Quantum error rejection and fault tolerant quantum communication
Quantum communication utilizes the quantum state as information carrier. The transmission of quantum states is therefore a precondition for various quantum communication protocols. Photons play a central role in quantum communication since they are fast, cheap, easy to control and interact weakly with the environment. However, the widely used polarization degree of freedom of photons is vulnerable to the noise during the transmission. In this article, we review two main methods to deal with the channel noise, i.e., the quantum error rejection scheme and fault tolerant quantum communication. To transmit an arbitrary single-photon state, Li and Deng proposed two faithful state transmission schemes only by resorting to passive linear optics. The success probability can be (2N+1-1)/2N+1 by introducing a wave splitter composed of N unbalance interferometers. Compared with other quantum error rejection schemes, these two scheme are practical both in maneuverability and resource consumption. They are not only suitable for single-photon pure state transmission but also able to be used for transmitting mixed state, which makes them useful for one-way quantum communication. The success probability of error rejection is usually less than 100% since some error cases are rejected. To realize complete fault tolerant quantum communication, decoherence free subspace can be used to encode quantum information. In 2008, Li et al. proposed two efficient quantum key distribution schemes over two different collective-noise channels. The noiseless subspaces are made up of two Bell states and the spatial degree of freedom is introduced to form two nonorthogonal bases. Although entangled states are employed, only single-photon measurements are required to read the information. Later, the scheme is generalized to an efficient one which transmits n-1 bits information via n Einstein-Podolsky-Rosen pairs and many fault tolerant quantum communication schemes were proposed. We compare the practicality of different anti-noise schemes based on maneuverability and resource consumption and a perspective of these two research directions is given in the last section.
Nanoscale magnetic field sensing and imaging based on nitrogen-vacancy center in diamond
Magnetic field measurement and imaging with nanometer resolution is a key tool in the study of magnetism. There have been several powerful techniques such as superconducting quantum interference device, hall sensor, electron microscopy, magnetic force microscopy and spin polarized scanning tunneling microscopy. However, they either have poor sensitivity or resolution, or need severe environment of cryogenic temperature or vacuum. The nitrogen-vacancy color center (NV center) in diamond, serving as a quantum magnetic sensor, has great advantages such as long decoherence time, atomic size, and ambient working conditions. The NV center consists of a substitutional nitrogen atom and an adjacent vacancy in diamond. Its electronic structure of ground state is a spin triplet. The spin state can be initialized to mS=0 state and read out by laser pulse, and coherently manipulated by microwave pulse. It is sensitive to the magnetic field by measuring the magnetic Zeeman splitting or quantum phase in quantum interferometer strategies. By using dynamical decoupling sequence to prolong the decoherence time, the sensitivities approach to nano tesla for a single NV center and pico tesla for the NV center ensemble, respectively. As a sensor with an atomic size, it reaches single-nuclear-spin sensitivity and sub-nanometer spatial resolution. Combining with scanning microscopy technology, it can accomplish high-sensitivity and high-resolution magnetic field imaging so that the stray field can be reconstructed quantitatively. The magnetic field is calculated from the two resonant frequencies by solving the Hamiltonian of NV center in order to obtain the value of stray field. Recently, this novel magnetic imaging technique has revealed the magnetization structures of many important objects in magnetism research. The polarity and chirality of magnetic vortex core are determined by imaging its stray field; laser induced domain wall hopping is observed quantitatively with a nanoscale resolution; non-linear antimagnetic order is imaged in real space by NV center. It was recently reported that magnetization of the magnetic skyrmion is imaged by NV center. The magnetization distribution is reconstructed from stray field imaging. With the topological number limited to one, the Néel type magnetization is uniquely determined. These results show that the magnetic imaging method has great advantages to resolve the emerging magnetic structure materials. The magnetic imaging technology based on the NV center will potentially become an important method to study magnetic materials under continuous development.
Overview and outlook of magnetic skyrmions
Magnetic skyrmions are topologically protected nano-scale spin textures. They normally exist in chiral magnets and magnetic thin films with broken inversion symmetry. The size of skyrmion ranges from 1 nm to several hundred nanometers, depending on the material parameters. The spins of skyrmion wrap around the unit sphere exactly once, thus facilitating the unit topological charge of a skyrmion. Due to their non-trivial topology, skyrmions exhibit exotic physics such as the topological Hall effect (THE) and the emergent electrodynamics. Skyrmions show particle-like dynamics and can be driven with ultra-low current density. Furthermore, they can be created, annihilated, manipulated and detected by all-electric methods, making skyrmion a promising candidate for next-generation information storage and processing technologies. On the other hand, combining skyrmions with superconductors and topological insulators may also lead to intriguing physics and applications such as the topological quantum computing. Over the past few years, the creation, annihilation and detection of skyrmion at room temperature have already been demonstrated, but the precise control of single skyrmion with size below 10 nm is still a challenge. In this paper, we first review the fundamental physics of skyrmion, from its topology to its emergent dynamics. Physical mechanisms of the Dzyaloshinskii-Moriya interaction, the emergent electrodynamics and the THE are discussed. Then the skyrmion material systems, including chiral magnets, magnetic thin films, artificial skyrmion systems, frustrated magnets, bi-skyrmion materials and antiskyrmion materials, are comprehensively summarized. The optimizations of materials and potential new skyrmion materials are also proposed for different material systems. Methods of creating, annihilating and detecting skyrmions, which also cover potential application methods other than electrical methods, are discussed from both theoretical and experimental point of view. The energy efficiencies and reliabilities of different creation and annihilation methods and the sensitivities of different detection methods are still unclear, these current bottlenecks and possible avenues towards skyrmion-based spintronics are described. Finally, we address some possible future directions of skyrmion research, such as the antiferromagnetic skyrmion and skyrmions in topological insulators, which may lead to the discovery of peculiar topological quantum physics and materials.
Topological Hall effect in ferromagnetic/non-ferromagnetic metals heterojunctions
In a magnetic system, the spin orbit coupling can combine with the exchange interaction to generate an anisotropic exchange interaction that favors a chiral arrangement of the magnetization. This is known as the Dzyaloshinskii-Moriya interaction (DMI). Contrary to the Heisenberg exchange interaction, which leads to collinear alignment of lattice spins, the form of DMI is therefore very often to cant the spins by a small angle. If DMI is strong enough to compete with the Heisenberg exchange interaction and the magnetic anisotropy, it can stabilize chiral domain wall structure such as skyrmion. When a conduction electron passes through a chiral domain wall, the spin of the conduction electron will experience a fictitious magnetic field (Berry curvature) in real space, which deflects the conduction electrons perpendicular to the current direction. Therefore, it will cause an additional contribution to the observed Hall signal that is termed topological Hall effect (THE). The THE has attracted much attention since it is a promising tool for probing magnetic skyrmions. Recent extensive experiments have focused on the the THE in the ferromagnetic/non-ferromagnetic metal heterojunctions due to the inherent tunability of magnetic interactions in two dimensions. We firstly review the THE in ferromagnetic multilayers, in which the domain wall energy with interfacial DMI can be written as σ=4√AK-πD, where Dis the effective DMI energy constant, A the exchange constant, K the anisotropy constant. For the most favorable chirality, it lowers the energy. The limit of this situation is when σ goes to zero, which defines the critical DMI energy constant Dc=4√AK/π. Therefore, the domain wall energy would be negative and the chiral domain walls should proliferate if D > Dc, and the methods that can modulate D and Dc to reduce σ have been explored. We have also reviewed the THE in MnGa/heavy metal bilayers. The largest THE signals have been found based on the MnGa films with smallest Dc, which correspondingly results in the smallest σ. The large topological portion of the Hall signal from the total Hall signal has been extracted in the whole temperature range from 5 to 300 K and the magnitude of fictitious magnetic field has been determined.
