Dynamics of a Pinned Magnetic Vortex

Abstract

We observe the dynamics of a single magnetic vortex in the presence of a random array of pinning sites. At low excitation amplitudes, the vortex core gyrates about its equilibrium position with a frequency that is characteristic of a single pinning site. At high amplitudes, the frequency of gyration is determined by the magnetostatic energy of the entire vortex, which is confined in a micron-scale disk. We observe a sharp transition between these two amplitude regimes that is due to depinning of the vortex core from a local defect. The distribution of pinning sites is determined by mapping fluctuations in the frequency as the vortex core is displaced by a static in-plane magnetic field.PACS numbers: 75.75.+a,75.40.Gb The excitation spectrum of a sub-micron ferromagnetic particle is influenced profoundly by its shape. An example of considerable interest is the vortex state of a soft ferromagnetic disk, in which the lowest frequency excitation is a translational mode of the vortex core. This mode, in which the vortex core gyrates about its equilibrium position, has been studied in several recent experiments [1,2,3,4,5,6]. Although the core has a diameter of the order of the exchange length (∼10 nm) [7,8], the eigenfrequency of the gyrotropic mode is determined only by the geometrical aspect ratio (diameter over thickness) of the disk in which it is confined [9,10]. In particular, the gyrotropic frequency should be independent of the location of the vortex core in the disk [5]. As demonstrated recently, however, the vortex core can be pinned by defects in a patterned thin film [11,12,13]. In the case of intrinsic defects, the range of the effective pinning potential appears to be on the order of ten nanometers [13]. This raises the question of how a nanoscale defect influences the vortex gyrotropic motion.In this Letter, we report that pinning has a pronounced effect on magnetic vortex dynamics at small amplitudes. The vortex gyrotropic frequency in 50 nm thick permalloy (Py) disks with diameters from 600 nm to 2 µm fluctuates by a factor of at least two as the core is displaced by a static magnetic field over length scales ∼ 10 nm. The dependence on core location indicates that the smallamplitude dynamics are influenced strongly by the characteristics of a particular pinning site. Each site has a critical excitation amplitude above which the vortex becomes depinned and gyrates at the frequency determined by the aspect ratio of the disk. We image the spatial distribution of pinning sites in a disk by displacing the vortex core in two dimensions while monitoring the gyrotropic frequency. Using this approach, we find a density of up to ∼ 2×10 11 cm −2 for the pinning sites in our films. Although this density cannot be correlated directly with the physical morphology of the permalloy films, the extreme sensitivity to core displacement indicates that the magnetic microstructure fluctuates strongly on nanometer scales.The samples were patterned from 50 nm thick films of Py (Ni 0.81 Fe 0.19 ), which has negligible mag...

Direct dynamic imaging of non-adiabatic spin torque effects

“…The orbital tilts are sensitive to the relative magnitudes of all three driving contributions: adiabatic, non-adiabatic and Oersted. Hence, mapping the tilt angle with respect to frequency may allow the additional determination of the degree of spin polarization, P, though in practice, local pinning effects can influence low-amplitude oscillations and may complicate the interpretation of P 18,21 .…”

“…We carefully tuned the frequency in the experiments until the maximum core trajectory is observed and fit the resonant amplitudes as a function of current for both chiralities to obtain β. Currents were chosen such that the maximum vortex core displacements were only 6.5% of the disc width to prevent anharmonic contributions to the motion, but to still maintain large enough displacements to minimize the pinning effects that are present for static or weakly driven excitations 18,21 . This represents one of the key advantages of our approach, as pinning can lead to large errors 6 .…”

“…The relative uncertainties in the core positions, and hence in β, were almost 50% due to the limited spatial resolution of the technique. Furthermore, the vortex core is static in these measurements so it is susceptible to influences from strong local pinning 18 . Reducing the uncertainty in β would require a greater vortex core displacement, better spatial resolution, a dynamic approach or a combination of the above.…”

Coherence and modality of driven interlayer-coupled magnetic vortices

“…Since we measured the real-space gyrotropic motion for individual discs with sub-5 nm resolution, the data points are directly related to the vortices' response to the HF excitation and local structure. The deviations of the measured orbital amplitudes from the fitted Lorentzian curves are unique to each disc and are related to the inherent microstructure 43 . For example, the asymmetry of the data for the single vortex disc r ¼ 1150 nm demonstrates good agreement with the fit in the onset of the curve but a more linear trend towards the end where the orbital amplitude tails off.…”

Influence of material defects on current-driven vortex domain wall mobility

“…Nevertheless, real Permalloy nanowire samples contain defects in their microstructure, e.g., surface roughness and/or grain boundaries, which can act as pinning centers for the domain walls. From experiments [25][26][27][28][29] it is known that these are randomly distributed throughout the wire with a density σ ranging from 690 to 2000 μm −2 , and give rise to a pinning potential for a vortex that is approximately 2 eV deep and has an interaction range roughly equal to the size of the vortex core. In this contribution we numerically investigate the influence of such distributed disorder on the domain wall mobility.…”