Dense skyrmion crystal stabilized through interfacial exchange coupling: Role of in-plane anisotropy

A Monte Carlo simulated-annealing algorithm was used to study the magnetic state in an in-plane helimagnet layer on triangular lattice that exchange couples to an underlayer with strong out-of-plane anisotropy. In the single helimagnet layer with in-plane anisotropy (K), the formation of labyrinthlike domains with local spin spirals, instead of parallel stripes, is favored, and these domains rapidly transform into dense skyrmion crystals with increasing interfacial exchange coupling (J′), equivalent to a virtual magnetic field, and finally evolve to an out-of-plane uniform state at large enough J′. Moreover, with increasing K, the skyrmion crystal state can vary from regular 6-nearest-neighboring circular skyrmion arrangement to irregular squeezed skyrmions with less than 6 nearest neighbors when the in-plane anisotropy energy is higher than the interfacial exchange energy as the skyrmion number is maximized. Finally, we demonstrated that the antiferromagnetic underlayer cannot induce skyrmions while the chirality inversion can be achieved on top of an out-of-plane magnetization underlayer with 180◦ domain walls, supporting the experimental findings in FeGe thin film. This compelling advantage offers a fertile playground for exploring emergent phenomena that arise from interfacing magnetic skyrmions with additional functionalities.     

磁畴壁手性和磁斯格明子的拓扑性表征及其调控

磁性斯格明子由于拓扑的保护性,具有很高的稳定性和较小的临界驱动电流,有望应用于未来的赛道存储器件中.而在中心对称体系,由于偶极作用的各向同性,磁泡的拓扑性和螺旋度都呈现出多样性的特征.其中非平庸的磁泡即等同于磁性斯格明子.我们通过近期实验结果,结合微磁学模拟的方法,发现在中心对称体系中磁斯格明子的拓扑性会受到体系垂直各向异性的调控.另外在加磁场的演变过程中,会很大程度上依赖于基态畴的畴壁特性.磁场的倾斜或者一定的面内各向异性也会改变磁斯格明子的形态.通过对材料的基态磁结构及磁各向异性的调节,辅助以面内分量的控制,可以对基态磁畴、进而对磁斯格明子的拓扑性实现调控.这对磁斯格明子在电流驱动存储器件中的应用具有重要意义.     

Dynamics of Magnetic Skyrmions in Nanodots

Bloch and Neel magnetic skyrmions have been studied in systems of confined geometry (nanodots, a linear array of nanodots). The spectra of low- and high-frequency excitation modes of a skyrmion state have been calculated. It has been shown that skyrmion spectrum asymmetry, namely, the characteristic difference between the frequencies of the azimuthal modes of the azimuthal skyrmion modes rotating clockwise and counterclockwise, is associated with asymmetry in the magnetization profiles of high-frequency spin waves propagating on the background of a skyrmion state in a nanodot. The low-frequency spectrum contains the only gyrotropic mode localized near the center of a nanodot. The gyrotropic frequency depends on the material parameters of a nanodot and the size of a skyrmion. The eigenfrequency of the gyrotropic mode of an isolated skyrmion in a nanodot in ultrathin films (L ~ 1 nm) does not depend on the internal structure of a skyrmion and is the same for Bloch and Neel skyrmions. The interaction of skyrmions, in particular, in a linear chain of nanodots with the ground skyrmion state, leads to distinctions in low-frequency spectra. The structure of a skyrmion (of Bloch or Neel type) is exhibited as a shift of dispersion curves and a difference between the frequencies of ferromagnetic resonance in a system of interacting skyrmions.     

Brownian motion of massive skyrmions in magnetic thin films

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.     

磁斯格明子拓扑特性及其动力学微磁学模拟研究进展

具有非平庸拓扑性的新型磁结构斯格明子,由于其拓扑稳定性、尺寸小、低电流驱动等方面的显著优势,有望应用于自旋电子学储存器件.拓扑和凝聚态物理学的结合,使得斯格明子展现出很多有趣的拓扑物理现象,吸引了众多的研究兴趣,同时这些性质也是其电流驱动下动力学特点的重要影响因素.本文从斯格明子的拓扑物理学基础及其自旋电子学器件应用相关动力学两个方面介绍了相关研究进展.在拓扑物理基础方面,介绍了斯格明子的拓扑霍尔效应、斯格明子霍尔效应以及自旋轨道转矩等拓扑性质,由此讨论了斯格明子的动力学性质及其计算方法;在动力学方面,从非均匀电流驱动生成斯格明子、电流驱动下的稳定输运、产生湮灭过程的人工控制几个赛道存储应用关心的问题简要地介绍了相关微磁学模拟研究最新进展.     

