Stable Vortex State Research Articles

Artificial Neuron Based on the Bloch-Point Domain Wall in Ferromagnetic Nanowires.

Nanomagnetism and spintronics are currently active areas of research, with one of the main goals being the creation of low-energy-consuming magnetic memories based on nanomagnet switching. These types of devices could also be implemented in neuromorphic computing by crafting artificial neurons (ANs) that emulate the characteristics of biological neurons through the implementation of neuron models such as the widely used leaky integrate-and-fire (LIF) with a refractory period. In this study, we have carried out numerical simulations of a 120 nm diameter, 250 nm length ferromagnetic nanowire (NW) with the aim of exploring the design of an artificial neuron based on the creation and destruction of a Bloch-point domain wall. To replicate signal integration, we applied pulsed trains of spin currents to the opposite faces of the ferromagnetic NW. These pulsed currents (previously studied only in the continuous form) are responsible for inducing transitions between the stable single vortex (SV) state and the metastable Bloch point domain wall (BP-DW) state. To ensure the system exhibits leak and refractory properties, the NW was placed in a homogeneous magnetic field of the order of mT in the axial direction. The suggested configuration fulfills the requirements and characteristics of a biological neuron, potentially leading to the future creation of artificial neural networks (ANNs) based on reversible changes in the topology of magnetic NWs.

Magnetization reversal and stability of vortex state in convex shaped cylindrical nanodisks

Cylindrical nanodisks typically exhibit in-plane magnetization reversal comprising of nucleation and propagation of a vortex closure state. Present work investigates the magnetization reversal process in a cylindrical disk of radius ranging from 20 nm to 100 nm in which the flat surfaces at top and bottom are modified to convex shaped surfaces. It is found that the nucleation of vortex state no longer occurs as a result of this surface modification. Instead, a buckled magnetization state is nucleated which transforms to reverse buckled state yielding a square hysteresis loop. However, the out-of-plane hysteresis loop exhibits a vortex state at remanence. Analytical calculation of total free energy of both vortex as well as buckled state and the comparison thereof shows that the vortex state is ground state if radius of nanodisk is above 60 nm . Below this critical radius, buckled state is the ground state. But the non-appearance of vortex state at remanence in in-plane hysteresis loop of all of the nanodisks indicates a presence of energy barrier between vortex and buckled state. Height of the energy barrier is estimated using nudged elastic band method (NEBM) in all cases which proves that the energy barrier for vortex state weakens and the barrier for buckled state intensifies with the reduction of nanodisk size. At the critical radius of 60 nm , crossover of the two barrier heights occurs. Eventually, at the radius of 30 nm , the vortex state becomes totally unstable which can be toppled to buckled state with the slightest of perturbation.

Geometric frustration in polygons of polariton condensates creating vortices of varying topological charge

Vorticity is a key ingredient to a broad variety of fluid phenomena, and its quantised version is considered to be the hallmark of superfluidity. Circulating flows that correspond to vortices of a large topological charge, termed giant vortices, are notoriously difficult to realise and even when externally imprinted, they are unstable, breaking into many vortices of a single charge. In spite of many theoretical proposals on the formation and stabilisation of giant vortices in ultra-cold atomic Bose-Einstein condensates and other superfluid systems, their experimental realisation remains elusive. Polariton condensates stand out from other superfluid systems due to their particularly strong interparticle interactions combined with their non-equilibrium nature, and as such provide an alternative testbed for the study of vortices. Here, we non-resonantly excite an odd number of polariton condensates at the vertices of a regular polygon and we observe the formation of a stable discrete vortex state with a large topological charge as a consequence of antibonding frustration between nearest neighbouring condensates.

A new form of liquid matter: Quantum droplets

This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) self-trapped states in Bose-Einstein condensates (BECs), which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee-Huang-Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D → 3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect.

