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We excite the gyrotropic mode of a magnetic vortex and observe the resulting effect on the spin state of a nearby nitrogen-vacancy (NV) defect in diamond. Thin permalloy disks fabricated on a diamond sample are magnetized in a vortex state in which the magnetization curls around a central core. The magnetization dynamics of this configuration are described by a discrete spectrum of confined magnon modes, as well as a low-frequency gyrotropic mode in which the vortex core precesses about its equilibrium position. Despite the spin transition frequencies being far-detuned from the modes of the ferromagnet, we observe enhanced relaxation of the NV spin when driving the gyrotropic mode. Moreover, we map the spatial dependence of the interaction between the vortex and the spin by translating the vortex core within the disk with an applied magnetic field, resulting in steplike motion as the vortex is pinned and de-pinned. The strong spin relaxation is observed when the vortex core is within approximately 250 nm of the NV center defect. We attribute this effect to the higher frequencies in the spectrum of the magnetic fringe field arising from the soliton-like nature of the gyrotropic mode when driven with sufficiently large amplitude., Comment: 7 pages, 5 figures

We explored, by micromagnetic simulations, a novel conceptual time- and frequency-division demultiplexer using coupled-vortex-gyration-mode propagations in specially designed vortex-state arrays composed of circular- and chopped-shape disk dots. Coupled-vortex-gyration modes are characteristic of resonant excitations in given vortex-state arrays, which are controllable with bias static fields applied to given array structures as well as with different configurations of circular- and chopped-shape disks. As examples, we designed two array structures composed of five-vortex-state disk arrays of different combinations of circular and chopped shapes. By changing the direction of the in-plane bias fields, either leftward or rightward propagation of specific coupled-gyration-mode signals can be manipulated by exciting one of the coupled gyration modes of specific resonance frequency from an input disk, which allows for time- and frequency-division demultiplexing functions. This device concept offers an energy-efficient means of information processing without joule heating in cases where a low-damping magnetic material is used in micro-to-nanometer-scale magnonic circuits.

Hemispherical caps of in-plane exchange biased IrMn/CoFe layer systems have been fabricated on top of regularly arranged spherical silica particles by magnetron sputtering, creating magnetic Janus particles. In this thin film layer system cap, the magnetic shape anisotropy of the topographically non-flat hemispheres competes with the unidirectional anisotropy induced by the exchange bias. The magnetic properties of this non-trivial system have been investigated by longitudinal magneto-optical Kerr effect magnetometry, where a characterization method has been developed considering both the curved layer system and the signal contributions of flat parts of the sputtered thin film system. Both remagnetization curves, from Kerr magnetometry and the magnetic force microscopy images, reveal an onion state in the magnetic caps of the ensemble. Additional micromagnetic simulations show a stabilization of the onion state due to the introduced unidirectional anisotropy also in individual hollow hemispheres as compared to the vortex state exhibited by purely ferromagnetic caps.

We explored the reliable control of high-efficiency specific-loss power (SLP) using magnetic nanoparticles in the vortex state, where the value of power is one order of magnitude higher than those of the conventional mechanisms of SLP reported thus far. The underlying mechanism is based on the precession of a single vortex core and subsequent dissipation due to the intrinsic damping when the vortex-state spheres are resonantly excited. Owing to the dynamic characteristics of vortex-state nanoparticles, the resonant excitation of vortex-core precession is variable with particle size as well as tunable by the size-specific resonant frequency and strength of ac magnetic fields applied to the particles. The ac magnetic-field energy absorbed by the particles can be converted very efficiently to other energy forms such as heat. We derived, semi-analytically and by micromagnetic simulations, the quantitative relationships of the SLP quantity with the particle size and intrinsic damping constant of nanoparticles, and with externally controllable parameters including the frequency and strength of ac magnetic fields and dc magnetic-field strength. This work provides a reliable means of control as well as an optimal design of high-value SLPs for high-efficiency hyperthermia bio-applications.

The stability of the vortex magnetization state in circular cylindrical soft magnetic dots is calculated analytically and by micromagnetic simulations. For the cases considered the dot thickness is comparable to the material exchange length and dot radii are in the submicron range. The equation for the vortex magnetization distribution is analyzed taking exact account of the magnetostatic field inside dot. The limitations and applicability of a previously proposed “exchange-dominated” vortex ansatz are discussed. It is shown that for the transition from the vortex to perpendicular single-domain state the magnetization distribution changes continuously while retaining the axial symmetry. The zero-field critical line of the transition is calculated analytically as a function of dot size and is compared with micromagnetic simulations of the vortex magnetization profile.

