Coupled Vortex Oscillations in Spatially Separated Permalloy Squares

Abstract

The influence of the magnetostatic interaction on vortex dynamics in arrays of ferromagnetic disks is investigated by means of a broadband ferromagnetic-resonance setup. Transmission spectra reveal a strong dependence of the resonance frequency of vortex-core motion on the ratio between the center-tocenter distance and the element size. For a decreasing ratio, a considerable broadening of the absorption peak is observed following an inverse sixth power law. An analogy between the vortex system and rotating dipoles is confirmed by micromagnetic simulations. DOI: 10.1103/PhysRevLett.105.037201 PACS numbers: 75.75.Àc, 75.25.Àj, 75.40.Gb, 76.50.+g Vortex dynamics can be observed in many physical systems such as ferromagnets, superconductors, and Bose-Einstein condensates. Explanations of flow phenomena in modern fluid mechanics are often predicated on the dynamics of vortices. In recent years, small ferromagnetic structures with vortex magnetization configuration have gained intense scientific interest because of their dynamics on the subnanosecond time scale and potential technological applications, such as ultrafast and highdensity digital storage devices [1][2][3][4]. Even medical applications have lately been discussed [5]. Understanding the influence of the various internal and external parameters on the dynamic properties of the magnetic vortex is an important issue for further development. The gyrotropic mode and switching of single vortex cores have been studied intensely [6][7][8][9][10]. However, investigation of the interaction between several vortices [11][12][13][14] is still required. Coupling of magnetic vortices, e.g., provides a model system in fundamental research and could also determine the packing density in storage devices.To describe the magnetic behavior of an array of ferromagnetic disks, the magnetostatic interaction between single elements has to be considered when the interelement distance is less than the lateral size of one disk [15]. An increase of the initial susceptibility and a decrease of the vortex nucleation and annihilation fields are observed [16]. Analytical and numerical calculations using the rigid vortex model predict a shift of the eigenfrequency of vortexcore motions in adjacent ferromagnetic disks depending on the core polarizations and the distance between the disk centers [11,17].Here, we experimentally study the influence of the magnetostatic interaction on the resonance frequency of vortices trapped in arrays of 4 Â N ferromagnetic disks by varying the distance and the size of the elements. Energy absorption in radio-frequency magnetic fields has been determined via a broadband ferromagnetic-resonance (FMR) setup using a vector-network analyzer. The vortex resonance frequency strongly depends on the magnetostatic coupling within the array. The relative broadening of the absorption peak due to resonant vortex-core motion varies with the inverse sixth power of the normalized center-to-center distance. This kind of distance dependence is a prominent feature of the f...

Simultaneous control of magnetic topologies for reconfigurable vortex arrays

“…1,2 Because both circularity and polarity can be specified by two independent values, that is, c = ± 1 and p = ± 1, four distinct spin states can exist in a single magnetic element with the combination of circularity and polarity. Magnetic vortices have been intensively studied due to their compelling physical behavior [3][4][5][6][7] and their potential in a wide range of applications such as data storage, 8,9 signal transfer, [10][11][12] logic devices, 13 transistors 14 and artificial skyrmion crystals. [15][16][17][18] With respect to practical application of magnetic vortices in advanced nanotechnologies, one of the critical factors is the effective reconfigurability of two topologies, c and p, particularly within large and densely packed arrays of magnetic elements.…”

Resonance in magnetostatically coupled transverse domain walls

“…These interactions can modify existing resonant behavior [1,2], lead to the appearance of new coupled modes [3][4][5], or result in a combination of these [6][7][8]. The coupling of DWs has also been proposed as a scheme towards increasing the output power of spin-torque oscillators [9], and will have an impact on the design of DW-logic-based devices as well.…”

Spectroscopy and Imaging of Edge Modes in Permalloy Nanodisks

“…A very challenging variation is near-field Brillouin scattering, which has been used to image edge mode dynamics with resolution below 55 nm [17]. X-ray microscopy based on magnetic circular dichroism also provides dynamic magnetic imaging [18][19][20] with resolution as fine as 25 nm. [18] In parallel, ferromagnetic resonance force microscopy (FMRFM) [21][22][23][24] has been developed and proven to be a useful tool for various areas in magnetic dynamics, such as spin wave dynamics in confined structures [22,[25][26][27][28][29][30], spin-transfer torque device dynamics [31], defect detection in an array [32], and spin wave localization [33][34][35][36].…”