Lower Critical Field of Layered Organic Superconductor with Asymmetrical Donor κ-(MDT-TTF)<sub>2</sub>AuI<sub>2</sub>

We report magnetization measurement in the superconducting state of a type-II organic layered superconductor with asymmetrical donor k-(MDT-TTF)2AuI2. The demagnetization factor of a plate-like shape of the single crystal has been taken into account for the measurement by applying an external field perpendicular to the conducting plane. The superconducting transition temperature TC is determined to be 4.7 K through the detection of demagnetization signal. The lower critical field is 10.5±1.4 G. This result implies that the stable vortex state of k-(MDT-TTF)2AuI2 can be reached at the applied magnetic field above 105 Oe

Quantized vortices in spinor Bose–Einstein condensates with time–space modulated interactions and stability analysis**Project supported by the Beijing Natural Science Foundation, China (Grand No. 1182009) and the National Natural Science Foundation of China (Grant No. 11471182).

The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex solutions of the spinor BECs with spatiotemporally modulated interactions are worked out by similarity transformation. Theoretical analysis and numerical simulation of vortex states are demonstrated. Stable vortex states are obtained by adjusting the frequency of the external potential and the spatiotemporally modulated interaction.

Topological spinor vortex matter on spherical surface induced by non-Abelian spin-orbital-angular-momentum coupling

We propose a scheme to implement non-Abelian spin-orbital-angular-momentum (SOAM) coupling in spinor Bose–Einstein condensates using magnetic gradient coupling. For a spherical surface trap addressable using high-order Hermite–Gaussian beams, we show that this system supports various degenerate ground states carrying different total angular momenta J, and the degeneracy can be tuned by changing the strength of SOAM coupling. For spinor condensates with hyperfine spin F = 1, the system supports various meta-ferromagnetic phases and meta-polar states always described by quantized total mean angular momentum in case of weak interactions. Polar states with Z2 symmetry and Thomson lattices formed by defects of spin vortices are also discussed. The system can be used to prepare various stable spin vortex states with nontrivial topology, and serve as a platform to investigate strong-correlated physics of neutral atoms with tunable ground-state degeneracy.

Skyrmions and composite vortex states in three-component Bose–Einstein condensates with spin–orbit coupling

Stable and metastable vortex states in two-dimensional three-component Bose–Einstein condensates are studied in the presence of spin–orbit coupling. The ground states exhibit two skyrmion structures which respectively correspond to the d-skyrmion in antiferromagnetic or the F-skyrmion in ferromagnetic condensates. The half skyrmion and full skyrmion can be controlled by changing the strength of the spin–orbit coupling. We also find a stable composite vortex state which is associated to mixing of the ferromagnetic and antiferromagnetic manifolds.

Vortex and double-vortex nucleation during magnetization reversal in Fe nanodots of different dimensions

Abstract Magnetic nanodots are of high technological importance in diverse storage and spintronics applications, especially in bit patterned media. Magnetization reversal in such nanodots typically occurs either by coherent rotation of the magnetization or along a vortex state. Other mechanisms of magnetization reversal are scarcely described in the literature. Understanding and predicting the magnetization reversal processes, however, is of utmost importance due to the varying stray fields in the different states under evolution, influencing neighboring nanodots in an array or matrix-like structure. Besides, the stability of vortex states against magnetic field changes – which corresponds to typically broad field ranges with reversible modifications of the magnetic state – influences the robustness of magnetically stored information as well as the necessary external fields for writing new information. Here we report on micromagnetic simulations on nanodots with 10 different, representative diameters and 10 dot thicknesses, respectively, giving rise to 8 possible magnetization reversal processes and suggesting the preconditions for the nucleation and propagation of one or two vortices in cylindrical iron disks. We show the impact of the dimensions and aspect ratios on all phases of magnetization reversal. This study results in a phase diagram of the different magnetization reversal processes.

