Reorientation transition between square and hexagonal skyrmion lattices near the saturation into the homogeneous state in quasi-two-dimensional chiral magnets
I revisit the well-known phase transition between the hexagonal skyrmion lattice and the homogeneous state within the phenomenological Dzyaloshinskii theory for chiral magnets which includes only the exchange, Dzyaloshinskii-Moriya and Zeeman energy contributions. I show that, in a narrow field range near the saturation field, the hexagonal skyrmion order gradually transforms into a square arrangement of skyrmions. Then, by the second-order phase transition during which the lattice period diverges, the square skyrmion lattice releases a set of repulsive isolated skyrmions. On decreasing magnetic field, isolated skyrmions re-condense into the square lattice at the same critical field as soon as their eigen-energy becomes negative with respect to the field-aligned state. The underlying reason of the reorientation transition between two skyrmion orders can be deduced from the energy density distribution within isolated skyrmions surrounded by the homogeneous state. When the negative energy within the ring-shaped area at the skyrmion outskirt outweighs the positive energy amount around the skyrmion axis, skyrmions tend to form the square lattice, in which the overlap of skyrmion profiles results in smaller energy losses as compared with the hexagonal crystal. With the further decreasing field, the hexagonal lattice achieves smaller energy density in comparison with the square one due to the denser packing of individual skyrmions.
We obtain the lowest energy solutions for the skymion field equations and their corresponding vortex structures. Two nondegenerate solutions emerge with their vortex swirls in opposite directions. The solutions are associated with an extremum property, which favors an array of almost hexagonal shape. We predict that a regular hexagonal lattice must have a mix of skyrmions of both swirls. Although our solutions could not keep the norm of the magnetization constant at unity, their greatest deviation from unity occurred in regions where the spins are far from planar; we show how to improve this s…
Magnetic skyrmions are nontrivial spin textures which resist external perturbations, being promising candidates for the next generation recording devices. Nevertheless, a major challenge in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures under ambient conditions and zero applied field. Here, we demonstrate for the first time the formation and stabilization of magnetic skyrmions on arrays of self-assembled hexagonal nanodomes taking advantage of the intrinsic properties of its curved geometry. Magnetic force microscopy images from the arrays of 100…
Thin magnetic films with Dzyaloshinskii-Moriya interactions are known to host skyrmion crystals, which typically have a hexagonal lattice structure. We investigate skyrmion-lattice configurations in synthetic antiferromagnets, i.e., a bilayer of thin magnetic films that is coupled antiferromagnetically. By means of Monte-Carlo simulations, we find that by tuning the interlayer coupling the skyrmion lattice structure can be tuned from square to hexagonal. We give a simple interpretation for the existence of this transition based on the fact that for synthetic antiferromagnetic coupling the skyr…
Acoustic phonons, spin-phonon coupling and spin relaxation via the lattice reorientation mechanism in hexagonal germanium nanowires
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN-BME-BCE Quantum Technology Research Group, Budapest University of Technology and Economics（匈牙利研究与创新网络-布达佩斯技术与经济大学-基础与交叉中心量子技术研究组）
We have utilised a high spatial resolution imaging method, Differential Phase Contrast (DPC) performed in a scanning transmission electron microscope (STEM), for precise measurement of the magnetic induction distribution in skyrmion states in noncentrosymmetric magnetically ordered materials. Applied to investigate the internal structure of hexagonal skyrmion lattice cells, stabilised by an out-plane applied magnetic field in an FeGe nanowedge specimen, mapping of the in-plane component of magnetic induction has yielded "average" skyrmion profiles and observation of internal six-fold symmetry.…
Meron-mediated phase transitions in quasi-two-dimensional chiral magnets with easy-plane anisotropy: successive transformation of the hexagonal skyrmion lattice into the square lattice and into the tilted FM state
Microelectromechanical systems, which can be moved or rotated with nanometre precision, already find applications in such fields like radio-frequency electronics, micro-attenuators, sensors and many others. Especially interesting are those which allow fine control over the motion on atomic scale due to self-alignment mechanisms and forces acting on the atomic level. Such machines can produce well-controlled movements as a reaction to small changes of the external parameters. Here we demonstrate that, for the system of graphene on hexagonal boron nitride, the interplay between the van der Waals…
