Trajectory and frequency of vortex gyration in a multi-nanocontact geometry

Nonlinear vortex gyrotropic motion in a three-nanocontacts system is investigated by micromagnetic simulations and analytical calculations. Three out-of-plane spin-polarized currents are injected into a nanodisk through a centered nanocontact and two off-centered nanocontacts, respectively. For current combination(ip1, ip0, ip2) =(-1, 1,-1), the trajectory of the vortex core is a peanut-like orbit, but it is an elliptical orbit for(ip1, ip0, ip2) =(1, 1,-1). Moreover, the gyrotropic frequency displays peaks for both current combinations. Analytical calculations based on the Thiele equation show that the changes of frequency can be ascribed mainly to the forces generated by the Oersted field accompanying the currents. We also demonstrate a dependence of eigenfrequency shifts on the direction and distance of the applied currents.     

Effects of damping constant on gyrotropic motion and switching of vortex core in permalloy disk

We investigate the influence of damping constant on the dynamics process of the magnetic vortex in submicron-size permalloy disks by micromagnetic simulations and analytical calculations. Both of them reveal that damping constant influences the trajectory of vortex core gyrotropic motion strongly. Comparing with the case of no damping constant, the steady-state trajectory of vortex core motion becomes ellipse as the amplitude of the oscillating magnetic filed is small. The ellipse becomes more slab-sided and tilting with increasing of damping constant, and the tilting direction is also dependent on the vortex core polarization. As the amplitude of the magnetic field increases to a value, the polarization of the vortex core will reverse and a new vortex with opposite polarization will be produced. With increasing of damping constant, the minimum oscillating magnetic field amplitude H_S0 that can reverse the polarization of the vortex core increases proportionally.     

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.     

Interactions of spin waves with a magnetic vortex

We have investigated azimuthal spin-wave modes in magnetic vortex structures using time-resolved Kerr microscopy. Spatially resolved phase and amplitude spectra of ferromagnetic disks with diameters from 5 microm down to 500 nm reveal that the lowest order azimuthal spin-wave mode splits into a doublet as the disk size decreases. We demonstrate that the splitting is due to the coupling between spin waves and the gyrotropic motion of the vortex core.     

Excitation of spin dynamics by spin-polarized current in vortex state magnetic disks

A spin-polarized current with the polarization direction perpendicular to a disk in the vortex ground state will result in renormalization of the effective damping of excitations on this state. As the current is increased to a threshold current Ic the effective damping will be zero and the lowest threshold current corresponds to the vortex gyrotropic mode. For larger values of the current the excitation is a nonlinear gyrotropic mode having nonsmall amplitudes and larger frequency than the linear mode. This effect occurs for any mode of the vortex-state disk, and the value of Ic is proportional to the mode frequency.     

Importance of the internal shape mode in magnetic vortex dynamics

We investigate the motion of a nonplanar vortex in a circular easy-plane magnet with a rotating in-plane magnetic field. Our numerical simulations of the Landau-Lifshitz equations show that the vortex tends to a circular limit trajectory, with an orbit frequency which is lower than the driving field frequency. To describe this we develop a new collective variable theory by introducing additional variables which account for the internal degrees of freedom of the vortex core, strongly coupled to the translational motion. We derive the evolution equations for these collective variables and find limit-cycle solutions whose characteristics are in qualitative agreement with the simulations of the many-spin system.     

Dynamics of a pinned magnetic vortex

We observe the dynamics of a single magnetic vortex pinned by a defect in a ferromagnetic film. At low excitation amplitudes, the vortex core gyrates about its equilibrium position with a frequency that is characteristic of a single pinning site. At high amplitudes, the frequency of gyration is determined by the magnetostatic energy of the entire vortex, which is confined in a micron-scale disk. We observe a sharp transition between these two amplitude regimes that is due to depinning of the vortex core from a local defect. The distribution of pinning sites is determined by mapping fluctuations in the frequency as the vortex core is displaced by a static in-plane magnetic field.     

Current-driven resonant excitation of magnetic vortices

A magnetic vortex core in a ferromagnetic circular nanodot has a resonance frequency originating from the confinement of the vortex core. By the micromagnetic simulation including the spin-transfer torque, we show that the vortex core can be resonantly excited by an ac (spin-polarized) current through the dot and that the resonance frequency can be tuned by the dot shape. The resistance measurement under the ac current successfully detects the resonance at the frequency consistent with the simulation.     

Antivortex gyrotropic motion in a nanocontact

A vortex-antivortex pair can form in the free layer of a nanocontact device as a result of the Oersted field produced by the current. In a large-scale free layer having uniform magnetization boundary conditions an in-plane external magnetic field will tend to confine the vortex-antivortex pair, which undergoes gyrotropic motion about the nanocontact after an initial displacement from the static equilibrium position. With the vortex pinned to a defect at the nanocontact the antivortex dynamics can be isolated and gyrotropic precession of the antivortex will be the dominant mode. The frequency of antivortex precession increases as the external magnetic field increases, and the frequency decreases as the nanocontact current increases.     

