Magnetic Nanostripes Research Articles

Suppression of the intrinsic stochastic pinning of domain walls in magnetic nanostripes

Nanofabrication has allowed the development of new concepts such as magnetic logic and race-track memory, both of which are based on the displacement of magnetic domain walls on magnetic nanostripes. One of the issues that has to be solved before devices can meet the market demands is the stochastic behaviour of the domain wall movement in magnetic nanostripes. Here we show that the stochastic nature of the domain wall motion in permalloy nanostripes can be suppressed at very low fields (0.6–2.7 Oe). We also find different field regimes for this stochastic motion that match well with the domain wall propagation modes. The highest pinning probability is found around the precessional mode and, interestingly, it does not depend on the external field in this regime. These results constitute an experimental evidence of the intrinsic nature of the stochastic pinning of domain walls in soft magnetic nanostripes.

Domain Wall Manipulation with a Magnetic Tip

A theoretical concept of local manipulation of magnetic domain walls is introduced. In the proposed procedure, a domain wall is driven by a spin-polarized current induced by a magnetic tip, as used in a scanning tunneling microscope, placed above a magnetic nanostripe and then moved along its long axis with a current flowing through the vacuum barrier. The angular momentum from the spin-polarized current exerts a torque on the magnetic moments underneath the tip and leads to a displacement of the domain wall. Particularly, the manipulation of a ferromagnetic 180° transverse domain wall has been studied by means of Landau-Lifshitz-Gilbert dynamics and Monte Carlo simulations. Different relative orientations of the tip and the sample magnetization have been considered.

Non-Planar Dzyaloshinskii Spirals and Magnetic Domain Walls in Non-Centrosymmetric Systems with Orthorhombic Anisotropy

The basic micromagnetic models of Landau, Lifshitz, and Dzyaloshinskii, are extended by an anisotropy term with two independent parameters. The resulting ground states of the magnetic domains and the domain-wall profiles are discussed for crystal lattices with orthorhombic unit cells. In these simple geometries, the magnetization is not confined to a single plane. Depending on the relations between the spin-stiffness, anisotropy, and Dzyaloshinskii-Moriya interaction several different zero-temperature phases of the magnetic structure are found. The corresponding phase diagrams are obtained numerically. Analytical results are given for some special cases. The studied model is of particular relevance for magnetic wires, nanostripes and ultrathin magnetic films deposited on non-magnetic surfaces.

Thermally activated domain wall dynamics in a disordered magnetic nanostrip

We consider the effect of disorder on the dynamics of a transverse domain wall in thin and narrow magnetic strips made of soft magnetic materials such as permalloy. Motivated by the micromagnetic description of such a domain wall, we construct a model based on two coupled flexible lines enclosing the domain wall transition region. The model captures both the finite width and the characteristic V-shape of the wall. Disorder is included via randomly distributed pinning centers interacting with the two lines, describing, e.g., thickness fluctuations of the strip. We study the thermally activated creep motion of the domain wall driven by an applied field in a disordered nanostrip, and demonstrate how such inherently stochastic motion leads to a broad distribution of the domain wall velocities, in agreement with experimental observations.

Structural characterization of magnetic nanostripes by fast domain wall injection

The process of injection of a magnetic domain wall (DW) by means of a 25--100 ns current pulse flowing through an adjacent conductive track has been studied in detail. We find that the probability of creating a DW through this method is 100% for a wide range of amplitudes of the current pulse and of the external magnetic field, including zero external magnetic field. Micromagnetic simulations show that the DW is created in the first nanosecond of the pulse, and its movement is strongly influenced by the induced Oersted field, which can reach considerable values, especially in the perpendicular-to-plane direction. The edge roughness and temperature play also a crucial role in determining the type of DW that travels through the wire. Experimentally we show that a map of the probability of injection of a DW by a current pulse can be a very powerful method to check the structural quality of the nanostripe, which has very important practical consequences for research in this area.

Direct observation of Oersted-field-induced magnetization dynamics in magnetic nanostripes

We have used time-resolved x-ray photoemission electron microscopy to investigate the magnetization dynamics induced by nanosecond current pulses in NiFe/Cu/Co nanostripes. A large tilt of the NiFe magnetization in the direction transverse to the stripe is observed during the pulses. We show that this effect cannot be quantitatively understood from the amplitude of the Oersted field and the shape anisotropy. High-frequency oscillations observed at the onset of the pulses are attributed to precessional motion of the NiFe magnetization about the effective field. We discuss the possible origins of the large magnetization tilt and the potential implications of the static and dynamic effects of the Oersted field on current-induced domain-wall motion in such stripes.