中心对称的阻挫磁体中斯格明子直径的调节

在带有垂直各向异性的二维三角晶格磁体中,当同时存在最近邻铁磁性和第三近邻反铁磁性交换作用时,垂直于膜面施加外磁场会使体系内自旋沿着非共面的方向排列,甚至出现拓扑稳定的斯格明子自旋结构.基于蒙特卡罗模拟方法,本文研究了在该二维阻挫磁体中,竞争性交换作用和外磁场对斯格明子直径的影响.与常规非中心对称的手性磁体中的斯格明子性质类似,外磁场会磁化斯格明子外围自旋而减小斯格明子直径.但是,磁体中反铁磁性交换作用的增强会整体压缩斯格明子.本文结合自旋波理论和蒙特卡罗模拟,首次量化了此类阻挫磁体中斯格明子的直径.结果表明:在弱的反铁磁性交换作用磁体中,斯格明子直径随磁场增大而快速线性减小;随着反铁磁性交换作用的增大,斯格明子直径随外磁场增大的减小变得相对平缓,但在强磁场下也会造成斯格明子直径的加速减小;随着反铁磁性交换作用的增强,斯格明子在不同外磁场下的直径的最大值和中值均从逐渐减小到渐趋稳定,而直径的最小值则从快速减小到表现出很大的涨落.这些现象都可以通过分析斯格明子在不同交换作用和外磁场下的构型和磁能变化加以解释.该项工作阐明了在中心对称的阻挫磁体中斯格明子直径的可调节性,不仅完善了我们对斯格明子本身物理机理的认识,同时也为发展基于斯格明子的新一代存储和逻辑器件提供了理论支撑.     

Tunable in-plane spin orientation in Fe/Si(557) film by step-induced competing magnetic anisotropies

Although the spin-reorientation transition from out-of-plane to in-plane in Fe/Si film is widely reported, the tuning of in-plane spin orientation is not yet well developed. Here, we report the thickness-, temperature- and Cu-adsorptioninduced in-plane spin-reorientation transition processes in Fe/Si(557) film, which can be attributed to the coexistence of two competing step-induced uniaxial magnetic anisotropies, i.e., surface magnetic anisotropy with magnetization easy axis perpendicular to the step and volume magnetic anisotropy with magnetization easy axis parallel to the step. For Fe film thickness smaller than 32 monolayer(ML), the magnitudes of two effects under various temperatures are extracted from the thickness dependence of uniaxial magnetic anisotropy. For Fe film thickness larger than 32 ML, the deviation of experimental results from fitting results is understood by the strain-relief-induced reduction of volume magnetic anisotropy.Additionally, the surface and volume magnetic anisotropies are both greatly reduced after covering Cu capping layer on Fe/Si(557) film while no significant influence of Na Cl capping layer on step-induced magnetic anisotropies is observed.The experimental results reported here provide various practical methods for manipulating in-plane spin orientation of Fe/Si films and improve the understanding of step-induced magnetic anisotropies.     

Magnetic surfaces

The magnetic ground state, magnetic anisotropies and spin excitations of surfaces, interfaces and ultra-thin films of ferromagnetic 3d-metals are discussed. Enhanced magnetic ground state moments and altered hyperfine fields as predicted by ab initio band calculations have not been conclusively verified by experiments up to now. Future calculations should take into account dipolar fields and the role of interface roughness. Very large magnetic anisotropies are observed at magnetic surfaces and interfaces. In Ni/Cu multilayered films, the superposition of surface and stress-induced anisotropies was used to switch the easy axis of magnetization from the film plane to a perpendicular orientation by a proper choice of the Ni layer thickness. This could be an attractive possibility to develop new magnetic materials for technical applications. The temperature dependence of the spontaneous magnetization at surfaces and in ultra-thin films deviates from the behaviour of bulk material. Size effects as well as surface effects of spin wave excitations are discussed, comparing theoretical and experimental results. The need for more complete theories including surface exchange, surface anisotropy and realistic surface structures is emphasized.     

Structural and Magnetic Properties of [Fe/Ni]N Multilayers

[Fe/Ni]N multilayered structure grows epitaxially on the single crystalline MgO substrate. Due to the different directions of magnetic easy axes of Fe and Ni and the strong strain, large anisotropy dispersion is assumed. According to the layer model, the magnetization of Fe and Ni layers cannot follow each easy axis because of exchange coupling, and then the anisotropies are averaged out. The reduction of the effective anisotropy enhances with the decrease of periodic thickness. Thus, the coercivity of [Fe/Ni]N multilayers reduces with decreasing periodic thickness.     

