We demonstrate a novel method allowing the study of the magnetic state dynamics of a single nanoparticle by means of electron transport measurements. Elliptical 550 nm x 240 nm permalloy nanoparticles are wired with non-magnetic leads for magnetotransport measurements in the presence of a radio-frequency (RF) field. Their resistance exhibits sharp jumps due to the anisotropic magnetoresistance even at room temperature. An RF field induces DC voltage across the nanoparticle which can be partially depleted at a certain RF frequency when a magnetic vortex core resonance is present. An application of an additional DC magnetic field eliminates the vortex and reinstates the unperturbed DC voltage level. The vortex core resonance frequencies are found and the smallest resonance widths are estimated to be less than 6 MHz.
We report on the switching of a magnetic vortex core in a sub-micron Permalloy disk, induced by a short current pulse applied in the film plane. Micromagnetic simulations including the adiabatic and non-adiabatic spin-torque terms are used to investigate the current-driven magnetization dynamics. We predict that a core reversal can be triggered by current bursts a tenth of a nanosecond long. The vortex core reversal process is found to be the same as when an external field pulse is applied. The control of a vortex core's orientation using current pulses introduces the technologically relevant …
Permalloy nanoparticles containing bacterial cellulose hydrogel obtained after reduction was compressed into a xerogel flexible sheet by hot pressing at 60 C at different pressures. The permalloy nanoparticles with an ordered structure have a bimodal size distribution centered around 25 nm and 190 nm. The smaller nanoparticles are superparamagnetic while the larger particles are ferromagnetic at room temperature. The sheets have a room temperature magnetisation of 20 emu/g and a coercivity of 32 Oe. The electrical conductivity of the flexible sheets increases with hot pressing pressure from 7 …
We study vortex domain wall dynamics in wide Permalloy strips driven by applied magnetic fields and spin-polarized electric currents. As recently reported [V. Estévez and L. Laurson, Phys. Rev. B, 93, 064403 (2016)], for sufficiently wide strips and above a threshold field, periodic dynamics of the vortex core are localized in the vicinity of one of the strip edges, and the velocity drop typically observed for narrow strips is replaced by a high-velocity plateau. Here, we analyze this behavior in more detail by means of micromagnetic simulations. We show that the high-velocity plateau originat…
The induced motion of a magnetic vortex in a micron-sized ferromagnetic disk due to the DC current injection is studied by measuring planar Hall effect. The DC current injection is found to induce the spin torque that sweeps the vortex out of the disk at the critical current while bias magnetic field are applied. The current-induced vortex core displacement deduced from the change in planar Hall resistance is quantitatively consistent with theoretical prediction. Peak structures similar to those originated from spin wave excitations are observed in the differential planar Hall resistance curve…
We study the dynamics of flat circular permalloy nanomagnets for 1.) magnetic vortex and 2.) single-domain configurations, using micromagnetic simulation. Dynamical studies for isolated vortex structures show that both the vorticity and the central polarity of the out-of-plane component can be switched fast (50-100 ps) and independently. Micromagnetic simulations of the switching process in thin cylindrical Permalloy (Py) nanoparticles with an initial stable single-domain state show nearly homogeneous single-domain behaviour followed by excitation of spin waves.