We present a magnetoresistance study of controlled spin switching and domain wall pinning effects in mesoscopic narrow ferromagnetic Permalloy ring structures containing notches. It is found that notches create an attractive potential well for the transverse domain walls present in these structures. The strength and size of this potential well is measured and found to stretch far beyond the physical dimensions of the notch. Measuring the resistance, a minimum at remanence is found to occur when a transverse domain wall is pinned at the notch, in agreement with the results of numerical simulations of the anisotropic magnetoresistance. Applying a field in the direction corresponding to a potential well edge, a magnetic state with a very wide domain wall is stabilized, leading to a dip in the magnetoresistance at such angles. Using notches of different sizes, it is demonstrated that controlled switching is achieved, which means that the circulation direction of the vortex state can be selected.

In this article, we present an analytical approximation for calculating the magnetic energy in circular nanostructures for the vortex phase (closed magnetic flux) and the single domain phase. Comparing these energies in remanent state lead to a magnetic phase boundary between single domain phase and vortex phase, given by a critical thickness, which depends on the radius of the circular nanostructure. Experimental data and micromagnetic simulations have verified the analytical results.

Manipulation of vortex states in magnetic media provides new routes towards information storage and processing technology. The typical slow relaxation times (∼100 ns) of magnetic vortex dynamics may present an obstacle to the realization of these applications. Here, we investigate how a vortex state in a ferromagnetic microdisk can be manipulated in a way that translates the vortex core while enhancing energy dissipation to rapidly damp the vortex dynamics. We use time-resolved differential magneto-optical Kerr effect microscopy to measure the motion of the vortex core in response to applied magnetic fields. We first map out how the vortex core becomes sequentially trapped by pinning sites as it translates across the disk. After applying a fast magnetic field step to translate the vortex from one pinning site to another, we observe long-lived dynamics of the vortex as it settles to the new equilibrium. We then demonstrate how the addition of a short (

In magnetic random access memory, free layers are used to store data bits as “0” or “1.” For free layers with slotted nanoring structures, the magnetization configuration of counterclockwise vortex state can be defined as “0” state, while clockwise vortex state as “1” state. It is important to have a controllable and stable state transition process to make sure that “0” state can switch to “1” state and vice versa. Up to now, it has seldom been reported that the transition process is heavily affected by the static anisotropy field Hk-stat of free layers. A sufficient Hk-stat will substantially reduce the probability of successful state transition. To increase the accuracy of writing data, the free layers must be prepared with a low anisotropy field. In this paper, we present a rotational sputtering method, which can finish the desired isotropic film preparation, and thus realize a stable state transition.

Submicron permalloy magnetic dots have a vortex ground state because of competition between the exchange and magnetostatic interactions, and the application of an in-plane magnetic pulse will result in precession of the vortex about the dot axis at a frequency in the sub-GHz range. The precession frequency of this mode is calculated using a perturbation technique based on vortex–magnon scattering including the magnetostatic interaction. These calculations show that the frequencies vary between 0.2 and 0.8 GHz for 60 nm disks or radii between 250 nm and 1000 nm, which agrees with recent experimental data.

We have fabricated nanoscale ferromagnetic rings using electron-beam lithography with a lift-off process for pattern transfer. The resist thickness and electron-beam dose were tailored to produce 10 nm thick rings with outer diameters down to 90 nm. Arrays of rings were produced for magneto-optical Kerr effect measurements which show that down to the smallest diameters, reproducible magnetic switching into the flux-closure vortex state is maintained.

Magnetic structure and magnetization reversal of permalloy ring arrays and elongated permalloy particle array were studied by magnetic force microscopy (MFM). For single domain permalloy particles, the hysteresis loop is constructed by counting the percentage of switched elements imaged at remanence. For permalloy ring elements, two different states are energetically stable: a vortex state and an onion state. Their hysteresis loop is obtained by MFM imaging at a field between the switching fields of these two states. The magnetostatic coupling among these ring elements is directly revealed.

Current-induced magnetization switching (CIMS) in low resistance tunnel junctions is reported at critical current densities of 1.9×106 A/cm2 for tunnel junction areas ranging from 2 to 3 μm2, and junction resistances from 6 to 20 Ω μm2. Typical tunnel magnetic resistance values for these junctions range from 15% to 21% (measured in an external magnetic field) and 10% to 14% resistance changes are obtained by CIMS. Micromagnetic simulation indicates that vortex fields and spin transfer effects cannot fully account for the observed current-induced switching. Although able to explain the observed transition from a parallel or antiparallel state to a vortex state, it fails to explain the switch back to the original state, at a comparable but symmetrical critical current density.