In situ electron holography of magnetic skyrmions in nanostructures
Understanding the correlations between magnetic skyrmions and the microstructural characteristics of the crystals that host skyrmions is a key issue for fundamental research and practical applications of novel type of magnetic materials. Magnetic skyrmion has received great attention due to its non-trivial topological properties and stability. Here we focus on two important points:1) dimensional confinement effects on magnetic skyrmions in magnetic nanostructures, specifically, the magnetic evolution, its related topological properties and energetic stability in confined nanostructured geometries; 2) effects of crystallographic defects on magnetic skyrmions, such as the pinning effect of magnetic skyrmion by crystal defects, and the effect of crystallographic-magnetic chirality reversal at crystal grain boundaries. For the study of dimensional effects on skyrmions in confined nanoscale geometries, we use state-of-the-art electron holography to directly image the morphology and nucleation of magnetic skyrmions in a wedge-shaped FeGe nanostripe that has a width in a range of 45-150 nm. Our experimental results reveal that geometrically-confined skyrmions are able to adopt a wide range of sizes and ellipticity in a nanostripe, which are not existent in thin films nor bulk materials and can be created from a helical magnetic state with a distorted edge twist in a simple and efficient manner. We further perform micromagnetic simulations to confirm our experimental results. The flexibility and ease of formation of geometrically confined magnetic skyrmions may help to optimize the design of skyrmion-based memory devices. For studying the effects of crystallographic defects on magnetic skyrmions, we use in situ Lorentz microscopy and off-axis electron holography to investigate the formation and characteristics of skyrmion lattice defects and their relationship to the underlying crystallographic structure of a B20 FeGe thin film. The measurements of spin configurations at grain boundaries reveal the crystallographic and magnetic chirality across adjacent grains, resulting in the formation of interface spin stripes at the grain boundaries. In the absence of material defects, our results show that skyrmion lattices possess dislocations and domain boundaries, in analogy to atomic crystals. Moreover, the distorted skyrmions can flexibly change their size and shape to accommodate local geometry, especially at sites of dislocations in the skyrmion lattice. These findings offer an insight into the elasticity of topologically protected skyrmions and their correlation with underlying material defects. Our electron holography results provide a quantitative determination of the fine skyrmionic spin textures in magnetic nanostructures. The resolved spin textures will be correlated with the material microstructures to provide important information about the relationship between the magnetic functions and the material microstructures. Our experiments also highlight the applicability of state-of-the-art electron holography for the study of complex spin textures in nanostructures.
Skyrmions in magnetic thin film heterostructures
Magnetic skyrmion is expected to function as an ideal information carrier for ultra-high density magnetic storage and logic functional device in the future due to its superior properties, such as topological protection, small size, and low driving current density for motion. In order to meet the basic requirements for writing and reading information in devices, one needs to be able to accurately generate, manipulate, and probe skyrmion at room temperature. Given that the history and latest developments of the skyrmion research will be reviewed comprehensively in other articles, in order to avoid repetition, in this article we briefly review a series of recent research advances we have made in magnetic multilayer materials in recent years, and discuss the advantages of relevant device applications and problems that need to be solved. They are included in three aspects as follows. 1) The room temperature skyrmion was observed in a wedge film Ta (5 nm)/Co20Fe60B20 (CoFeB) (1 nm)/Ta (t)/MgO (2 nm)/Ta (2 nm) by a polar magneto-optical Kerr microscope. Results showed that skyrmion can be created at room temperature by controlling the perpendicular magnetic anisotropy of magnetic thin film. In the following, we designed a thin film heterojunction containing an antiferromagnetic layer IrMn. The introduction of antiferromagnetic material can produce an exchange bias field in the magnetic layer, which can play the same role as an external magnetic field, making it possible to realize zero-field skyrmion. In this study, we have successfully observed a stable skyrmion at room temperature and zero magnetic field. 2) The spin-orbit torque generated by the current proved to be able to be used to manipulate the created skyrmion. In the fourth part of this review, we discuss the dynamic process of skyrmion driven by spin-orbit torque in IrMn/CoFeB heterojunctions, and the chirality of skyrmion can be deduced by the direction of its longitudinal motion driven by an applied current. Finally, a principle device based on the skyrmion is further fabricated. In this device, a set of binary data was recorded in the “track” in the presence and absence of skyrmion. Generating and manipulating numbers of skyrmions were realized by using a series of pulse currents with different amplitudes and widths. The detection of a skyrmion can be achieved by using a magnetic tunnel junction at the right end of the device. 3) The advantages of skyrmion as a storage device and the problems that need to be solved for practical applications were discussed.
Overview and advances in skyrmionics
Microelectronic technologies have been developing rapidly in the past half-century following the famous Moore's Law. However, this tendency is beginning to break down due to the thermal effects induced by the leakage current and data traffic. Spintronics sheds light on eliminating this bottleneck by using the spin degree of electron, which attracts great attention from both the academia and industry. The magnetic skyrmion is a particle-like spin texture with topological protection, envisioned as an energy efficient spintronic information carrier due to its nanoscale size, ultra-low driven energy, and high thermal stability. Recent research progress shows that the nucleation, transportation, and detection of skyrmion in room temperature, which affirm its potential application in electronics, lead to a new research field called skyrmionics.
In this review article, we first introduce the fundamental concepts and recent progress of magnetic skyrmions, from both the theoretical and experimental point of view. Different types of magnetic skyrmions have different properties due to their physical dynamics. We only focus on the skyrmions stabilized by Dzyaloshinskii-Moriya interaction (DMI) in the ultra-thin film structures as their small size, high mobility and room temperature stability can provide the perspectives for electronic devices. The skyrmions have already been extensively investigated from both the theoretical and experimental aspects in recent years. Micromagnetic simulation is the main approach to theoretically studying the dynamics of skyrmions and their applications. Most of the innovative skyrmionic devices have first been demonstrated by this method. Experimentally, skyrmions can be measured by various methods, such as the neutron scattering, Lorentz transmission electron microscopy, scanning X-ray transmission microscopy, polar magneto-optical Kerr effect microscope, etc.
In the third part of this paper, we present four basic functions of skyrmionic devices ranging from nucleation, motion, detection, to manipulation. The nucleation of skyrmions, corresponding to the information writing in skyrmionic devices, has been widely investigated. A skyrmion can be nucleated by conversion from domain wall pairs, local spin injection, local heating, and spin waves. Then, we focus on the current induced skyrmion motion and compare the two different torques:the spin transfer torque and the spin orbit torque. To read the data, it is necessary to detect skyrmions electrically. One way is to measure the topological Hall effect in a Hall bar. More commonly, skyrmions can be detected through magnetoresistance effects, i.e., giant magnetoresistance/anisotropic magnetoresistance, tunnel magnetore sistance, and non-collinear magnetoresistance, in a junction geometry. For manipulation, it is mainly demonstrated by the voltage controlled magnetic anisotropy (VCMA).
Finally we discuss several representative skyrmionic nano-devices in memory, logic, and neuromorphic applications. The magnetic tunnel junction and the racetrack are two common designs for skyrmionic memory devices. The former can store multiple values in one bit, and the latter can realize fast and efficient data transmission. To control the skyrmionic data in these memories, the VCMA effect is one of the promising approaches, which is used in several designs. For the skyrmionic logic devices, they can be divided into two main types:the transistor and the logic gate. However, until now, these ideas are only demonstrated in simulation, and more efforts in experiment are needed. Besides, novel devices such as artificial synapses and neurons can be realized more naturally by skyrmion due to its particle-like property.
In summary, skyrmionics is promising in several aspects, including performance improvement, emerging function and architecture design, and bio-inspired computing. Remarkable progress has been made in the past few years, however the device integration, the materials, and the data transmission still restrict its application. We hope this overview article may present a clear picture about skyrmionics and receive more attention, thus promoting its fast research and development in the future.