Switching of vortex polarization in 2D easy-plane magnets by magnetic fields

We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations, due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made clear, through an analogy with a generalized Thiele equation. Received 6 June 2002 / Received in final form 4 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: juan.zagorodny@uni-bayreuth.de     

Excitation of Eigenwaves by a Vortex Electromagnetic Beam in a Semi-Infinite Cylinder Filled with a Gyrotropic Medium

Radiophysics and Quantum Electronics - We study the diffraction of a Laguerre–Gaussian electromagnetic vortex beam by the end of a semi-infinite cylinder filled with a gyrotropic medium. A...     

The effect of the single-spin defect on the stability of the in-plane vortex state in 2D magnetic nanodots

The aim of this study is to analyse the stability of the single in-plane vortex state in two-dimensional magnetic nanodots with a nonmagnetic impurity (single-spin defect) at the centre. Small square and circular dots including up to a few thousand of spins are studied by means of a microscopic theory with nearest-neighbour exchange interactions and dipolar interactions fully taken into account. We calculate the spin-wave frequencies versus the dipolar-to-exchange interaction ratio d to find the values of d for which the assumed state is stable. Transitions to other states and their dependence on d and the vortex size are investigated as well, with two types of transition found: vortex core formation for small d values (strong exchange interactions), and in-plane reorientation of spins for large d values (strong dipolar interactions). Various types of localized spin waves responsible for these transitions are identified.     

Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap

The dynamics of a dark soliton has been investigated in a Bose--Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.     

Spectroscopy of magnetic excitations in magnetic superconductors using vortex motion

In magnetic superconductors a moving vortex lattice is accompanied by an ac magnetic field which leads to the generation of spin waves. At resonance conditions the dynamics of vortices in magnetic superconductors changes drastically, resulting in strong peaks in the dc I-V characteristics at voltages at which the washboard frequency of the vortex lattice matches the spin wave frequency omegaS(g), where g are the reciprocal vortex lattice vectors. We show that if the washboard frequency lies above the magnetic gap, measurement of the I-V characteristics provides a new method to obtain information on the spectrum of magnetic excitations in borocarbides and cuprate layered magnetic superconductors.     

Observation and modelling of magnetic vortex core structure in Permalloy nanoparticles

We use an approximate micromagnetic model, based on geometrical simplifications of the problem, to describe the vortex core structure observed in spherical Permalloy nanoparticles using off-axis electron holography. The magnetisation distribution inside the vortex core is directly calculated by minimising the micromagnetic energy functional and is compared with the experimental results. The symmetry constraints underlying the model are discussed envisaging possible generalisation to the case of vortex cores with structure strongly dependent on the coordinate directed along the axis of the vortex. Moreover the many-body effect associated with the presence of two small satellite particles is described by rescaling the size of the particle.     

Images of a spin-torque-driven magnetic nano-oscillator

We present the first space- and time-resolved images of the spin-torque-induced steady-state oscillation of a magnetic vortex in a spin-valve nanostructure. We find that the vortex structure in a nanopillar is considerably more complicated than the 2D idealized structure often-assumed, which has important implications for the driving efficiency. The sense of the vortex gyration is uniquely determined by the vortex core polarity, confirming that the spin-torque acts as a source of negative damping even in such a strongly nonuniform magnetic system. The orbit radius is ～10 nm, in agreement with micromagnetic simulations.     

Marginal Fermi liquid resonance induced by a quantum magnetic impurity in d-wave superconductors

We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.     

Quantum magnetic impurities in magnetically ordered systems

We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group methods and accurate numerical renormalization group we show that contrary to other dissipative models there is quantum frustration of decoherence and quasiscaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility. Our results may also have relevance to quantum computation.     

Vortices in dipolar Bose–Einstein condensates in synthetic magnetic field

We study the formation of vortices in a dipolar Bose–Einstein condensate in a synthetic magnetic field by numerically solving the Gross–Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.     

Strong magnetic fluctuations in a superconducting state of CeCoIn5

We show results on the vortex core dissipation through current-voltage measurements under applied pressure and magnetic field in the superconducting phase of CeCoIn{5}. We find that as soon as the system becomes superconducting, the vortex core resistivity increases sharply as the temperature and magnetic field decrease. The sharp increase in flux-flow resistivity is due to quasiparticle scattering on critical antiferromagnetic fluctuations. The strength of magnetic fluctuations below the superconducting transition suggests that magnetism is complementary to superconductivity and therefore must be considered in order to fully account for the low-temperature properties of CeCoIn{5}.