Spin dynamics characterization in magnetic dots

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 such a dot have also been calculated in both phases by the linearized equation of motion method. These results have also been reproduced f rom the Fourier transform of the spin autocorrelation function. From the magnon Density Of States (DOS), it is possible to identify the magnetic phase of the dot. Furthermore, the magnon modes have been characterized for both the ferromagnetic and the vortex phase, and the magnon instability mechanism leading to the vortex-ferro transition has also been identified. The results can also be used to compute finite temperature magnetization or vort icity of magnetic dots.Comment: 11 figures (12 figure files + 1 tex file

Stability of magnetic vortex in soft magnetic nano-sized circular cylinder

Stability of magnetic vortex with respect to displacement of its center in a nano-scale circular cylinder made of soft ferromagnetic material is studied theoretically. The mode of vortex displacement producing no magnetic charges on the cylinder side is proposed and the corresponding absolute single-domain radius of the cylinder is calculated as a function of its thickness and the exchange length of the material. In cylinders with the radii less than the single-domain radius the vortex state is unstable and is absolutely prohibited (except if pinned by material imperfections), so that the distribution of the magnetization vector in such cylinders in no applied magnetic field is uniform (or quasi-uniform). The phase diagram of nano-scale cylinders including the stability line and the metastability region obtained here is presented.Comment: 3 pages, 2 figures, RevTex 4, presented at JEMS'01, accepted to JMM

Broadband probing magnetization dynamics of the coupled vortex state permalloy layers in nanopillars

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 (although more gradual) changes occur also in the exchange coupled Py(25 nm)/Cu(1 nm)/Py(25 nm) tri-layer nanopillars. These findings are in qualitative agreement with micromagnetic dynamic simulations

Nonlinear gyrotropic vortex dynamics in ferromagnetic dots

The quasistationary and transient (nanosecond) regimes of nonlinear vortex dynamics in a soft magnetic dot driven by an oscillating external field are studied. We derive a nonlinear dynamical system of equations for the vortex core position and phase, assuming that the main source of nonlinearity comes from the magnetostatic energy. In the stationary regime, we demonstrate the occurrence of a fold-over bifurcation and calculate analytically the resonant nonlinear vortex frequencies as a function of the amplitude and frequency of the applied driving field. In the transient regime, we show that the vortex core dynamics are described by an oscillating trajectory radius. The resulting dynamics contain multiple frequencies with amplitude decaying in time. Finally, we evaluate the ranges of the system parameters leading to a vortex core instability (core polarization reversal)

Dynamics of ferromagnetic nanomagnets with vortex or single-domain configuration

We study the dynamics of flat circular permalloy nanomagnets for 1.) magnetic vortex and 2.) single-domain configurations, using micromagnetic simulation. Dynamical studies for isolated vortex structures show that both the vorticity and the central polarity of the out-of-plane component can be switched fast (50-100 ps) and independently. Micromagnetic simulations of the switching process in thin cylindrical Permalloy (Py) nanoparticles with an initial stable single-domain state show nearly homogeneous single-domain behaviour followed by excitation of spin waves.Comment: 2 pages with 3 eps-figures, --> ICM2003 Rome 28.7.-1.8.03, --> JMM

Magnetic Vortex Resonance in Patterned Ferromagnetic Dots

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 the characteristic vortex annihilation field. Resonances at 162 and 272 MHz were detected for 2.2 and 1.1 um disks with thickness 40 nm, respectively. A resonance peak at 83 MHz was detected for 20-nm thick, 2-um diameter disks. The resonance frequencies exhibit weak field dependence, and scale as a function of the dot geometrical aspect ratio. The measured frequencies are well described by micromagnetic and analytical calculations that rely only on known properties of the dots (such as the dot diameter, thickness, saturation magnetization, and exchange stiffness constant) without any adjustable parameters. We find that the observed resonance originates from the translational motion of the magnetic vortex core.Comment: submitted to PRB, 17 pages, 5 Fig