We report on detailed broadband ferromagnetic resonance measurements of azimuthal and radial spin wave excitations in circular Permalloy dots in the vortex ground state. Dots with aspect ratio (Beta =height over radius) varied from 0.03 to 0.1 were explored. We found that for Beta exceeding approximately 0.05, variation of the spin wave eigenfrequencies with Beta deviates from the predicted dependence. The frequency splitting of two lowest azimuthal modes was observed. The experimentally observed dependence of the frequency splitting on beta was reasonably well described by dynamic splitting model accounting the spin-waves and, vortex gyrotropic mode interaction.
We have studied magnetic vortex oscillations in soft sub-micron cylindrical dots with variable thickness and diameter by an analytical approach and micromagnetic simulations. We have considered two kinds of modes of the vortex magnetization oscillations: 1) low-frequency translation mode, corresponding to the movement of the vortex as a whole near its equilibrium position; 2) high-frequency vortex modes, which correspond to radially symmetric oscillations of the vortex magnetization, mainly outside the vortex core. The vortex translational eigenmode was calculated numerically in frequency and …
The magnetization reversal and spin structure in circular Co/insulator/Ni80Fe20 trilayer dots has been investigated numerically. The effect of dipolar coupling between a soft ferromagnetic Permalloy (Py=Ni80Fe20) layer and a hard ferromagnetic Cobalt layer inside one stack is studied. We find either a stabilization or even a triggering of the vortex state in the Py layer due to the magnetic stray field of the Co layer, while the Co magnetization remains in a single-domain state. Furthermore, for thin Py layers a 360 deg-domain wall is observed. We construct a phase diagram, where regions of vo…
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…
Shape asymmetries in nominally circular nanomagnets provide a potential means for vortex chirality control. However, in realistic arrays their effects are challenging to probe since asymmetric magnetization reversal processes are often averaged to include distributions over all angles. Here we investigate how shape asymmetry influences the vortex reversal in arrays of sub-micron edge-cut Co dots. We find that the vortices can be manipulated to annihilate at particular sites under different field orientations and cycle sequences. The vortex annihilation field and degree of chirality control dep…
Vortex dynamics in a restricted geometry is considered for a magnetic system consisting of ferromagnetic cylindrical dots. To describe the vortex dynamic susceptibility and relaxation the equation of motion for the vortex center position is applied. The dependencies of the vortex dynamic susceptibility and resonance linewidth on geometrical parameters are calculated. A new method of extracting damping parameter from the vortex low-frequency resonance peaks is proposed and applied for interpretation of resonance data on FeNi circular dots.
Reproducible control of the magnetic vortex state in nanomagnets is of critical importance. We report on chirality control by manipulating the size and/or thickness of asymmetric Co dots. Below a critical diameter and/or thickness, chirality control is achieved by the nucleation of single vortex. Interestingly, above these critical dimensions chirality control is realized by the nucleation and subsequent coalescence of two vortices, resulting in a single vortex with the opposite chirality as found in smaller dots. Micromagnetic simulations and magnetic force microscopy highlight the role of ed…
Time-resolved soft X-ray transmission microscopy is applied to image the current-induced resonant dynamics of the magnetic vortex core realized in a micronsized Permalloy disk. The high spatial resolution better than 25 nm enables us to observe the resonant motion of the vortex core. The result also provides the spin polarization of the current to be 0.67 +/-0.16 for Permalloy by fitting the experimental results with an analytical model in the framework of the spin-transfer torque.