Magnetization reversal in 300 nm Co squares has been investigated by semiconductor transport magnetometry using a Hall bar containing a two-dimensional electron gas. In this technique the local field from a regular array of magnetic elements patterned on top of the Hall bar changes the measured longitudinal magnetoresistance, enabling the magnetization of the elements to be deduced. Hysteresis loops obtained from the magnetoresistance curve showed a zero magnetization state at zero applied field, which was confirmed by transmission electron microscopy imaging and micromagnetic modelling to represent a vortex state. Repeatable fields were found for vortex expulsion and re-entry, with strong dependence on element size but rather weak dependence on film thickness.

The results of recent micromagnetic simulations of deep submicron supermalloy disks are presented. A recent experimental measurement of the hysteresis and magnetic domain structure in supermalloy disks with diameters ranging from 55 to 500 nm and thickness ranging from 6 to 15 nm has been reported. Our micromagnetic simulations show remarkable agreement with the experimental hysteresis loops. The simulation results show that for thin or small diameter disks a single magnetic domain exists with all spins aligned. The hysteresis loop represents free rotation of these spins. For larger diameter disks or as the thickness increases the hysteresis loops change shape due to the appearance of a single vortex state appearing at low applied fields.

A high temporal resolution magneto-optical system is employed to follow the crystallization process of the quasiordered vortex state in Bi2Sr2CaCu2O8+δ crystals following a sudden change in the applied magnetic field. Two types of experiments are performed. In the first one the sample is suddenly exposed to a steady magnetic field smaller than the vortex order–disorder transition field, Bod. In the second type of experiment the sample is initially exposed to an external field larger than Bod, and then the field is suddenly reduced. The two types of experiments reveal growth of the quasiordered state proceeding in opposite directions: from the sample center toward its edge in the first experiment, and from the sample edge toward the center in the second experiment. This motion enables tracing of the time evolution of the thermodynamic quasiordered vortex phase in the early stages of its formation.

Magnetic imaging in the transmission electron microscope (TEM) has been used to examine submicron elements with the aim of discovering down to what element size complex domain patterns can form. The elements were squares, circles, triangles, and pentagons in the size range 100–500 nm and were made from 36 nm Co films or 8 nm Ni80Fe20 (NiFe) with in-plane magnetization. The magnetic domain structures in these elements were imaged at high resolution using the differential phase contrast imaging mode in a TEM. Nonuniform magnetization structures were seen in the images. Vortices were present at remanence in all shapes of 36-nm-thick Co elements down to 100 nm size and in circular NiFe elements down to 116 nm diameter. Triangular NiFe elements did not have a vortex state at remanence, instead the magnetization curved round within the element but did not achieve complete flux closure. In simulations of square and circular NiFe elements, it was found that defects at the edges of the elements encouraged reversal...

Micromagnetic structures in submicron size circular permalloy elements of various thickness (5–50 nm) have been experimentally studied using a magnetic force microscope (MFM). One and two vortex micromagnetic states were observed in the elements. It was found that one vortex state is more favorable under external field of low values, while two vortex state forms under high fields. Switching between one and two vortex states results in a hysteresis in the micromagnetic response of the elements. The transition field from one to two vortex state increases with the increase of element thickness and, therefore, with the increase of the demagnetizing effect of the element edges. The two vortex state was not observed in the elements with a thickness of 50 nm or greater. The micromagnetic behavior correlates with hysteresis loops of a free layer in a magnetic tunnel junction of size, shape, and free layer thickness similar to elements examined with the MFM.

Properties of a type II triplet superconductor with equal spin pairing are investigated using the phenomenological Ginzburg–Landau approach. It is shown that there exist two kinds of fluxons: vortices and magnetic skyrmions. Vector nature of the order parameter allows a direct coupling of the effective spin of the condensate to a magnetic field. This coupling, which is reminiscent to Zeeman interaction in the form, significantly modifies the structure of an isolated vortex, as compared to the usual Abrikosov vortex, and changes the energetics of a vortex lattice. If the coupling is sufficiently strong, then magnetization of the triplet superconductor becomes positive at high magnetic fields. Formation of spontaneous vortex state is also possible.