Magnetoelastic phenomena and mechanisms of magnetic skyrmion crystal
Recently, a novel two-dimensional spin structure with non-trivial topological properties, called magnetic skyrmion, has been found in many chiral magnets. In most cases, magnetic skyrmions assemble spontaneously and form a lattice structure, called magnetic skyrmion crystal (SkX). SkX, as a novel macroscopic magnetic phase, may interact with different types of external fields through the intrinsic multi-field coupling of the material, resulting in many peculiar physical phenomena. It is found that due to the intrinsic magnetoelastic coupling of chiral magnets, SkX not only influences the mechanical properties of the materials, but also has “emergent elastic properties” when subjected to external forces. In this review, we first introduce and categorize various types of SkX-related magnetoelastic phenomena, and then introduce a unified theoretical framework to analyze these magnetoelastic phenomena. Specifically, we establish the Landau-Ginzburg free energy functional with a comprehensive description of the magnetoelastic effect for B20 chiral magnets obtained through symmetry analysis, and prove that SkX should be described by a Fourier series due to its wave nature. We show quantitative agreement between theoretical results and experimental results for three types of phenomena:1) the temperature-magnetic field phase diagrams of MnSi suffering uniaxial compression, it is found that uniaxial compression in the direction[0, 0, 1]T constricts the stable region of the skyrmion phase in the phase diagram, while uniaxial compression in the direction[1, 1, 0]T extends the stable region of the skyrmion phase in the phase diagram; 2) the emergent elastic behavior of SkX, it is found that this property derives from the magnetoelastic effect of the underlying material, and the linear constitutive equation (with coefficient matrix λ) which determines the emergent deformation of SkX, is briefly introduced; 3) the variations of elastic coefficients C11, C33, C44, and C66 with the external magnetic field for MnSi, and the predictions of the variation of C12 and C13 are provided by the theory. Based on the theoretical framework, the analytical solutions of the eigenstrain problems for chiral magnets hosting SkX and the surface configuration of SkX in a half-space magnet are introduced. In this process, we show how to use the theoretical framework to deal with different problems. Finally, we make a summary and suggest several directions for the future development of this field.
Dzyaloshinsky-Moriya interaction in δ-(Zn, Cr)S(111) surface: First principle calculations
According to density functional theory calculations, we elucidate the atomic and electronic structure of δ-(Zn, Cr)S(111) surface. The magnetic interaction between Cr atoms is via S atoms close to the Cr layer. This interaction is shown by the analysis of spin charge contour plot and partial density of states (DOS) of each atom. The DOSs of other S atoms are non magnetic and have no magnetic exchange with the Cr layer. E(q) and E(-q) are the dispersions between energy E and wave vector q of spin spiral in the opposite directions. They are calculated with generalized Bloch equations and all the magnetic moments of Cr atoms are arranged in the plane perpendicular to the δ-(Zn, Cr)S(111) film. The differences between E(q) and E(-q) are caused by the interface of δ-(Zn, Cr)S(111), where the symmetry of space perpendicular to the film is broken. Effective Heisenberg exchange interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors (Ji and di) are derived by well fitting the ab initio spin spiral dispersion E(q) to HBI with DMI model and E(q)-E(-q) to DMI model, respectively. The J2 plays a major role with a large negative value of -9.04 meV. The J1 is about 2/5 of J2, and J3 is about 1/4 of J2 with positive value. The DMI d1 is -0.53 meV, and d2 is 0.07 meV. With these HBI parameters, E(0) is the largest one at which δ-(Zn, Cr)S(111) has no ferromagnetic interface. The E(q) has its lowest energy with the q at M=b1/2 in the first Brillouin zone. Hence, δ-(Zn, Cr)S(111) is an M-type antiferromagnetic (AFM) material. In this type of AFM configuration, magnetic moments of Cr atom in a line along b2 are parallel to each other, and antiparallel to the magnetic moments in adjacent lines. The E(q) at K=b1/2+ b2/2 is almost as large as that at Γ point. The value of DMI parameter d1 is about 1/5 of that on Co/Pt3 interface and 1/2 of Co/graphene. However, it is a negative number, which shows the clockwise chirality. The δ-(Zn, Cr)S(111) interface has obvious DMI, and skyrmion may be formed at this transition-metal/semiconductor (TM/S) interface. It is a good option to search for DMI in different kinds of TM/S heterojunctions. The material that combines the advantage of heterojunction, and DMI may have new magnetic phenomenon, which is usefulfor the magnetic storage. This paper enriches the research on DMI.
Critical behaviors of helimagnetic ordering systems relating to skyrmion
Study of critical phenomena plays a key role in developing the theory of phase transition. In this article, we mainly review some new experimental results about the critical phenomena reported recently in the helimagentic ordering materials. These materials exhibit a kind of a vortex-like spin texture so-called skyrmion phase. The skyrmion phase has great potential applications in the new spin-based storage due to the topologically protected stability, nanometric size, and current-driven motion. Generally, the skyrmion state exists in a helimagentic system due to the DzyaloshinskiiMoriya (DM) interaction which forms in the crystal structure without inversion symmetry. It usually emerges just below the helimagentic phase transition temperature TC under a certain temperature and magnetic field. In this review article, firstly, we introduce some basic concepts about the phase transition, such as critical phenomenon, critical exponents, scaling law, and universality. Secondly, we discuss two different methods which can help us to obtain the critical exponents, i.e., the iteration method based on the isothermal dc-magnetization and the fitting technique based on the magnetic entropy change. Both methods are extensively used in the current study of critical phenomena Thirdly, we analyze and outline some latest studies of critical behaviors and critical exponents for several typical helimagnetic systems with skyrmion state, such as MnSi, FeGe, Cu2OSeO3, Fe1-xCoxSi, and Fe1.5-xCoxRh0.5MoN. The B20 compound MnSi is a typical skyrmion material, which undergoes a paramagnetic-to-helimagnetic phase transition at ~30.5 K and the skyrmion phase appears just below TC as an appropriate external magnetic field is applied. Investigations show that critical exponents of MnSi belong in the universality class of a tricritical mean-field model, implying the existence of a long-rang magnetic interaction in this system. The critical behavior of MnSi reveals that its first-order phase transition can be driven into a second-order phase transition by the action of external magnetic field, where a field-induced tricritical point is found among the helimagnetic, conical, and paramagnetic phases in MnSi system. Unlike MnSi, the critical exponent of the near-room-temperature skyrmion system FeGe, which undergoes a helimagentic phase transition at ∼278 K, belong to the three-dimensional Heisenberg model. The critical behavior of Cu2OSeO3 is similar to that of FeGe, which indicates that the magnetic interactions in these two systems are dominated by the short-range nearestneighbor isotropic magnetic coupling. In addition, studies revealed that magnetic interaction and critical behavior of the skyrmion system can be effectively modulated by doping. The critical exponents of Fe1-xCoxSi and the newly founded skyrmion system of Fe1.5-xCoxRh0.5MoN indicated that the doping concentration of Co can change and affect their critical behaviors. In addition, it was demonstrated that the doping of Co enhanced the anisotropic magnetic coupling in Fe1-xCoxSi while it suppressed that in Fe1.5-xCoxRh0.5MoN. Fourthly, according to the universality and the scaling equations, we proposed a method to construct the detailed H-T phase diagram around the phase transition temperature in the system exhibiting field-induced phase transition. Finally, we make a brief summary and suggest our perspectives of the study of critical phenomena in helimagentic system. The results of critical behaviors indicate that although all these helimagentic systems exhibit a similar skyrmion phase, their essential magnetic interactions belong in different universality classes, indicating different types of magnetic coupling in these systems. Furthermore, the results also suggest that magnetic coupling can also be effectively tuned by the external modulation.