Ultrafast magnetization dynamics probes the most fundamental properties of magnetic materials, exploring questions about the fundamental interactions responsible for magnetic phenomena. Thermal effects are known to be extremely important for laser-induced dynamics in metallic systems, but the dynamics of topological magnetic structures are little understood. Here we apply a massively parallel atomistic spin dynamics simulation to study the response of a permalloy vortex to a 50 fs laser pulse. We find that macroscopically the short timescale dynamics are indistinguishable from the bulk, but th…
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 conducted a thorough experimental and numerical study of the micromagnetic properties of Permalloy (Ni$_{80}$Fe$_{20}$) microdisks exhibiting target domain structures at remanence. Vortex configurations are quite common in such microdisks and correspond to an in-plane flux closure configuration of cylindrical symmetry with an out-of-plane magnetized core. In contrast, target domain configuration are observed in thicker microdisks and are characterized by a vortex configuration of the in-plane component of the magnetization superposed to an out-of-plane component of magnetization which oscil…
Domain walls in soft permalloy strips may exhibit various equilibrium micromagnetic structures depending on the width and thickness of the strip, ranging from the well-known transverse and vortex walls in narrow and thin strips to double and triple vortex walls recently reported in wider strips [V. Estévez and L. Laurson, Phys. Rev. B {\bf 91}, 054407 (2015)]. Here we analyze the field driven dynamics of such domain walls in permalloy strips of widths from 240 nm up to 6 $μ$m, using the known equilibrium domain wall structures as initial configurations. Our micromagnetic simulations show that …
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 employed micro-Hall magnetometry and micromagnetic simulations to investigate magnetic vortex pinning at single point defects in individual submicron-sized permalloy disks. Small ferromagnetic particles containing artificial point defects can be fabricated by using an image reversal electron beam lithography process. Corresponding micromagnetic calculations, modeling the defects within the disks as holes, give reasonable agreement between experimental and simulated pinning and depinning field values.
Phase transformation in finite-size ferroelectrics is of fundamental relevance for understanding collective behaviors and balance of competing interactions in low-dimensional systems. We report a first-principles effective Hamiltonian study of vortex-to-polarization transformation in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles, caused by homogeneous electric fields normal to the vortex plane. The transformation is shown to (1) follow an unusual {\it macroscopic} path that is symmetry non-conforming and characterized by the occurrence of a previously unknown structure as the bridging phase; (2)…
It is well known that azimuthal spin wave modes of magnetic vortex state in permalloy nanodisks have circular symmetry. Intuitively, magnetic materials having magnetocrystalline anisotropy is not compatible with the circular symmetry of the azimuthal modes. In this article, however, we report cubic azimuthal modes in heterogeneous nanodisks consisting of a permalloy core and a Fe shell. The fourfold symmetry of azimuthal modes is due to the exchange, and magneto-static, interactions between the permalloy core and the Fe shell. In comparison to results of circular azimuthal mode, the vortex swi…
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…
We investigate the interaction between spherical magnetic nanoparticles which present either a single domain or a vortex structure. First the magnetic structure of a uniaxial soft sphere is revisited, and then the interaction energy is calculated from a micromagnetic simulation. In the vortex regime the orientation of the vortex relative to the easy axis depends on both the particle size and the anisotropy constant. We show that the leading term of the interaction is the dipolar interaction energy between the magnetic moments. For particles presenting a vortex structure, we show that the polar…
Three-dimensional linear spin-wave eigenmodes of a Permalloy disk having finite thickness are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The eigenmodes found in the simulations are interpreted as linear superpositions (hybridizations) of 'approximate' three-dimensional eigenmodes, which are the fundamental gyromode $G_0$, the spin-wave modes and the higher-order gyromodes $G_N$ (flexure modes), the thickness dependence of which is represented by perpendicular standing spin waves. This hybridization leads to new and surprising dependencies of the mode fr…
We present an ultrafast route for a controlled, toggle switching of magnetic vortex cores with ultrashort unipolar magnetic field pulses. The switching process is found to be largely insensitive to extrinsic parameters, like sample size and shape, and it is faster than any field-driven magnetization reversal process previously known from micromagnetic theory. Micromagnetic simulations demonstrate that the vortex core reversal is mediated by a rapid sequence of vortex-antivortex pair-creation and annihilation sub-processes. Specific combinations of field pulse strength and duration are required…
To verify the exact underlying mechanism of ultrafast vortex-core reversal as well as the vortex state stability we conducted numerical calculations of the dynamic evolution of magnetic vortices in Permalloy cylindrical nanodots under an oscillating in-plane magnetic field over a wide range of the frequency and amplitude. The calculated results reveal different kinds of the non-trivial dynamic responses of vortices to the driving external field. In particular, the results offer insight into the 10 ps scale underlying physics of the ulrafast vortex-core reversals driven by small amplitude (~10 …
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…
The interaction between spherical magnetic nanoparticles is investigated from micromagnetic simulations and ananlysed in terms of the leading dipolar interaction energy between magnetic dipoles. We focus mainly on the case where the particles present a vortex structure. In a first step the local magnetic structure in the isolated particle is revisited. For particles bearing a uniaxial magnetocrystaline anisotropy, it is shown that the vortex core orientation relative to the easy axis depends on both the particle size and the anisotropy constant. When the particles magnetization present a vorte…
Using first-principles based effective Hamiltonian and finite temperature Monte Carlo simulations we investigate cooperative responses, as well as microscopic mechanism for vortex switching, in zero-dimensional Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles under curled electric fields. We find that the generally accepted domain coexistence mechanism is not valid for toroid switching. Instead dipoles are shown to display unusual collective behaviors by forming a new vortex with perpendicular (but not opposite) toroid moment. The strong correlation between the new and original vortices is revealed…
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 have characterized a new Magnetic Force Microscopy (MFM) probe based on an iron filled carbon nanotube (FeCNT) using MFM imaging on permalloy (Py) disks saturated in a high magnetic field perpendicular to the disk plane. The experimental data are accurately modeled by describing the FeCNT probe as having a single magnetic monopole at its tip whose effective magnetic charge is determined by the diameter of the iron wire enclosed in the carbon nanotube and its saturation magnetization 4 πM_s ~ 2.2 x 10^4 G. A magnetic monopole probe enables quantitative measurements of the magnetic field grad…
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.