We report a high-resolution experimental detection of the resonant behavior of magnetic vortices confined in small disk-shaped ferromagnetic dots. The samples are magnetically soft Fe-Ni disks of diameter 1.1 and 2.2 um, and thickness 20 and 40 nm patterned via electron beam lithography onto microwave co-planar waveguides. The vortex excitation spectra were probed by a vector network analyzer operating in reflection mode, which records the derivative of the real and the imaginary impedance as a function of frequency. The spectra show well-defined resonance peaks in magnetic fields smaller than…
Dipole-dipole interactions in a square planar array of sub-micron magnetic disks (magnetic dots) have been studied theoretically. Under a normal magnetic field the ground-state of the array undergoes many structural transitions between the limiting chessboard antiferromagnetic state at zero field and the ferromagnet at a threshold field. At intermediate fields, numerous ferrimagnetic states having mean magnetic moments between zero and that of the ferromagnetic state are favorable energetically. The structures and energies of a selection of states are calculated and plotted, as are the fields …
In planar structures, the vortex resonance frequency changes little as a function of an in-plane magnetic field as long as the vortex state persists. Altering the topography of the element leads to a vastly different dynamic response that arises due to the local vortex core confinement effect. In this work, we studied the magnetic excitations in non-planar ferromagnetic dots using a broadband microwave spectroscopy technique. Two distinct resonance frequency ranges were observed depending on the position of the vortex core controllable by applying a relatively small magnetic field. The microma…
The magnetization in a magnetic microdot made from soft magnetic materials can have a vortex-like ground state structure resulting from competition between the exchange and dipolar interactions. Normal mode magnon frequencies for such dots are calculated taking into account both exchange and magnetostatic effects. The presence of a low-lying mode as well as doublet structure with small splitting is demonstrated. Estimates of the mode frequencies for permalloy dots are obtained, and the possibility of experimental detection of such modes is discussed.
A spin wave theory explaining experimentally observed frequency splitting of dynamical excitations with azimuthal symmetry of a magnetic dot in a vortex ground state is developed. It is shown that this splitting is a result of the dipolar hybridization of three spin wave modes of a dot having azimuthal indices |m|=1: two high-frequency azimuthal excitation modes of the in-plane part of the vortex with indices m = +/-1 and a low-frequency m= +1 gyrotropic mode describing the translational motion of the vortex core. The analytically calculated magnitude of the frequency splitting is proportional…
Ensemble-averaged exchange bias in arrays of Fe/FeF2 nanodots has been deconvoluted into local, microscopic, bias separately experienced by nanodots going through different reversal modes. The relative fraction of dots in each mode can be modified by exchange bias. Single domain dots exhibit a simple loop shift, while vortex state dots have asymmetric shifts in the vortex nucleation and annihilation fields, manifesting local incomplete domain walls in these nanodots as magnetic vortices with tilted cores.
We developed the self-assembly of epitaxial submicrometer-sized face-centered-cubic (fcc) Co(111) dots using pulsed laser deposition. The dots display atomically-fl at facets, from which the ratios of surface and interface energies for fcc Co are deduced. Zero- field magnetic structures are investigated with magnetic force and lorentz microscopies, revealing vortex-based flux-closure patterns. A good agreement is found with micromagnetic simulations.
We have used Monte Carlo simulations to investigate the magnetic properties of asymmetric dots as a function of their geometry. The asymmetry of round dots is produced by cutting off a fraction of the dot and is characterized by an asymmetry parameter $α$. This shape asymmetry has interesting effects on the coercivity ($H_{c}$), remanence ($M_{r}$), and barrier for vortex and C- state formation. The dependences of $H_{c}$ and $M_{r}$ are non monotonic as a function of $α$ with a well defined minima in these parameters. The vortex enters the most asymmetric part and exits through the symmetric …
This study conducts a comprehensive investigation into the reversal mechanism of magnetic vortex cores in a nanopillar system composed of two coupled ferromagnetic dots under zero magnetic field conditions. The research employs a combination of experimental and simulation methods to gain a deeper understanding of the dynamics of magnetic vortex cores. The findings reveal that by applying a constant direct current, the orientation of the vortex cores can be manipulated, resulting in a switch in one of the dots at a specific current value. The micromagnetic simulations provide evidence that this…
We report direct imaging by means of x-ray photoemission electron microscopy of the dynamics of magnetic vortices confined in micron-size circular Permalloy dots that are 30 nm thick. The vortex core positions oscillate on a 10-ns timescale in a self-induced magnetostatic potential well after the in-plane magnetic field is turned off. The measured oscillation frequencies as a function of the aspect ratio (thickness/radius) of the dots are in agreement with theoretical calculations presented for the same geometry.
We study the interactions of the vortex lattice with a periodic square array of holes in a superconducting Nb film using magnetic and resistive measurements. Three different temperature regions have been observed. They are governed by interplay between vortex-vortex interactions and pinning by holes. At low temperatures flux jumps suppress the commensurability anomalies. In all measurements a peak has been observed close to commensurate states 5-7. The Cole-Cole plot reveals significant changes in the flux penetration mechanism at this point.