Modulation of skyrmion diameter in centrosymmetric frustrated magnet
Magnetic skyrmions were first observed in a bulk B20 chiral magnet where the unit cell of the crystal lacks inversion symmetry, i. e. it is noncentrosymmetric, due to the Dzyaloshinskii-Moriya interaction (DMI). The breaking of structural inversion symmetry can also be achieved artificially in extremely thin FM layers adjacent to heavy elements, to induce a nonzero DMI. Many skyrmion properties in the DMI-based system are revealed such as the skyrmion diameters simply inversely proportional to the DMI constant. On the contrary, the triangular lattice, providing a simple realization of a high-symmetry system with six equivalent orientations for the helix, is centrosymmetric. In a two-dimensional triangular lattice magnet with the magnetocrystalline anisotropy perpendicular to the film plane, the magnetic frustration can arise from the coexistence of a nearest -neighbor ferromagnetic exchange interaction and a third-neighbor antiferromagnetic exchange interaction. When an external magnetic field is applied parallelly to the anisotropy, the non-coplanar alignments of spins are favored and even the topologically protected magnetic skyrmions also appear. Based on the Monte Carlo simulation, the dependence of magnetic-field-induced magnetic phase transitions in such magnetic frustrated magnets, including the magnetic phase of skyrmion crystals, and the skyrmion diameters on competing exchange interaction and magnetic field is studied. The results indicate that the diameters of magnetic skyrmions strongly depend on the competing exchange interactions and external magnetic field. Like the diameter features of magnetic skyrmions observed in the conventional DMI-based chiral magnets, the external magnetic field can magnetize the skyrmion periphery spins to reduce the skyrmion diameters. However, the enhanced antiferromagnetic exchange interaction can compress the entire skyrmions. In the framework of the spin wave theory and Monte Carlo simulation results, the diameters of magnetic skyrmions in exchange-interaction-frustrated systems are quantified. The skyrmion diameter decreases linearly with the increase of magnetic field for weak antiferromagnetic exchange interaction. With the increase of antiferromagnetic exchange interaction, the decrease of the skyrmion diameter with increasing magnetic field becomes slow, while the strong magnetic fields may rapidly reduce the skyrmion diameter. With the increase of antiferromagnetic exchange interaction, the maximum and median skyrmion diameters decrease to level-off roughly, while the minimum skyrmion diameters show a rapid decrease first and a great fluctuation later. The phenomena are explained through discussing the variations of configurations and magnetic energies of skyrmions. This work demonstrates the adjustability of skyrmion diameter in centrosymmetric frustrated magnet, which not only improves the understanding of origin of skyrmions, but also supports theoretically the development of new generation of skyrmion-based storage and logic devices.
Control of skyrmion movement in nanotrack by using periodic strain
Magnetic skyrmions are a topologically stable and particle-like chiral spin configuration. They are appealing because of their potential applications in racetrack memory and other spintronic devices. These applications are strongly dependent on the skyrmion motion in confined geometry. Therefore, it is important to study the moving behaviors of skyrmions in a nanotrack to make them have more practical applications. Mechanical strain and stress have been demonstrated theoretically and experimentally to be able to effectively control the skyrmion phase. It can stabilize the skyrmion lattice in a broad range, and change the shape of the skyrmion crystal. In this paper, we study the moving behaviors of ferromagnetic skyrmions and antiferromagnetic skyrmions under the action of sinusoidally distributed strain in a nanotrack by using micromagnetic simulation. We assume that strain is uniaxial and perpendicular to the plane of the nanotrack. Its strength varies sinusoidally along the x-axis. Meanwhile, we apply an in-pane current along the nanotrack to drive the skyrmion moving towards the right side. We first find that there is a threshold current density that is defined as the minimum current that can drive skyrmion moving continuously. When the current density is larger than the threshold current density, the skyrmion can move continuously in the nanotrack. The threshold current density increases with the amplitude of strain increasing, but decreases with the period of strain increasing. Second, we find that the trajectory of skyrmion changes under the action of the sinusoidal distributed strains. For ferromagnetic skyrmion, its trajectory changes from straight line to periodic wavy line. Also, we find that the longitudinal velocity of skyrmion is affected by the boundary of the nanotrack. When the skyrmion is close to the upper boundary of the nanotrack, the longitudinal velocity increases sharply and it will form a peak in the velocity curve, but when the skyrmion is close to the lower boundary of the nanotrack, the longitudinal velocity decreases and it will form a valley in the velocity curve. The transverse velocity of skyrmion relates to the strain gradient. It is inversely proportional to the strain gradient. For antiferromagnetic skyrmion, we find that the movement trajectory of antiferromagnetic skyrmion does not change under the stress control. However, its diameter and velocity change periodically. Its velocity can vary between 103 m/s and 0. Our results demonstrate that the sinusoidal strain can control the skyrmion motion. This work may provide guidance in designing and developing of the spintronic devices based on magnetic skyrmions.
Research progress of micromagnetic magnetic skyrmions and applications
Magnetic skyrmion, as a quasi-particle, with topologically protected property has received wide attention. In this article, We first review the existence conditions and transport characteristics of magnetic skyrmions theoretically, then view recent micromagnetic simulation researches on creation and controlling as well as the device design, which includes racetrack memories, spin transfer nano-oscillators, transistors and logic gates. We hope this paper can provide a reference for the applications of magnetic skyrmions in the future.
Overview of magnetic skyrmion-based devices and applications
Magnetic skyrmions possess topologically non-trivial particle-like nanoscale domain wall structures, which have reasonably good stability and unique dynamic properties and can be controlled by magnetic fields, electric fields, and electric currents. Therefore, magnetic skyrmions are expected to be used as novel information carriers in the next-generation high-density, low-energy-consumption, and non-volatile information storage and logic computing devices. Since the first experimental observation of magnetic skyrmions in 2009, a number of skyrmion-based device prototypes have been proposed. In this article, we review the recently proposed skyrmion-based devices and applications, including skyrmion-based racetrack memory, logic computing device, transistor-like functional device, and nano-oscillator. We first discuss advantages of skyrmion-based racetrack memory and solutions for some problems we are facing currently. We then introduce the duplication and merging of magnetic skyrmions and the skyrmion-based logic OR and AND gates. We also introduce the switch function of skyrmion-based transistor-like functional device. The switch function is realized via a voltage gate and controlled by the applied voltage as well as the driving spin current. Besides, a brief introduction of the skyrmion-based nano-oscillator is given. In addition, we introduce several possible methods to encode binary information in skyrmion-based devices. Finally, we discuss some possible future novel applications based on magnetic skyrmions.
Research progress on topological properties and micro-magnetic simulation study in dynamics of magnetic skyrmions
Skyrmions, as a nontrivial topological magnetic structure, have the advantages of topological stability, small size and low driving electrical current, showing potential applications in spintronic memory device. There are several mechanisms for skyrmion formation in magnets. One major mechanism is, in chiral-lattice ferromagnets, the competition between the Dzyaloshinskii-Moriya and ferromagnetic exchange interactions, due to the lack of spatial inversion symmetry. The combination of topology and condensed physics demonstrates various new topological phenomena of skyrmions, which also determine their dynamics. In this review, recent progress on the topological physics foundation of Skyrmions, as well as their dynamics of application in spintronics devices, is reviewed.
The topological physics foundations of skyrmions is introduced. Firstly, the structure of skyrmions, which shows a special nontrivial topology in the real space, is presented accompanied with the formation of skyrmions caused by Dzyaloshinskii Moriya interactions in chiral magnets. Secondly, due to the importance of the describable method of the topology of a skyrmion, the topological charge, that characterize the topology, as well as the calculation method are introduced. Also, the arising topological stability is discussed here. Then, the typical topological effects arising from the topology of a skyrmion, including topological Hall effect and the skyrmion Hall effect are reviewed. The next is the introduction of the helical and the spiral spin configuration, the alternatives for Bloch and Néal type skyrmions respectively, which show up under lower external magnetic field with the same interaction. Also the phase transition of the helical/spiral state to skyrmions and the Monte Carlo method to simulate the spin configuration of a chiral magnet are introduced. At last, the spin orbital torque and the spin transfer torque, that describe the driven effect of a skyrmion by an electrical current or a thermal field, are reviewed. The consequence dynamics of skyrmions, the Landau-LifshitzGilbert equation, are also introduced.