Motion of transverse domain walls in thin magnetic nanostripes under transverse magnetic fields

The motion of transverse magnetic domain walls (TDW) in thin magnetic nanostripes under transverse magnetic fields (TMF) is investigated. In the absence of axial fields, an approximate static TDW profile is obtained under a TMF with an arbitrary orientation. This profile becomes exact if the TMF is parallel or perpendicular to the stripe plane. Under nonzero axial fields, the TDW becomes asymmetric and twisted, and it moves along the wire axis with two different propagation modes, rigid-body mode and precession mode, depending on the strength of the axial field. The critical strength separating these two modes is called modified Walker limit HW′. The TMF dependence of HW′, the TDW velocity and maximum twisting angle at HW′ were investigated both numerically and analytically. Moreover, it is shown that an early proposed velocity-field relationship fits well to the average velocities of a TDW above HW′. These results should be important for future developments of magnetic nanodevices based on DW propagation.

Numerical Analysis of the Influence of Geometry and Temperature on Switching Processes in Magnetic Nanostrips

The present paper numerically investigates the micromagnetic behavior of permalloy nanostrips, starting from the space-time integration of the Landau-Lifshitz-Gilbert equation. The analysis is performed on objects with variable longitudinal size of the order of some hundreds of nanometers. The attention is focused on the role of geometrical properties (e.g., scaling factor and end shape) and of thermal agitation on magnetization reversal processes. The thermal effects are included in the model following the Langevin approach.

Splitting of a moving transverse domain wall in a magnetic nanostripe in a transverse field

The field-driven domain-wall dynamics in magnetic nanostripes under the influence of transverse fields was examined experimentally and by numerical simulations. For a small range of transverse fields in a regime below the Walker field an unexpected instantaneous change in the domain-wall velocity was found. Micromagnetic simulations have shown that this peculiar behavior is caused by a transformation of the moving asymmetric transverse wall: the wall is stretched along the nanostripe due to different velocities of the upper and lower half antivortices constituting the domain wall.

Detection of Continuous Spinwaves Along Magnetic Nanostripes Using Magnetoresistive Devices

In this study, we have theoretically investigated the scheme to detect continuous spinwaves using magnetoresistive devices. First, the spinwaves along a magnetic nanostripe related to this detection scheme have been characterized using a linearization approach on the Landau-Lifshitz-Gilbert equation. Then, the frequency (wavelength) responses of the magnetoresistive devices have been derived from the giant- or tunneling-magnetoresistive effect. The frequency (wavelength) responses have been compared with those of the conventional detection methods using microstrip lines or coplanar waveguides. Finally, we have qualitatively analyzed the impact of noise in spinwave detection, from which this detection scheme can be improved.

Critical nucleation size of vortex core for domain wall transformation in soft magnetic thin film nanostrips

We report on the criterion for the dynamic transformation of the internal structure of moving domain walls (DWs) in soft magnetic thin-film nanostripes above the Walker threshold field, Hw. In order for the process of transformation from transverse wall (TW) to vortex wall (VW) or antivortex wall (AVW) occurs, the edge-soliton core of the TW-type DW should grow sufficiently to the full width at half maximum of the out-of-plane magnetizations of the core area of the stabilized vortex (or antivortex) by moving inward along the transverse (width) direction. Upon completion of the nucleation of the vortex (antivortex) core, the VW (AVW) is stabilized, and then its core accompanies the gyrotropic motion in a potential well (hill) of a given nanostripe. Field strengths exceeding the Hw, which is the onset field of DW velocity breakdown, are not sufficient but necessary conditions for dynamic DW transformation.

Magnetic domain-wall motion by propagating spin waves

We found by micromagnetic simulations that the motion of a transverse wall (TW)–type domain wall in magnetic thin-film nanostripes can be manipulated via interaction with spin waves (SWs) propagating through the TW. The velocity of the TW motion can be controlled by changes of the frequency and amplitude of the propagating SWs. Moreover, the TW motion is efficiently driven by specific SW frequencies that coincide with the resonant frequencies of the local modes existing inside the TW structure. The use of propagating SWs, whose frequencies are tuned to those of the intrinsic TW modes, is an alternative approach for controlling TW motion in nanostripes.

Antivortex dynamics in magnetic nanostripes

In a thin magnetic nanostripe, an antivortex nucleates inside a moving domain wall when driven by an in-plane magnetic field greater than the so-called Walker field. The nucleated antivortex must cross the width of the nanostripe before the domain wall can propagate again, leading to low average domain wall speeds. A large out-of-plane magnetic field, applied perpendicularly to the plane of the nanostripe, inhibits the nucleation of the antivortex leading to fast domain wall speeds for all in-plane driving fields. We present micromagnetic simulation results relating the antivortex dynamics to the strength of the out-of-plane field. An asymmetry in the motion is observed which depends on the alignment of the antivortex core magnetic moments to the direction of the out-of-plane field. The size of the core is directly related to its crossing speed, both depending on the strength of the perpendicular field and the alignment of the core moments and direction of the out-of-plane field.

