Flux-Closure Magnetic States in Triangular Cobalt Ring Elements

Ferromagnetic ring elements on the micrometer and submicrometer scale exhibit flux-closure magnetic vortex states in an intermediate step of their magnetization reversal. These clockwise or counterclockwise flux-closure states are of interest for applications that encode binary information in magnetic elements. Here, we study the magnetization reversal process of triangular cobalt rings made by e-beam lithography and lift-off. We demonstrate that full control over the direction of flux-closure magnetic states can be achieved solely by homogeneous external magnetic fields applied in particular directions. We have extracted statistical experimental data pertaining to the range of critical field values that trigger magnetization reversal from magnetic force microscopy images, and we explain the results on the basis of micromagnetic simulations     

Superconducting Vortex Lattice Configurations on Periodic Potentials: Simulation and Experiment

Nb films have been fabricated on top of array of Ni nanodots. The array of periodic pinning potentials modifies the vortex lattice for specific values of the external applied magnetic field. By means of an implemented code developed from scratch, computer simulations based only on the vortex?Cvortex and the vortex?Cnanodot interactions provide the total interaction between vortices and pinning sites as well as the position of the vortices in the array unit cell. This simulation approach could be performed on square, rectangular or triangular arrays of nanodefects of different size.     

The advantages of the magnetic structure in ferromagnetic-film-coated carbon nanotube probes

The magnetic structures of ferromagnetic-film-coated carbon nanotube (CNT) probes and conventional pyramidal probes for a magnetic force microscope (MFM) were simulated using three-dimensional micromagnetic simulation. The CNT-MFM probes with a total probe diameter less than 60?nm are almost uniformly magnetized along the longitudinal direction of the CNT, which is the ideal magnetic structure for MFM observations. On the other hand, the pyramidal probes had a vortex structure around the point tip, which suggests that they require a greater thickness of the ferromagnetic film because only part of the magnetic moment participates in the detection of the z-component of the stray field from samples. The advantages of the CNT-MFM probe are uniform magnetization along the longitudinal direction and magnetic imaging ability using a smaller coating thickness.     

Vortex domain wall formation in permalloy nanowires with geometric pinning sites

An optimal geometric pinning site on Permalloy nanowires of varying widths has been investigated and applied in a magnetic memory scenario using micromagnetic simulations. Minimal limits on two key factors; the applied field length and the domain wall formation length are established such that vortex domain walls are reliably formed in the structures to facilitate lower powered domain wall movement using spin-polarised current. The symmetric wires with the nanoconstrictions at both sides have been found to favour the formation of the vortex domain wall compared with the asymmetric wires with the nanoconstrictions at only one side of the wires. The detailed micromagnetic simulations show that the domain wall formation length and the applied field length are optimal to form the vortex domain walls when they are equal to the nanowire width.     

Ginzburg–Landau Study of Superconductor with Regular Pinning Array

The vortex distributions and dynamics in superconductors with triangular and honeycomb pinning arrays are investigated by numerical simulation of the two- dimensional (2-D) time-dependent Ginzburg–Landau equations. Periodic boundary conditions are implemented through specific gauge transformations under lattice translations. We model the pinning sites as holes. The simulation results at different magnetic fields are presented. For film with regular triangular pinning array, the vortices are all captured within the holes for a wide range of magnetic fields. For film with regular honeycomb pinning array, the interstitial vortices appear at relatively low magnetic fields. With an increase of magnetic field, the new vortices may enter the holes again and keep the number of vortices at the interstitial positions unchanged. These results confirm our explanations of the experimental results we obtained earlier.     

Dzyaloshinskii–Moriya-Interaction-Like Behavior in Confined Permalloy Nanostructures via Coupled Magnetic Vortices

Dzyaloshinskii–Moriya interaction (DMI), one of antisymmetric exchanges, originates from the combination of low structural symmetry and large spin-orbit coupling and favors magnetization rotations with fixed chirality. Herein, this work reports a DMI-like behavior in permalloy via coupled vortices in confined structures. Under the in-plane magnetic fields, continuous reversals of different coupled vortices are directly observed by in situ Lorentz transmission electron microscopy, and reproduced by complementary micromagnetic simulations. The statistical results show that coupled vortices with opposite chirality appear more frequently with the frequency up to about 60%. Such an asymmetric phenomenon mainly arises from a DMI-like behavior, associated with the increased total energy difference between different ground-state coupled vortices. Moreover, in the reversal process, the junction between disks accelerates the annihilation of vortices moving toward it and is also the starting point of vortex nucleation. These results provide an effective method to generate a DMI-like behavior in magnetic systems with symmetry breaking surface and benefit the future development of vortex-based spintronic devices.     

