counter to intuition, the apparent velocity of domain walls can increase as the defect density increases. However, when we closely investigate the propagating front of the domain wall, we find that it is not unified but can be rough, indicating the presence of multiple nucleated domains in advance of the primary wall. We therefore ascribe the increased apparent velocity with defect density to actually derive from nucleation-aided motion. To further investigate the effect of engineered pinning centers, we spatially confined the defect regions and then propagated domain walls in that direction. We found that, given a sufficiently high defect density, walls can be pinned indefinitely at sub-threshold voltages. Finally, we outline a method to create domain wall propagation channels in which the wall is confined to a low defect region bordered by high defect density regions.

19pPSB-48 フェリ磁性体GdFeCo細線における磁場駆動磁壁移動速度の温度依存性

19pPSB-48 フェリ磁性体GdFeCo細線における磁場駆動磁壁移動速度の温度依存性

Understanding the role of damping and Dzyaloshinskii-Moriya interaction on dynamic domain wall behaviour in platinum-ferromagnet nanowires

Heavy metal layers, exemplified by Pt, are known to play a significant role in the magnetization behaviour of thin-film ferromagnets by three distinct mechanisms that can each contribute to the reversal process. These include modifying the local magnetization state via an interfacial Dzyaloshinskii-Moriya interaction (IDMI), enhancement of the damping, via d-d hybridisation and spin-pumping across the interface, and the mediation of the magnetization switching, with the flow of current through a system, via the spin-Hall effect. Here we show for a system with weak interfacial DMI (NiFe/Pt) that the measurement of magnetic field-driven magnetization reversal, mediated by domain wall (DW) motion, is dominated by the enhanced intrinsic damping contribution as a function of the Pt capping layer thickness. But, we also show micromagnetically that the IDMI and damping also combine to modify the domain wall velocity behaviour when the damping is larger. It is also noted that Walker breakdown occurs at lower fields and peak DW velocity decreases in the presence of IDMI. These results highlight the significance of the relative contributions of the damping and the IDMI from the heavy metal layer on the magnetization reversal and provide a route to controlling the DW behaviour in nanoscale device structures.

Thermally Assisted Current-Induced Domain Wall Motion in Tb/Co Magnetic Multilayered Wire With a High Domain Wall Propagation Field

We investigated the current-induced domain wall (DW) motion in Tb/Co multilayered wire with various substrate temperatures ( $T_{s}$ ). The coercivity and DW propagation field of the Tb/Co multilayered film are 10 and 8 kOe, respectively. In the Tb/Co wire, the DW velocity is 2.4 m/s for a current density of $4.5 \times 10^{11}$ A/ $\text{m}^{2}$ at room temperature. At $T_{s} = 343$ K, we also found that the DW velocity is about two times higher than that at room temperature. The enhancement of DW velocity can be attributed to thermally activated creep DW motion and/or the reduction of the depinning current density.

Dramatic influence of curvature of nanowire on chiral domain wall velocity.

The use of current pulses to move domain walls along nanowires is one of the most exciting developments in spintronics over the past decade. We show that changing the sign of the curvature of a nanowire changes the speed of chiral Néel domain walls in perpendicularly magnetized nanowires by up to a factor of 10. The domain walls have an increased or decreased velocity in wires of a given curvature, independent of the domain wall chirality and the sign of the current-induced spin-orbit torques. Thus, adjacent domain walls move at different speeds. For steady motion of domain walls along the curved nanowire, the torque must increase linearly with the radius, which thereby results in a width-dependent tilting of the domain wall. We show that by using synthetic antiferromagnetic nanowires, the influence of the curvature on the domain wall's velocity is eliminated, and all domain walls move together, emphasizing the use of such structures for spintronic applications.

Domain-wall dynamics in magnetoelastic nanostripes

We numerically demonstrate the possibility to manipulate domain walls in magnetoelastic nanostripes by means of uniform mechanical stresses. The symmetry breaking of the magnetic states in unidimensional ferromagnets allows the control of the domain-wall position or velocity in geometrically tailored nanostripes coupled to piezoelectric substrates. We further predict that this approach yields unusual domain-wall configurations with velocities of the same order of magnitude as that induced by magnetic fields or spin-polarized currents, while the energy consumption is considerably smaller.

Universal absence of Walker breakdown and linear current-velocity relation via spin-orbit torques in coupled and single domain wall motion

We consider theoretically domain wall motion driven by spin-orbit and spin Hall torques. We find that it is possible to achieve universal absence of Walker breakdown for all spin-orbit torques using experimentally relevant spin-orbit coupling strengths. For spin-orbit torques other than the pure Rashba spin-orbit torque, this gives a linear current-velocity relation instead of a saturation of the velocity at high current densities. The effect is very robust and is found in both soft and hard magnetic materials, as well as in the presence of the Dzyaloshinskii-Moriya interaction and in coupled domain walls in synthetic antiferromagnets, where it leads to very high domain wall velocities. Moreover, recent experiments have demonstrated that the switching of a synthetic antiferromagnet does not obey the usual spin Hall angle-dependence, but that domain expansion and contraction can be selectively controlled toggling only the applied in-plane magnetic field magnitude and not its sign. We show for the first time that the combination of spin Hall torques and interlayer exchange coupling produces the necessary relative velocities for this switching to occur.

