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 describes 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.
In a thin magnetic nanostripe, an anti-vortex nucleates inside a moving domain wall when driven by an in-plane magnetic field greater than the so-called Walker field. The nucleated anti-vortex 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 anti-vortex leading to fast domain wall speeds for all in-plane driving fields. We present micromagnetic simulation results relating the anti-vortex dynamics…
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 th…
In this report we demonstrate a simple model for the motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field. The model 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 motion becomes underdamped as the vortex moves periodically across the strip; these oscillations are accompanied by a slow drift with a decreasing velocity. At still higher fields the drift velocity starts rising linearly with the field agai…
A concept of magnetic vortex guide is proposed and numerically studied. Similar to the waveguides of electromagnetic waves, a magnetic vortex guide allows a vortex domain wall to move along a nanostrip without annihilation at the strip edges. It is shown by micromagnetic simulations that a magnetic nanostrip of a properly designed superlattice structure or bilayered structure can serve as vortex guides.
We express 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.
Controlling domain wall motion is important due to the impact on the viability of proposed nanowire devices. One hurdle is slow domain wall speed when driven by fields greater than the Walker field, due to nucleation of vortices in the wall. We present simulation results detailing the dynamics of these vortices; including the nucleation and subsequent fast ejection of the vortex core leading to fast domain wall speeds. The ejection is due to the reversal of the core moments by an out-of-plane field. The technique can be used to produce domain walls of known orientation independent of the initi…
Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The as…
It is known that oscillatory domain-wall (DW) motions in soft magnetic thin-film nanostripes above the Walker critical field lead to a remarkable reduction 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 origin and detailed mechanism of this unexpected behavior. We associate the mechanism with the serial dynamic processes of the nucleation of vortex-antivortex (V-AV) pairs inside the stripe or at its edges, th…
We investigated head-to-head domain walls in nanostrips of epitaxial $\mathrm{Fe}_4\mathrm{N}(001)$ thin films, displaying a fourfold magnetic anisotropy. Magnetic force microscopy and micromagnetic simulations show that the domain walls have specific properties, compared to soft magnetic materials. In particular, strips aligned along a hard axis of magnetization are wrapped by partial flux-closure concertina domains below a critical width, while progressively transforming to zigzag walls for wider strips. Transverse walls are favored upon initial application of a magnetic field transverse to …
We present experimental evidence of metastable magnetic domains in cylindrical CoNi nanowires. Transverse (perpendicular) domains have been previously observed only in flat nanostrips. Here they are found together with more conventional vortex domains along the same cylindrical nanowire, denoting a bistable system with similar free energies. The surface and the inner magnetization distribution in both types of domains are analyzed by Photo-Emission Electron Microscopy (PEEM) with X-ray magnetic circular dichroism (XMCD) contrast, and hysteresis loop in individual nanowires are measured by Magn…
The dispersion relations for collective magnon modes for square-planar arrays of vortex-state magnetic dots, having closure magnetic flux are calculated. The array dots have no direct contact between each other, and the sole source of their interaction is the magnetic dipolar interaction. The magnon formalism using Bose operators along with translational symmetry of the lattice, with the knowledge of mode structure for the isolated dot, allows the diagonalization of the system Hamiltonian giving the dispersion relation. Arrays of vortex-state dots show a large variety of collective mode proper…
Phase transformation in finite-size ferroelectrics is of fundamental relevance for understanding collective behaviors and balance of competing interactions in low-dimensional systems. We report a first-principles effective Hamiltonian study of vortex-to-polarization transformation in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles, caused by homogeneous electric fields normal to the vortex plane. The transformation is shown to (1) follow an unusual {\it macroscopic} path that is symmetry non-conforming and characterized by the occurrence of a previously unknown structure as the bridging phase; (2)…
The critical current density shown by a superconductor at the extreme type-II limit is predicted to follow an inverse square-root power law with external magnetic field if the vortex lattice is weakly pinned by material line defects. It acquires an additional inverse dependence with thickness along the line direction once pinning of the interstitial vortex lines by material point defects is included. Moderate quantitative agreement with the critical current density shown by second-generation wires of high-temperature superconductors in kG magnetic fields is achieved at liquid-nitrogen temperat…
Using first-principles based effective Hamiltonian and finite temperature Monte Carlo simulations we investigate cooperative responses, as well as microscopic mechanism for vortex switching, in zero-dimensional Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles under curled electric fields. We find that the generally accepted domain coexistence mechanism is not valid for toroid switching. Instead dipoles are shown to display unusual collective behaviors by forming a new vortex with perpendicular (but not opposite) toroid moment. The strong correlation between the new and original vortices is revealed…
Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of…
We calculate the magnon modes in the presence of a vortex in a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S-matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasi-local translational modes are identified with the frequencies which appear in the trajectory X(t) of the vortex center in recent Molecular Dynamics simulations of the full many-spin model. Using these quasi-local mode…
We report the growth and characterization of single crystals of iron chalcogenide superconductor FeCr$_{0.02}$Se. There is an enhancement of the superconducting transition temperature (T$_{\rm c}$) as compared to the T$_{\rm c}$ of the single crystals of the parent compound Fe$_{1+x}$Se by about 25%. The superconducting parameters such as the critical fields, coherence length, penetration depth and the Ginzburg-Landau parameter have been estimated for these single crystals. Analysis of the critical current data suggests a fluctuation in electronic mean free path induced ($δl$) pinning mechanis…