The recent progress of typical dynamics of skyrmions on several concerned problems in practical applications are reviewed. The applications in spintronics memory require skyrmions have steady transportation driven by electrical current and controllable creation and annihilation process. Firstly, skyrmion can be generated by the spatial nonuniform electric current with a certain geometry constrain. Especially for the Néal type skyrmion, nonuniformity of the spin orbital torque, come from the non-uniform electric current, play an important role in the skyrmion generation process. Secondly, skyrmion moves with a perpendicular velocity under an electrical current, because of the skyrmion Hall effect. So the elimination of skyrmion Hall effect is practically concerned to make the transportation steady. The anti-ferromagnetic skyrmion and antiferromagnetic coupled skyrmion bilayer are found with no skyrmion Hall effect by have two opposite component cancel out. Finally, with topological stability, skyrmions are hard to convert from and to a nontrivial topological spin configuration at low temperature. So the manipulation of skyrmion creation and annihilation are discussed accompanied with their difference of Bloch and Néal type skyrmiom.
Multi-field control on magnetic skyrmions
The concept of skyrmion is proposed by Tony Skyrme, a British particle physicist, to describe a state of particles as a topological soliton. Magnetic skyrmion is a novel spin structure with topological behavior, whose size is on a nanometer scale. The space between skyrmions is tunable from a few nanometers to micrometer. Magnetic skyrmion can be stable in a large temperature range, from lower temperatures, to room temperature, and even to higher temperature. The materials with magnetic skyrmions include not only low temperature B20-type ferromagnets with centrosymmetry breaking and weak ferromagnets with helical magnetic ordering, but also the hexagonal MnNiGa alloy and ferromagnetic multilayers over room temperature. By using topological spin structure of skyrmions, an electrical current can be applied to driving or flipping the skyrmions, similar to the spin transfer torque effect in spin-valves and magnetic tunnel junctions. The critical current density is on the order of 102 A/cm2, which is five orders lower than that in magnetic multilayered structures such as 107 A/cm2. This critical value is much lower than the channel current density in Si-based semiconductor technology, thus leading to great potential applications in the future magnetic information devices. In this review paper, we first introduce the discovery, a brief development history of magnetic skyrmions. Then, we summarize the materials with skyrmion spin structures, focusing on the key physical properties. Finally, we mention the recent progress of the multi-field (such as magnetic field, electrical current, and temperature) control on magnetic skyrmions in hexagonal MnNiGa alloy and Pt/Co/Ta magnetic multilayers, together with the creation, annihilation, and dynamic behavior of skyrmions.
Magnetic domain chirality and tuning of skyrmion topology
Owing to the topologically protected properties, magnetic skyrmions possess high stability and small critical driving current, thus making them potentially applied to future racetrack memory devices. Skyrmions have been identified in several material systems. One large class contains the centrosymmetric materials, where skyrmions emerge as the competition between perpendicular magnetic anisotropy and magnetic dipolar interactions. The recently reported skyrmion host includes La-Sr-Mn-O, hexagonal MnNiGa, Fe3Sn2, etc. In these systems, due to the isotropic characteristic of the dipolar interaction, magnetic bubble can exhibit various topologies and helicities. The common types of bubbles existing in the materials are the trivial one with n=0 (n is the topological charge) and the non-trivial one with n=1, and the latter is taken to be equivalent to magnetic skyrmion. In this article, we investigate the formation of skyrmions under various magnetic parameters and the role of stripe domain chairity in tuning the bubble topology. The main method we use here is micromagnetic simulation with the Object Oriented MicroMagnetic Framework (OOMMF) code. Also some recent experimental results on MnNiGa and Fe3Sn2 are exhibited and compared with the simulation prediction. Under a fixed magnetization (Ms), by tuning the exchange constant A and magnetic anisotropy Ku, we find that the domains can evolve into a bubble state under a moderate anisotropy value, and to some extent, large anisotropy favors the formation of n=1 topological skyrmion. In the case of the stripe domains, it is found that different initial configuration can lead to different domain wall charity and further change the process of skyrmion formation. When the magnetization in the domain wall orients in the same direction, n=0 bubble will form upon applying magnetic field. While the magnetization in the wall orients alternatively up and down, a topological skyrmion is directly formed. In the stripe domains with inversed 180° Bloch wall, in-plane magnetization dominates and no bubble or skyrmion can form. In addition, the tilt of the magnetic field and uniaxial anisotropy can also change the morphology and topology of the skyrmions, which has been verified in our experiments. According to the above results, we propose to tune the topology of skyrmions in centrosymmetric material through adjusting the ground magnetic state, magnetic anisotropy and in-plane components, which can be realized by element doping at different sites and appropriately designing the sample.
Observation of new-type magnetic skymrions with extremerely high temperature stability and fabrication of skyrmion-based race-track memory device
Nanoscle magnetic skyrmions are topologically protected vortex-like spin textures that have been regarded as a promising candidate for the transport of information in further spintronic applications based on the racetrack memory concept due to their nanoscale dimension, stable particle-like feature, and an ultralow threshold for current-driven motion. Recently, most of the skyrmions are observed in chiral magnetic materials, such as MnSi, FeGe, Co-Mn-Zn, where the Dzyaloshinskii-Moriya interaction is active. However, their overall low thermal stability is one of the major factors hindering the practical applications. In this paper, we report the observation of a new-type magnetic skyrmion with extremerely high temperature stability in the centrosymmetric frustrated magnet Fe3Sn2, and the fabrication of skyrmion-based race-track memory device based on Fe3Sn2 by using focused ion beam. This compound is a rare example of ferromagnetic frustrated magnet that exhibits a high Curie temperature Tc up to 640 K. As the temperature decreases from 640 K to 100 K, it undergoes a spin reorientation during which the easy axis rotates gradually from the c-axis to the ab-plane. The Fe3Sn2 has a layered rhombohedral structure with the alternate stacking of the Sn layer and the Fe-Sn bilayer along the c-axis. By a high-temperature flux method, we grow high-quality Fe3Sn2 single crystal. The in-situ Lorentz transmission electron microscopy (LTEM) observations demonstrate that this compound can host skyrmions at room temperature (RT). In contrast to the skyrmions of the chiral magnets, they possess various spin textures and are transformed from topologically trivial bubbles under a high external magnetic field of 800 mT. By using the FIB technique, we fabricate a geometrically confined nanostripe with a width of 600 nm and thickness of 250 nm. The in-situ LTEM observations demonstrate that a single chain of skyrmions with uniform spin textures can be created at RT. The investigations on the temperature stability of the single skyrmion chain reveal that it shows an extremerely high temperature stability that the size of and the distance between the skyrmions in the chain can keep unchanged at temperatures varying from RT up to a record-high temperature of 630 K. The observation of a highly stable single skyrmion chain in the geometrically confined Fe3Sn2 nanostripe can be attributed to (1) the weak temperaturedependent magnetic anisotropy Ku of the Fe3Sn2 crystal, and (2) the formation of edge states at the boundaries of the nanostripes. The observation of new-type magnetic skymrion with extremerely high temperature stability and the fabrication of skyrmion-based race-track memory devices are very important steps towards the applications in skyrmionbased spintronic devices.
