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 circularly rotating magnetic field were calculated, which offer practical guidance for implementing nanodots in vortex states into future solid-state information-storage devices.
The effect of dipolar interactions among cylindrical nanodots, with a vortex-core magnetic configuration, is analyzed by means of analytical calculations. The cylinders are placed in a N x N square array in two configurations - core oriented parallel to each other and with antiparallel alignment between nearest neighbors. Results comprise the variation in the core radius with the number of interacting dots, the distance between them and dot height. The dipolar interdot coupling leads to a decrease (increase) of the core radius for parallel (antiparallel) arrays.
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 …
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…
Magnetic vortex dynamics in lithographically prepared nanodots is currently a subject of intensive research, particularly after recent demonstration that the vortex polarity can be controlled by in-plane magnetic field. This has stimulated the proposals of non-volatile vortex magnetic random access memories. In this work, we demonstrate that triangular nanodots offer a real alternative where vortex chirality, in addition to polarity, can be controlled. In the static regime, we show that vortex chirality can be tailored by applying in-plane magnetic field, which is experimentally imaged by mean…
Sub-100 nm nanomagnets not only are technologically important, but also exhibit complex magnetization reversal behaviors as their dimensions are comparable to typical magnetic domain wall widths. Here we capture magnetic "fingerprints" of 1 billion Fe nanodots as they undergo a single domain to vortex state transition, using a first-order reversal curve (FORC) method. As the nanodot size increases from 52 nm to 67 nm, the FORC diagrams reveal striking differences, despite only subtle changes in their major hysteresis loops. The 52 nm nanodots exhibit single domain behavior and the coercivity d…
We have explored the electric field controlled magnetization in the nanodot CoFe2O4/SrRuO3/PMN-PT heterostructures. Ordered ferromagnetic CFO nanodots (~300 nm lateral dimension) are developed on the PMN-PT substrate (ferroelectric as well as piezoelectric) using a nanostencil-mask pattering method during pulsed laser deposition. The nanostructures reveal electric field induced magnetization reversal in the single domain CFO nanodots through transfer of piezostrains from the piezoelectric PMN-PT substrate to the CFO. Further, electric field modulated spin structure of CFO nanomagnets is analys…
Controlling the polarization switching in the ferroelectric nanocrystals, nanowires and nanodots has an inherent specificity related to the emergence of depolarization field that is associated with the spontaneous polarization. This field splits the finite-size ferroelectric sample into polarization domains. Here, based on 3D numerical simulations, we study the formation of 180$^{\circ }$ polarization domains in a nanoplatelet, made of uniaxial ferroelectric material, and show that in addition to the polarized monodomain state, the multidomain structures, notably of stripe and cylindrical shap…
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…
New results are reported of the computer simulations on the magnetic behaviour of magnetic arrays of nanoscopic dots, placed in cells of the square lattice. We show that the remanence magnetization $M_r$ decreases with the array size. For arrays 50x50, we investigate also the stability of the magnetic structure of an array in an oscillating magnetic field. The damage spreading technique reveals that this stability increases with the standard deviation $σ$ of the switching field of individual elements of the array. On the other hand, $M_r$ decreases with $σ$. An optimalization of the system (la…
Power consumption is the main limitation in the development of new high performance random access memory for portable electronic devices. Magnetic RAM (MRAM) with CoFeB/MgO based magnetic tunnel junctions (MTJs) is a promising candidate for reducing the power consumption given its non-volatile nature while achieveing high performance. The dynamic properties and switching mechanisms of MTJs are critical to understanding device operation and to enable scaling of devices below 30 nm in diameter. Here we show that the magnetic reversal mechanism is incoherent and that the switching is thermally nu…
A micromagnetic numerical study of the precessional motion of the vortex and antivortex states in soft ferromagnetic circular nanodots is presented using Landau-Lifshitz-Gilbert dynamics. For sufficiently small dot thickness and diameter, the vortex state is metastable and spirals toward the center of the dot when its initial displacement is smaller than a critical value. Otherwise, the vortex spirals away from the center and eventually exits the dot which remains in a state of in-plane magnetization (ground state). In contrast, the antivortex is always unstable and performs damped precession …
The spin dynamics are calculated for a model system consisting of magnetically soft, layered nanomagnets, in which two ferromagnetic (F) cylindrical dots, each with a magnetic vortex ground state, are separated by a non-magnetic spacer (N). This permits a study of the effects of interlayer magnetostatic interactions on the vortex dynamics. The system was explored by applying the equations of motion for the vortex core positions. The restoring force was calculated taking into account the magnetostatic interactions assuming a realistic surface charge free spin distribution. For tri-layer F/N/F d…