Broadband optomechanical transduction of nanomagnetic spin modes

The stable vortex state that occurs in micron-scale magnetic disks is one of the most interesting and potentially useful phenomena in nanomagnetism. A variety of tools have been applied to study the vortex state and collective spin excitations corresponding to harmonic motion of the vortex, but to-date, these tools either have measured strongly driven vortex resonances or have been unable to simultaneously measure static properties such as the magnetization. Here, we show that by combining the sensitivity of cavity optomechanics with the technique of torque-mixing magnetic resonance spectroscopy, we are able to measure the magnetization, in-plane susceptibility, and spin resonances of individual vortices in the low-drive limit. These measurements demonstrate the complex behavior of the vortex as it moves through the pinning landscape of the disk. Furthermore, we observe gyrotropic resonances as high as 1.1 GHz, suggesting the use of engineered defects for applications such as microwave-to-optical wavelength conversion.

Origin and Manipulation of Stable Vortex Ground States in Permalloy Nanotubes.

We present a detailed study on the static magnetic properties of individual permalloy nanotubes (NTs) with hexagonal cross-sections. Anisotropic magnetoresistance (AMR) measurements and scanning transmission X-ray microscopy (STXM) are used to investigate their magnetic ground states and its stability. We find that the magnetization in zero applied magnetic field is in a very stable vortex state. Its origin is attributed to a strong growth-induced anisotropy with easy axis perpendicular to the long axis of the tubes. AMR measurements of individual NTs in combination with micromagnetic simulations allow the determination of the magnitude of the growth-induced anisotropy for different types of NT coatings. We show that the strength of the anisotropy can be controlled by introducing a buffer layer underneath the magnetic layer. The magnetic ground states depend on the external magnetic field history and are directly imaged using STXM. Stable vortex domains can be introduced by external magnetic fields and can be erased by radio-frequency magnetic fields applied at the center of the tubes via a strip line antenna.

Elliptical vortex necklaces in Mathieu lattices

We demonstrate unusual kinds of discrete vortex beams, elliptical necklaces, realized by Mathieu photonic lattices. Varying the order of the Mathieu lattices and their ellipticity, we can control the shape and size of such necklaces. Besides stable vortex states, we observe oscillatory dipole states or dynamical instabilities and study their orbital angular momentum. Dynamical instabilities occur for higher beam power and higher-order vortices. Also the decay of higher-order phase singularities and their separation is observed in dependence on the ellipticity.

The control of magnetic vortex state in rectangular nanomagnet

We study the magnetic vortex states in rectangular nanomagnet with aspect ratio close to two by micro-magnetic simulations and experiments comparatively, and propose a simple way to manipulate both the chirality and polarity independently by tuning the direction of the in-plane magnetic field. There are always two vortices which have opposite chirality with Neel type wall and identical polarity for the rectangular nanomagnet with aspect ratio close to two. Four stable vortex states can be genetated from the uniformly magnetized state by in-plane magnetic field, and specific vortex states depend on the direction of the initial magnetization. The phenomenont of the formation of vortex states was explained based on the vortex dynamics. Also the reliability of proposed method was confirmed by domain structure using magnetic force microscopy (MFM) in experiment.

Strain-mediated magnetoelectric effect for the electric-field control of magnetic states in nanomagnets

Electric-field control of magnetism without electric currents potentially revolutionizes spintronics toward 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 a 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 electric field can drive the single-domain nanomagnet into an equilibrium vortex state. The nanomagnet remains in the vortex state even after removing the electric field or applying a reverse electric field, i.e., the vortex state is extremely stable and nonvolatile. Only by utilizing the precessional magnetization dynamics, the 180 $$^\circ $$ magnetization switching is possible in small-sized nanomagnets which are free of the stable vortex state. Electric-field pulses can realize the deterministic 180 $$^\circ $$ switching if the electric-field magnitude, pulse width, and ramp time are carefully designed. The minimum switching time is found to be less than 10 ns. These results provide useful information for the design of low-power, reliable, and fast electric-field-controlled spintronics.