Stabilizing vortices in interacting nano-objects: a chemical approach

We report a chemical method to prepare metallic Fe porous nanocubes. The presence of pores embedded inside the cubes was attested by electron tomography. Thanks to electronic holography and micromagnetic simulations, we show that the presence of these defects stabilizes the vortices in assembly of interacting cubes. These results open new perspectives toward magnetic vortex stabilization at relatively low cost for various applications (microelectronics, magnetic recording, or biological applications).     

Vortices with Fractional Flux Quanta in Multi-Band Superconductors

In superconductors with three or more components, time-reversal symmetry may be broken when the inter-component couplings are repulsive, leading to a superconducting state with twofold degeneracy. When prepared carefully, there is a stable domain wall on a constriction which connects two bulks in states with opposite chiralities. Applying external magnetic field, vortices in different components dissociate with each other, resulting in a ribbon shape distribution of magnetic field at the domain wall.     

Comparison of Micromagnetic and Point Probe Model in Magnetic Force Microscope Simulation

We developed a micromagnetic model of magnetic force microscopy (MFM) tip to compare it with the simple point probe model. We simulated the MFM signal to provide an understanding of the measurement of the field generated by the write head in perpendicular recording hard disk drives. When the magnetic pole density at the air-bearing surface of the head's main pole is increased from 0.2 T to 1 T, the MFM tip with vertical anisotropy shows a flower-state magnetization, while the tip with horizontal anisotropy has more complicated switching modes. It is found that the signal ratio of the two MFM tips with vertical/horizontal anisotropy does have a one-to-one correspondence to the average magnetic field in the tip; however, the signal ratio may change sign because of the magnetic moments' switching in the tip with vertical anisotropy. The result of micromagnetic simulation is quite similar to that of the point probe model, and has good agreement with experiments.     

Magnetic dynamic behavior of nanomagnets studied by Magnetic Force Microscopy with external field

The micro/nanomagnetic behavior of magnetic systems is a key issue as the size of magnetic devices is reduced to or under the micrometer range. We study the magnetic behavior of nanomagnets under different applied magnetic field conditions by Magnetic Force Microscopy (MFM). MFM is sensitive mainly to magnetization distributions that generate magnetic fields. CoCr Magnets were deposited by electropulsed SPM onto a Si substrate with sizes ranging from 400×100 to 800×400 nm and thickness between 2 and 3 nm. MFM measurements were performed using a Digital Instruments (DI) Dimension 3100 SPM upgraded for measurements with an external magnetic field applied to the sample. The home-designed modification consists in an electromagnet with field guides towards the scanning region while measuring. Different magnetic fields up to 400 Oe were applied to the samples in-plane during the MFM measurements. The magnetic configuration for the different applied fields was then imaged by MFM.     

Vortex Dynamics in Bi2Sr2CaCu2O8 Single Crystal with Low Density Columnar Defects Studied by Magnetic Force Microscope

We have studied vortex dynamics in Bi₂Sr₂CaCu₂O₈ single crystal with low density columnar defects by using a magnetic force microscope. Single crystal Bi₂Sr₂CaCu₂O₈ sample was irradiated by 1.3 GeV uranium ion to form artificial pinning centers along the crystalline c-axis. The irradiation dose corresponded to a matching field of 20 gauss. The radius of an individual vortex is approximately 140 nm, which is close to the penetration depth of this material. Magnetic force microscope (MFM) images show that intrinsic crystalline defects such as stacking fault dislocations are very effective pinning centers for vortices in addition to the pinning centers due to ion bombardment. By counting the number of vortex, we found that the flux trapped at each pinning center is a single flux quantum. At higher magnetic field, the vortex structure showed an Abrikosov lattice disturbed only by immobile vortices located at pinning centers. When increasing or decreasing the external magnetic field, the spatial distribution of vortices showed a Bean model like behavior.     

