Field-driven Domain Wall Motion Research Articles

Adjustment of Demagnetizing Field in Permalloy Nanowires to Control Domain Wall Motion

The domain wall motion in permalloy nanowires has been investigated widely due to its potential for a new type of memory. In this paper. we use the LLG Simulator based on the Landau-Lifshitz-Gilbert (LLG) equation to investigate the field-driven domain-wall motion in a long, straight ferromagnetic strip. An injection field of 60 Oe is applied to inject a domain wall from an extended disk into the nanowire. We found a dependence of nanowire dimensions with the velocity of domain wall. By increasing the width of the nanowire, the velocity of the domain wall motion also increases, while the Walker breakdown field ( HWB) decreases. On the other hand, increasing the thicknesses of the nanowire, the domain wall velocity, HWB, and demagnetizing field all decrease. By applying a vertical field from 0 to 1000 Oe in order to enhance the demagnetizing field, it is found the HWB is increased from 16 to 20 Oe.

Universal magnetic domain wall dynamics in the presence of weak disorder

Abstract The motion of elastic interfaces in disordered media is a broad topic relevant to many branches of physics. Field-driven magnetic domain wall motion in ultrathin ferromagnetic Pt/Co/Pt films can be well interpreted within the framework of theories developed to describe elastic interface dynamics in the presence of weak disorder. Indeed, the three theoretically predicted dynamic regimes of creep, depinning, and flow have all been directly evidenced in this model experimental system. We discuss these dynamic regimes and demonstrate how field-driven creep can be controlled not only by temperature and pinning, but also via interactions with magnetic entities located inside or outside the magnetic layer. Consequences of confinement effects in nano-devices are briefly reviewed, as some recent results on domain wall motion driven by an electric current or assisted by an electric field. Finally new theoretical developments and perspectives are discussed.

Time-resolved measurements of field-driven domain wall motion in a submicron strip with perpendicular magnetic anisotropy

The motion of domain walls (DWs), driven by magnetic field and spanning almost eight orders of magnitude in velocity, has been studied in a submicron-wide strip of Co/Pt with perpendicular magnetic anisotropy. A scanning magneto-optic Kerr effect (MOKE) system is used to conduct time-resolved measurements of DW dynamics in both the thermally activated and viscous flow regimes. MOKE signal transients in the thermally activated regime reveal distributions of stochastic DW propagation events. Transients in the viscous flow regime show deterministic DW motion with velocities ∼20 m/s. The transition between the two dynamic regimes is observed as the relationship between the DW velocity and the driving magnetic field changes from exponential to linear.

Controlled pinning and depinning of domain walls in nanowires with perpendicular magnetic anisotropy

We investigate switching and field-driven domain wall motion in nanowires with perpendicular magnetic anisotropy comprising local modifications of the material parameters. Intentional nucleation and pinning sites with various geometries inside the nanowires are realized via a local reduction of the anisotropy constant. Micromagnetic simulations and analytical calculations are employed to determine the switching fields and to characterize the pinning potentials and the depinning fields. Nucleation sites in the simulations cause a significant reduction of the switching field and are in excellent agreement with analytical calculations. Pinning potentials and depinning fields caused by the pinning sites strongly depend on their shapes and are well explained by analytical calculations.

Domain wall motion in perpendicular anisotropy nanowires with edge roughness

We study field-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy using finite element micromagnetic simulations. Edge roughness is introduced by deforming the finite element mesh, and we vary the correlation length and magnitude of the roughness deformation separately. We observe the Walker breakdown both with and without roughness, with steady DW motion for applied fields below the critical Walker field Hc, and oscillatory motion for larger fields. The value of Hc is not altered in the presence of roughness. The edge roughness introduces a depinning field. During the transient process of depinning, from the initial configuration to steady DW motion, the DW velocity is significantly reduced in comparison to that for a wire without roughness. The asymptotic DW velocity, on the other hand, is virtually unaffected by the roughness, even though the magnetization reacts to the edge distortions during the entire course of motion, both above and below the Walker breakdown. A moving DW can become pinned again at some later point (‘dynamic pinning’). Dynamic pinning is a stochastic process and is observed both for small fields below Hc and for fields of any strength above Hc. In the latter case, where the DW shows oscillatory motion and the magnetization in the DW rotates in the film plane, pinning can only occur at positions where the DW reverses direction and the instantaneous velocity is zero, i.e., at the beginning or in the middle of a positional oscillation cycle. In our simulations pinning was only observed at the beginnings of cycles, where the magnetization is pointing along the wire. The depinning field depends linearly on the magnitude of the edge roughness. The strongest pinning fields are observed for roughness correlation lengths that match the domain wall width.