Nanopatterned FePt nano-dots often exhibit low coercivity and a broad switching field distribution, which could arise due to edge damage during the patterning process causing a reduction in the $L1_{0}$ ordering required for a high magnetocrystalline anisotropy. Using an atomistic spin model, we study the magnetization reversal behavior of $L1_{0}$ FePt nanodots with soft magnetic edges. We show that reversal is initiated by nucleation for the whole range of edge widths studied. For narrow soft edges the individual nucleation events dominate reversal; for wider edges, multiple nucleation at th…
Asymmetric dots as a function of their geometry have been investigated using three-dimensional (3D) object oriented micromagnetic framework (OOMMF) code. The effect of shape asymmetry of the disk on coercivity and remanence is studied. Angular dependence of the remanence and coercivity is also addressed. Asymmetric dots are found to reverse their magnetization by nucleation and propagation of a vortex, when the field is applied parallel to the direction of asymmetry. However, complex reversal modes appear when the angle at which the external field is applied is varied, leading to a non monoton…
For a circular magnetic nanodot in a vortex ground state we study how the critical velocity $v_c$ of the vortex core reversal depends on the magnitude $H$ of a bias magnetic field applied perpendicularly to the dot plane. We find that, similarly to the case $H$ = 0, the critical velocity does not depend on the size of the dot. The critical velocity is dramatically reduced when the negative (i.e. opposite to the vortex core direction) bias field approaches the value, at which a \emph{static} core reversal takes place. A simple analytical model shows good agreement with our numerical result.
We report a new reversal mechanism of magnetic vortex cores in nanodot elements driven by out-of-plane currents, occurring through two coupled edge-solitons via dynamic transformations between magnetic solitons of different topological charges. This mechanism differs completely from the well known switching process mediated by the creation and annihilation of vortex-antivortex pairs in terms of the associated topological solitons, energies, and spin-wave emissions. Strongly localized out-of-plane gyrotropic fields induced by the fast motion of the two coupled edge-solitons enable a magnetizati…
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…
Field-induced switching of ferroelectric domains with a topological vortex configuration is studied by atomic imaging and electrical biasing in an electron microscope, revealing the role of topological defects on the topologically-guided change of domain-wall pairs in a hexagonal manganite.
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 …
We describe ferroelectric thin films with circular electrodes and develop a thermodynamic theory that explains previously mysterious experiments. It is found to be especially useful for restricted geometries such as microstructures for which boundary conditions are well known to play an important role in ferroelectric properties. We have explored a new switching mechanism, which consists of an inhomogeneous rotational motion of the polarization and leads to an extended vortex state. The vortex appearance exhibits characteristic properties of a first-order field-induced phase transition: three …
We experimentally demonstrate low-power-consumption vortex-core switching in magnetic nanodisks using tailored rotating magnetic fields that are produced with orthogonal and unipolar Gaussian-pulse currents. Optimal width of the orthogonal pulses and their time delay are found to be determined only by the angular eigenfrequency ω_D for a given vortex-state disk of its polarization p, such that σ = 1/ω_D and Δt = πp/2ω_D, as studied from analytical and micromagnetic numerical calculations. The estimated optimal pulse parameters are in good agreements with the experimentally found results. This …
We show experimental switching data on microscale capacitors of lead-zirconate-titanate (PZT), which reveal time-resolved domain behavior during switching on a 100-ns scale. For small circular capacitors, an unswitched domain remains in the center while complete switching is observed in square capacitors. The observed effect is attributed to the formation of vortex domain during polarization switching in circular capacitors. This dynamical behavior is modeled using the Landau-Liftshitz-Gilbert equations and found to be in detailed agreement with experiment. This simulation implies rotational m…
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…
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…
We fabricated a current-perpendicular-to-plane pseudo-spin-valve nanopillar comprising a thick and a thin Co rings with deep submicron lateral sizes. The dc current can effectively induce the flux-closure vortex states in the rings with desired chiralities. Abrupt transitions between the vortex states are also realized by the dc current and detected with the giant magnetoresistance effect. Both Oersted field and spin-transfer torque are found important to the magnetic transitions, but the former is dominant. They can be designed to cooperate with each other in the vortex-to-vortex transitions …
