Gyrotropic Motion Research Articles

Spin-torque-driven vortex dynamics in a spin-valve pillar with a perpendicular polarizer

Spin-torque-driven vortex dynamics are studied by micromagnetic modeling in a spin-valve pillar which contains a perpendicular polarizer and a vortex free layer. Two kinds of transient oscillations mediated by the vortex-core motion are observed. The oscillations are treated as the competition among the spin torque, gyroforce, Gilbert damping, and the restoring force, governed by the generalized Thiele equation [A. A. Thiele, J. Appl. Phys. 45, 377 (1974)]. The fundamental frequency is dominated by the gyrotropic motion, while the high-frequency oscillation is triggered by the balance of the spin torque and demagnetizing field. The polarity of the vortex core can be switched through a vortex-antivortex pair creation and annihilation process.

Soft x-ray imaging of spin dynamics at high spatial and temporal resolution

Soft x-ray microscopy provides element specific magnetic imaging with a spatial resolution down to 15 nm. At XM-1, the full-field soft x-ray microscope at the Advanced Light Source in Berkeley, a stroboscopic pump and probe setup has been developed to study fast magnetization dynamics in ferromagnetic elements with a time resolution of 70 ps, which is set by the width of the x-ray pulses from the synchrotron. Results obtained from a 2 μm×4 μm×45 nm rectangular permalloy sample exhibiting a seven domain Landau pattern reveal dynamics up to several nanoseconds after the exciting magnetic field pulse. Domain wall motion, a gyrotropic vortex motion, and a coupling between vortices in the rectangular geometry are observed.

Nanocontact spin-transfer oscillators based on perpendicular anisotropy in the free layer

Micromagnetic simulations are used to predict the behavior exhibited by spin-transfer oscillators when materials with perpendicular anisotropy are introduced in the “free” layer of nanocontact devices. Under a perpendicular-to-plane bias field, the frequency exhibits nonlinear dependence on the anisotropy field, mostly originated by the exchange-dominated propagating nature of spin-wave modes. The increase of frequency without using large bias fields makes it suitable for potential technological applications. A study of the feasibility of bias-field-free devices has been also performed deriving multiharmonic signals at gigahertz frequencies. Here, the magnetization describes a gyrotropic motion where both vortex-core polarization and rotation sense switch periodically.

Simple Harmonic Oscillation of Ferromagnetic Vortex Core

Here we report a theoretical description of ferromagnetic vortex dynamics. Based on Thiele's formulation of the Landau-Lifshitz-Gilbert equation, the motion of the vortex core could be described by a function of the vortex core position. Under a parabolic potential generated in the circular magnetic patterns, the vortex core showed a circular rotation-namely the gyrotropic motion, which could be described by a 2-dimensional simple harmonic oscillator. The gyrotropic frequency and apparent damping constant were predicted and compared with the values obtained micromagnetic calculation.

Mode degeneracy due to vortex core removal in magnetic disks

The mode spectrum of micrometer-sized ferromagnetic Permalloy disks, exhibiting a vortex ground state, is investigated by means of time-resolved scanning Kerr microscopy. The temporal evolution of the magnetization is probed after application of a fast in-plane field pulse. The lowest order azimuthal mode, a mode with only one diametric node, splits into a doublet as the disk diameter decreases. Theoretical models show that this splitting is a consequence of the interaction of the mode with the gyrotropic motion of the vortex core. Our experiments and micromagnetic simulations confirm that by removing the vortex core from the disk, the mode splitting vanishes.

Direct observation of the vortex core magnetization and its dynamics

Square-shaped thin film structures with a single magnetic vortex were investigated using a scanning transmission x-ray microscope. The authors report on the direct observation of the vortex core in 500×500nm2, 40nm thick soft magnetic Ni–Fe samples. The static configuration of the vortex core was imaged as well as the gyrotropic motion of the core under excitation with an in-plane alternating magnetic field. This enabled them to directly visualize the direction of the out-of-plane magnetization in the vortex core (up or down). The reversal of the core was effected by short bursts of an alternating magnetic field. An asymmetry appears in the core’s trajectory for its orientation pointing up and down, respectively.

Vortex dynamics in Permalloy disks with artificial defects: Suppression of the gyrotropic mode

The dynamics of magnetic vortices in thin Permalloy disks having artificial defects in the form of small holes at different locations within the disk has been investigated by means of frequency-domain spatially resolved ferromagnetic resonance. It is found that the vortex can be effectively captured by such a defect. Consequently the commonly observed gyrotropic vortex motion in an applied microwave field of 1mT is suppressed. However, if in addition a static magnetic field of at least 4.3mT is applied, the vortex core is nucleated from the artificial defect and a modified gyrotropic motion starts again.