Magnetic soft x-ray microscopy of the domain wall depinning process in permalloy magnetic nanowires

Full-field magnetic transmission x-ray microscopy at high spatial resolution down to 20 nm is used to directly observe field-driven domain wall motion in notch-patterned permalloy nanowires. The depinning process of a domain wall around a notch exhibits a stochastic nature in most nanowires. The stochasticity of the domain wall depinning sensitively depends on the geometry of the nanowire such as the wire thickness, the wire width, and the notch depth. We propose an optimized design of the nanowire for deterministic domain wall depinning field at a notch.

Effect of Enhanced Damping Due to Spin-Motive Force on Field-Driven Domain Wall Motion

Temporal and spatial variation of magnetization generates an additional damping torque due to spin-motive force. We performed semi-one-dimensional (1-D) and two-dimensional (2-D) micromagnetic simulations to investigate effect of the additional damping on the field-driven transverse wall dynamics in a magnetic nanowire. At the magnetic field above the Walker breakdown field, the additional damping due to the spin-motive force causes an increase of domain wall velocity. In semi-1-D model, the amount of increased domain wall velocity is linearly proportional to the external magnetic field as predicted by theory. However, in 2-D model, it is inversely proportional to the field owing to the periodic injection of antivortex.

Magnetic domain wall motion triggered by electric field

We propose the new approach to the problem of electrically controlled magnetic state: the electric field driven domain wall motion. The effect is demonstrated in iron garnet films in ambient conditions. The theoretical model based on inhomogenous magnetoelectric interaction provides with the necessary criteria of the effect and the way to maximize it.

Observation of asymmetrical pinning of domain walls in notched Permalloy nanowires using electron holography

Field-driven domain-wall motion and pinning in notched Permalloy nanowires have been observed using electron holography and Lorentz microscopy. Transverse domain walls (TDWs) were identified and different aspects of their behavior, including nucleation, injection, pinning, and depinning, were studied. The relative chirality (i.e., sense of field rotation) of the notch and the nucleation pad had a major influence in determining the TDW propagation: the walls were preferentially pinned for a notch of opposite chirality, but simply passed through when the notch had the same chirality. This asymmetrical TDW pinning accounts for the observed asymmetrical hysteresis hoop.

Concept of the field-driven domain wall motion memory

In this paper, the concept of field-driven domain wall motion memory is presented. It is confirmed that a domain is shifted with a carefully designed non-uniform field by micromagnetic simulations. The shift of a domain—a bit—can be established by the motion of two domain walls to the same direction and the same distance. In order to get a better understanding of the domain wall motion under the non-uniform transverse magnetic field, we investigate the motion of the transverse Néel-type domain wall by micromagnetic simulations and the collective coordinate approach. The validity of the equation of motion for the domain wall is confirmed by the micromagnetic simulations as functions of the gradient of the non-uniform field, the saturation magnetization, and the Gilbert damping parameter α.

Current- and Field-Driven Domain Wall Motion in L- and C-Shaped Permalloy Nanowires With Different Wire Widths

We investigated the pulse-current-driven and magnetic-field-driven domain wall (DW) motion in permalloy nanowires with different shapes and wire widths. Two different nanowire types, 600 nm wide L- and 300 nm wide C- shaped, were considered by means of magnetic force microscope and anisotropic magnetoresistance measurement. We confirmed that every time head-to-head vortex DWs were placed at the specific places as we intended for both types of nanowires. We found similar critical current densities (~5 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> A/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and DW velocity (~2.0 m/s) for both nanowires in spite of their different shapes and widths. Multiple vortex DWs were also observed when the applied current density exceeded only a few percent of the critical values. We also performed magnetic-field-driven DW propagations. From the pinning and depinning images and anisotropic magnetoresistance measurement, we found the magnetoresistance value of the single vortex type DW for the L-shaped permalloy nanowire.