The antivortex is a fundamental magnetization structure which is the topological counterpart of the well-known magnetic vortex. We study here the ultrafast dynamic behavior of an isolated antivortex in a patterned Permalloy thin-film element. Using micromagnetic simulations we predict that the antivortex response to an ultrashort external field pulse is characterized by the production of a new antivortex as well as of a temporary vortex, followed by an annihilation process. These processes are complementary to the recently reported response of a vortex and, like for the vortex, lead to the rev…
The magnetoresistivity and critical current density of well characterized Si-nanoparticle doped and undoped Cu-sheathed MgB$_{2}$ tapes have been measured at temperatures $T\geq 28$ K in magnetic fields $B\leq 0.9$ T. The irreversibility line $B_{irr}(T)$ for doped tape shows a stepwise variation with a kink around 0.3 T. Such $B_{irr}(T)$ variation is typical for high-temperature superconductors with columnar defects (a kink occurs near the matching field $% B_ϕ$) and is very different from a smooth $B_{irr}(T)$ variation in undoped MgB$_{2}$ samples. The microstructure studies of nanoparticl…
Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The as…
Reduced vortex descriptors linking polycrystallinity in magnetic nanoparticles with polarized magnetic small-angle neutron scattering
Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；Center for Free-Electron Laser Science（自由电子激光科学中心）；Ghent University（根特大学）；University of Luxembourg（卢森堡大学）；Institute for Advanced Studies, University of Luxembourg（卢森堡大学高等研究院）
In the framework of the Landau-Ginzburg-Devonshire approach coupled with electrostatic equations, we performed finite element modeling of the polarization behavior in a ferroelectric barium titanate core covered with a tunable paraelectric strontium titanate shell placed in a polymer or liquid medium. A stable two-dimensional vortex is formed in the core after a zero-field relaxation of an initial random or poly-domain distribution of the polarization, where the vortex axis is directed along one of the core crystallographic axes. Subsequently, sinusoidal pulses of a homogeneous electric field …
We report on a study of the dynamics of a magnetic antivortex in a submicron, asteroid shaped, permalloy ferromagnet using micromagnetic simulations. As with vortex states in disk and square geometries, a gyrotropic mode was found in which a shifted antivortex core orbits about the center of the asteroid. Pulsed magnetic fields were used to generate azimuthal or radial spin wave modes, depending on the field orientation. The degeneracy of low frequency azimuthal mode frequencies is lifted by gyrotropic motion of the antivortex core, and restored by inserting a hole in the center of the particl…
The micromagnetic distribution in a dielectric nanoparticle is theoretically considered. It is shown that the existence of inhomogeneous magnetoelectric interaction in magnetic dielectrics provides the possibility to stabilize the vortex and antivortex state. The estimation of the critical voltage necessary for vortex/antivortex nucleation in bismuth ferrite and iron garnet nanoparticles yields a value of +/-150 V. This system can be considered as electrically switchable two state-logic magnetic element.