Skyrmions in electron gas with nonlocal exchange in a strong magnetic field

The energy and action for skyrmions in two-dimensional electron gas with nonlocal exchange have been calculated. The energy of positively charged skyrmions is considerably lower than the energy of negatively charged skyrmions and does not contain an exchange contribution. The action has been calculated taking into account collective skyrmion null modes. Zh. éksp. Teor. Fiz. 115, 716–725 (February 1999)     

Quantum Hall skyrmions with higher topological charge

We have investigated quantum Hall skyrmions with more than one unit of topological, and hence electric, charge. Using a combination of analytic and numerical methods we find the counterintuitive result that when the Zeeman energy is tuned to values much smaller than the interaction energy ( ), the creation energy of a charge two skyrmion becomes less than twice the creation energy of a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged skyrmions are stable to further accretion of charge and exhibit a larger spin per unit charge than charge one skyrmions which would, in principle, signal this pairing. 1997 Elsevier Science B.V. All rights reserved.     

Topological charge analysis of dynamic process of transition to Néel-type skyrmion: Role of domain wall skyrmions

Magnetic skyrmions are intriguing topological spin textures that promise future high-density spintronic devices. The creation of magnetic skyrmions has been understood based on the energetics of skyrmions, but the detailed dynamic process of the skyrmion creation remains unclear. Here topological evolution in conversion from uneven domains to Néel-skyrmions is investigated using micromagnetic simulations. We find that, rather than the overall topological charge, annihilation of novel topological defects, i.e., recently suggested domain wall skyrmions, dominantly govern the skyrmion creation process. Also, the topological charge evolution is interpreted in terms of the number and the combination of such topological defects.     

Symmetry-breaking induced exchange bias in ferromagnetic Ni-Cu-Co and Ni-Fe-Co sandwiches grown on a vicinal Cu(001) surface

Ferromagnetic Ni-Cu-Co and Ni-Fe-Co sandwiches were grown epitaxially onto a vicinal Cu(001) substrate and investigated using magneto-optical Kerr effect and x-ray magnetic circular dichroism techniques. We find that the atomic steps of the vicinal surface break the magnetic reversal symmetry to induce an exchange bias in the Ni perpendicular magnetic hysteresis loop. The Ni exchange bias direction can be switched by changing the direction of the in-plane Co magnetization. In addition, the exchange bias can be tailored by changing the Cu or Fe spacer layer thickness.     

Magnetic skyrmion dynamics in thin cylindrical dots

We calculate high‐frequency spin excitations of the skyrmion ground state cylindrical magnetic dots. The skyrmion is assumed to be stabilized at room temperature due to interplay of the isotropic and Dzyaloshinskii–Moriya exchange interactions, perpendicular magnetic anisotropy and magnetostatic interaction. The Skyrmion ground state is represented as combination of two radially symmetric bubble domains. To consider the Bloch‐ and Néel‐type magnetic skyrmion dynamics we apply an approximation of ultrathin domain wall between the circular domains and assume that the magnetic dot is thin enough (magnetization does not depend on the thickness coordinate). The eigenfunctions/eigenfrequencies of spin wave excitations over the skyrmion background are calculated as a function of the skyrmion radius. The developed approach allows predicting spin wave eigenfrequencies in the skyrmion ground state magnetic dots. Recent experiments on magnetic skyrmion dynamics are discussed. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

周期性应变调控斯格明子在纳米条带中的运动

斯格明子是一种拓扑稳定的手性自旋结构,凭借其在磁性赛道存储器和自旋电子器件方面的巨大应用潜力而受到研究人员的广泛关注.为了使斯格明子能够更好地应用于磁性赛道存储器,研究斯格明子在纳米条带中的运动行为就变得非常重要.本文主要研究了存在周期性应变的纳米条带中铁磁斯格明子和反铁磁斯格明子在电流驱动下的运动行为.研究结果表明:周期性应变使得驱动电流存在一个临界电流密度,只有当电流密度大于临界电流密度时斯格明子才能够在纳米条带中连续移动.临界电流密度随应变振幅的增加而增加,随应变周期的增加而减小.铁磁斯格明子在周期性应变的调制下会产生周期性运动,轨迹为波浪式,其横向速度受到边界的影响,而纵向速度则与应变梯度成正比.反铁磁斯格明子在周期性应变调控下运动方向不变,但其移动速度则剧烈变化.     

Non-volatile multi-state magnetic domain transformation in a Hall balance

High performance of the generation, stabilization and manipulation of magnetic skyrmions prompts the application of topological multilayers in spintronic devices. Skyrmions in synthetic antiferromagnets (SAF) have been considered as a promising alternative to overcome the limitations of ferromagnetic skyrmions, such as the skyrmion Hall effect and stray magnetic field. Here, by using the Lorentz transmission electron microscopy, the interconversion between the single domain, labyrinth domain and skyrmion state can be observed by the combined manipulation of electric current and magnetic field in a Hall balance (a SAF with the core structure of [Co/Pt]₄/NiO/[Co/Pt]₄ showing perpendicular magnetic anisotropy). Furthermore, high-density room temperature skyrmions can be stabilized at zero field while the external stimulus is removed and the skyrmion density is tunable. The generation and manipulation method of skyrmions in Hall balance in this study opens up a promising way to engineer SAF-skyrmion-based memory devices.     