Skyrmions-based magnetic racetrack memory
Magnetic skyrmions are topologically stable spin configurations with small size, which can be driven into motion by a small current. They are widely regarded as building blocks for next-generation magnetic storage. The main advantage of skyrmions lies in their particular dynamic behaviors, especially in their ability to move stably in racetrack under the action of small spin-polarized currents. The writing, driving and reading methods of skyrmions in racetrack are reviewed in detail in this paper, including the most recent research findings. The review focuses on the most commonly used driving method, i.e., driving skyrmions by applying spin-polarized currents. The clogging and annihilation of skyrmions in racetrack are analyzed, with the skyrmion Hall effect discussed which may lead skyrmion signals to lose. Methods to avoid skyrmion Hall effect are introduced and hence the optimized designs for skyrmion-based racetrack are also reviewed. Finally, some challenges of skyrmion-based racetrack memory are discussed.
First-principles study of optical properties of germanium doped with phosphorus and bismuth
Using first-principles calculations based on density functional theory, we investigate the electronic structures and optical properties of germanium doped by phosphorus and bismuth with different concentrations. By analyzing the electronic structures and optical properties of the doped systems, we can theoretically analyze and predict the optical and electrical practical applications of N-doped germanium semiconductors. By analyzing and comparing the densities of electronic states before and after doped, we can draw some conclusions. The conclusions show that the Fermi level moves in the direction of conduction band after being doped. Although germanium is an indirect band gap luminescent material, the doped systems all become direct band gap luminescence. Doping more or less affects various optical properties in different energy ranges. In a low energy range, the dielectric function and refractive index of the doped systems are affected. When the doping concentration is 2.083%, the dielectric function and refractive index of the doped system both have a special change. And the absorption of the doped system is changed in the high energy. As the energy increases after the absorption peak, the absorption of the doped system drops faster. The reflectance of the doped system is affected in all the energy ranges. The reflectance of the doped system increases in medium energy. And the reflectance of the doped system is reduced in low energy and high energy range. However, when the doping concentration is 2.083% and the energy is less than 1.7 eV, the reflectance of the doped system is higher than that of the undoped system. The conductivity of the doped system forms two peaks, adding a peak in low energy. The additional peaks in the systems where the doping concentrations are 1.563% and 2.083% are obvious. The peak of the loss function increases after being doped. However, as the doping concentration increases, the increment of the loss function decreases. As the doping concentration increases, the peak is formed at a higher energy. The conclusions are of significance for guiding the optical applications of N-type doped germanium. According to the conclusions, we can adjust the doping concentration and energy range in the optical applications of N-doped germanium.
Method of picking up carbon nanotubes inside scanning electron microscope
In this paper a promising method of recognizing spatial contact state between carbon nanotubes (CNTs) and atomic force microscope (AFM) probe inside scanning electron microscope (SEM) is proposed. The CNTs can be picked up simply and effectively by van der Waals force without knowing depth information of SEM images by using this method. And a micro-nanorobotic manipulation system with 16 DOFs, which allows the automatic pick-up of CNTs based on visual feedback, is presented. The micro-nanorobotic manipulators are assembled into 4 units with 4 DOFs individually. Namely, a manipulator has 4 DOFs i.e., three linear motions and a rotational motion. Manipulators are actuated by picomotors with better than 30 nm linear resolution and less than 1 micro-rad rotary resolution. The van der Waals force mechanics model between CNTs and AFM probe in the picking up manuplation is established. In reality, the van der Waals force is the main attractive force under the vacuum condition inside SEM when the influence of staticelectricity is ignored. It is shown that the van der Waals force under horizontal (sphere-plane) contact model is significantly larger with appropriate overlapping length. Though the positions in both x and y directions of the CNTs and AFM cantilever are acquired, the relative positions of those two objects in the z direction remain unclear. In the gradually ascending process of AFM cantilever to contact the CNTs, the CNTs abruptly drop on the surface of AFM probe due to the van der Waals force. According to the relative coordinate system of SEM visual feedback images, the detection of contact state between carbon nanotubes and AFM probe are completed by using the inclination changing value of fitting line. The experimental results suggest that the abrupt contact between CNTs and AFM probe happens when the inclination changing value of the regression line is found to be 3.0263°. The spatial contact state between carbon nanotubes and AFM probe includes line contact (Model a) and point contact (Model b, Model c). Then the dynamic difference method is introduced to identify the spatial contact model of CNTs and AFM probe. The results demonstrate that contact model of CNTs and AFM probe is line contact when the dynamic difference is approximately zero. The position of carbon nanotubes is corrected by moving AFM cantilever automatically underneath the CNTs. The picking-up of CNTs from substrate under line contact model is completed by choosing the optimum contact angle, contact length and pickup speed.
Growth of Tl-1223 superconducting thin films by rapidly heating-up sintering technology
Owing to high critical temperature (125 K) and high upper critical field, TlBa2Ca2Cu3O9 (Tl-1223) superconductor is a kind of superconducting power transmission material working at liquefied natural gas temperature, and it has a great potential application value in the strong and weak electric field. In this work, the Tl-1223 superconducting films are fabricated by rapidly heating-up sintering technology (RHST) on (00l) lanthanum aluminate substrates. The Tl-Ba-Ca-Cu-O target is used as a sputtering source to deposit the precursor films by the radio-frequency magnetron sputtering technique. The Tl-contained pellets, named annealing targets, are fabricated by the solid-state reaction of stoichiometric quantities of Tl2O3, BaO2, CaO and CuO powders with an initial cation ratio of m Tl:Ba:Ca:Cu=0.4-1.8:2:2:3. The amorphous precursors together with the annealing target providing Tl source are sealed in a silver foil and annealed at 820℃ for 5 min in argon atmosphere, then converted into Tl-1223 superconducting phase. The heating rates are set at 2.5℃/s from room temperature to 350℃, 5℃/s from 350℃ to 650℃, and 35℃/s from 650℃ to 820℃, respectively. The prepared films are characterized by X-ray diffraction and scanning electron microscope. In the conventional low heating rate process, all of the precursor films sintered together with the annealing targets containing different Tl content are first converted into Tl-2212 superconducting phase. That is because the sample residence time in the phase transition temperature range of Tl-2212 is longer, while the phase-formed temperature of Tl-2212 is lower than that of Tl-1223. In the RHST, when the metal ion molar ratio of Tl to Ba in the annealing target is 1.8:2, the main phase of the film is (00l)-oriented Tl-2212. In addition, the film also contains a small number of Tl-2223 grains. On reducing the ratio to 1:2, the film is composed of Tl-1212, Tl-2212, Tl-1223 and Tl-2223 grains. As the ratio decreases to 0.8:2, the film contains the (00l)-oriented Tl-1223 grains and traces of Tl-2223 grains. With the ratio decreasing to 0.4:2, purely c-axis oriented Tl-1223 film is obtained. The critical transition temperature Tc onset of the as-grown film is only 103 K. The film annealed again in oxygen gas has a dense crystal structure and excellent electrical properties. The Tc onset of the sample is about 116 K, and the critical current density Jc is about 1.5 MA/cm2 (77 K, 0 T). The experimental results show that the new sintering process to grow Tl-based films has several advantages such as the short processing cycles, less raw-material consumption, and low production cost.
