Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile,while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Creation and annihilation of artificial magnetic skyrmions with the electric field

Recent theory and experiments show that artificial magnetic skyrmions can be stabilized at room temperature without the need for the external magnetic field,casting strong potentials for the device applications.In this work,we study the electric field manipulation of artificial magnetic skyrmions imprinted by Co disks on CoPt multilayers utilizing the micromagnetic simulations.We find that the reversible annihilation and creation of skyrmions can be realized with the electric field via the strain mediated magnetoelastic coupling.In addition,we also demonstrate controllable manipulation of individual skyrmion,which opens a new platform for constructing magnetic field-free and low-energy dissipation skyrmion based media.

Skyrmion-based logic gates controlled by electric currents in synthetic antiferromagnet

Skyrmions in synthetic antiferromagnetic(SAF) systems have attracted much attention in recent years due to their superior stability, high-speed mobility, and completely compensated skyrmion Hall effect. They are promising building blocks for the next generation of magnetic storage and computing devices with ultra-low energy and ultra-high density.Here, we theoretically investigate the motion of a skyrmion in an SAF bilayer racetrack and find the velocity of a skyrmion can be controlled jointly by the edge effect and the driving force induced by the spin current. Furthermore, we propose a logic gate that can realize different logic functions of logic AND, OR, NOT, NAND, NOR, and XOR gates. Several effects including the spin–orbit torque, the skyrmion Hall effect, skyrmion–skyrmion repulsion, and skyrmion–edge interaction are considered in this design. Our work may provide a way to utilize the SAF skyrmion as a versatile information carrier for future energy-efficient logic gates.

Gate-voltage control of alternating-current-driven skyrmion propagation in ferromagnetic nanotrack devices

Magnetic skyrmions, with topologically protected particle-like magnetization configurations, are promising information carriers for future spintronics devices with ultralow energy consumption. Generally, during motion, skyrmions suffer from the skyrmion Hall effect(Sk HE) wherein the skyrmions deflect away from the intended path of the driving force.Numerous methods have been proposed to avoid this detrimental effect. In this study, we propose controllable alternating current(AC)-driven skyrmion propagation in a ferromagnetic nanowire based on combination of gate-voltage-controlled magnetic anisotropy(VCMA) and Sk HE. Micromagnetic simulations show that a skyrmion oscillatory closed-loop-like in situ motion driven by AC can be transformed into directional ratchet-like propagation along the nanotrack by creating a VCMA-gate barrier. Additionally, we show that the skyrmion propagation conditions depend on the gate barrier potential and driving AC parameters, and they can be used for the optimal design of nanotrack devices. Moreover, this mechanism could be used to control skyrmion macroscopic propagation directions by dynamically alternating the voltage of another series of gates. We further show the dynamic control of the long-distance propagation of skyrmions along with the pinning state. The study results provide a promising route for designing future skyrmion-based spintronics logical and memory devices.

In-plane spin excitation of skyrmion bags

Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current(AC) magnetic field, we investigate the spinwave modes of skyrmion bags, which behave differently from the clockwise(CW) rotation mode and the counterclockwise(CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion–inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.

Room-temperature creation and manipulation of skyrmions in MgO/FeNiB/Mo multilayers

Magnetic skyrmions in multilayer structures are considered as a new direction for the next generation of storage due to their small size,strong anti-interference ability,high current-driven mobility,and compatibility with existing spintronic technology.In this work,we present a tunable room temperature skyrmion platform based on multilayer stacks of MgO/FeNiB/Mo.We systematically studied the creation of magnetic skyrmions in MgO/FeNiB/Mo multilayer structures with perpendicular magnetic anisotropy(PMA).In these structures,the magnetic anisotropy changes from PMA to in-plane magnetic anisotropy(IMA)as the thickness of FeNiB layer increases.By adjusting the applied magnetic field and electric current,stable and high-density skyrmions can be obtained in the material system.The discovery of this material broadens the exploration of new materials for skyrmion and promotes the development of spintronic devices based on skyrmions.

另一种Skyrmion的稳定项和内部结构

在“Ｓｋｙｒｍｅ模型中的一个问题及其简单的讨论”的基础上提出了两个问题：一是对Ｈｉｇｇｓ场形成的Ｓｋｙｒｍｉｏｎ其拉氏量中的Ｓｋｙｒｍｅ项可否用矢量介子作用项代替？另一个是对Ｈｉｇｇｓ场形成的Ｓｋｙｒｍｉｏｎ可否引进内部结构？对前一个问题找到了用规范矢量玻色子Ｚ０的作用作为Ｈｉｇｇｓ形成的Ｓｋｙｒｍｉｏｎ的稳定项；对后一间题接线性σ模型的方法引进了Ｈｉｇｇｓ形成的Ｓｋｙｒｍｉｏｎ的内部结构．获得这两个模型的方程组，并借助于别人的结果，得知这些方程组的某些信息．

Lorentz transmission electron microscopy for magnetic skyrmions imaging

Magnetic skyrmions have interesting properties,including their small size,topological stability,and extremely low threshold current for current-driven motion.Therefore,they are regarded as promising candidates for next-generation magnetic memory devices.Lorentz transmission electron microscopy(TEM)has an ultrahigh magnetic domain resolution(~2 nm),it is thus an ideal method for direct real-space imaging of fine magnetic configurations of ultra-small skyrmions.In this paper,we describe the basic principles of Lorentz-TEM and off-axis electron holography and review recent experimental developments in magnetic skyrmion imaging using these two methods.