Direct observation and control of the Walker breakdown process during a field driven domain wall motion

We report the real-time study of a domain wall motion in giant magnetoresistance nanostrips. We have visualized the Walker breakdown process (WBP) [N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 (1974)] in single shot experiments. The domain wall motion above the Walker breakdown is highly nonperiodic. Surprisingly, the time intervals of movement are equal or larger than those where the domain wall nearly stops. When an additional transversal magnetic field is applied, domain wall motion becomes more regular, enabling the study of the WBP in more detail. A sufficiently large transverse field can suppress the WBP completely.

Equation of motion for a domain wall movement under a nonuniform transverse magnetic field

We investigate the dynamics of the domain wall in a nonuniform field driven domain wall motion memory concept. The equation of motion for a transverse Néel-type domain wall under a nonuniform transverse magnetic field is obtained with a collective coordinate approach. The validity of the equation of the motion is confirmed with micromagnetic simulations. We find that the domain wall velocity depends on the domain wall width, Gilbert damping parameter α, saturation magnetization, and the gradient of the field. The domain wall velocity of ∼100m∕s is obtained with typical material as Permalloy with a moderate field gradient (100Oe∕μm). It has promising results for memory applications.

Domain Wall Dynamics in Annealed GaMnAs Epilayers

We study magnetic field-driven domain wall motion in a GaMnAs thin film. The velocity is measured as function of the applied field. It varies over 6 orders of magnitude in a field range of 2.5 mT. Two regimes are identified. At low field, the domain wall motion follows a creep regime: it is controlled by defects and the domain wall velocity increases exponentially with the applied field. At higher fields, the domain wall motion follows a depinning regime: pinning defects are less efficient and the wall velocity increases linearly with the field. The highest measured domain wall velocity is 14 m s−1.

Quantum dissipation theory of slow magnetic relaxation mediated by domain-wall motion in the one-dimensional chain compound[Mn(hfac)2BNOH]

Based on a quantum dissipation theory of open systems, we present a theoretical study of slow dynamics of magnetization for the ordered state of the new molecule-based magnetic complex [Mn(hfac)_{2}BNO_{H}] composed from antiferromagnetically coupled ferrimagnetic (5/2,1) spin chains. Experimental investigations of the magnetization process in pulsed fields have shown that this compound exhibits a metamagnetic AF-FI transition at a critical field in the order of the interchain coupling. A strong frequency dependence for the ac-susceptibility has been revealed in the vicinity of the AF-FI transition and was associated with an AF-FI interface kink motion. We model these processes by a field-driven domain-wall motion along the field-unfavorable chains correlated with a dissipation effect due to a magnetic system-bath coupling. The calculated longitudinal magnetization has a two-step relaxation after the field is switched off and are found in good agreement with the experiment. The relaxation time determined from the imaginary part of the model ac-susceptibility agrees qualitatively with that found from the remanent magnetization data.

Influence of Current on Field-Driven Domain Wall Motion in Permalloy Nanowires from Time Resolved Measurements of Anisotropic Magnetoresistance

The motion of magnetic domain walls in permalloy nanowires is investigated by real-time resistance measurements. The domain wall velocity is measured as a function of the magnetic field in the presence of a current flowing through the nanowire. We show that the current can significantly increase or decrease the domain wall velocity, depending on its direction. These results are understood within a one-dimensional model of the domain wall dynamics which includes the spin transfer torque.