Do Images of Biskyrmions Show Type‐II Bubbles?

The intense research effort investigating magnetic skyrmions and their applications for spintronics has yielded reports of more exotic objects including the biskyrmion, which consists of a bound pair of counter‐rotating vortices of magnetization. Biskyrmions have been identified only from transmission electron microscopy images and have not been observed by other techniques, nor seen in simulations carried out under realistic conditions. Here, quantitative Lorentz transmission electron microscopy, X‐ray holography, and micromagnetic simulations are combined to search for biskyrmions in MnNiGa, a material in which they have been reported. Only type‐I and type‐II magnetic bubbles are found and images purported to show biskyrmions can be explained as type‐II bubbles viewed at an angle to their axes. It is not the magnetization but the magnetic flux density resulting from this object that forms the counter‐rotating vortices.     

Observation of the Curved and Entangled Vortex Tubes in 3D Mesoscopic Cubic Superconductors

The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for the superconducting samples with a cubic shape in a uniform external magnetic field. We obtain the different vortex patterns as a function of the magnetic field perpendicular to its surface. The vortex tubes must reach the surface perpendicularly in order to avoid a supercurrent component pointing outwards the surface. At the same time, we observed the arrangement of spiral vortices in the cubic superconductor. These results show that our approach is an effective and useful to interpret experimental data on vortex states in the mesoscopic superconductors.     

Majorana States in 2D Topological Superconductor Hosting Abrikosov Vortices

We study Majorana states near Abrikosov vortices in a 2D topological superconductor in the applied magnetic field B. The Majorana fermions always arise in pairs. In the considered case, the first Majorana fermion localizes in the vortex core while the second, exterior, Majorana fermion localizes at the distance r ∝ 1/B away from the core. We calculate the hybridization between the vortex-core and the exterior Majorana fermions in the cases of a single vortex, two vortices, and the Abrikosov vortex lattice. We show that the hybridization can be effectively governed by the applied magnetic field if the chemical potential is tuned near the Dirac point. We also show that in the case of the vortex lattice, the hybridization between the vortex-core and external Majorana fermions affects significantly low-energy spectrum giving rise to the gap between two lowest Majorana energy bands.     

High resolution magnetic force microscopy of patterned L1(0)-FePt dot arrays by nanosphere lithography

High resolution magnetic force microscopy (MFM) has been carried out on L1(0)-FePt dot arrays patterned by plasma modified nanosphere lithography. An ex situ tip magnetization reversal experiment is carried out to determine the magnetic domains and verify the imaging stability of MFM and the mutual perturbations between the magnetic tip and the sample. We have identified that the critical size for the single domain region is about 90?nm across. Comparison with MFM image simulation also suggests that the magnetizations of the triangular dots in both single and double domain states are parallel to one edge of the dots, indicating the large uniaxial magnetocrystalline anisotropy of the L1(0)-FePt phase and the need for decreasing the magnetostatic energy.     

Magnetic vortex state stability, reversal and dynamics in restricted geometries

Magnetic vortices are typically the ground states in geometrically confined ferromagnets with small magnetocrystalline anisotropy. In this article I review static and dynamic properties of the magnetic vortex state in small particles with nanoscale thickness and sub-micron and micron lateral sizes (magnetic dots). Magnetic dots made of soft magnetic material shaped as flat circular and elliptic cylinders are considered. Such mesoscopic dots undergo magnetization reversal through successive nucleation, displacement and annihilation of magnetic vortices. The reversal process depends on the stability of different possible zero-field magnetization configurations with respect to the dot geometrical parameters and application of an external magnetic field. The interdot magnetostatic interaction plays an important role in magnetization reversal for dot arrays with a small dot-to-dot distance, leading to decreases in the vortex nucleation and annihilation fields. Magnetic vortices reveal rich, non-trivial dynamical properties due to existance of the vortex core bearing topological charges. The vortex ground state magnetization distribution leads to a considerable modification of the nature of spin excitations in comparison to those in the uniformly magnetized state. A magnetic vortex confined in a magnetically soft ferromagnet with micron-sized lateral dimensions possesses a characteristic dynamic excitation known as a translational mode that corresponds to spiral-like precession of the vortex core around its equilibrium position. The translation motions of coupled vortices are considered. There are, above the vortex translation mode eigenfrequencies, several dynamic magnetization eigenmodes localized outside the vortex core whose frequencies are determined principally by dynamic demagnetizing fields appearing due to restricted dot geometry. The vortex excitation modes are classified as translation modes and radially or azimuthally symmetric spin waves over the vortex ground state. Studying the spin eigenmodes in such systems provides valuable information to relate the particle dynamical response to geometrical parameters. Unresolved problems are identified to attract attention of researchers working in the area of nanomagnetism.     