Rotating skyrmions of the (2 + 1)-dimensional Skyrme gauge model with a Chern-Simons term

The (2 + 1)-dimensional Skyrme gauge model with a Chern-Simons term is considered. The presence of the Chern-Simons term makes possible the existence of two-dimensional skyrmions in this model, which carry magnetic flux and have an electric charge and a nonzero angular momentum. It is shown that the model also admits the existence of two-dimensional skyrmions with a nonzero phase frequency of rotation. Due to the nontrivial topological properties of the model, the magnetic flux, the electric charge, and the angular momentum of a two-dimensional rotating skyrmion turn out to be interrelated. Analytic and numerical investigations of the properties of rotating two-dimensional skyrmions are carried out.     

纳米结构中磁斯格明子的原位电子全息研究

斯格明子(skyrmion)磁序结构与晶体微观结构的关联是新型功能磁材料和器件研发的重要问题.本文利用微纳加工技术制备了形状、尺寸均可控的磁纳米结构,通过电子全息术观察定量地分析了斯格明子磁序结构,确定了材料晶格缺陷和空间受限效应对斯格明子磁结构形成和稳定机制的影响,系统地分析了斯格明子基元的磁功能与材料微结构的关联.文中主要探讨了两个问题:1)斯格明子在磁纳米结构中的空间受限效应.重点研究斯格明子磁序随外磁场和温度变化的演变规律,探索其演变过程的拓扑属性和稳定性;2)晶格缺陷对斯格明子磁结构的影响,重点考察晶界原子结构手性反转对斯格明子磁序的影响.这些研究结果可为研发以磁斯格明子为基元的磁信息存储器及自旋电子学器件提供重要实验基础.     

磁性斯格明子的研究现状和展望

磁性斯格明子是具有拓扑保护性质的纳米尺度涡旋磁结构.斯格明子主要存在于非中心对称的手性磁性材料以及界面镜面对称性破缺的磁性薄膜材料中.因具有实空间的非平庸拓扑性,磁性斯格明子展现出丰富新奇的物理学特性,例如拓扑霍尔效应,新兴电磁动力学等,为研究拓扑自旋电子学提供了新的平台.另一方面,由于其具有尺寸小,高稳定性和易操控的特性,磁性斯格明子在未来高密度,低能耗,非易失性计算和存储器件中也具有潜在应用.现阶段的研究已经初步发现一系列磁斯格明子材料,并证明能够通过电流操控室温下稳定的磁性斯格明子,但是室温下单个斯格明子的精确产生、湮灭以及探测在实验上仍具有挑战性.本文阐述了磁性斯格明子的基础理论以及动力学研究现状,并对现有的斯格明子材料和斯格明子的产生,湮灭以及探测方法进行了总结,最后还对未来磁性斯格明子的物理理论研究以及应用发展中的挑战和机遇进行了讨论.     

磁性斯格明子的多场调控研究

斯格明子(skyrmion)的概念最早是由英国的粒子物理学家Tony Skyrme提出,它被用来描述粒子的一个状态,是一种拓扑孤立子.磁性斯格明子是一种具有拓扑行为的新型磁结构,其空间尺寸为纳米量级,空间距离从纳米到微米量级可调;其存在温度涵盖从低温、室温到高温的宽温区;其材料体系不仅包括早期发现的低温区B20型中心对称破缺的铁磁体和螺旋磁有序的弱铁磁材料,也包括近期发现的室温及以上的中心对称六角结构磁性MnNiGa金属合金和磁性薄膜/多层膜体系.利用磁性斯格明子的拓扑磁结构可以实现类似于自旋阀或者磁性隧道结中的自旋转移矩效应,即外加电流可以驱动斯格明子,其临界电流密度比传统翻转磁性多层膜体系中磁矩的电流密度(一般为10~7A/cm~2)要低5个数量级,约为10~2A/cm~2,该临界值远低于硅基半导体技术中沟道电流密度的上限,在未来的磁信息技术中具有广泛的应用前景.本综述简单介绍了磁性斯格明子的发展历程,归纳总结了磁性斯格明子的材料体系,介绍了观察磁性斯格明子的实验手段,重点介绍了多场(磁场、电流、温度场)调控作用下中心对称MnNiGa合金和Pt/Co/Ta磁性多层膜体系中磁性斯格明子的产生、消失以及外场调控演变等动态行为.