We discuss a new class of phenomena based on strong interaction between magnetic superstructures and vortices in superconductors in combined heterogeneous structures. An inhomogeneous magnetization can pin vortices or create them spontaneously changing drastically properties of the superconductor. On the other hand, the interaction between magnetic moments mediated by vortices can result in specific types of magnetic ordering. The same interaction can create coupled magnetic-superconducting defects. We discuss possible experimental observation of magnetism controlled vortex matter in supercond…
Using the ultra low damping NiMnSb half-Heusler alloy patterned into vortex-state magnetic nano-dots, we demonstrate a new concept of non-volatile memory controlled by the frequency. A perpendicular bias magnetic field is used to split the frequency of the vortex core gyrotropic rotation into two distinct frequencies, depending on the sign of the vortex core polarity $p=\pm1$ inside the dot. A magnetic resonance force microscope and microwave pulses applied at one of these two resonant frequencies allow for local and deterministic addressing of binary information (core polarity).
We show that the flux-flow transport of the Josephson vortex lattice (JVL) in layered high-temperature superconductors provides a convenient probe for both components of quasiparticle conductivity, $σ_{c}$ and $σ_{ab}$. We found that the JVL flux-flow resistivity, $ρ_{ff}$, in a wide range of magnetic fields is mainly determined by the in-plane dissipation. In the dense lattice regime ($B>1$ T) $ρ_{ff}(B)$ dependence is well fitted by the theoretical formula for that limit. That allows us to independently extract from the experimental data the values of $σ_{c}$ and of the ratio $σ_{ab}/(σ_{c}γ…
The spin structure in a magnetic dot, which is an example of a quantum few-body system, is studied as a function of exchange coupling strength and dot size with in the semiclassical approximation on a discrete lattice. As the exchange coupli ng is decreased or the size is increased, the ground state undergoes a phase cha nge from a single domain ferromagnet to a spin vortex. The line separating these two phases has been calculated numerically for small system sizes. %, and analytically for larger dots. The dipolar interaction has been fully included in our calculations. Magnon frequencies in s…
We investigate the magnetization dynamics in circular Permalloy dots with spatially separated magnetic vortices interconnected by domain walls (double vortex state). We identify a novel type of quasi one-dimensional (1D) localised spin wave modes confined along domain walls, connecting each of two vortex cores with two edge half-antivortices. Variation of the mode eigenfrequencies with the dot size is in quantitative agreement with the developed model, which considers a dipolar origin of the localized 1D spin waves or so-called Winterś magnons [J.M. Winter, Phys.Rev. 124, 452 (1961)]. These sp…
Broadband magnetization response of coupled vortex state magnetic dots in layered nanopillars was explored as a function of in-plane magnetic field and interlayer separation. For dipolarly coupled circular Py(25 nm)/Cu(20 nm)/Py(25 nm) nanopillars of 600 nm diameter, a small in-plane field splits the eigenfrequencies of azimuthal spin wave modes inducing an abrupt transition between in-phase and out-of-phase kinds of the low-lying coupled spin wave modes. The critical field for this splitting is determined by antiparallel chiralities of the vortices in the layers. Qualitatively similar (althou…
Magnetic configurations in heterostructures are often difficult to probe when the magnetic entities are buried inside. In this study we have captured magnetic and magnetoresistance "fingerprints" of Co nanodiscs embedded in Co/Cu multilayered nanowires using a first-order reversal curve method. In 200nm diameter nanowires, the magnetic configurations can be tuned by adjusting the Co nanodisc aspect ratio. Nanowires with the thinnest Co nanodiscs exhibit single domain behavior, while those with thicker Co reverse via vortex states. A superposition of giant and anisotropic magnetoresistance is o…
In this paper we show that the vortex states can be created not only in magnetically soft "small" (with the dipolar and exchange energy competition) cylindrical dots, but also in magnetically saturated "big" (when the exchange is neglected) cylindrical dots. A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a ferrite disk with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. In this case the scalar (magnetostatic-potential) wave functions may have a phase singularity in a center of a dot.…
The spin dynamics are calculated for a model system consisting of magnetically soft, layered nanomagnets, in which two ferromagnetic (F) cylindrical dots, each with a magnetic vortex ground state, are separated by a non-magnetic spacer (N). This permits a study of the effects of interlayer magnetostatic interactions on the vortex dynamics. The system was explored by applying the equations of motion for the vortex core positions. The restoring force was calculated taking into account the magnetostatic interactions assuming a realistic surface charge free spin distribution. For tri-layer F/N/F d…