In our earlier work [Appl. Phys. Lett. 92, 022509 (2008)], we proposed nonvolatile vortex random access memory (VRAM) based on the energetically stable twofold ground state of vortex-core magnetizations as information carrier. Here we experimentally demonstrate reliable memory bit selection and low-power-consumption recording in a two-by-two vortex-state dot array. The bit selection and core switching is made by flowing currents along two orthogonal addressing electrode lines chosen among the other crossed electrodes. Tailored pulse-type rotating magnetic fields are used for efficiently switch…
We report on the switching of the magnetic vortex core in a Pac-man disk using a magnetic field pulse, investigated via micromagnetic simulations. The minimum core switching field is reduced by 72 % compared to that of a circular disk with the same diameter and thickness. However, the core switches irregularly with respect to both the field pulse amplitude and duration. This irregularity is induced by magnetization oscillations which arise due to excitation of the spin waves when the core annihilates. We show that the core switching can be controlled with the assist magnetic field and by chang…
In the micro- and nanoscale ferroelectric samples, the formation and the growth of domains are the usual stages of the polarization switching mechanism. By assuming the weak polarization anisotropy and by solving the Ginzburg-Landau-Khalatnikov equation we have explored an alternative mechanism which consists in ferroelectric switching induced by vortex formation. We have studied the polarization dynamics inside a ferroelectric circular capacitor where switching leads to formation of a metastable vortex state with a rotational motion of polarization. Our results are consistent with recent firs…
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…
In a ferromagnetic nanodisk, the magnetization tends to swirl around in the plane of the disk and can point either up or down at the center of this magnetic vortex. This binary state can be useful for information storage. It is demonstrated that a single nanosecond current pulse can switch the core polarity. This method also provides the precise control of the core direction, which constitutes fundamental technology for realizing a vortex core memory.
A magnetic vortex is a curling magnetic structure realized in a ferromagnetic disk, which is a promising candidate of a memory cell for future nonvolatile data storage devices. Thus, understanding of the stability and dynamical behaviour of the magnetic vortex is a major requirement for developing magnetic data storage technology. Since the experimental proof of the existence of a nanometre-scale core with out-of-plane magnetisation in the magnetic vortex, the dynamics of a vortex has been investigated intensively. However, the way to electrically control the core magnetisation, which is a key…
We investigate the influence of artificial defects (small holes) inserted into magnetic nanodisks on the vortex core dynamics. One and two holes (antidots) are considered. In general, the core falls into the hole but, in particular, we would like to remark an interesting phenomenon not yet observed, which is the vortex core switching induced by the vortex-hole interactions. It occurs for the case with only one hole and for very special conditions involving the hole size and position as well as the disk size. Any small deformation in the disk geometry such as the presence of a second antidot ch…
We report manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (of nominal dimensions ~ 340 nm x 270 nm x 12 nm) delineated on bulk 128° Y-cut lithium niobate with Surface Acoustic Waves (SAWs) launched from interdigitated electrodes. Isolated nanomagnets that are initially magnetized to a single domain state with magnetization pointing along the major axis of the ellipse are driven into a vortex state by surface acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong m…
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…
Electric-field control of magnetism without electric currents potentially revolutionizes spintronics towards ultralow power. Here by using mechanically coupled phase field simulations, we computationally demonstrate the application of the strain-mediated magnetoelectric effect for the electric-field control of magnetic states in heterostructure. In the model heterostructure constituted of the soft nanomagnet Co and the piezoelectric substrate PMN-PT, both the volatility of magnetic states and the magnetization switching dynamics excited by the electric field are explored. It is found that an e…
Magnetic vortices are characterized by the senses of in-plane magnetization chirality and by the polarity of the vortex core. The electrical control of vortex polarity and chirality is highly demanded not only for fundamental understanding on spin dynamics in nano-disks under different circumstances, but also for technological applications, such as magnetic non-volatile memories and spin torque oscillators for neuromorphic computing. Here we report a novel approach that enables one to electrically control both the vortex chirality and polarity with low energy consumption. Thorough micromagneti…