In this paper, we show that multiaxial fields can induce time-averaged, noncentrosymmetric interactions between particles having polarization anisotropy, yet the multiaxial field itself does not exert either a force or a torque on an isolated particle. These induced interactions lead to particle assemblies whose energy is strongly dependent on both the translational and orientational degrees of freedom of the system. The situation is similar to a collection of permanent dipoles, but the symmetry of the time-averaged interaction is quite distinct, and the scale of the system energy can be dynamically controlled by the magnitude of the applied multiaxial field. In this paper, the case of polarizable rods is considered in detail, and it is suggested that collections of rods embedded in spheres can be used to create a material with a dynamically tunable magnetic permeability or dielectric permittivity. We report on Monte Carlo simulations performed to investigate the behavior of assemblies of both multiaxial-field induced dipoles and permanent dipoles arranged onto two-dimensional lattices. The ground state of the induced dipoles is an orientational soft mode of aligned dipoles, whereas that of the permanent dipoles is a vortex state.

We present a detailed study of the magnetic states in sub-micron nickel disks in the diameter range of 300–900 nm and thickness of 15–55 nm using magnetic force microscopy and micromagnetic simulations. In this dimensional range, we find three main magnetic states, namely: the single domain state, the vortex state, and the stripe domain state. We identify the crossover dimensions between these magnetic states, demonstrating that the disk thickness is the dominant parameter, which is further supported by the fact that the magnetocrystalline anisotropy of the Ni films is thickness dependant and plays a dominant role at large thicknesses. Experimental results are in a very good agreement with micromagnetic modelling using the out-of-plane effective anisotropy constant. Using in-situ high resolution Magnetic Force Microscopy techniques, we investigate in detail the motion of the vortex core under applied in-plane magnetic field and find that vortex nucleates and annihilates at ∼100 Oe.

The formation of the vortex-antivortex-vortex (v-av-v) metastable remanent states in elongated magnetic elements have been systematically investigated using micromagnetic modeling. It is demonstrated that the v-av-v magnetization pattern can be effectively stabilized by exciting the single vortex state with an external RF field. Furthermore, we show that a set of different polarity combinations of the vortex cores can be achieved by adjusting the frequency and amplitude of the excitation field. The corresponding dynamic response in time- and frequency-domain has also been presented. Owing to the diversity of the collective modes with different vortex-antivortex combinations, this system may open promising perspectives in the area of spin transfer torque oscillators.

The hysteretic transport properties of vortex states in sub-micron nickel disks are measured using the anisotropic magnetoresistance (AMR) effect and correlated with the magnetization state of the disks using in-situ magnetic force microscopy and micromagnetic modelling. The magnetoresistance behavior is described by a simple AMR model; however, the nucleation and annihilation fields of the vortex state differ when the magnetic field is applied parallel (0°) or perpendicular (90°) to the applied current within the sample plane. In the 0° orientation, the vortex magnetoresistance behaves similar to that reported in the literature. However, in the 90° orientation, the vortex nucleates and annihilates at lower applied fields than in the 0° orientation. Moreover, in the latter orientation, the annihilation process occurs in a two-step transition. This difference is attributed to the effect of the inhomogeneous current distribution within the magnetic disk.

Magneto-optical Kerr effect (MOKE) is used to investigate 1-D arrays of hexagonally arranged Co Y-junction nanostructures embedded in Anodic aluminium oxide (AAO) templates. MOKE in reflection mode clearly distinguishes the magnetic response on the front and back sides of two magnetic samples, i.e., in the form of solid nanowires and as hollow nanotubes. MOKE, being a surface sensitive technique, clearly shows the effect of magnetic interactions and density on magnetization reversal measurements. The experimental measurements complement well with the simulation results using MAGPAR. Simulations suggest the formation of closed vortex state in hollow nanotubes prominently and are found to be consistent with the MOKE measurements. Our approach also clearly shows that it is possible to study and model the exact profile of the Y-shaped nanowires. Their magnetization state is important and will have a significant impact on the overall magnetization as well as the switching behaviour of the nanowires.

The rare-earth (R) magnetism and grain-size dependencies of magnetic field distributions in RBa2Cu3O7−δ (RBCO) vortex states have been studied. A maximum-entropy technique has been applied to transverse field muon-spin-relaxation data of several polycrystalline cuprate superconductors. The main vortex signals for R=Er, Gd, and Ho reveal signs of two peaks in the field distribution below the applied field (Bext=1 kOe) as predicted for d-wave superconductivity. For the RBCO (R=Er, Gd, Ho, Eu, Y) vortex states, we have confirmed low-field tails in the field distributions well below Bext. The low-field tail may be caused by magnetic frustration in the vortex state or possible CuO-chain superconductivity below 25 K. Any interpretation of these (magnetic) vortex anomalies should comprise unconventional non-Bardeen–Cooper–Schrieffer-like fundamental properties of the cuprate vortex states.