Vortex dynamics in coupled ferromagnetic multilayer structures

Magnetization dynamics in ferromagnetic multilayer structures was studied by time-resolved transmission x-ray microscopy. A square-shaped 1×1μm2 trilayer structure consisting of Co(20nm)∕Cu(10nm)∕Permalloy Ni80Fe20(20nm) was investigated. Each ferromagnetic layer showed a Landau-like domain configuration with a single vortex. A gyrotropic vortex motion was excited by an in-plane magnetic field alternating at a frequency of 250 MHz. The movement of the magnetic vortex in each individual magnetic layer was imaged by taking advantage of the element specificity of the x-ray magnetic circular dichroism. A 180° phase shift between the gyrotropic vortex motion in the Permalloy and the Co layer was observed. This phase shift can be ascribed to the magnetic coupling between the layers.

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.

Micromagnetic simulations of vortex-state excitations in soft magnetic nanostructures

The dynamic susceptibility spectra of Permalloy nanodots, supporting a vortex-type magnetic configuration, are studied within the frequency range $0.2--20\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ as a function of dot thickness $(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\ensuremath{\leqslant}{L}_{z}\ensuremath{\leqslant}80\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ by means of three-dimensional dynamic micromagnetic simulations. In addition to the low-frequency vortex translation mode (gyrotropic motion of the vortex core), a second vortex core mode is revealed at a higher frequency for thicker nanodots (in-plane pumping field). This mode whose resonance frequency decreases rapidly with increasing dot thickness originates from the nonuniform vortex structure along the dot normal axis. Higher frequency modes are also observed for both in-plane and perpendicular pumping field orientations and correspond mostly to spin excitations localized outside the vortex core. The possible detection of the two vortex core modes within an individual nanodot using resonance experiments is discussed on the basis of the dispersion relation frequency versus perpendicular static magnetic field.

One-dimensional model of a vortex in an easy-plane ferromagnet

A simple one-dimensional model of a ferromagnet in a vortex configuration is proposed for qualitative description of the structure and dynamics of a vortex in a two-dimensional magnetic system. The model describes a system of four parallel spin chains with single-ion anisotropy of the easy-plane type and includes elements of both the continuum (along the chains) and discrete (perpendicular to the chains) descriptions. An analytical study is made of the static vortices and moving vortex solutions of stationary profile. The analytical results of a calculation of the static structure of the vortices are supplemented by a numerical analysis for the analogous discrete systems and are in good agreement with the numerical data. The approach is generalized to the case of the description of gyrotropic motion of vortices of stationary profile in the framework of the collective variables method for the combined continuum–discrete description. The results are analyzed and compared with the data for two-dimensional magnets.

Imaging of spin dynamics in closure domain and vortex structures

Time-resolved Kerr microscopy is used to study the excitations of individual micron-scale ferromagnetic thin-film elements in their remnant state. Thin (18 nm) square elements with edge dimensions between 1 and $10\ensuremath{\mu}\mathrm{m}$ form closure domain structures with 90 deg N\'eel walls between domains. We identify two classes of excitations in these systems. The first corresponds to precession of the magnetization about the local demagnetizing field in each quadrant, while the second excitation is localized in the domain walls. Two modes are also identified in ferromagnetic disks with thicknesses of 60 nm and diameters from $2\ensuremath{\mu}\mathrm{m}$ down to 500 nm. The equilibrium state of each disk is a vortex with a singularity at the center. As in the squares, the higher-frequency mode is due to precession about the internal field, but in this case the lower-frequency mode corresponds to gyrotropic motion of the entire vortex. These results demonstrate clearly the existence of well-defined excitations in inhomogeneously magnetized microstructures.

Viscous Forces in Velocity Boundary Layers around Planetary Ionospheres.

A discussion is presented to examine the role of viscous forces in the transport of solar wind momentum to the ionospheric plasma of weakly magnetized planets (Venus and Mars). Observational data are used to make a comparison of the Reynolds and Maxwell stresses that are operative in the interaction of the solar wind with local plasma (planetary ionospheres). Measurements show the presence of a velocity boundary layer formed around the flanks of the ionosphere where the shocked solar wind has reached super-Alfvénic speeds. It is found that the Reynolds stresses in the solar wind at that region can be larger than the Maxwell stresses and thus are necessary in the local acceleration of the ionospheric plasma. From an order-of-magnitude calculation of the Reynolds stresses, it is possible to derive values of the kinematic viscosity and the Reynolds number that are suitable to the gyrotropic motion of the solar wind particles across the boundary layer. The value of the kinematic viscosity is comparable to those inferred from studies of the transport of solar wind momentum to the earth's magnetosphere and thus suggest a common property of the solar wind around planetary obstacles. Similar conditions could also be applicable to velocity boundary layers formed in other plasma interaction problems in astrophysics.

Domain rotation in magnetic garnet films

The behavior of ring-shaped and dumbbell-shaped domains was investigated in epitaxial magnetic garnet films with uniaxial anisotropy perpendicular to the film surface. A series of rectangular field pulses applied to the sample can cause rotation of each of the structures. Rotation of the ring-shaped domains was described by a model based on gyrotropic motion of vertical bloch lines, similar to the earlier published model of the dumbbell rotation. An effect of a successive involvement of dumbbells into rotation was observed when the film was heated. On cooling the film again, the dumbbells stopped to rotate in their reversed order. Temperature hysteresis of the process was registered. The observed effects were explained on the basis of the domain models and of the temperature dependence of the domain-wall coercivity.