Perpendicular MgO-based Magnetic Tunnel Junctions are optimal candidates as building block of Spin Transfer Torque (STT) magnetoresistive memories. However, up to now, the only STT is not enough to achieve switching current density below 106 A/cm2. A recent work [Wang et al., Nature Mater., vol. 11, pp 64-68, Jan. 2012] has experimentally demonstrated the possibility to perform magnetization switching assisted by an electric-field at ultra-low current density. Theoretically, this switching has been studied by using a macrospin approach only. Here, we show a full micromagnetic study. We found t…
Symmetry classification of the magnetic vortices and skyrmions has been suggested. Relation between symmetry based predictions and direct calculation has been shown. It was shown, that electric dipole moment of the vortex is located inside the small vortex core. The antivortices and antiskyrmions do not carry the total core electric dipole induced by the flexomagnetoelectric interaction in the hexoctahedral cubic crystal. The volumetric bound electric charge is distributed around the core. Switching of the core electric dipole direction produces the switching of the core magnetization or vorte…
We investigate the vortex excitations induced by a spin-polarized current in a magnetic nanopillar by means of micromagnetic simulations and analytical calculations. Damped motion, stationary vortex rotation and the switching of the vortex core are successively observed for increasing values of the current. We demonstrate that even for small amplitude of the vortex motion, the analytical description based the classical Thiele approach can yield quantitatively and qualitatively unsound results. We suggest and validate a new analytical technique based on the calculation of the energy dissipation…
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…
Ferromagnetic rings exhibit many novel physical phenomena with promise for potential applications. Here, we focus on switching processes which are fundamental properties of magnetic systems and are especially crucial for data storage applications. A brief introduction on the advantages of ring geometries is presented, followed by a background survey of the model and methods to study nanomagnetic elements. The relevant magnetic states identified until now are discussed, with special emphasis given to vortex, onion, and twisted states. Such states are potential candidates for data storage applic…
The stability of the superconducting dissipationless and resistive states in single-crystalline NbSe2 nanobelts is characterized by transport measurements in an external magnetic field (H). Current-driven electrical measurements show voltage steps, indicating the nucleation of phase-slip structures. Well below the critical temperature, the position of the voltage steps exhibits a sharp, periodic dependence as a function of H. This phenomenon is discussed in the context of two possible mechanisms: the interference of the order parameter and the periodic rearrangement of the vortex lattice withi…
Micromagnetic sensors play a major role towards the miniaturization in the industrial society. The adoption of new and emerging sensor technologies like anisotropic magnetoresistance (AMR), giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR) sensors are mainly driven by their integrability and enhanced sensitivity. At the core of such sensors, a microstructured ferromagnetic thin film element transduces the magnetic signal. Such elements usually switch via multi-domain, C- or S-shaped magnetization states and, therefore, often exhibit an open non-linear hysteresis curve. Linearity…
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…
Transmission electron microscopy is one of the most powerful techniques to characterize nanoscale magnetic structures. In light of the importance of fast control schemes of magnetic states, time-resolved microscopy techniques are highly sought after in fundamental and applied research. Here, we implement time-resolved Lorentz imaging in combination with synchronous radio-frequency excitation using an ultrafast transmission electron microscope. As a model system, we examine the current-driven gyration of a vortex core in a 2 $\mathrmμ$m-sized magnetic nanoisland. We record the trajectory of the…
In this paper we propose a new method for the study and visualization of dynamic processes in magnetic nanostructures, and for the accurate calculation of rates for such processes. The method is illustrated for the case of switching of a grain of an exchange-coupled recording medium, which switches through domain wall nucleation and motion, but is generalizable to other rate processes such as vortex formation and annihilation. The method involves calculating the most probable (lowest energy) switching path and projecting the motion onto that path. The motion is conveniently visualized in a two…
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…
We present an experimental investigation of radial spin-wave modes in magnetic nano-disks with a vortex ground state. The spin-wave amplitude was measured using a frequency-resolved magneto optical network analyzer, allowing for high-resolution resonance curves to be recorded. It was found that with increasing excitation amplitude up to about 10 mT, the lowest-order mode behaves strongly non-linearly as the mode frequency redshifts and the resonance peak strongly deforms. This behavior was quantitatively reproduced by micromagnetic simulations. At higher excitation the spinwaves are transforme…
