Time-resolved soft X-ray transmission microscopy is applied to image the current-induced resonant dynamics of the magnetic vortex core realized in a micronsized Permalloy disk. The high spatial resolution better than 25 nm enables us to observe the resonant motion of the vortex core. The result also provides the spin polarization of the current to be 0.67 +/-0.16 for Permalloy by fitting the experimental results with an analytical model in the framework of the spin-transfer torque.
We report on detailed broadband ferromagnetic resonance measurements of azimuthal and radial spin wave excitations in circular Permalloy dots in the vortex ground state. Dots with aspect ratio (Beta =height over radius) varied from 0.03 to 0.1 were explored. We found that for Beta exceeding approximately 0.05, variation of the spin wave eigenfrequencies with Beta deviates from the predicted dependence. The frequency splitting of two lowest azimuthal modes was observed. The experimentally observed dependence of the frequency splitting on beta was reasonably well described by dynamic splitting m…
We have studied magnetic vortex oscillations in soft sub-micron cylindrical dots with variable thickness and diameter by an analytical approach and micromagnetic simulations. We have considered two kinds of modes of the vortex magnetization oscillations: 1) low-frequency translation mode, corresponding to the movement of the vortex as a whole near its equilibrium position; 2) high-frequency vortex modes, which correspond to radially symmetric oscillations of the vortex magnetization, mainly outside the vortex core. The vortex translational eigenmode was calculated numerically in frequency and …
The magnetic vortex with the in-plane curling magnetization and the out-of-plane magnetization at the core is a unique ground state in nanoscale magnetic elements. This kind of magnetic vortex can be used as a memory unit for information storage, through its downward or upward core-orientation and, thus, controllable core switching deserves some special attention. Our analytical and micromagnetic calculations reveal that the origin of the vortex core reversal is a gyrotropic field. This field is induced by vortex dynamic motion and is proportional to the velocity of the moving vortex. Our calc…
The universal criterion for ultrafast vortex-core switching between the up- and down-core bistates in soft magnetic nanodots was investigated by micromagnetic simulations along with analytical calculations. Vortex-core switching occurs whenever the velocity of vortex-core motion reaches the critical velocity that is expressed as (e.g. m/s for Permalloy), where Aex is the exchange stiffness, and is the gyromagnetic ratio. On the basis of the above results, phase diagrams for the vortex-core switching event and switching times with respect to both the amplitude and frequency of applied circularl…
We show that the flux-flow transport of the Josephson vortex lattice (JVL) in layered high-temperature superconductors provides a convenient probe for both components of quasiparticle conductivity, $σ_{c}$ and $σ_{ab}$. We found that the JVL flux-flow resistivity, $ρ_{ff}$, in a wide range of magnetic fields is mainly determined by the in-plane dissipation. In the dense lattice regime ($B>1$ T) $ρ_{ff}(B)$ dependence is well fitted by the theoretical formula for that limit. That allows us to independently extract from the experimental data the values of $σ_{c}$ and of the ratio $σ_{ab}/(σ_{c}γ…
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 (althou…
We report on the criterion for the dynamic transformation of the internal structure of moving domain walls (DWs) in soft magnetic thin-film nanostripes above the Walker threshold field, Hw. In order for the process of transformation from transverse wall (TW) to vortex wall (VW) or antivortex wall (AVW) occurs, the edge-soliton core of the TW-type DW should grow sufficiently to the full width at half maximum of the out-of-plane magnetizations of the core area of the stabilized vortex (or antivortex) by moving inward along the transverse (width) direction. Upon completion of the nucleation of th…
Magnetic configurations in heterostructures are often difficult to probe when the magnetic entities are buried inside. In this study we have captured magnetic and magnetoresistance "fingerprints" of Co nanodiscs embedded in Co/Cu multilayered nanowires using a first-order reversal curve method. In 200nm diameter nanowires, the magnetic configurations can be tuned by adjusting the Co nanodisc aspect ratio. Nanowires with the thinnest Co nanodiscs exhibit single domain behavior, while those with thicker Co reverse via vortex states. A superposition of giant and anisotropic magnetoresistance is o…
We found, by micromagnetic numerical and analytical calculations, that the clockwise (CW) and counterclockwise (CCW) circular-rotational motions of a magnetic vortex core in a soft magnetic circular nanodot are the elementary eigenmodes existing in the gyrotropic motion with respect to the corresponding CW and CCW circular-rotational-field eigenbasis. Any steady-state vortex gyrotropic motions driven by a linearly polarized oscillating in-plane magnetic field in the linear regime can be perfectly understood according to the superposition of the two circular eigenmodes, which show asymmetric re…
We analyze scattering of the transverse optic modes by spherically symmetric Polarized Nano Regions (PNR) in the paraelectric phase of relaxor ferroelectrics. Calculations have done in the frame of mean-field model early supposed by E.Iolin & J.Toulouse but depolarization field effects, DF, were taken into account. Elementary excitations of the system are found to be of two types - Vortex (V) and Quasi Polar (QP). DF decreases temperature of the local QP phase transition. The local phase transition temperature is found to be lower (higher) for Vortex than for QP excitations for the case of sma…
Microwave measurements have recently been successfully applied to measure ferroelectric materials on the nanoscale, including detection of polarization switching and ferroelectric domain walls. Here we discuss the question whether scanning probe microscopy (SPM) operating at microwave frequency can identify the changes associated with the soft phonon dynamics in a ferroic. The analytical expressions for the electric potential, complex impedance and dielectric losses are derived and analyzed, since these physical quantities are linked to experimentally-measurable properties of the ferroic. As a…
The motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a velocity proportional to the field. Above a critical field the viscous motion breaks down giving way to oscillations accompanied by a slow drift of the wall. At still higher fields the drift velocity starts rising with the field again but with a much lower mobility dv/dH than in the viscous regime. To describe the dynamics of the wall we use the method of collec…
Vortex crystals are commonly observed in ultra-thin ferroelectrics. However, a clear physical picture of origin of this topological state is currently lacking. Here, we show that vortex crystallization in ultra-thin Pb(Zr0.4,Ti0.6)O3 films stems from the softening of a phonon mode and can be thus described as a SU(2) symmetry-breaking transition. This result sheds light on the topology of the polar vortex patterns and bridges polar vortices with smectic phases, spin spirals, and other modulated states. Finally, we predict an ac-field driven resonant switching of the vortex tube orientation whi…
Although pinning of domain walls in ferromagnets is ubiquitous, the absence of an appropriate characterization tool has limited the ability to correlate the physical and magnetic microstructures of ferromagnetic films with specific pinning mechanisms. Here, we show that the pinning of a magnetic vortex, the simplest possible domain structure in soft ferromagnets, is strongly correlated with surface roughness, and we make a quantitative comparison of the pinning energy and spatial range in films of various thickness. The results demonstrate that thickness fluctuations on the lateral length scal…
The magnetization in a magnetic microdot made from soft magnetic materials can have a vortex-like ground state structure resulting from competition between the exchange and dipolar interactions. Normal mode magnon frequencies for such dots are calculated taking into account both exchange and magnetostatic effects. The presence of a low-lying mode as well as doublet structure with small splitting is demonstrated. Estimates of the mode frequencies for permalloy dots are obtained, and the possibility of experimental detection of such modes is discussed.
The magnetization reversal and spin structure in circular Co/insulator/Ni80Fe20 trilayer dots has been investigated numerically. The effect of dipolar coupling between a soft ferromagnetic Permalloy (Py=Ni80Fe20) layer and a hard ferromagnetic Cobalt layer inside one stack is studied. We find either a stabilization or even a triggering of the vortex state in the Py layer due to the magnetic stray field of the Co layer, while the Co magnetization remains in a single-domain state. Furthermore, for thin Py layers a 360 deg-domain wall is observed. We construct a phase diagram, where regions of vo…
A recent article by Sassa et al. [Phys. Rev. B 91, 045114 (2015)] reports on a soft x-ray angle-resolved photoemission study of MgB2. The analysis and/or presentation of the collected data and the corresponding calculations appear to be partially inconsistent. The aim of this comment is to provide a guide to these inconsistencies and to discuss their influence on the presented conclusions.
We study theoretically the interaction between soft magnetic and superconducting films. It is shown that the vortex induces a magnetization distribution in the magnetic film, thus modifying the magnetic field as well as the interactions with e.g. Bloch walls. In particular, the field from the vortex may change sign close to the core as a result of the vortex-induced magnetization, thus resulting in a crossover from attraction to repulsion between vortices and Bloch walls. Moreover, we show that by tuning the anisotropy field of the magnetic film, one may enhance the interaction between Bloch w…
A magnetic vortex has attracted significant attention since it is a topologically stable magnetic structure in a soft magnetic nanodisk. Many studies have been devoted to understanding the nature of magnetic vortex in isolated systems. Here we show a new aspect of a magnetic vortex the dynamics of which strongly affects the magnetic structures of environment. We exploit a nanodot of an exchange-coupled bilayer with a soft magnetic Ni81Fe19 (permalloy; Py) having a magnetic vortex and a perpendicularly magnetized L10-FePt exhibiting a large switching field (Hsw). The vortex dynamics with azimut…
Spin-polarized radio frequency (RF) currents and RF-Oersted fields resonantly excite a magnetic vortex core confined in a micron-scale soft magnetic disk. In this study, we measured the rectifying voltage spectra caused by the anisotropic magnetoresistance oscillation due to the gyration of the vortex with different polarity and chirality. The measured spectra are presented such that we can determine the vortex properties and strength of the spin torques and Oersted field accurately and directly through analytical calculation.
Synergistic approach to probing the dynamics and mechanics of patchy soft matter
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of the Basque Country（巴斯克大学）；University of Padua（帕多瓦大学）；Istituto Nazionale Di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Institute of Nanotechnology, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院纳米技术研究所）；Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院人机交互与机器人研究所）；University of Edinburgh（爱丁堡大学）
Within the framework of the Landau-Ginzburg-Devonshire approach we explore the impact of elastic anisotropy, electrostriction, flexoelectric couplings, and mismatch strain on the domain structure morphology in ferroelectric core-shell nanoparticles of spherical shape. We perform finite element modelling (FEM) for multiaxial ferroelectric nanoparticle cores covered with an elastically-isotropic soft or elastically-anisotropic rigid paraelectric shell, with and without mismatch strains. In the case of a core covered with a soft shell, the FEM results show that at room temperature a single polari…