Magnetic field dependence of most stable vortex states in the chiral helimagnet / superconductor bilayer system

We have studied vortex states in chiral helimagnet / superconductor bilayer systems. An effect of a chiral helimagnet on a superconductor is taken as an external magnetic field. Solving the Ginzburg-Landau equations, we obtain various vortex configurations. In order to find a stable vortex state, we compare the Ginzburg-Landau free energies of these states. Under the large magnetic field from the chiral helimagnet, the state in which vortices appear in a row becomes more stable.

Dynamics of supersolid crystals in microcavity polariton condensates

The possible existence of quantum crystals phase of polariton condensate in two-dimensional microcavity polariton was studied by using mean-field method for bosons at zero temperature. In this study, we observe the supersolid crystallized (hexagonal, square) and a quantized winding number of the phase in a regime of strong- field interaction in rotating exciton–polariton condensates. First, the ground state of the condensate was found; and the solution was further extended for dynamics state to reach the equilibrium steady-state as well as their density profile and energy diagrams. The supersolid crystal is the result of the considerable deviation induced by the interaction of polaritons of both ground and dynamic states of a dressed dipolar Bose–Einstein condensate. Here, the researchers demonstrated the formation of a hexagonal lattice in the nonlinear regime at high polariton-density where polariton–polariton interactions dominate the behavior of the system. It was identified that stability regimes for ground state increases as the polariton–polariton interaction strength increases. The phase diagram for the stable vortex state will be useful for conducting experimental and theoretical studies on rotating dipolar quantum gases and many other exotic systems.

Pinning of scroll waves to flat and highly branched unexcitable heterogeneities.

System heterogeneities such as organelles, cells, and anatomical features strongly affect nonlinear wave patterns in biological systems. These effects are more readily studied in otherwise homogeneous chemical reactions that allow the introduction of tailored structures. Following this approach, we investigate the dynamics of three-dimensional excitation vortices pinned to inert sheets with circular holes arranged on a hexagonal lattice. Experiments with the Belousov-Zhabotinsky reaction and numerical simulations of an excitable reaction-diffusion model reveal vortex pinning that circumvents the rapid collapse of free vortex rings. The pinned scroll waves are affected by the topological mismatch between their looplike rotation backbone and the branched pinning structure. Depending on the initial condition, a multitude of stable vortex states exist, all of which obey topological constraints, suggesting spinlike states for the involved obstacle holes.

Vortex states in a superconductor under a helical magnetic field

We have studied vortex states in a chiral helimagnet / superconductor bilayer system numerically. We consider a two-dimensional superconductor subsystem. An effect of a chiral helimagnet on a superconductor is taken as a magnetic field, which oscillates spatially. Solving the Ginzburg-Landau equations, we obtain various vortex states. Comparing free energies, we find the most stable vortex states under only the oscillating magnetic field HCHM and under the HCHM and the homogeneous applied magnetic field Happl.

Three-dimensional vortex structures in a rotating dipolar Bose–Einstein condensate

We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio (λ) and dipole–dipole interaction strength (D) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.

Single crystalline cylindrical nanowires - toward dense 3D arrays of magnetic vortices.

Magnetic vortex-based media have recently been proposed for several applications of nanotechnology; however, because lithography is typically used for their preparation, their low-cost, large-scale fabrication is a challenge. One solution may be to use arrays of densely packed cobalt nanowires that have been efficiently fabricated by electrodeposition. In this work, we present this type of nanoscale magnetic structures that can hold multiple stable magnetic vortex domains at remanence with different chiralities. The stable vortex state is observed in arrays of monocrystalline cobalt nanowires with diameters as small as 45 nm and lengths longer than 200 nm with vanishing magnetic cross talk between closely packed neighboring wires in the array. Lorentz microscopy, electron holography and magnetic force microscopy, supported by micromagnetic simulations, show that the structure of the vortex state can be adjusted by varying the aspect ratio of the nanowires. The data we present here introduce a route toward the concept of 3-dimensional vortex-based magnetic memories.