Domain wall dynamics and Barkhausen jumps in thin-film permalloy microstructures

Domain wall jump-amplitude and velocity distributions associated with Barkhausen jumps in a 300-\AA{}-thick thin-film permalloy and a $200\ifmmode\times\else\texttimes\fi{}200\phantom{\rule{0.3em}{0ex}}{(\ensuremath{\mu}\mathrm{m})}^{2}\ifmmode\times\else\texttimes\fi{}220\text{\ensuremath{-}}\mathrm{\AA{}}$-thick permalloy sample microstructrue are measured using a high-speed magneto-optic Kerr effect polarimeter. The jump-amplitude and velocity distributions are obtained for applied-field sweep rates from $0.9\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}∕\mathrm{s}$ to $6.3\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}∕\mathrm{s}$. The velocity distributions exhibit statistical properties consistent with the stochastic description of field-driven domain wall motion developed by ABBM [B. Alessandro, C. Beatrice, G. Bertotti, and A. Montorsi, J. Appl. Phys. 68, 2901 (1990)]. Averaged velocity distributions exhibit the expected increase of dynamic coercivity as the sweep rate is increased, and the maximum domain wall velocity measured as a function of the applied field at the stochastic depinning threshold is shown to be governed by the mobility limit imposed by local spin damping. The averaged velocity $⟨\ensuremath{\nu}(H\ensuremath{-}{H}_{0})⟩$ obtained from the distributions is observed to depart from the commonly accepted linear-dependence model, especially at higher drive-field sweep rates. This departure is interpreted as an indication of a sweep-rate-dependent mobility. Sweep-rate-dependent jump-amplitude distributions $P(\ensuremath{\Delta}M)$ versus $\ensuremath{\Delta}M$ are obtained from the Barkhausen effect data. These distributions exhibit power-law behavior with a sharp cutoff at large values of $\ensuremath{\Delta}M$. Attempts to reconcile the measured jump-amplitude distributions and sweep-rate-dependent exponents with various models of universal scaling are described. Power-law fits to $P(\ensuremath{\Delta}M)$ distributions measured to optimize temporal resolution (required for the velocity-distribution studies) yield a sweep-rate-dependent exponent that varies from $\ensuremath{\beta}=1.45\ifmmode\pm\else\textpm\fi{}0.05$ to $\ensuremath{\beta}=1.0$ as $dH∕dt$ is varied from $25\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}∕\mathrm{s}$ to $6.3\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}∕\mathrm{s}$. This range of sweep-rate-dependent $\ensuremath{\beta}$ agrees with the ABBM model and is consistent with the sweep-rate dependence exponent rule that predicts linear sweep-rate scaling for the adiabatic value $\ensuremath{\beta}=3∕2$ [R. A. White and K. A. Dahmen, Phys. Rev. Lett. 91, 085702 (2003)]. Additional experiments on both 300-\AA{}-thick continuous films and the same microstructures optimized for $\ensuremath{\Delta}M$ sensitivity yield a more accurate value of $\ensuremath{\beta}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\beta}=1.33\ifmmode\pm\else\textpm\fi{}0.01)$, which corresponds to a CZDS model $(\ensuremath{\beta}=4∕3)$ [C. Cizeau, S. Zapperi, G. Durin, and H. E. Stanley, Phys. Rev. Lett. 79, 4669 (1997); Phys. Rev. B 58, 6353 (1998)]. Adiabatic limit values of $\ensuremath{\beta}$ determined from all of the experiments are definitively outside the range $\ensuremath{\beta}\ensuremath{\sim}1.0$ for self-organized criticality in a two-dimensional system [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)], and also appear to be inconsistent with experimental results for 900 \AA{} Fe films on MgO in which $\ensuremath{\beta}=1.1$ was obtained from rescaled $P(\ensuremath{\Delta}M)$ distributions [E. Puppin, Phys. Rev. Lett. 84, 5415 (2000)]. The sweep-rate dependence of $\ensuremath{\beta}$ determined in a system that manifests an adiabatic limit of $\ensuremath{\beta}$ that is not equal to $3∕2$ also violates the model of White and Dahman that prohibits sweep-rate-dependent scaling for $\ensuremath{\beta}=4∕3$.