Voltage-controllable magnetic skyrmion dynamics for spiking neuron device applications

Voltage-controlled magnetic skyrmions have attracted special attention because they satisfy the requirements for well-controlled high-efficiency and energy saving for future skyrmion-based neuron device applications.In this work,we propose a compact leaky-integrate-fire(LIF)spiking neuron device by using the voltage-driven skyrmion dynamics in a multiferroic nanodisk structure.The skyrmion dynamics is controlled by well tailoring voltage-induced piezostrains,where the skyrmion radius can be effectively modulated by applying the piezostrain pulses.Like the biological neuron,the proposed skyrmionic neuron will accumulate a membrane potential as skyrmion radius is varied by inputting the continuous piezostrain spikes,and the skyrmion radius will return to the initial state in the absence of piezostrain.Therefore,this skyrmion radius-based membrane potential will reach a definite threshold value by the strain stimuli and then reset by removing the stimuli.Such the LIF neuronal functionality and the behaviors of the proposed skyrmionic neuron device are elucidated through the micromagnetic simulation studies.Our results may benefit the utilization of skyrmionic neuron for constructing the future energy-efficient and voltage-tunable spiking neural networks.

Zero-field skyrmions in FeGe thin films stabilized through attaching a perpendicularly magnetized single-domain Ni layer

A numerical study reports that the zero-field skyrmions in Fe Ge thin films are stabilized when a Fe Ge layer is exchange coupled to a single-domain Ni layer,which has been magnetized perpendicularly.Due to the small thickness,an easy-plane anisotropy in the Fe Ge layer is taken into account,and the skyrmion-crystal state is favored to appear for low anisotropies and intermediate Fe Ge/Ni interlayer exchange couplings,and finally transformed from a labyrinth-like and into an out-ofplane uniform state for the large couplings or into an in-plane state for the high anisotropies.Furthermore,the maximum skyrmion charge number is bigger for the periodic and fixed boundary conditions with an out-of-plane magnetization;on the contrary,the Bloch-type skyrmions can be frozen and stabilized for the larger couplings on the fixed boundary with an in-plane magnetization,similar to the experimental results of the magnetic-field-induced skyrmions.Finally,the skyrmion charge number and diameter both decrease if the nonmagnetic defects exist,and the skyrmion centers are prone to being captured by defect sites.This work evidences that the ensembles of homochiral skyrmions stabilized in the multilayers fabricated by well-established technologies present a roadmap to design new classes of the materials that can host skyrmions.

磁性Skyrmions信息存储器的微磁学模拟

为了解决当前存储信息技术的发展问题,人们发现了一种新型的高密度信息载体——磁性Skyrmions.实现对磁性Skyrmions生成和输运的微观调控是完成其器件化过程中至关重要的一步.本文基于微磁学模拟方法,通过OOMMF软件首先在纳米盘模型中详细研究了自旋极化电流注入对磁性Skyrmions生成的影响.在局域电流注入过程中,调节自旋极化电流密度、电流注入时间和注入电流面积,得到了不同注入电流面积下阈值电流密度以及注入时间对Skyrmions拓扑数的影响;在全局电流注入中,实现了两种手性Skyrmions的生成,并讨论了模型尺寸对于Skyrmions拓扑数和尺寸的影响,对于低能耗、高密度新型Skymions信息存储器的研发提供了理论指导.

Control of Hall angle of Skyrmion driven by electric current

Skyrmions are very promising for applications in spintronics and magnetic memory.It is desired to manipulate and operate a single skyrmion.Here we report on the thermal effect on the motion of current-driven magnetic Skyrmions in magnetic metal.The results show that the magnon current induced by the thermal gradient acts on Skyrmions via magnonic spin-transfer torque,an effect of the transverse and longitudinal Skyrmions drift velocities,thus leading to the effective manipulation of the Hall angle through the ratio of thermal gradient to electric current density,which can be used as a Skyrmion valve.

SKYRMIONS IN GROSS-PITAEVSKII FUNCTIONALS

In Bose-Einstein condensates （BECs）, skyrmions can be characterized by pairs of linking vortex rings coming from two-component wave functions. Here we construct skyrmions by studying critical points of Gross-Pitaevskii functionals with two-component wave functions. Using localized energy method, we rigorously prove the existence, and describe the configurations of skyrmions in such BECs.

