Dynamics of coupled vortices in layered magnetic nanodots

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 dots with opposite chiralities and the same core polarizations (lowest energy state), two eigenmodes are predicted analytically and confirmed via micromagnetic simulations. One mode is in the sub-GHz range for submicron dot diameters and corresponds to quasi-circular rotation of the cores about the dot center. A second mode is in the MHz range corresponding to a small amplitude rotation of the mean core position. The eigenfrequencies depend strongly on the geometrical parameters of the system, suggesting that magnetostatic effects play a dominant role in determining the vortex dynamics.Comment: One PDF file including text and 4 figure

Low-frequency vortex dynamic susceptibility and relaxation in mesoscopic ferromagnetic dots

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

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

Magnetic Vortex Core Dynamics in a Ferromagnetic Dot

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.Comment: 18 pages including 4 figure

Boundary conditions for magnetization in magnetic nano-elements

We show that the dynamic magnetization at the edges of a thin magnetic element with finite lateral size can be described by new effective boundary conditions that take into account inhomogeneous demagnetizing fields near the element edges. These fields play a dominant role in the effective pinning of the dynamic magnetization at the boundaries of mesoscopic and nano-sized magnetic elements. The derived effective boundary conditions generalize well-known Rado-Weertman boundary conditions and are reduced to them in the limiting case of a very thin magnetic element

Evolution and stability of a magnetic vortex in small cylindrical ferromagnetic particle under applied field

The energy of a displaced magnetic vortex in a cylindrical particle made of isotropic ferromagnetic material (magnetic dot) is calculated taking into account the magnetic dipolar and the exchange interactions. Under the simplifying assumption of small dot thickness the closed-form expressions for the dot energy is written in a non-perturbative way as a function of the coordinate of the vortex center. Then, the process of losing the stability of the vortex under the influence of the externally applied magnetic field is considered. The field destabilizing the vortex as well as the field when the vortex energy is equal to the energy of a uniformly magnetized state are calculated and presented as a function of dot geometry. The results (containing no adjustable parameters) are compared to the recent experiment and are in good agreement.Comment: 4 pages, 2 figures, RevTe

Origin of four-fold anisotropy in square lattices of circular ferromagnetic dots

We discuss the four-fold anisotropy of in-plane ferromagnetic resonance (FMR) field $H_r$, found in a square lattice of circular Permalloy dots when the interdot distance $a$ gets comparable to the dot diameter $d$. The minimum $H_r$, along the lattice $$axes, and the maximum, along the$$ axes, differ by $\sim$ 50 Oe at $a/d$ = 1.1. This anisotropy, not expected in uniformly magnetized dots, is explained by a non-uniform magnetization \bm(\br) in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variational procedure.Comment: 4 pages, 3 figures, revtex, details of analytic calculation and new references are adde

Magnetization reversal in magnetostatically coupled dot arrays

科研費報告書収録論文(課題番号:13555087・基盤研究(B)(2) ・H13～H15/研究代表者:北上, 修/ナノ磁性ドット規則配列格子の磁気的挙動の解明と超高密度メモリーへの応用

Theory of vortex states in magnetic nanodisks with induced Dzyaloshinskii-Moriya interactions

Vortex states in magnetic nanodisks are essentially affected by surface/interface induced Dzyaloshinskii-Moriya interactions. Within a micromagnetic approach we calculate the equilibrium sizes and shape of the vortices as functions of magnetic field, the material and geometrical parameters of nanodisks. It was found that the Dzyaloshinskii-Moriya coupling can considerably increase sizes of vortices with "right" chirality and suppress vortices with opposite chirality. This allows to form a bistable system of homochiral vortices as a basic element for storage applications.Comment: 8 pages, 8 figure