Magnetization Curling Research Articles

An exact, time-dependent analytical solution for the magnetic field in the inner heliosheath

We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic divergence constraint. To this end, we assume that the magnetic field is frozen into a plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. Furthermore, we make use of the ideal Ohm’s law for the magnetic vector potential and the electric scalar potential. By employing a suitable gauge condition that relates the potentials and working with a characteristic coordinate representation, we thus obtain an inhomogeneous first-order system of ordinary differential equations for the magnetic vector potential. Then, using the general solution of this system, we compute the magnetic field via the magnetic curl relation. Finally, we analyze the well-posedness of the corresponding Dirichlet-type initial-boundary value problem, specify compatibility conditions for the initial-boundary values, and outline the implementation of initial-boundary conditions.

Wide-Band Electromagnetic Wave Propagation and Resonance in Long Cobalt Nanoprisms

Electromagnetic wave interaction with confined metallic magnetic structures is complex due to the excitation of nonuniform electromagnetic fields and magnetic precession and spin-wave modes over length scales that are dependent on the geometric, electromagnetic, and micromagnetic properties of the magnetic structures. Here, we solve the coupled system of Maxwell's equations and the Landau-Lifshitz-Gilbert equation using a stable algorithm based on the finite-difference time-domain method to study the transient wide-band electromagnetic propagation and resonance in infinitely long cobalt nanoprisms with a square cross section of side lengths 50--1000 nm. In particular, we identify the resonance mechanisms through studying the local transient and spectral distributions of magnetization in the prisms. The nanoprisms are excited by an axially polarized plane wave at normal incidence with a 70 GHz Gaussian pulse profile. For this incident wave condition, the simulations confirm that resonance in the cobalt prisms is excited mainly by the current-induced magnetic fields and indicate a magnetization curling resonance mode for prism side lengths less than 100 nm. The eigenfrequencies for the curling mode are confirmed theoretically using a model for an equivalent long circular cylinder with radial spin-wave modes. For prism side lengths longer than 100 nm (but less than the nonmagnetic skin depth), the magnetic response is confined to thin regions along the prism edges due to resonance-induced skin effects. The simulations indicate predominately uniform magnetization precession in the confined edge regions with increased pinning in the corners. The uniform resonance mode in the central part of the edge regions increases in intensity with prism size, with frequency described using Kittel's ferromagnetic resonance frequency of a thin planar structure. A higher-frequency size-independent uniform resonance mode is observed in the corner regions with frequency determined by the local demagnetizing factors. Local and integrated power absorption spectra are calculated using the simulated transient magnetization and fields, and confirm the resonance modes and frequencies in the cobalt prisms and their size dependence. The profile of the local power absorption spectra is also used to estimate the thickness of the confined edge regions or magnetic skin depth in the cobalt prisms at the fundamental resonance mode and is found to be approximately 50 nm. The outcomes of this work would benefit the design and engineering of lightweight and compact materials and devices incorporating metallic magnetic nanostructures. This work also provides a foundation for further modeling and understanding of electromagnetic transmission and propagation in more complex metallic ferromagnetic structures and composites excited by different electromagnetic wave conditions.

Uniaxial magnetization reversal process in electrodeposited high-density iron nanowire arrays with ultra-large aspect ratio

In this study, magnetization reversal modes of iron nanowire arrays with large aspect ratios were investigated by Shtrikman’s micromagnetic theory. The iron nanowire arrays were potentiostatically electrodeposited into anodized aluminum oxide nanochannels with average diameters, Dp, of ca. 33 nm, 52 nm, 67 nm, and 85 nm. The growth rate of the iron nanowires was ca. 105 nm s−1 at the cathode potential of −1.2 V (vs. an Ag/AgCl reference), and the axial length, Lw, reached up to ca. 60 µm. Maximum aspect ratio, Lw/Dw of the iron nanowires was found to be ca. 1800, and the axial direction coincided with 〈1 1 0〉 direction of the bcc-Fe crystal structure. The effect of the average diameter size on the coercivity of iron nanowire arrays corresponded well to the theoretical estimate, which was calculated by the magnetization curling mode in Shtrikman’s micromagnetic theory. As the average diameter of the iron nanowires was decreased, coercivity and squareness of the nanowire arrays increased up to 1.63 kOe and 0.87, respectively.