We discuss distinctive features of spiral states in bulk chiral magnets such as MnSi and Cu$_2$OSeO$_3$ that stem from the effect of the cubic magneto-crystalline anisotropy. First of all, at both the helical-to-conical and the conical-to-ferromagnetic transitions, taking place at H$_{c1}$ and H$_{c2}$, respectively, the cubic anisotropy leads to reversible or irreversible jump-like reorientations of the spiral wavevectors. The subtle interplay between the easy and hard anisotropy axes gives rise to a phase transition between elliptically distorted conical states almost without any detectable …
Spin-polarized scanning tunneling microscopy has been applied to study non-collinear spin textures of a Mn monolayer on a four-fold symmetric W(001) substrate revealing a zero-field spin spiral ground state and two different types of rotational domain walls. With an applied magnetic field of 9 T, we observe a coexistence of the spin spiral and the skyrmion phase, even though a previous theoretical study reported that the phase transition occurs at 18 T. The skyrmions show a roughly hexagonal arrangement despite the square lattice symmetry of the W(001) substrate. Based on a reduced set of ener…
Axisymmetric solitonic states (chiral skyrmions) have been predicted theoretically more than two decades ago. However, until recently they have been observed in a form of skyrmionic condensates (hexagonal lattices and other mesophases). In this paper we report experimental and theoretical investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers two years ago (Science 341 , 636 (2013)). The results of spin-polarized scanning tunneling microscopy analyzed within the continuum and discrete models provide a consistent description of isolated skyrmions in thin layers. The exi…
Emergent phenomena and functions arising from topological electron-spin textures in real space or momentum space are attracting growing interest for new concept of states of matter as well as for possible applications to spintronics. One such example is a magnetic skyrmion, a topologically stable nanoscale spin vortex structure characterized by a topological index. Real-space regular arrays of skyrmions are described by combination of multi-directional spin helixes. Nanoscale configurations and characteristics of the two-dimensional skyrmion hexagonal-lattice have been revealed extensively by …
Recently, there has been substantial interest in realizations of skyrmions, in particular in 2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the 2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symme…
Cu$_2$OSeO$_3$ is an insulating skyrmion-host material with a magnetoelectric coupling giving rise to an electric polarization with a characteristic dependence on the magnetic field $\vec H$. We report magnetic force microscopy imaging of the helical real-space spin structure on the surface of a bulk single crystal of Cu$_2$OSeO$_3$. In the presence of a magnetic field, the helimagnetic order in general reorients and acquires a homogeneous component of the magnetization, resulting in a conical arrangement at larger fields. We investigate this reorientation process at a temperature of 10~K for …
The internal and lattice structures of magnetic skyrmions in B20-type FeGe are investigated using off-axis electron holography. The temperature, magnetic field and angular dependence of the magnetic moments of individual skyrmions are analyzed. Whereas the internal skyrmion shape is found to vary with magnetic field, the inter-skyrmion distance remains almost unchanged in the lattice phase. The amplitude of the local magnetic moment is found to depend on temperature, while the skyrmion shape does not. Deviations from a circular to a hexagonal skyrmion structure are observed in the lattice phas…
Controlling Skyrmion Lattice Orientation with Local Magnetic Field Gradients
Institute of Physics, Johannes Gutenberg University Mainz（约翰内斯·古腾堡大学美因茨分校物理研究所）；Department of Physics and Materials Science, University of Luxembourg（卢森堡大学物理与材料科学系）；Department of Materials Science and Engineering, Norwegian University of Science and Technology (NTNU)（挪威科技大学材料与工程系）；Centre for Quantum Spintronics, Norwegian University of Science and Technology (NTNU)（挪威科技大学量子自旋电子学中心）；Faculty of Physics, University of Duisburg-Essen（杜伊斯堡-埃森大学物理学院）
We determine the nature of the magnetic order on the surface of a topological insulator (TI) which develops due to hexagonal warping and the resulting Fermi surface (FS) nesting in the presence of a repulsive Hubbard interaction. For this purpose we investigate the spin susceptibility and derive a Landau theory to compare the different accessible phases. For a nearly hexagonal FS and sufficiently strong interaction the magnetic ground state is formed by a skyrmion lattice, i.e., by a superposition of three helical spin density waves which preserves C$_3$ symmetry. The magnetic ground state is …