Realization of artificial skyrmion in CoCrPt/NiFe bilayers

Skyrmion, as a quasi-particle structure, has attracted much attention due to its potential applications in future spintronic devices. Artificial skyrmion structure has aroused great interest as it can be stabilized at room temperature, without needing to incorporate materials with Dzyaloshinskii–Moriya interaction(DMI) into it. In this paper, it is found that the artificial skyrmion structure can be realized in CoCrPt/NiFe bilayers by micromagnetic simulations. The critical magnetic field of the core decreases as the diameter of the NiFe soft magnetic layer increases. The artificial skyrmion has excellent topological protection, and the critical magnetic field of plane is about 76 mT(760 Oe, 1 Oe = 79.5775 A·m-1). The external magnetic field plays a key role in determining the core diameter of the skyrmion, and the artificial skyrmion can be realized in CoCrPt/Cu/CoCrPt/NiFe four-layer with a diameter of 13 nm.

Dynamics of magnetic skyrmions

We review the recent progress on the magnetic skyrmions in chiral magnetic materials. The magnetic skyrmion is a topological spin configuration with localized spatial extent, which could be thought of as an emergent rigid particle, owing to its particular topological and chiral properties. Static skyrmionic configurations have been found in various materials with different transport and thermodynamic properties. The magnetic skyrmions respond to externally applied fields in a very unique way, and their coupling to other quasiparticles in solid-state systems gives rise to the emergent electrodynamics.Being not only theoretically important, the magnetic skyrmion is also very promising to be the information carrier in next generation spintronic devices.

Skyrmion crystals in pseudo-spin-1/2 Bose–Einstein condensates

Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose-Einstein condensates, which are de- scribed by the coupled nonlinear Gross-Pitaevskii equations where the intra-and inter-species coupling constants are as- sumed to be equal. The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions. The stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, a crystal of skyrmion-anti-skyrmion pairs is formed in the soliton limit.

Skyrmion transport driven by pure voltage generated strain gradient

The magnetic skyrmion transport driven by pure voltage-induced strain gradient is proposed and studied via micromagnetic simulation.Through combining the skyrmion with multiferroic heterojunction,a voltage-induced uniaxial strain gradient is adjusted to move skyrmions.In the system,a pair of short-circuited trapezoidal top electrodes can generate the symmetric strain.Due to the symmetry of strain,the magnetic skyrmion can be driven with a linear motion in the middle of the nanostrip without deviation.We calculate the strain distribution generated by the trapezoidal top electrodes pair,and further investigate the influence of the strain intensity as well as the strain gradient on the skyrmion velocity.Our findings provide a stable and low-energy regulation method for skyrmion transport.

Spin transfer nano-oscillator based on synthetic antiferromagnetic skyrmion pair assisted by perpendicular fixed magnetic field

As a microwave generator, spin transfer nano-oscillator(STNO) based on skyrmion promises to become one of the next-generation spintronic devices. However, there still exist a few limitations to the practical applications. In this paper, we propose a new STNO based on synthetic antiferromagnetic(SAF) skyrmion pair assisted by a perpendicular fixed magnetic field. It is found that the oscillation frequency of this kind of STNO can reach up to 5.0 GHz, and the multiple oscillation peak with higher frequency can be realized under a fixed out-of-plane magnetic field. Further investigation shows that the skyrmion stability is improved by bilayer antiferromagnetic coupling, which guarantees the stability process of skyrmion under higher spin-polarized current density. Our results provide the alternative possibilities for designing new skyrmionbased STNO to further improve the oscillation frequency, and realize the output of multiple frequency microwave signal.

Current-driven dynamics of skyrmion bubbles in achiral uniaxial magnets

We report dynamics of skyrmion bubbles driven by spin-transfer torque in achiral ferromagnetic nanostripes using micromagnetic simulations.In a three-dimensional uniaxial ferromagnet with a quality factor that is smaller than 1,the skyrmion bubble is forced to stay at the central nanostripe by a repulsive force from the geometry border.The coherent motion of skyrmion bubbles in the nanostripe can be realized by increasing the quality factor to~3.8.Our results should propel the design for future spintronic devices such as artificial neural computing and racetrack memory based on dipolestabilized skyrmion bubbles.

Progress and challenges in magnetic skyrmionics

Magnetic skyrmions are two-dimensional localized topological spin-structures characterized by the skyrmion number that measures the number of times of spins wrapping the Bloch sphere. Skyrmions behave like particles under an external stimulus and are promising information carriers. Skyrmions can exist as an isolated object as well as skyrmion condensates in crystal structures, helical/conical states, mazes or irregular stripy states with emergent electromagnetic fields. Thus,skyrmions provide a nice platform for studying fundamental physics, other than its applications in spintronics. In this perspective, we briefly review some recent progress in the field and present an outlook of the fundamental challenges in device applications.