We investigate the transitions of spin configurations in ultrathin nanostructures by tuning the perpendicular anisotropy (Kz) and out-of-plane magnetic field (H), using the Monte Carlo simulation. It is revealed that enhancing the anisotropy Kz can drive the evolution of in-plane vortex state into intriguing saturated magnetization states under various H, such as the bubble domain state and quadruple-block-domain state etc. The spin configurations of these states exhibit remarkable H-dependence. In addition, the strong effects of geometry and size on the spin configurations of nanostructures are observed. In particular, a series of edged states occur in the circular disk-shaped lattices, and rich intricate saturated magnetization patterns appear in big lattices. It is suggested that the magnetic states can be manipulated by varying the perpendicular anisotropy, magnetic field, and geometry/size of the nanostructures. Furthermore, the stability (retention capacity) of the saturated magnetization states upo...

Previous simulation reports have shown that the magnetization reversal mechanism in the asymmetric rings with the global vortex state is dominated by domain wall movement. This work investigates the asymmetric Co rings with relatively large sizes and thick arms with simulation. Results show that the magnetization reversal processes are dominated by the formation, movement, and annihilation of localized vortex states. 90° decenter of the inner core is favorable for a stable global vortex state with controllable chirality. Either a larger 90° decenter distance or a thicker thickness brings about a higher stability of global vortex state. However, the global vortex state cannot be obtained at remanence in these rings. In the smaller rings, with the global vortex state obtained at remanence, the stability of global vortex state is enhanced when the inner core size grows larger, and it is due to the reduced possibility of the formation of localized vortex state.

The evolution of the magnetic state of a soft ferromagnetic nanoparticle with its size is usually thought to be from superparamagnetic single domain to blocked single domain to a blocked multidomain structure. Neel pointed out that a vortex configuration produces practically no stray field at the cost of an increase in the exchange energy, of the order of RJS2lnR/c, where JS2 is the bond energy, R is the particle radius, and c is of the order of the exchange length. A vortex structure is energetically cheaper than single domain when the radius is greater than a certain value. The correct sequence should include a vortex configuration between the single domain and the multidomain states. The critical size is calculated for spherical particles of four important materials (nickel, magnetite, permalloy, and iron) both numerically and analytically. A vortex state is favored in materials with high magnetisation.

This paper presents a numerical model for the study of micro-Hall magnetometry applications, aiming at evaluating the sensitivity of semiconductor miniaturized devices to the stray field of permalloy nanostructures with ring and disk geometry. The procedure couples a micromagnetic code, for the calculation of the stray field generated by the nanomagnet, to a 2D classical transport model for the determination of the electric potential distribution inside the Hall plate. The model is applied to study the sensitivity of a micro-Hall device in the detection of magnetization switching processes characterized by vortex state, focusing on the influence of magnetic nanostructure position.

The dynamics of magnetization (M) reversal and relaxation as a function of temperature (T) are reported in three non-interacting NiFe ring arrays having fixed ring outer diameter and varying widths. Additionally, the dependence of M(H) loop on the angle (θ) between magnetic field (H) and the plane of the rings is addressed. The M(H) loops show a double step transition from onion state (OS) to vortex state (VS) at all temperatures (T = 3 to 300 K) and angles (θ = 0 to 90°). The critical reversal fields HC1 (OS to VS) and HC2 (VS to OS) show a pronounced dependence on T, ring width, and θ. Estimation of the transverse and vortex domain wall energies reveals that the latter is favored in the OS. The OS is also the remanent state in the smallest rings and decays with the effective energy scale (U0/T) of 50 and 32 meV/K at 10 and 300 K, respectively. The robust in-plane anisotropy of magnetization of ring assemblies is established by scaling the M(H) with θ.

We study theoretically two-dimensional nanorings assumed to have the in-plane vortex magnetic configuration. Using a discrete dipole model we examine the spectrum of normal spin-wave modes vs. the dipolar-to-exchange interaction ratio. We systematize the spin-wave excitations by their azimuthal and radial wave numbers. The lowest-frequency mode, the fundamental (quasiuniform) mode, and the mode hybridization are analyzed; the discussion of the influence of effective pinning at the ring boundaries is provided as well. We study the stability of the in-plane vortex state and discuss the role of the size of the ring and the type of lattice arrangement of the magnetic moments within it. To facilitate comparison with our results we provide the relationships between microscopic parameters, used in our model, and those used in the case of continuous medium.