Magnetic vortex gyration in a 500 nm wide, 50 nm thick Permalloy square platelet was investigated using time-resolved scanning transmission x-ray microscopy and micromagnetic simulations. The response of the vortex core on an in-plane oscillating magnetic field was studied as a function of the excitation frequency and amplitude. Non-linear behavior was observed in the form of a redshift of the gyrotropic resonance. I.e., when the excitation amplitude was increased, the resonance frequency was found to decrease. The nonlinearity is in agreement with extensive micromagnetic simulations. This wor…
Nano-scale visualization of magnetic vortices in metal nanoparticles
Institute of Engineering Innovation, School of Engineering, The University of Tokyo（东京大学工学部工程创新研究所）；JEOL Ltd.（日本电子株式会社）；Nanostructures Research Laboratory, Japan Fine Ceramics Center（日本先进陶瓷中心纳米结构研究实验室）；WPI Research Center, Advanced Institute for Materials Research, Tohoku University（东北大学材料研究高等机构WPI研究中心）；Quantum-Phase Electronics Center (QPEC), The University of Tokyo（东京大学量子相电子中心）
Understanding the fundamental dynamics of topological vortex and antivortex naturally formed in micro/nanoscale ferromagnetic building blocks under external perturbations is crucial to magnetic vortex based information processing and spintronic devices. All previous studies have focused on magnetic vortex-core switching via external magnetic fields, spin-polarized currents, or spin waves, which have largely prohibited the investigation of novel spin configurations that could emerge from the ground states in ferromagnetic disks and their underlying dynamics. Here, we report in situ visualizatio…
Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic spherical inclusions using large-scale numerical simulations of time-dependent Ginzburg-Landau equations. We found the size and density of particles for which the highest critical current is realized in a fixed magnetic field. For each particle size and magnetic field, the critical current reaches a maximum value at a certain particle density, which typically corre…
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…
Time-resolved X-ray microscopy is used to image the influence of alternating high-density currents on the magnetization dynamics of ferromagnetic vortices. Spin-torque induced vortex gyration is observed in micrometer-sized permalloy squares. The phases of the gyration in structures with different chirality are compared to an analytical model and micromagnetic simulations, considering both alternating spinpolarized currents and the current's Oersted field. In our case the driving force due to spin-transfer torque is about 70% of the total excitation while the remainder originates from the curr…
Magnetic vortex is topologically nontrivial and commonly found in ferromagnetic nanodisks. So far, three classes spin-wave eigenmodes, i.e., gyrotropic, azimuthal and radial modes, have been identified in ferromagnetic nanodisks. Here, using micromagnetic simulation and analytical calculation, we reveal twisted spin-wave modes in a thick permalloy (Ni0.8Fe0.2) nanodisk. The twisted spin-waves carry topological charges, which sign depends on the core polarity of the magnetic vortex in the nanodisk. By applying rotating magnetic fields at one end of the sample, we observe continuous generation o…
Within the framework of the Landau-Lifshitz-Gilbert equation, using permalloy parameters, we study the statics and dynamics of flat circular magnetic nano-structures with an in-plane magnetic vortex configuration, putting particular emphasis on the (planar) vorticity of the magnetic state and on the (perpendicular) polarisation of the vortex center (which may be shifted with respect to the center of the circle). These binary degrees of freedom can in principle be used to manipulate two independent bits of information. Studying switching processes induced by in-plane and out-of plane field puls…
A detailed investigation of the scaling relations recently proposed by [J. d'Albuquerque e Castro, D. Altbir, J. C. Retamal, and P. Vargas, Phys. Rev. Lett. 88, 237202 (2002)] to study the magnetic properties of nanoparticles is presented. Analytical expressions for the total energy of three characteristic internal configurations of the particles are obtained, in terms of which the behavior of the magnetic phase diagram for those particles upon scaling of the exchange interaction is discussed. The exponent $η$ in scaling relations is shown to be dependent on the geometry of the vortex core, an…
Confinement alters the energy landscape of nanoscale magnets, leading to the appearance of unusual magnetic states, such as vortices, for example. Many basic questions concerning dynamical and interaction effects remain unanswered, and nanomagnets are convenient model systems for studying these fundamental physical phenomena. A single vortex in restricted geometry, also known as a non-localized soliton, possesses a characteristic translational excitation mode that corresponds to spiral-like motion of the vortex core around its equilibrium position. Here, we investigate, by a microwave reflecti…
We investigate the magnetization dynamics in circular Permalloy dots with spatially separated magnetic vortices interconnected by domain walls (double vortex state). We identify a novel type of quasi one-dimensional (1D) localised spin wave modes confined along domain walls, connecting each of two vortex cores with two edge half-antivortices. Variation of the mode eigenfrequencies with the dot size is in quantitative agreement with the developed model, which considers a dipolar origin of the localized 1D spin waves or so-called Winterś magnons [J.M. Winter, Phys.Rev. 124, 452 (1961)]. These sp…
Ultrasonic irradiation of magnesium diboride slurries in decalin produces material with significant inter-grain fusion. Sonication in the presence of Fe(CO)5 produces magnetic Fe2O3 nanoparticles embedded in the MgB2 bulk. The resulting superconductor-ferromagnet composite exhibits considerable enhancement of the magnetic hysteresis, which implies an increase of vortex pinning strength due to embedded magnetic nanoparticles.