Influence of sloped electric field on magnetic-field-induced domain wall creep in a perpendicularly magnetized Co wire

A creep motion of the magnetic domain wall (DW) in a perpendicularly magnetized Co wire, where the DW energy is artificially varied by applying a sloped electric field, is studied. Under the sloped electric field and a constant external magnetic field, the DW velocity gradually changes according to the position of the wire owing to the spatially varying DW energy. Although the sloped DW energy can be a source to drive a DW, no clear electric-field-induced DW motion is observed, most likely because the effective magnetic field induced by the sloped electric field is very small in the present system.

Domain growth dynamics in (K, Na)NbO 3 ferroelectric thin films

(K,Na)NbO3 (KNN) based lead-free materials have gained great progress and drawn much attention recently, due to their attractive piezoelectric performance and the demand for environmental protection. As is known, domain motion is essential for piezoelectric output; however, there is limited understanding on this topic for KNN. In the present study, the domain growth process of the KNN thin film is studied by piezoresponse force microscopy (PFM). The domain size shows a linear dependence on the pulse voltage and a complex dependence, unlike the commonly accepted logarithmic relationship, on the pulse duration. Meanwhile, a power decay relationship between the domain wall velocity and the domain size is observed. The extremely low dynamical exponent proves that our sample is influenced by extremely strong pinning effects caused by defects, resulting in the uncommon pulse duration dependence of domain size.

Effect of annealing on magnetic properties and structure of Fe-Ni based magnetic microwires

We studied the magnetic properties and domain wall (DW) dynamics of Fe47.4Ni26.6Si11B13C2 and Fe77.5Si7.5B15 microwires. Both samples present rectangular hysteresis loop and fast magnetization switching. Considerable enhancement of DW velocity is observed in Fe77.5Si7.5B15, while DW velocity of samples Fe47.4Ni26.6Si11B13C2 is less affected by annealing. The other difference is the magnetic field range of the linear region on dependence of domain wall velocity upon magnetic field: in Fe47.4Ni26.6Si11B13C2 sample is considerably shorter and drastically decreases after annealing. We discussed the influence of annealing on DW dynamics considering different magnetoelastic anisotropy of studied microwires and defects within the amorphous state in Fe47.4Ni26.6Si11B13C2. Consequently we studied the structure of Fe47.4Ni26.6Si11B13C2 sample using X-ray diffraction and the atom probe tomography. The results obtained using the atom probe tomography supports the formation of the B-depleted and Si-enriched precipitates in the metallic nucleus of Fe-Ni based microwires.

Switching processes of thin ferroelectric films

The influence of size effects on dielectric and switching characteristics of lead titanate and lead zirconate titanate thin films with various thicknesses was studied. It was shown that with decreasing the film thickness the “creep” regime of domain wall movement is expanded due to shortening area where the sliding motion of domain walls occurs. In weak electric fields a deviation from the strictly exponential dependence of domain wall velocity V on the strength of an applied electric field was established with the appearance of an exponent in dependence V∼exp[−C/Eμ], where C – constant and μ – dynamic factor. For lower thicknesses of films with polycrystalline structure the values of this factor approach to unity due to an increase of the orientation of crystallite axis. For strong fields with decreasing film thickness the domain wall mobility decreases due to an increase of near-surface defect contribution to domain wall motion.

Steady motion of skyrmions and domains walls under diffusive spin torques

We explore the role of the spin diffusion of conducting electrons in two-dimensional magnetic textures (domain walls and skyrmions) with spatial variation of the order of the spin precession length ${\ensuremath{\lambda}}_{\text{ex}}$. The effect of diffusion reflects in four additional torques that are third order in spatial derivatives of magnetization and bilinear in ${\ensuremath{\lambda}}_{\text{ex}}$ and in the nonadiabatic parameter ${\ensuremath{\beta}}^{\ensuremath{'}}$. In order to study the dynamics of the solitons when these diffusive torques are present, we derive the Thiele equation in the limit of steady motion and we compare the results with the nondiffusive limit. When considering a homogenous current these torques increase the longitudinal velocity of transverse domain walls of width $\mathrm{\ensuremath{\Delta}}$ by a factor ${({\ensuremath{\lambda}}_{\text{ex}}/\mathrm{\ensuremath{\Delta}})}^{2}(\ensuremath{\alpha}/3), \ensuremath{\alpha}$ being the magnetic damping constant. In the case of single skyrmions with core radius ${r}_{0}$ these new contributions tend to increase the Magnus effect in an amount proportional to ${({\ensuremath{\lambda}}_{\text{ex}}/{r}_{0})}^{2}(1+2\ensuremath{\alpha}{\ensuremath{\beta}}^{\ensuremath{'}})$.