Axial multi-particle trapping and real-time direct observation
The optical tweezers with the special advantages of non-mechanical contact and the accurate measurement of positions of particles, are a powerful manipulating tool in numerous applications such as in colloidal physics and life science. However, the standard optical tweezers system uses a single objective lens for both trapping and imaging. As a result, the trapping and imaging regions are confined to the volume near the focal plane of the objective lens, making it difficult to track the trapped particles arranged in the axial direction. Therefore, multiple trapping along axial direction remains a challenge. The three-dimensional imaging technology can realize the monitoring of the axial plane, but neither the laser scanning microscopy nor the wide-field imaging technology can meet the requirement of the real-time imaging. To address this issue, we propose a modified axial-plane Gerchberg-Saxton (GS) iterative algorithm based on the Fourier transform in the axial plane. Compared with the direct algorithm such as the Fresnel lens method, the modified axial-plane GS iterative algorithm has a higher modulation efficiency, and the generated axial distribution has a sharper intensity. In theory, the traps generated each have an ideal Gaussian intensity distribution independently, which is proved by the simulation of reconstructed field. With such an iterative algorithm, we can directly create multiple point-trap array arranged along the axial direction. We also develop an axial-imaging scheme. In this scheme, the particles are trapped and a right-angled silver-coated 45° reflector is used to realize axial-plane imaging. The scheme is verified by imaging silica particles in an axial plane and a lateral plane simultaneously. Furthermore, we combine the axial-plane imaging technique with holographic optical tweezers, and demonstrate the simultaneous optical trapping in 2×2 trap array and the monitoring of multiple silica particles in the axial plane. The trap stiffness of traps array in axial plane is calibrated by measuring the Brownian motion of the trapped particles in the axial trap array with digital video microscopy. The proposed technique provides a new perspective for optical micromanipulation, and enriches the functionality of optical micromanipulation technology, and thus it will have many applications in biological and physical research.
Electronic structures of stable Cu-centered Cu-Zr icosahedral clusters studied by density functional theory
Cu-Zr alloy system,as a representative of transition metal-transition metal (TM-TM) metallic glass (MG),has attracted considerable attention due to its high glass-forming ability in a wide range of compositions.Many researchers have realized that the GFA of Cu-Zr alloy is intimately related to Cu-centered Cu-Zr icosahedral atomic cluster in supercooled liquid and rapidly solidified into amorphous solid.And lots of molecular dynamics simulations have shown that Cu-centered Cu-Zr icosahedral clusters not only affect the thermo-dynamical properties of metal or alloy melts,but also exhibit excellent structural stability and configuration heredity ability during the rapid solidification.Hereof a model of the metallic glass structure based on like icosahedron has become widely accepted,which plays an important role in the glass transition and its strong kinetic constraint on nucleation.However,though more and more standard and distorted Cu-Zr icosahedral clusters have been found and reported in Cu-Zr metallic glass,the fundamental understanding of these Cu-Zr icosahedral clusters of MGs is still lacking.More essential properties of Cu-centered Cu-Zr icosahedral cluster, especially on the electronic structure are still unclear.Based on this,as a further step towards in depth understanding the electronic structures of those icosahedral clusters,we will investigate the electronic structures of the stable Cucentered CunZr13-n (n=6,7,8,9) icosahedral clusters in this work,and consider all the possible atomic configurations for given chemical composition in view of originate in theory And a DMol3 molecular orbital package based on density functional theory (DFT) is adopted to calculate the energetics and electronic structures of Cu-centered Cu-Zr icosahedral clusters.During optimization and total energy calculation,electronic exchange-correlation energy functions in reciprocal space with the Perdew-Burke-Emzerhof type under general gradient approximate are used.A double-numerical basis set together with d-polarization functions (DNP) is chosen to describe the electronic wave functions of Cu and Zr atoms. And only core electrons described by the DFT Semi-core Pseudopots are calculated.All atomic positions in Cu-centered CunZr13-n (n=6,7,8,9) icosahedral clusters are relaxed by geometry optimization under a root mean square (RMS) force of 0.002 Ha/Å and RMS displacement of 0.005 Å.The calculations of total energy and electronic structure are followed by the geometry optimization with self-consistent field tolerance of 1×10-5 Ha.It is found that homogeneous atoms in the shell of clusters with low binding energy prefer to bond to each other.In this case,the results of electronic structures reveal this segregation at low energy and stable configurations can be attributed to their low N (EF) at EF to some extent.A further analysis of Mulliken'population shows that these 4s and 4p of shell Cu atoms are all donees in the formation of icosahedral cluster,different from the donations of 3d and 4s of core Cu atoms and 5s of shell Zr atoms, and this charge transfer tendency does not change with order parameter nor chemical composition of Cu-centered Cu-Zr icosahedral cluster.In addition,calculating the infrared vibration spectrum of Cu-Zr icosahedral cluster is a new idea for accurately characterizing the cluster structure.
Dependence of peak width of energy distribution on profile of combined field
In this paper, we use the quantum field theory to solve the generation process of particle-anti-particle pairs (PAPs), and study the generation characteristics of PAPs by changing the profile of the field combining an oscillating field and a static electric field. We find a way to increase the generation of PAPs and change the energy distribution. As the field strength of the oscillating field increases, the quantity of particle pairs generated increases. Increasing the field strength of a static electric field yields higher energy pairs of particles. If the frequency of the oscillating field becomes higher, the peak of the energy distribution shifts to higher energy but the width of the peak remains unchanged. The reduction of the field width of the oscillating field increases the generated quantity of PAPs on the one hand, and reduces the peak width of the energy distribution on the other hand. Therefore, we can obtain a narrower range of the energy distribution and more PAPs at less energy cost. Meanwhile, the relationship among the generation yield, the width of energy distribution and the width of the oscillation field is obtained. The width of the oscillating field only significantly narrows the peak width of the energy distribution in a range and reaches a limit after that. This provides useful details for future experiments, and suggests an appropriate width of the oscillating field to produce enough quantity of PAPs with concentrated energy distribution. According to previous studies, varying field width will inevitably lead to the change in the intensity of the electric field. It will be shown that the concentrating of the energy distribution is induced by narrowing the oscillating field instead of increasing the electric field intensity. Therefore, more concentrated PAPs will be obtained and their mutual annihilation will lead to the generation of γ -ray, which can be used as a γ -ray in experiments that follow. We suggest reducing the width of the oscillating field to improve the energy concentration of both particles and anti-particles while their quantities are still large enough.
Weighting inversion of dynamic light scattering based on particle-size information distribution character
In particle sizing with dynamic light scattering (DLS) technique, the determination of particle size distribution (PSD), via inversing the autocorrelation function (ACF) of scattering light, is usually limited by the inherently low particle size information in ACF data and, the lack of targeted inversion on the noise restriction and the particle size information utilization. For the ACF data in DLS measurement, most of particle size information is centrally contained in the decay section and the larger noise is contained in the larger delay section. However, no consideration of the particle size information distribution in the ACF data for the routine inversion method increases the difficulty of the accurate PSD inversion, especially the broad and bimodal PSDs. Until now, it is still a difficult problem to obtain an accurate recovery of the broad and bimodal PSDs, specifically the bimodal PSD with a peak position ratio less than 2:1 and containing large particles (>350 nm). In this paper, a character-weighted constrained regularization (CW-CR) method is proposed, in which, the particle size information distribution in the ACF as the base and the adjustment parameter as the exponent are used to weight the ACF. By using the weighting coefficients corresponding to the particle size information distribution along the delay time in ACF, the CW-CR method can enhance the utilization of the particle size information in ACF data, and effectively weaken the effect of noise at large delay time. With this method, the closely spaced bimodal PSD (with nominal diameters of m 350 nm:500 nm in simulation, m 300 nm:502 nm in experiment) is recovered successfully at a high noise level of 0.01. It shows that the CW-CR method, combined with the multiangle DLS (MDLS) measurement, can effectively make the best use of the particle size information hiding in the noisy ACF data, and improve the resolution of bimodal PSD as well as the capability of noise suppression. So it can make the advantages of MDLS more highlighted than the routine method in the recovery of the broad and bimodal PSDs.