Iron Oxide Nanoparticles for Magnetic Hyperthermia

Assemblies of magnetic nanoparticles show a great potential for application in biomedicine, particularly, magnetic hyperthermia. However, to achieve desired therapeutic effect in magnetic hyperthermia, the assembly of nanoparticles should have a sufficiently high specific absorption rate (SAR) in alternating magnetic field of moderate amplitude and frequency. Using the Landau–Lifshitz stochastic equation, it is shown that dilute assemblies of iron oxide nanoparticles of optimal diameters are capable of providing SAR of the order of 400–600[Formula: see text]W/g in alternating magnetic field with the amplitude [Formula: see text][Formula: see text]Oe in the frequency range f = 300–500[Formula: see text]kHz. Unfortunately, in dense clusters of magnetic nanoparticles, which are often formed in a biological medium, there is a sharp decrease in SAR due to the influence of strong magneto-dipole interaction of closest nanoparticles. To overcome this difficulty, it is suggested covering the nanoparticles with nonmagnetic shells of sufficient thickness or using non-single-domain nanoparticles being in magnetization curling states.

Magnetization Reversal Modes in Short Nanotubes with Chiral Vortex Domain Walls.

Micromagnetic simulations of magnetization reversal were performed for magnetic nanotubes of a finite length, L, equal to 1 and 2 μm, 50 and 100 nm radii, R, and uniaxial anisotropy with “easy axis” parallel to the tube length. I.e., we considered relatively short nanotubes with the aspect ratio L/R in the range 10–40. The non-uniform curling magnetization states on both ends of the nanotubes can be treated as vortex domain walls (DW). The domain wall length, Lc, depends on the tube geometric parameters and the anisotropy constant Ku, and determines the magnetization reversal mode, as well as the switching field value. For nanotubes with relative small values of Lc (Lc/L < 0.2) the magnetization reversal process is characterized by flipping of the magnetization in the middle uniform state. Whereas, for relative large values of Lc, in the reverse magnetic field, coupling of two vortex domain walls with opposite magnetization rotation directions results in the formation of a specific narrow Néel type DW in the middle of the nanotube. The nanotube magnetization suddenly aligns to the applied field at the switching field, collapsing the central DW.

Photon Gas Is the Medium of Electromagnetic Waves

The aim of this paper is to find the carrier or medium of electromagnetic waves that has been searched for many years. The thermal radiation is composed of the shot noise and the wave noise, so the Planck formula can be separated mathematically into two parts. Assume every photon has the same proper magnetic moment and an equal rest mass which has been estimated from the cosmic background temperature in space where the photon gas is at an open state of thermal equilibrium. The magnetic-electric dynamic equation is established that means magnetic curl caused electric change, and the electric-magnetic dynamic equation is established that means electric curl caused magnetic change. After the wave equation is caught, it is clear that the photon gas is the medium of electromagnetic waves in vacuum.

Numerical assessment of low-frequency dosimetry from sampled magnetic fields

Low-frequency dosimetry is commonly assessed by evaluating the electric field in the human body using the scalar potential finite difference method. This method is effective only when the sources of the magnetic field are completely known and the magnetic vector potential can be analytically computed. The aim of the paper is to present a rigorous method to characterize the source term when only the magnetic flux density is available at discrete points, e.g. in case of field measurements. The method is based on the solution of the discrete magnetic curl equation. The system is restricted to the independent set of magnetic fluxes and circulations of magnetic vector potential using the topological information of the computational mesh. The solenoidality of the magnetic flux density is preserved using a divergence-free interpolator based on vector radial basis functions. The analysis of a benchmark problem shows that the complexity of the proposed algorithm is linearly dependent on the number of elements with a controllable accuracy. The method proposed in this paper also proves to be useful and effective when applied to a real world scenario, where the magnetic flux density is measured in proximity of a power transformer. A 8 million voxel body model is then used for the numerical dosimetric analysis. The complete assessment is completed in less than 5 min, that is more than acceptable for these problems.

