Micromagnetic study of domain wall depinning driven by nanosecond current pulse in notched Permalloy nanowires

The complete understanding of domain wall (DW) dynamics is important in the design of future spintronic devices. The characteristics of faster time-scale and lower current amplitude to move DW along nanowire are crucial in fabrication upgrade. In this study, we have investigated depinning behavior of magnetic domain wall triggered by nanosecond current pulse in notched Permalloy nanowires by means of micromagnetic simulation. We introduced double-triangular notch as the constrictions in the nanowire. The non-adiabaticity of the spin-transfer-torque is considered in simulation by varying the non-adiabatic constant (β) value. We observed that the depinning current density (J_d) was not significantly affected by β for notch size (s) < 50 nm. Interestingly, we found that the depinning time (t_d) for β ≥ 0.04 was slightly constant for all the cases with s > 70 nm, where the DW structure was kept to be a transverse structure during the depinning process. The broadly applicable depinning behavior is considered to contribute to the development of high-speed memory storage devices based on magnetic domain wall.     

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.     

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.     

Magnetization reversal of single domain permalloy nanowires

Magnetization reversal process and magnetoresistance (MR) hysteresis of single domain permalloy nanowires are numerically investigated by using OOMMF. It is shown that the abrupt jumps in the magnetoresistance are due to the domain formation and domain wall propagation so that a magnetic domain suddenly switches from one state into another. A nonmonotonic angular dependence of the jump (switching) field is found. Coherent rotation mode is responsible for the smooth variation of MR curves. The nucleation pattern of newly born domains depends on the tilted angle of external field.     

Current driven domain wall velocities exceeding the spin angular momentum transfer rate in permalloy nanowires

The velocity of domain walls driven by current in zero magnetic field is measured in permalloy nanowires using real-time resistance measurements. The domain wall velocity increases with increasing current density, reaching a maximum velocity of approximately 110 m/s when the current density in the nanowire reaches approximately 1.5 x 10(8) A/cm(2). Such high current driven domain wall velocities exceed the estimated rate at which spin angular momentum is transferred to the domain wall from the flow of spin polarized conduction electrons, suggesting that other driving mechanisms, such as linear momentum transfer, need to be taken into account.     

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.     

Stability of uniformly driven domain walls

An infinite ferromagnetic medium with orthorombic crystal field anisotropy and with a constantdc field applied along the easy axis is considered in the framework of micromagnetics. It is shown that in the presence of Gilbert damping the uniformly driven plane domain wall (Walker wall) with positive Döring mass is linearly stable for any strengthH of the applied field below a critical valueH ₀, where it connects to an unstable wall configuration with negative Döring mass. The critical fieldH ₀ is lower than the existence limitH _W (Walker limit) of the solitary travelling-wave type domain wall solutions, and represents the threshold of the field regionH _{0 W} where negative wall mobilities occur. The instability atH=H ₀ is associated with a nonuniform localized relaxation mode (corrugating mode) of the plane domain wall. If coupling to the external circuit is taken into account, negative-mobility walls also become unstable against uniform perturbations for sufficiently small circuit resistance.Work supported by the Swiss National Science Foundation     

Statistics of irreversible displacements of domain walls in nanowires

The process of quasistatic displacement of domain walls is considered in a nanowire represented as a one-dimensional chain of ferromagnet crystallites. The domain wall pinning due to spatial fluctuations of the anisotropy axes is analyzed. Based on the theory of overshoots of random processes, we have calculated the distribution functions of the initial susceptibility and of the maximal force of interaction of the domain wall with inhomogeneities. These functions are found to be non-Gaussian. We have derived expressions for the magnetization curve and the coercive force, which depend on the length of the chain.     

Tunable remote pinning of domain walls in magnetic nanowires

Domain wall (DW) pinning in ferromagnetic nanowires is in general a complex process. Distortions of the DW shape make quantitative agreement between modeling and experiment difficult. Here we demonstrate pinning using nanometer scale localized stray fields. This type of interaction gives well-characterized, tailorable potential landscapes that do not appreciably distort the DW. Our experimental results are in excellent quantitative agreement with an Arrhenius-Néel model of depinning--a result only possible when the modeled potential profile agrees fully with that experienced by the DW.     

Effect of substrate roughness on the domain structure of permalloy

The effect of substrate roughness on the magnetic properties of a permalloy film is studied. It is shown theoretically that an anisotropic distribution of roughness leads to effective anisotropy in the plane of the film.     