The angular dependence of magnetic properties was investigated in Co nanowire (NW) array with varying length grown by pulse electrochemical route. In these investigations, three different NW lengths, 200, 400, and 1000 nm were considered. Detail structural investigation revealed the formation of hcp (002) texture for NW of length 200 nm. However, the existence of both hcp (002) and hcp (100) oriented texture was observed in longer NW of length 1000 nm. It was established that these two phases were well separated along the axis of the NW with lower segment having hcp (002) and upper segment with hcp (100) oriented texture. Micromagnetic simulation was carried out to correlate the experimentally obtained angular dependent magnetization reversal results with simulated data considering the different crystallographic structures as a function of NW length, and with the variation of angle between the applied magnetic field and NW axis. Inference was drawn from these correlations that the magnetization reversal occurs by coherent rotation in case of NW with sole hcp (002) structure, whereas vortex state formation plays an important role for hcp (100) structure. In case of bilayer structure, the interaction between these two states leads to a gradual crossover from a coherent state to a vortex one along the NW axis. Effort has also been made to explain the angular dependence of coercive field by micromagnetic simulation irrespective of the NW length.

The deviation of magnetization (M) relaxation from logarithmic time dependence is due to both the low pinning potential influenced by the driving energy formed by the gradient of flux lines and the large thermal activation. Considering the structural relaxation of the vortex state under the action of the driving force and thermal activation, the dependence of M on time t can be obtained as M=A+Bt−β, where A, B, and β keep constant at a given field and temperature.

We have studied the magnetic properties of single‐crystal Dy and Tb in the temperature range from 4.2 to 250 K. We observe the Neel transition for Dy and Tb at 180 and 230 K, respectively. The Curie temperature was found to be 90 and 220 K for Dy and Tb, respectively. These values for TN and TC agree well with earlier measurements by Behrendt (1958) and Koehler (1963). In addition to these transitions, we observe a new anomaly in single‐crystal Dy near 4.5 K manifested by a reduction of the magnetization in the basal plane with a simultaneous rise in the magnetization along the c axis. This suggests the magnetic moments may rise out of the basal plane of Dy and form a component along the c axis at low temperatures. We also observe a small broad peak in the ac susceptibility of Dy near 167 K which is likely due to the vortex state of Dy. The ac susceptibility along the b axis of single‐crystal Tb shows a rapid decrease below 30 K while the c‐axis susceptibility shows a corresponding increase.

We discuss a new mechanism of changing the magnetic vortex gyrotropic motion in a permalloy/nonmagnet bi-layers system. In this system, a spin current characterized by an in-plane polarizer is injected from the nonmagnetic layer to the permalloy disk. We introduce current density gradient to the spin current, and find that the interplay between the planar polarizer and current gradient can change the damping of the vortex motion. This change originates from a spin-transfer force acting on the vortex. The influence of the spin-transfer force on the vortex motion is dependent on the direction of the planar polarizer, the orientation of the current density gradient, and the vortex state.

Magnetic vortices in soft ferromagnetic nano-disks have been extensively studied for at least several decades both for their applied (non-volatile information storage) as well as fundamental value. Here, it is shown that there is another vortex ground state with large radius-dependent core profile in nano-scale ferromagnetic disks of several exchange lengths in size. Its energy is computed numerically and its stability is studied analytically, which allows to plot it on magnetic phase diagram. Large vortices may exist on par with the classical ones, while being separated by an energy barrier, controllable by tuning the geometry and material of ferromagnetic disk.

Quasi-static magnetic properties of microscopic Ni80Fe20 disks, rings, and double layered disks and rings were studied via longitudinal magneto-optical Kerr effect (MOKE) and magnetic force microscopy (MFM), concomitant with micromagnetic simulations to elucidate the systems' vortex properties and remagnetization behavior. The features were fabricated lithographically, with diameters between 0.6 and 2 micrometers, and thicknesses of 50 and 100 nm. Key results are: (i) Dual-vortex to single-vortex transitions were observed at nucleation in 100 nm thick disks. (ii) Vortex nucleation and annihilation fields increase with single layer disk thickness whereas they decrease with thickness in single layer ring features. (iii) Double-layer disks separated by a Ru spacer indicate interactions of vortex cores at nucleation and avoidance of vortex core movements, whereas double-layer rings show successive switching in- and out- of vortex states with strong interactions only at vortex-to-onion transition.