Magnetic skyrmions have attracted great research interest in recent years due to their exotic physical properties, scientific merit and potential applications in modern technology. Here, we apply a quantum computational method to investigate the spin configurations of Fe$_{0.5}$Co$_{0.5}$Si-Like quasi-two-dimensional ferromagnetic system with co-existence of Dzyaloshinsky-Moriya and Heisenberg exchange interactions. We find that within a weak magnetic field perpendicular to the film plane, skyrmion crystal (SkX) of hexagonal-close-packed pattern can be induced, the spin configurations evolve w…
We investigate the anomalous effects due to the Berry correction and the considerable perturbations in the silicene-like hexagonal lattice system. The Berry curvature in periodic Bloch band system which related to the electromagnetic field is explored, the induced transverse anomalous velocity gives rise to the intrinsic Hall conductivity (without the vertex correction) expecially in the quantum anomalous Hall phase. The quantum anomalous Hall effect which related to the anomalous velocity term is detected, including the band avoided corssing effect and the generated special band gap. %{Enlarg…
Magnetic skyrmions are topologically nontrivial spin textures which hold great promise as stable information carriers in spintronic devices at the nanoscale. One of the major challenges for developing novel skyrmion-based memory and logic devices is fast and controlled creation of magnetic skyrmions at ambient conditions. Here we demonstrate the single ultrafast (35-fs) laser pulse-induced generation of skyrmion bubbles and skyrmion bubble lattices from a ferromagnetic state in sputtered ultrathin magnetic films at room temperature. The skyrmion bubble density increases with the laser fluence …
We study quantum Hall ferromagnets with a finite density topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a $d$-component complex spinor field. In the absence of anisotropies, we find formation of a hexagonal Skyrmion lattice which completely breaks the underlying SU(d) symmetry. The ground state charge density modulation, which inevitably exists in these lattices, vanishes exponentially in $d$. We compute analytically the complete low-lying excitation spectrum, which separates into …
Chiral skyrmion states exist in non - centrosymmetric magnetic crystals as a consequence of the asymmetric exchange Dzyaloshinskii-Moriya interactions that destroy the homogeneous magnetic state and generally lead to twisted incommensurate magnetic spin-structures. Recently, skyrmion lattices and free skyrmions in magnetic layers of the chiral helimagnets with the noncentrosymmetric cubic B20 crystal structure have been observed. The stabilization of these states and their transformation properties impressively illustrate the theoretically predicted solitonic nature of these chiral two-dimensi…
Topological spin textures emerging in magnetic materials usually appear in crystalline states. A long-standing dilemma is whether we should understand these emergent crystals as gathering particles or coupling waves, the answer of which affects almost every aspect of our understanding on the subject. Here we prove that 2-D emergent crystals with long-range order in helimagnets, such as skyrmion crystals and dipole skyrmion crystals, have a wave nature. We systematically study their equilibrium properties, metastability, and phase transition path when unstable. We show that the robustness of a …
Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；Université Grenoble Alpes, CNRS, CEA, SPINTEC（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，法国原子能和替代能源委员会，SPINTEC）；Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University（东北大学电气通信研究所纳米电子与自旋电子学实验室）；Peter Grünberg Institute, Forschungszentrum Jülich and JARA（于利希研究中心和JARA的彼得·格林伯格研究所）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文学系）；Wallenberg Initiative Materials Science, WISE, Uppsala University（乌普萨拉大学瓦伦堡材料科学倡议WISE）；Helmholtz-Zentrum Berlin für Materialien und Energie GmbH（柏林亥姆霍兹材料与能源中心有限公司）
The control of domain walls is central to nearly all magnetic technologies, particularly for information storage and spintronics. Creative attempts to increase storage density need to overcome volatility due to thermal fluctuations of nanoscopic domains and heating limitations. Topological defects, such as solitons, skyrmions, and merons, may be much less susceptible to fluctuations, owing to topological constraints, while also being controllable with low current densities. Here, we present the first evidence for soliton/soliton and soliton/antisoliton domain walls in the hexagonal chiral magn…