Magnetic field driven domain-wall propagation in magnetic nanowires

The mechanism of magnetic field induced magnetic domain-wall (DW) propagation in a nanowire is revealed: A static DW cannot exist in a homogeneous magnetic nanowire when an external magnetic field is applied. Thus, a DW must vary with time under a static magnetic field. A moving DW must dissipate energy due to the Gilbert damping. As a result, the wire has to release its Zeeman energy through the DW propagation along the field direction. The DW propagation speed is proportional to the energy dissipation rate that is determined by the DW structure. The negative differential mobility in the intermediate field is due to the transition from high energy dissipation at low field to low energy dissipation at high field. For the field larger than the so-called Walker breakdown field, DW plane precesses around the wire, leading to the propagation speed oscillation.     

Tunable conductance of magnetic nanowires with structured domain walls

We show that in a magnetic nanowire with double magnetic domain walls, quantum interference results in spin-split quasistationary states localized mainly between the domain walls. Spin-flip-assisted transmission through the domain structure increases strongly when these size-quantized states are tuned on resonance with the Fermi energy, e.g., upon varying the distance between the domain walls which results in resonance-type peaks of the wire conductance. This novel phenomenon is shown to be utilizable to manipulate the spin density in the domain vicinity. The domain wall parameters are readily controllable, and the predicted effect is hence exploitable in spintronic devices.     

Measurements of the mobility of domain walls in permalloy films in a wide thickness range

The mobility of domain wallsg in permalloy films, thicknessd being from 150 to 5.6 m, has been measured with the aid of Kerr effect. The measurements have been carried out at small displacement of the wall to lessen the effect of a demagnetizing field from the edges of thick film. In accordance with the law the mobility in films over 1 m thick decreases with thickness asd ^–1. The values ofg are in full conformity with the theory of damping by eddy currents. Within the range of 1200–8000 the mobility does not practically change with thickness (6–8×10³ cm/sec Oe) and is far less than that of the theory. Yet, the change of mobilityg(d) in films less than 1 m thick, does not at all mean the change of the nature of magnetic losses. For thin film structural factors are of great importance. Observations of the powder patterns at high resolution show an uneven nature of the wall movement and a great influence of defects upon the damping of the wall.     

Hall micromagnetometry of domain-wall depinning in Permalloy nanowires

Experimental results of field-induced domain-wall depinning in Permalloy nanowires of submicron width and thicknesses between 10 and 30 nm are presented. Single domain walls pinned at notches in nanowires are detected by Hall micromagnetometry. The technique allows to study domain-wall propagation and depinning non-invasively in the temperature range between 2 and 50 K. The influence of sample thickness on domain-wall propagation properties is investigated. In nanowires with two notches of different pinning strength single domain walls are pinned in a toggle mode. The temperature dependence of domain-wall depinning fields in two-notch wires is analyzed.     

Periodical structure based on ferroelectric domain walls

The spectrum of specific states apearing in periodical structure based on ferroelectric domain walls is investigated by perturbation theorie method.     

Spin-wave eigenmodes of permalloy squares with a closure domain structure

Quantized spin-wave eigenmodes in single, 16 nm thick and 0.75 to 4 mum wide square permalloy islands with a fourfold closure domain structure have been investigated by microfocus Brillouin light scattering spectroscopy and time resolved scanning magneto-optical Kerr microscopy. Up to six eigenmodes were detected and classified. The main direction of the spin-wave quantization in the domains was found to be perpendicular to the local static magnetization. An additional less pronounced quantization along the direction parallel to the static magnetization was also observed.     

Effect of the inner structure of domain walls on the stability of an isolated stripe domain in a pulsed field

This paper studies the effect of the inner structure of domain walls on the stability of an isolated stripe domain localized in a thin ferromagnetic film against a pulse of magnetic field applied perpendicularly to the film surface. It is found that the value of the critical amplitude of the pulsed signal strongly depends on the value of the magnetizing field in which the system was initially placed. It is also established that the difference on stability of domains with unipolar and bipolar walls in pulsed fields diminishes as the amplitude of the magnetizing field decreases. Finally, the dependence of the region of stability in a pulse field on the parameters of the system is determined for various domain types. Zh. éksp. Teor. Fiz. 116, 1694–1705 (November 1999)