Topological magnetic textures are of great interest in various scientific and technological fields. To allow for precise control of nanoscale magnetism, it is of great importance to understand the role of intrinsic defects in the host material. Here, we use conventional and time-resolved Lorentz microscopy to study the effect of grain size in polycrystalline permalloy films on the pinning and gyration orbits of vortex cores inside magnetic nanoislands. To assess static pinning, we use in-plane magnetic fields to shift the core across the island while recording its position. This enables us to …
Signature of surface anisotropy in the spin-flip neutron scattering cross section of spherical nanoparticles: atomistic simulations and analytical theory
We studied the temperature dependence of the magnetization reversal in individual submicron permalloy disks with micro-Hall and bend-resistance magnetometry. The nucleation field exhibits a nonmonotonic dependence with positive and negative slopes at low and high temperatures, respectively, while the annihilation field monotonically decreases with increasing temperature, but with distinctly different slopes at low and high temperatures. Our analysis suggests that at low temperatures vortex nucleation and annihilation proceeds via thermal activation over an energy barrier, while at high tempera…
In this paper we have tried to understand the precise nature of magnetism in ZnO nanoparticles. Cooling field dependence of magnetic hysteresis and coercive field was observed for high temperature annealed sample indicating cooperative magnetic correlation and ordering within the agglomerated nanograins. The increasing induced internal magnetic field along the direction of external field for the high temperature annealed sample has been fitted with the modified Weiss-Brillouin model indicating emergence of long range intergrain interaction among the superparamagnetic grains. We propose a simpl…
Vortex magnetic structure in artificial honeycomb lattice provides a unique platform to explore emergent properties due to the additional Berry phase curvature imparted by chiral magnetization to circulating electrons via direct interaction. We argue that while the perpendicularly-aligned magnetic component leads to the quantized flux of monopole at the center of the Berry sphere, the in-plane vortex circulation of magnetization gives rise to unexpected non-trivial topological Berry phase due to the gauge field transformation. The unprecedented effect signifies the importance of vector potenti…
We have investigated, by the Monte Carlo simulation, spin systems which represent moments of arrayed magnetic nanoparticles interacting with each other only by the dipole-dipole interaction. In the present paper we aim the understanding of finite size effects on the magnetic nanoparticles arrayed in hexagonal columns cut out from the close-packing structures or from those with uniaxial compression. In columns with the genuine close-packing structures, we observe a single vortex state which is also observed previously in finite 2-dimensional systems. On the other hand in the system with the int…
The ability of type-II superconductors to carry large amounts of current at high magnetic fields is a key requirement for future design innovations in high-field magnets for accelerators and compact fusion reactors and largely depends on the vortex pinning landscape comprised of material defects. The complex interaction of vortices with defects that can be grown chemically, e.g., self-assembled nanoparticles and nanorods, or introduced by post-synthesis particle irradiation precludes a priori prediction of the critical current and can result in highly non-trivial effects on the critical curren…