Induced magnetic anisotropies dependent micromagnetic structure of epitaxial Co nanostrip arrays

Dipole-dipole interaction in the arrays of closely packed magnetic nanostrips plays an important role in the magnetization reversal processes and significantly affects the critical fields, spin dynamics, and magnetotransport properties. Shape anisotropy in such arrays leads to the closure of the magnetic flux at the poles of adjacent nanostrips. If to induce the magnetic anisotropy oriented across the nanostrip long axis, this will change the micromagnetic configuration of each nanostrip in the array due to the appearance of the domain structure formed by domains with an antiparallel orientation of the magnetization. In this paper, we study the field-dependent behavior of vortex and Neel domain walls of the laminar domain structure of the dipolarly coupled epitaxial Co/Pd nanostrips with mutually perpendicular anisotropies induced by the atomic steps on the surface and by the long shape of nanostrips. We investigate the effect of dipole–dipole interaction between nanostrips on the magnetization reversal modes and switching fields depending on direction of the applied magnetic field. Our investigation reveals rather complex mechanisms of magnetization reversal of the nanostrip arrays, which can be described using a combination of processes including magnetization curling, transverse domain wall nucleation and motion as well as coherent rotation of spins within domains.

Unconventional spin distributions in thick Ni80Fe20 nanodisks

We study the spin distributions in permalloy (Py: Ni80Fe20) nanodisks as a function of diameter D (300 nm ≤ D ≤ 1 μm) and thickness L (30 nm ≤ L ≤ 100 nm). We observed that beyond a certain thickness, for a fixed disk diameter, an unconventional spin topology precipitates which is marked by the presence of a divergence field within the magnetic vortex curl. The strength of this divergence changes anti-symmetrically from negative to positive—depending on the core polarity—along the axis of the cylindrical nanodisk. This is also accompanied by a skyrmion-like out-of-plane bending of the spin vectors farther away from the disk center. Additionally, the vortex core dilates significantly when compared to its typical size. This has been directly observed using magnetic force microscopy. We determined from the ferromagnetic resonance spectroscopy measurements that the unconventional topology in the thicker nanodisks gyrated at a frequency, which is significantly lower than what is predicted by a magnetic vortex based analytical model. Micromagnetic simulations involving dipolar and exchange interactions appear to satisfactorily reproduce the experimentally observed static and dynamic behaviors. Besides providing a physical example of an unconventional topology, these results can also aid the design of topologically protected memory elements.

Nanoscale switch for vortex polarization mediated by Bloch core formation in magnetic hybrid systems.

Vortices are fundamental magnetic topological structures characterized by a curling magnetization around a highly stable nanometric core. The control of the polarization of this core and its gyration is key to the utilization of vortices in technological applications. So far polarization control has been achieved in single-material structures using magnetic fields, spin-polarized currents or spin waves. Here we demonstrate local control of the vortex core orientation in hybrid structures where the vortex in an in-plane Permalloy film coexists with out-of-plane maze domains in a Co/Pd multilayer. The vortex core reverses its polarization on crossing a maze domain boundary. This reversal is mediated by a pair of magnetic singularities, known as Bloch points, and leads to the transient formation of a three-dimensional magnetization structure: a Bloch core. The interaction between vortex and domain wall thus acts as a nanoscale switch for the vortex core polarization.

Inertial spin alignment in a circular magnetic nanotube

In cobalt nanotubes with a curling magnetization, the orbital motion of the conduction electrons interacts with their spin. As the spin goes around the nanotube it cannot follow the magnetization, since with the Fermi velocity it moves too fast. Instead, we predict that the spin precesses about an axis that is almost parallel to the axis of the nanotube and that rotates with the angular velocity of the electron. Therefore, the (absolute) value of the magnetic energy of the spin |μ⋅B| is strongly reduced. The physics of the ferromagnet is considerably modified.