Vortex Molecules in Thin Films of Layered Superconductors

Both the equilibrium and transport properties of the vortex matter are essentially affected by the behavior of the intervortex interaction potential. In isotropic bulk superconductors this potential is well known to be repulsive and is screened at intervortex distances R greater than the London penetration depth λ. As a result, in perfect crystals quantized Abrikosov vortices form a triangular lattice. In thin films of anisotropic superconductors this standard interaction potential behavior appears to be strongly modified because of the interplay between the long-ranged repulsion predicted in the pioneering work by J. Pearl and the attraction caused by the tilt of the vortex lines with respect to the anisotropy axes. This interplay results in a new type of vortex arrangement formed by finite-size vortex chains, i.e., vortex molecules. Tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or/and can arrange into multiquanta flux lattice. The magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number N of flux quanta. Thus, the increase in the field tilting (or varying temperature) should be accompanied by the series of the phase transitions between the vortex lattices with different N. A similar scenario should be realized in strongly anisotropic BSCCO high-T _c superconductors where in tilted field a crossing lattice of Abrikosov vortices (the stacks of pancakes in this case) and Josephson vortices appears. This crossing leads to the zigzag deformation of the pancakes stacks which is responsible for the attraction interaction competing with the long-ranged Pearl’s repulsion.     

Magnetic force microscopy and simulation studies on Co<Subscript>50</Subscript>Fe<Subscript>50</Subscript> elliptical nanomagnets

We studied the magnetization reversal mechanism of single-layered Co₅₀Fe₅₀ nanomagnets by measuring the magnetization reversal and using the micromagnetic simulations. The magnetization reversal strongly depends on the thickness of the nanomagnets. In the remanent state, the magnetic force microscopy studies and the simulation data showed the formation of single and vortex states depending on the thickness of nanomagnets.     

Spin Wave Excitations and Winter’s Magnons in Vertically Coupled Vortex State Permalloy Dots

Circular soft magnetic dots are the main elements of many proposed novel spintronics devices, capable of fascinating spin-based electronics applications, from extremely sensitive magnetic field sensors, to current-tunable microwave vortex oscillators. Here, we investigate static and broadband dynamic magnetization responses of vertically coupled Permalloy (Py) magnetic dots in the vortex state in layered nanopillars (experiment and simulations), which were explored as a function of in-plane magnetic field and interlayer separation. Under reduction of magnetic field from saturation for the field range just above vortex-vortex ground state. We observe a metastable double vortex state for each of the dots. In this state, novel kinds of spin waves (Winter’s magnons along domain walls between vortex cores and half-edge antivortex) are excited. For dipolarly coupled circular Py(25 nm)/Cu(20 nm)/Py(25 nm) trilayer nanopilars of diameter 600 nm, a small in-plane field splits the eigenfrequencies of azimuthal spin wave modes inducing an abrupt transition between acoustic (in-phase) and optic (out-of-phase) kinds of the low-lying coupled spin wave modes. Qualitatively similar changes (although more gradual and at higher values of in-plane fields) occur in the exchange coupled Py(25 nm)/Cu(1 nm)/Py(25 nm) trilayer nanopillars. These findings are in qualitative agreement with micromagnetic dynamic simulations.     

Magnetic Force Microscopy of Low-Coercivity Ferromagnetic Nanodiscs

We report the results of magnetic force microscopy (MFM) investigations of low-coercivity Co nanodiscs, with 50 nm lateral size and 20 nm height, fabricated by e-beam lithography and ion etching. We observed two types of MFM contrast in the form of Gaussian and ring distributions caused by strong probe–particle interaction. We compared experimentally the transformation of the MFM contrast from these low-coercivity nanodiscs caused by an external magnetic field applied in situ, and compared the experimental results with theoretical simulations.