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-to-center 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.

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...

Topological singularities occur as antivortices in ferromagnetic thin-film microstructures. Antivortices behave as two-dimensional oscillators with a gyrotropic eigenmode which can be excited resonantly by spin currents and magnetic fields. We show that the two excitation types couple in an opposing sense of rotation in the case of resonant antivortex excitation with circular-rotational currents. If the sense of rotation of the current coincides with the intrinsic sense of gyration of the antivortex, the coupling to the Oersted fields is suppressed and only the spin-torque contribution locks into the gyrotropic eigenmode. We report on the experimental observation of purely spin-torque induced antivortex-core reversal. The dynamic response of an isolated antivortex is imaged by time-resolved scanning transmission x-ray microscopy on its genuine time and length scale. DOI: 10.1103/PhysRevLett.105.137204 PACS numbers: 75.60.Jk, 68.37.Yz, 72.25.Àb, 75.60.Ch Magnetization dynamics in microstructures is not only an aspect of basic research. Its investigation is also motivated by the vision of engineering new storage devices. Magnetic antivortices and vortices are capable of storing binary information [1][2][3] represented by their core polarization p ¼ AE1 and behave as two-dimensional oscillators with a gyrotropic eigenmode which can be excited resonantly by spin currents and magnetic fields [4][5][6][7]. With the perspective of possible applications in storage devices, spin-torque induced core switching is preferred because in this case single elements can be addressed, which is obviously important for storage cells of high density. Another motivator to investigate the current induced dynamics of magnetization is the patent for the magnetic race track memory [8,9], which is based on the unidirectional control of magnetic domain walls in a nanowire by spinpolarized currents [10]. Thereto, a detailed understanding of the coupling between the spin of the conduction electrons and the magnetization of ferromagnets, namely, the spin-transfer torque [11][12][13], has to be gathered. Nevertheless, experiments on spin-torque driven magnetization dynamics come along with a general difficulty: the discrimination between the spin-transfer torque and the torque from parasitic Oersted fields as driving force [4][5][6][14][15][16]. Both torques are generated simultaneously by the applied current. In this Letter we show that both excitation types couple in an opposing sense of rotation in the case of resonant antivortex excitation with circular-rotational currents. The magnetic coupling is suppressed and only the spin-torque contribution locks into the gyrotropic eigenmode if the sense of rotation of the applied current coincides with the intrinsic sense of gyration of the antivortex. We report on the first experimental observation of purely spin-torque induced antivortex-core reversal.Antivortices and vortices form in ferromagnetic thinfilm structures [17][18][19] by a compromise between the shape anisotropy, which prefers the...

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Magnetic vortices and antivortices are usually observed coexisting in cross-tie walls within ferromagnetic thin films. An antivortex can be isolated by utilizing the shape anisotropy. The isolation offers the possibility to investigate its fundamental dynamics as a two-dimensional oscillator in a confining potential. Hitherto, the gyration mode of vortices and its excitation has been studied intensely. Here, a detailed investigation of the coupling of an antivortex to in-plane rotating magnetic fields is presented. The resonant response is imaged by time-resolved scanning transmission x-ray microscopy to determine the amplitude as well as the phase of the gyration. The experimental results are compared with the analytical model of a two-dimensional harmonic oscillator derived from the Thiele equation. As a cause for deviations from the model, a buckled energy landscape due to local defects is discussed

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We investigate the switching criteria of magnetic vortices in micron-sized Permalloy squares. The vortices are excited by high frequency magnetic fields. Continuous core reversal is demonstrated for a wide range of frequencies and amplitudes of excitation by ferromagnetic absorption spectroscopy and for selected frequencies and amplitudes with time-resolved scanning x-ray microscopy. The boundary of this switching regime is derived from the Thiele equation when a critical velocity of v crit ≈ 250 ms −1 is considered.