This study investigates the electrical observation of the formation of a 360° magnetic domain wall (360DW) in an elliptical Co ring structure. Because the 360DW consists of two 180° domain walls, a decrease in resistance is observed in the switching process due to anisotropic magnetoresistance (AMR). Certain AMR measurements exhibit an increase in the resistance in the switching process, indicating that a flux-closure vortex state is formed without first forming a 360DW state. The difference between the 360DW and vortex state in the switching process reflects differences in the DW depinning mechanism from the onion state. The minor loop of the AMR measurements is also dependent on the initial magnetic configuration between the 360DW and the vortex state.

We study two-dimensional circular nanorings composed of elementary magnetic moments arranged in sites of a square lattice. Using a microscopic approach that takes into account the dipolar and nearest-neighbor exchange interactions, we calculate the spin-wave frequencies and profiles to draw conclusions regarding the stability of the assumed magnetic configuration. We show that, in contrast to square rings, in circular rings the exchange-driven reorientation is sensitive to both the external and internal sizes of the ring. We associate this behavior with the delocalized character of the lowest spin-wave excitation, and show that, consequently, the in-plane vortex state can be stabilized even in the case of strong exchange interactions.

Magnetoresistance measurements at 300 K and 1.7 K are used to quantify the vortex state magnetic field duration in a series of Ni80Fe20 ring structures with two nm-sized gaps. The measured gap sizes are from 40 nm to 510 nm. The vortex magnetic field range of stability reduces on increasing gap size but then stabilizes and is predominantly determined by extrinsic domain wall pinning defects. Virtual domain wall mediated switching with the applied magnetic field direction parallel to the gap, reduces a stochastic switching behavior in these structures, compared to a continuous ring. A comparison of experiment with the predicted switching behavior from a micro-magnetic simulation is made and the stray fields are calculated in the vortex remanent state. The reduction in the vortex field duration with increasing gap size is more gradual than that predicted by the micro-magnetic simulation up to a gap size of ∼100 nm.

Triangular-shaped permalloy microstructures in the vortex magnetization state are studied via transmission soft x-ray microscopy, broadband-ferromagnetic resonance measurements, and micromagnetic simulations. The vortex chirality can be controlled via the direction of a saturating in-plane magnetic field applied before nucleation of the vortex state. The resonance frequencies of vortex gyration are probed for different equilibrium positions within the magnetic structure to determine the shape of the asymmetric confining potential. The experimental results are shown to coincide with micromagnetic simulations.

We study the influence of the vortex core on magnetotransport of ferromagnetic dots in a vortex state. The extraordinary Hall effect generated in the core region has a different field symmetry compared to contributions of anisotropic magnetoresistance and the planar Hall effect, which can be used to detect chirality and polarity of the vortex. We propose a method for realization of two-bit per dot magnetic random access memory, in which two states are contributed by clockwise and counter-clockwise chirality and two by up and down core polarity. Dependence of the signal on vortex location, core diameter, and other parameters is discussed.

Magnetite nanoring with vortex domain structure may form stable magnetic colloid for biomedical applications due to its weak magnetic interaction without superparamagnetic (SPM) limitation. In the present study, we perform three-dimensional (3 D) Landau-Liftshitz-Gilbert (LLG) micromagnetics simulation for magnetite nanorings. The ground state phase diagram and stable vortex area (SVA) as a function of outer diameter (Dout), thickness (T), and inner to outer diameter ratios (β) within 100 nm are obtained. The influence of notch, eccentricity, and crystallographic orientation are taken carefully into consideration. In the SVA, the vortex state is not only the ground state but also the remanence state after in-plane is fully magnetized. In particular, the results suggest that a 20 nm inter-rings distance for a typical magnetite nanoring (Dout = 70 nm, T = 50 nm, and β = 0.6) can achieve the stable colloid based on vortex domain structure. Furthermore, these simulation results have been confirmed experimentally and demonstrated by using phosphorylated-mPEG modified magnetite nanorings. The optimization of magnetite nanorings from both simulation and experiments in this work pave the way to achieve such novel and stable vortex domain based magnetic suspension for various biomedical applications.

The magnetization reversal processes of rectangular and circular permalloy ring arrays are compared. Rectangular rings reverse via two different processes, one of which includes the formation of a vortex state. The corners of the rectangular rings affect domain wall pinning and reverse domain nucleation processes and alter the field values for the two major transitions between magnetic states as compared to a circular ring. The effects of film thickness are also investigated. Micromagnetic simulations are compared with the experiment results.