Dynamics of Domain Walls in Soft Magnetic Nanostripes: Topological Soliton Approach

The motions of different types of domain walls (DWs) driven by direct current (dc) magnetic field in soft magnetic nanostripes were calculated. The DWs exhibit steady and transient motions in the low fields and oscillations of their internal structure above a critical field. A developed soliton model of the walls explains their dynamics by the motions of a limited number of magnetic topological solitons having nonzero gyrovectors such as vortex and antivortex. The model predicts the reduced DW velocity and critical field in the low-field regime, and increased wall-oscillation frequency in nanostripes, compared to the Walker solution for bulk magnets. The critical field and velocity are determined by the nanostripe thickness and width, whereas the oscillation frequency depends only on the field strength.

Dynamics of a vortex domain wall in a magnetic nanostrip: Application of the collective-coordinate approach

The motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a velocity proportional to the field. Above a critical field the viscous motion breaks down, giving way to oscillations accompanied by a slow drift of the wall. At still higher fields the drift velocity starts rising with the field again but with a much lower mobility $dv/dH$ than in the viscous regime. To describe the dynamics of the wall, we use the method of collective coordinates that focuses on soft modes of the system. By retaining two soft modes, parametrized by the coordinates of the vortex core, we obtain a simple description of the wall dynamics at low and intermediate applied fields that applies to both the viscous and oscillatory regimes below and above the breakdown. The calculated dynamics agrees well with micromagnetic simulations at low and intermediate values of the driving field. In higher fields, additional modes become soft and the two-mode approximation is no longer sufficient. We explain some of the significant features of vortex-domain-wall motion in high fields through the inclusion of additional modes associated with the half antivortices on the strip edge.

Underlying mechanism of domain-wall motions in soft magnetic thin-film nanostripes beyond the velocity-breakdown regime

It is known that oscillatory domain-wall (DW) motions in soft magnetic thin-film nanostripes above the Walker critical field lead to remarkable reductions in the average DW velocities. In a much-higher-field region beyond the velocity-breakdown regime, however, the DW velocities have been found to increase in response to a further increase of the applied field. We report on the physical underlying mechanism of this unexpected behavior. We associate the mechanism with the serial dynamic processes of the nucleation of vortex-antivortex pairs inside the stripe or at its edges, the nonlinear gyrotropic motions of vortices and antivortices, and their annihilation process. Moreover, this work evidences that a two-dimensional soliton model is required for adequate interpretation and understanding of DW motions in the linear- and oscillatory-DW-motion regimes as well as in the beyond-velocity-breakdown regime.

Dynamics of Domain Walls in Magnetic Nanostrips

We express the dynamics of domain walls in ferromagnetic nanowires in terms of collective coordinates, generalizing Thiele's steady-state results. For weak external perturbations the dynamics is dominated by a few soft modes. The general approach is illustrated on the example of a vortex wall relevant to recent experiments with flat nanowires. A two-mode approximation gives a quantitatively accurate description of both the steady viscous motion of the wall in weak magnetic fields and its oscillatory behavior in moderately high fields above the Walker breakdown.

Dynamic transformations of the internal structure of a moving domain wall in magnetic nanostripes

The magnetic field (or electric current) driven domain-wall motion in magnetic nanostripes is of considerable interest because it is essential to the performance of information-storage and logic devices. One of the current key problems is to understand the complex behaviors of oscillatory domain-wall motions under applied magnetic fields stronger than the so-called Walker field, beyond which the velocity of domain walls markedly drops. In a certain range just above the Walker field, the motions are not chaotic but rather periodic with different periodicities of dynamic transformations of a moving domain wall between the different types of its internal structure. In addition, three different periodicities of the dynamic transformations are calculated, which consist of different types of domain-wall structures that are transformed from one type to another. The transformation periods vary with the field strength and the nanostripe width. This phenomenon can be described by the dynamic motion of a limited number of magnetic topological solitons such as the vortex and antivortex confined in nanostripes. These results provide a considerably better understanding and details of the domain-wall motions in soft magnetic nanostripes.

Self-assembled magnetic nanostripes by organic patterning

Selective adsorption of Fe deposited on the organic molecule 3,4,9,10-perylene-tetracarboxylic-3, 4,9,10-dianhydride (PTCDA) is used to prepare a self assembled magnetic nanostripe structure on a vicinal Ag surface. Scanning tunneling microscopy reveals that after PTCDA deposition on the Ag(10 8 7) surface a grating-like domain pattern is formed. It consists of alternating stripes of molecule-covered facets and uncovered (111) terraces. Fe adsorption takes place selectively on the molecule-covered stripes forming disk-shaped super-paramagnetic islands with a polar easy magnetization axis.

Multilayered magnetic nanostrips studied by transmission X-ray microscopy

Transmission x-ray microscopy with the x-ray magnetic circular dichroism as a contrast mechanism was used to image the field dependent evolution of magnetic domains in artificially nanostructured strips of a multilayered Fe/Gd system. A diversity of domain configurations have been imaged for different strengths of the applied magnetic field and different widths of the strips, varying between 100 nm and 1 μm. Undulating domain patterns, analogous to those observed in other condensed matter systems could be found.