Electric-field-driven domain wall dynamics in perpendicularly magnetized multilayers

We report on reversible electric-field-driven magnetic domain wall motion in a Cu/Ni multilayer on a ferroelectric BaTiO3 substrate. In our heterostructure, strain-coupling to ferroelastic domains with in-plane and perpendicular polarization in the BaTiO3 substrate causes the formation of domains with perpendicular and in-plane magnetic anisotropy, respectively, in the Cu/Ni multilayer. Walls that separate magnetic domains are elastically pinned onto ferroelectric domain walls. Using magneto-optical Kerr effect microscopy, we demonstrate that out-of-plane electric field pulses across the BaTiO3 substrate move the magnetic and ferroelectric domain walls in unison. Our experiments indicate an exponential increase of domain wall velocity with electric field strength and opposite domain wall motion for positive and negative field pulses. The application of a magnetic field does not affect the velocity of magnetic domain walls, but independently tailors their internal spin structure, causing a change in domain wall dynamics at high velocities.

Current induced domain wall propagation in Co-rich amorphous microwires

We studied the influence of the AC current flowing through the magnetically bistable Co-rich microwire on the magnetization dynamics. We used previously developed Sixtus-Tonks modified set-up for evaluation of the domain wall (DW) velocity within the microwire, but instead of the magnetizing solenoid we used the current flowing through the microwire. We observed that the AC current flowing though the sample produces the remagnetization of the sample by fast domain wall propagation along the microwire. Estimated DW velocity is about 4.5 km/s, being similar and even higher to that reported for the magnetic field driven domain wall propagation in Fe and Co-rich microwires. Observed current induced DW propagation through the microwire we explained considering the magnetostatic interaction between the outer circumferentially magnetized shell and the inner axially magnetized core.

Analytical solution of the strain-controlled magnetic domain wall motion in bilayer piezoelectric/magnetostrictive nanostructures

The one-dimensional propagation of magnetic domain walls in an isotropic, linearly elastic, magnetostrictive material is investigated in the framework of the extended Landau-Lifshitz-Gilbert equation where the effects of a spin-polarized current and a rate-independent dry-friction dissipation are taken into account. In our analysis, it is assumed that the ferromagnet is subject to a spatially uniform biaxial in-plain stress generated by a piezoelectric substrate combined with the former in a multiferroic heterostructure. Moreover, a possible connection between the dry-friction mechanism and the piezo-induced strains is conjectured. By adopting the traveling waves ansatz, the effect of such a stress on the domain wall dynamics is explored in both steady and precessional regimes. In particular, it is proved that the magnetoelastic contribution, while it does not formally modify the classical solution, affects both the propagation threshold and the Walker Breakdown conditions involved in the steady regime, in agreement with recent experimental results. In the precessional regime, it is shown that the existence of a correlation between the piezo-induced strains and dry-friction leads to an upward shift of the domain wall velocity.

Magnetic Properties and Defects of Fe-Ni-Based Magnetic Microwires

We studied the magnetic properties and domain wall (DW) dynamics of Fe47.4Ni26.6Si11B13C2 and Fe77.5Si7.5B15 microwires. Both samples present a rectangular hysteresis loop and fast magnetization switching. The linear region of dependence of the DW velocity on the magnetic field in Fe47.4Ni26.6Si11B13C2 sample is considerably shorter. Consequently, we studied the structure of Fe47.4Ni26.6Si11B13C2 sample using X-ray diffraction and atom probe tomography. The results obtained using the atom probe tomography supports the formation of B-enriched precipitates in the interfacial layer and in the metallic nucleus after annealing.

Disorder-induced domain wall velocity shift at high fields in perpendicularly magnetized thin films

Domain wall dynamics in a perpendicularly magnetized system is studied by means of micromagnetic simulations in which disorder is introduced as a dispersion of both the easy-axis orientation and the anisotropy constant over regions reproducing a granular structure of the material. High field dynamics show a linear velocity-field relationship and an additional grain size dependent velocity shift, weakly dependent on both applied field and intrinsic Gilbert's damping parameter. We find the origin of this velocity shift in the nonhomogeneous in-plane effective field generated by the tilting of anisotropy easy axis introduced by disorder. We show that a one-dimensional analytical approach cannot predict the observed velocities and we augment it with the additional dissipation of energy arising from internal domain wall dynamics triggered by disorder. This way we prove that the main cause of higher velocity is the ability of the domain wall to irradiate energy into the domains, acquired with a precise feature of disorder.