Controlling of magnetic vortex chirality and polarity by spin-polarized current

For a nanodisk, magnetic vortex characterized by a curling magnetization is an energetically stable state. The magnetization in the center of the magnetic vortex is directed upward or downward, namely, the vortex core polarity p=+1 or p=-1 refers to up or down, respectively. The curling direction of magnetization, namely, the vortex chirality, is either counter-clockwise or clockwise. Thus, different combinations of chirality and polarity in a vortex structure demonstrate four stable magnetic states, which can be used to design a multibit memory cell. Such a multibit memory application requires the independent controlling of both the vortex chirality and vortex polarity, which has received considerable attention recently. Switching the vortex polarity has been achieved by using either a magnetic field or a current. The vortex chirality can be controlled by introducing asymmetric geometry of nanodisks. In this article, by using micromagnetic simulations, we present an effective method to simultaneously control the vortex chirality and polarity in a spin valve structure, in which the fixed spin polarizer layer is magnetized in the film plane when the free layer has a magnetic vortex configuration. The free layer is designed into a ladder shape with the right part being thicker than the left part. Our simulations indicate that a combination of desirable vortex chirality and polarity can be easily controlled by a Gaussian current pulse with proper strength and pulse duration through the spin-transfer torque effect. The insight into physical mechanism of the controllable vortex is demonstrated by a series of snapshots. If the magnetic moment of the free layer is saturated in the direction of 0θ θ is the angle between the magnetization and+x axis, the vortex with the counter-clockwise chirality will be generated after the pulse. In contrast, if the free layer magnetization is saturated along the direction πθ &lt;2π, after the pulse, the vortex will have the clockwise chirality. The core polarity of the remanent vortex state is determined by the sign of the magnetic charges which are formed in the step-side of nanodisk during the current pulse.

Higher order vortex gyrotropic modes in circular ferromagnetic nanodots

Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50–100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators.

Nanoscale characterization and magnetic property of NiCoCu/Cu multilayer nanowires

NiCo/Cu multilayer nanowires have been successfully fabricated by a pulse electrodeposition technique using anodic aluminum oxide templates, and their chemistry, crystal structure and magnetic properties characterized at the nanoscale. It was found that each individual nanowire had a regular periodic structure. The NiCo/Cu nanowires also displayed a continuous morphology, smooth surface and polycrystalline fcc structure. EDX elemental mappings confirmed the presence of nickel, cobalt and copper, which appear clearly with a periodic distribution throughout the samples. Both the NiCo and Cu layers were polycrystalline and the average length of the interlayers between NiCo and Cu layers was approximately 3–4 nm. The NiCo/Cu nanowire arrays had an easy axis parallel to the length of wire and exhibited a curling magnetization reversal mechanism. This study highlights the basis morphological, structural and chemical information for NiCoCu/Cu multilayer nanowires, which is critical for their applications in nanodevices and nanoelectronics.

From chaos to selective ordering of vortex cores in interacting mesomagnets

A spin vortex consists of an in-plane curling magnetization and a small core region (~10 nm) with out-of-plane magnetization. An oscillating field or current induce gyrotropic precession of the spin vortex. Dipole-dipole and exchange coupling between the interacting vortices may lead to excitation of collective modes whose frequencies depend on the core polarities. Here we demonstrate an effective method for controlling the relative core polarities in a model system of overlapping Ni(80)Fe(20) dots. This is achieved by driving the system to a chaotic regime of continuous core reversals and subsequently relaxing the cores to steady-state motion. It is shown that any particular core polarity combination (and therefore the spectral response of the entire system) can be deterministically preselected by tuning the excitation frequency or external magnetic field. We anticipate that this work would benefit the future development of magnonic crystals, spin-torque oscillators, magnetic storage and logic elements.