High sensitivity quantum Michelson interferometer
Michelson interferometer can be applied to not only the building block of the fundamental research of physics, but also the precise measurement, such as the direct observation of gravity wave signal. Therefore, high performance Michelson interferometer is the key step towards the implementation of direct observation of weak gravity wave signal. Recently, the vacuum noise was reduced by injecting squeezed vacuum into the unused port of Michelson interferomter, and the phase signal optical field in Mach-Zender interferometer is amplified based on the four-wave mixing in hot Rubidium atom. Here we study high sensitivity quantum Michelson interferometer. In the Michelson interferometer, the linear optical beam splitter is replaced by a non-degenerated optical parametric amplifier to realize the splitting and combining of optical fields, and the squeezed vacuum is also injected into the unused port of interferomter, so that the high signal-to-noise ratio and high sensitivity of phase measurement can be realized. Due to the inevitable optical losses, the losses inside and outside the Michelson interferometer are considered in our theoretical model. We investigate the influences of the losses inside and outside the Michelson interferometer on the sensitivity of phase measurement. By theoretical calculation, we analyze the dependence of sensitivity of phase measurement on system parameters, such as intensity of optical fields for phase sensing, gain factor of non-degenerated optical parametric amplifier, the losses inside and outside the Michelson interferometer, and the squeezing parameter of input squeezed vacuum, and thus the condition of high sensitivity nonlinear Michelson interferometer can be obtained. In a broad system parametric range, the quantum Michaleson interferometer can surpass standard quantum limit, and the nonlinear Michaleson interferometer with squeezed state injection can provide the optimal sensitivity for phase measurement. The nonlinear Michelson interferometer with squeezed state is suitable for weak signal measurement. While the gain factor of non-degenerated optical parametric amplifier is large enough, the nonlinear Michelson interferometer without injecting the squeezed vacuum can still reach the optimal sensitivity, which reduces the use of quantum resources. When the phase sensing optical field is strong, the linear Michelson interferometer with injecting the squeezed vacuum can also reach the optimal sensitivity, and the sensitivity is robust for both losses inside and outside the interferometer. All the kinds of interferometers are more sensitive to the loss inside the interferometer than outside the interferometer, and the sensitivity of phase measurement can be improved by reducing the loss inside the interferometer. Our result provides direct reference of experimental implementation of high performance interferometer for high precision quantum metrology.
Generation of Bessel-Gaussian vortex beam by combining technology
Bessel beam is an important member of the family of non-diffracting beams and has some unique properties which can be used in many areas, such as micro particle manipulating, material processing and optical communication. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, according to the coherent combining technology, we propose a method to generate a second-order Bessel-Gaussian (BG) beam by loading discrete vortex phase on specific spatially distributed Gaussian beam array. The coherent combining technology can enhance the output power by increasing the number of beams and use the phase-locking technique to maintain the beam quality. The experimental scheme is described as follows. The expanded Gaussian beam is first split by an amplitude-based spatial light modulator, then the Gaussian beam array is incident on a phase-only spatial light modulator to load the discrete vortex phase, and finally the Gaussian beam array loaded with phase can synthesize BG beam in free space. Due to the diffraction effect of the sub-beams, the optical field distribution between the adjacent sub-beams which are loaded with phase differences, are superimposed. As a result, the optical field distribution of the approximate beam can be obtained by coherent synthesis in free space. After that, the degree of similarity between simulated results and theoretical data is analyzed by correlation coefficient, including the comparison of light intensity between experiment and simulation, and the power-in-the-bucket is used to evaluate beam quality. In addition, the topological charge of the synthesized BG beams is verified by the interference method. By studying the number of beams, the waist radius and the radius of the ring, we find some interesting results which are summarized as follows. Firstly, the closed arrangement of Gaussian beam arrays can improve the quality of the synthesized BG beam. Secondly, the smaller the phase difference between the sub-beams, the more easily the discontinuous piston phase approaches to the vortex phase. Therefore, increasing the number of sub-beams can significantly improve the beam quality of the synthesized BG beam and obtain a higher order synthetic BG beam. Finally, we define the parameter k to represent the tightness of a circular array of Gaussian beams. The present study shows that when the parameter k is close to 1, the best experimental results can be obtained. Therefore, the proposed method has important guidance in generating various vortex beams or enhancing the vortex beam power.
Stability switching behavior of thermoacoustic oscillation in Rijke tube
Large-amplitude self-excited thermoacoustic oscillations arising due to the interaction between unsteady heat release and acoustic pressure fluctuations have been encountered in many thermal devices. These oscillations may lead to unwanted structural vibrations and efficiency reduction while emitting loud noises, and thus the predicting of such oscillations is very important. Physically, oscillation is a kind of instability, so stability analysis can be applied to understanding such a phenomenon. The present work focuses on the role of time delay between unsteady heat release and flow perturbation in the stability of thermoacoustic system. To this end, one-dimensional Rijke tube model with both open ends is numerically investigated. In the Rijke tube model, an electric heater is located at the first quarter of the Rijke tube and its unsteady heat release rate is modeled by an empirical model proposed by Heckl. Non-dimensional momentum equation and energy equation of the acoustic perturbation are derived and solved in time domain by using the Galerkin technique. The time evolution of the thermoacoustic oscillations with continuous increase in the time delay is calculated in two different acoustic damping cases, namely the heavily damped case and the weakly damped case, while other parameters are fixed. It is found that in both the heavily damped case and the weakly damped case, the system stability switches between stability and instability as the time delay increases, which is called stability switching and is a typical nonlinear phenomenon in a delay-dependent system. However, compared with in the heavily damped case, in the weakly damped case, the stability region is enlarged and the amplitude of the limit cycle oscillation is increased. Besides, in the weakly damped system, the dominating mode of system shifts in the first three modes instead of keeping in the first mode during increasing the time delay, which suggests that for the weakly damped system, the higher modes cannot be neglected and the system cannot be analyzed with a single-mode model either. Further, the bifurcation plots for the variation of the time delay for these two cases show that the system stability changes with time delay for a period of two, which is equal to the period of the first acoustic mode. As a conclusion, the results of present work indicate that the time delay between unsteady heat release and flow perturbations plays a critical role in generating thermoacoustic oscillations, and the findings of stability switching can help to understand the nonlinear phenomena in thermoacoustic systems.
Charging mechanism and application of lunar dust grains
Since the moon has an extremely rarefied atmosphere, the full spectrum of the electromagnetic radiation of the sun reaches the surface, charging the surface dust and affecting its current charge state. Lunar surface dust thus remains electrostatically charged at all times. Charged lunar dust will adversely affect the operations of most mechanical systems required by manned and unmanned exploration missions. Charged dust will also stubbornly adhere to solar panels and thermal radiators, thus reducing their efficiencies. Researches on the charged lunar dust can help to investigate lunar dusty environment as well as to solve those particle-induced problems by both simulation and experiment in laboratory. In this work, two different charging processes of charged lunar dust in the environment of electron beam and the radiation of ultraviolet source are considered. The computer numerical simulation method is used to analyze these two different charging processes of lunar dust, to explore the charging mechanisms of lunar dusts, and to choose an appropriate way of charging for the lunar environment simulation device in laboratory. On the basis of the classic dust charging equation, the charging equation of a dust in pure electron environment is given for the first time in this work. Meanwhile, the charging process under ultraviolet radiation is discussed and combined with the specific application of charging dusts. A solver of fourth-order Runge-Kutta algorithm is made to solve differential equations under two different irradiation sources. The main simulation results show that:1) in electron environment, the surface dust charge number increases as the particle size and the current intensity of electron guns increase, while the charge number increases as the beam spot radius of electron guns decreases; 2) under ultraviolet radiation, the dust charge number increases with the particle size and irradiance increasing, but charging efficiency is slow. A great dust charge number needs a long time radiation from sun (equivalent to 74 deuterium lamps), which means that more ultraviolet radiation sources are essential to speeding up the experiment in laboratory. Although the calculated efficiency of ultraviolet radiation is lower than electron irradiation, the secondary-electron emission, the scattering and the transmission process of electron irradiation are ignored, which can greatly reduce the efficiency of charging by energetic electron guns in the actual experiment. Therefore, comparing these two charging mechanisms and considering the actual design requirements for the space environment simulation device, charging by lots of ultraviolet radiation is an appropriate scheme for electrification of lunar dusts.