We investigate the enhancement of intrinsic spin Hall accumulation in a two-dimensional electron gas with Rashba and Dresselhaus (001) spin-orbit coupling. Employing the real-space Landauer–Keldysh Green’s function formalism, we show that intrinsic spin Hall accumulation can be strongly enhanced at the specific energy point where the system develops two charge current vortices with certain chirality. We find that the localized vortex state is accompanied by a conductance dip arising from the Fano–Rashba effect. The spin-orbit force picture is used to analyze the enhanced spin accumulation patterns.

We present calculations of the magnetization configuration and reversal behavior of magnetic nanotubes with uniaxial anisotropy by means of two-dimensional micromagnetic simulations and analytical methods. The tube radii R from 50 to 150 nm and the tube length /radius aspect ratio L/R≤20 were explored. For a finite length of magnetic nanotubes the magnetization configuration is characterized by a uniformly magnetized along the tube axis middle part and two nonuniform curling states of a length Lc in two ends of the tube with the same or opposite magnetization rotating senses, referring as C-state or B-state, respectively. We found that the magnetization configuration of the C-state exists for thin nanotubes with the tube thickness, ΔR, in the range of ΔR/R≤0.2. For thicker nanotubes the strong magnetostatic stray field forces the change of rotating senses of the end domains in opposite directions (the B-state). The transition from the C-state to a vortex state with in-plane magnetization is described as f...

The field-orientation dependence of magnetization reversal and spin wave modes in nanorings has been investigated by focused magneto-optical Kerr effect spectroscopy, Brillouin spectroscopy, and micromagnetic simulations. The samples studied are periodic arrays of 150 nm wide Ni80Fe20 rings with long axes of 850, 1200, and 1500 nm, and respective short axes of 550, 700, and 900 nm. For the smallest ring, the onion-to-vortex transition is observed for both the applied magnetic field directed along, and 5° from its magnetization easy axis. In contrast for the two larger rings, this transition is not observed for the field in the latter orientation. Splitting of spin wave modes is observed for the transition from the onion to vortex state. Micromagnetic simulations of magnetization reversal and spin waves are in good agreement with experiments. The simulated temporal recording of magnetization distributions during transition reveals that different switching mechanisms result from different applied magnetic f...

We used a micromagnetic model to study the head remanence of a perpendicular tapered main pole head. To reduce the head pole tip remanence, a single magnetic domain structure forming a vortex state from the pole tip to the tapered region is preferred. A tapered main pole structure with a trailing gap depth less than about 30 nm and a tapered angle (TGθ) equal to about 30° improved the writing efficiency. This was achieved with a head field value more than 1.3 times higher and with a head field gradient about 1.15 times higher than that of the conventional structure. Moreover, the pole tip remanence was reduced to a value closer to that of the conventional structure. The reduction in the throat height had less effect on the reduction in the head remanence in the tapered head than in the conventional head. We also discuss both single pole heads and shielded heads.

We present a complete investigation on the spin normal modes of triangular nanoparticles in the vortex, Y, and buckle states. In order to get a micromagnetic representation of an equilateral triangle, we choose a base side of 360 nm and a height of 310 nm, while the thickness is 20 nm. This choice allows the vortex state as an equilibrium configuration at zero applied field. We calculate the principal modes of the three magnetic configuration through the dynamical matrix method and discuss in detail their frequencies and their profiles on the basis of the internal field behavior. We also explain the onset of the irregular nodal surfaces in the mode profiles beyond a critical node number, depending on the underlying magnetic configuration. The modes with nodal surfaces parallel to the direction of variation of the internal field are found to occur in a series with identical node number but different localization: this is related to the reduced coherent length of the modes because of the strongly varying internal field. We present also the calculated Brillouin light scattering (BLS) spectrum for each magnetic configuration, with discussion on the reasons that allow some modes to be BLS active.

Spin dynamics of antivortices excited by sudden action of a spin-polarized dc is reported. Two main excitation modes are found with increased current density, involving a translational (gyrotropic) mode and a core reversal mode. The former mode can be described by Thiele’s equation, which accounts for the orbital distortion in view of the modified restoring force by nontrivial structures nucleated at sample edges. The final states of the system in the translational mode are obtained, being either a domain wall state or a vortex state, depending on the current density. The frequency of gyromotion is dependent on dot sizes. Within a threshold radius, the off-centered antivortex can freely relax back to the dot center.