Visualization of vortex core polarity in NiFe nanodots by tilted Fresnel images

We illustrate an approach which allows determining the out-of-plane component of the vortex core (polarity) in NiFe nanodots using Fresnel imaging in Lorentz electron microscopy. Using tilted Fresnel images, contribution of the polarity is introduced into the Fresnel image. However, this contribution is relatively small and a difference image from two symmetrically tilted Fresnel images must be used to eliminate the strong contribution from the in-plane curling magnetization and non-magnetic contrast. The sense of the polarity appears as a bipolar white-black contrast in the difference image on the tilt axis. A vortex core with a diameter of 16.5 ± 2.5 nm is experimentally measured. Image tilting, displacement and geometrical distortion may disturb the difference image, and hence subtraction of the difference image must be aligned by cross-correlation. The method is also justified by a study of the observed contrast characteristic due to misalignment. The method is confirmed to be superior to similar approach with direct interpretation of information and more information subtracted.

Magnetic vortex core reversal by excitation of spin waves

Micron-sized magnetic platelets in the flux-closed vortex state are characterized by an in-plane curling magnetization and a nanometer-sized perpendicularly magnetized vortex core. Having the simplest non-trivial configuration, these objects are of general interest to micromagnetics and may offer new routes for spintronics applications. Essential progress in the understanding of nonlinear vortex dynamics was achieved when low-field core toggling by excitation of the gyrotropic eigenmode at sub-GHz frequencies was established. At frequencies more than an order of magnitude higher vortex state structures possess spin wave eigenmodes arising from the magneto-static interaction. Here we demonstrate experimentally that the unidirectional vortex core reversal process also occurs when such azimuthal modes are excited. These results are confirmed by micromagnetic simulations, which clearly show the selection rules for this novel reversal mechanism. Our analysis reveals that for spin-wave excitation the concept of a critical velocity as the switching condition has to be modified.

Magnetization reversal in single domain Permalloy wires probed by magnetotransport

We have measured the in-plane magnetoresistance (MR) of a series of submicron single domain Permalloy wires to study two important magnetization reversal modes, coherent rotation and curling. With the consideration of both micromagnetic configurations, the MR curve can be decomposed in a reversibly bell-shaped curve and an irreversibly V-shaped discontinuity in low field, respectively. The discontinuity jump occurs at a switching field characterizing the curling mode. The angular dependence of the switching field is well described by the theoretical prediction of Aharoni model under the consideration of the whole volume curling. Moreover, we found that the low angle switching field decreases with increasing wire width (decreasing the aspect ratio) as 1/width, consistent with the curling model for a long slender ellipsoid.

Dynamic Origin of Vortex Core Switching in Soft Magnetic Nanodots

The magnetic vortex with in-plane curling magnetization and out-of-plane magnetization at the core is a unique ground state in nanoscale magnetic elements. This kind of magnetic vortex can be used, through its downward or upward core orientation, as a memory unit for information storage, and thus, controllable core switching deserves some special attention. Our analytical and micromagnetic calculations reveal that the origin of vortex core reversal is a gyrotropic field. This field is induced by vortex dynamic motion and is proportional to the velocity of the moving vortex. Our calculations elucidate the physical origin of the vortex core dynamic reversal, and, thereby, offer a key to effective manipulation of the vortex core orientation.

Magnetic vortex core reversal by excitation with short bursts of an alternating field

The vortex state, characterized by a curling magnetization, is one of the equilibrium configurations of soft magnetic materials and occurs in thin ferromagnetic square and disk-shaped elements of micrometre size and below. The interplay between the magnetostatic and the exchange energy favours an in-plane, closed flux domain structure. This curling magnetization turns out of the plane at the centre of the vortex structure, in an area with a radius of about 10 nanometres--the vortex core. The vortex state has a specific excitation mode: the in-plane gyration of the vortex structure about its equilibrium position. The sense of gyration is determined by the vortex core polarization. Here we report on the controlled manipulation of the vortex core polarization by excitation with small bursts of an alternating magnetic field. The vortex motion was imaged by time-resolved scanning transmission X-ray microscopy. We demonstrate that the sense of gyration of the vortex structure can be reversed by applying short bursts of the sinusoidal excitation field with amplitude of about 1.5 mT. This reversal unambiguously indicates a switching of the out-of-plane core polarization. The observed switching mechanism, which can be understood in the framework of micromagnetic theory, gives insights into basic magnetization dynamics and their possible application in data storage.