Three-dimensional topological solitons attract a great deal of interest in fields ranging from particle physics to cosmology but remain experimentally elusive in solid-state magnets. Here we numerically predict magnetic heliknotons, an embodiment of such nonzero-Hopf-index solitons localized in all spatial dimensions while embedded in a helical or conical background of chiral magnets. We describe conditions under which heliknotons emerge as metastable or ground-state localized nonsingular structures with fascinating knots of magnetization field in widely studied materials. We demonstrate magnetic control of three-dimensional spatial positions of such solitons, as well as show how they interact to form molecule-like clusters and possibly even crystalline phases comprising three-dimensional lattices of such solitons with both orientational and positional order. Finally, we discuss both fundamental importance and potential technological utility of magnetic heliknotons.
The formation of topological spin textures at the nanoscale has a significant impact on the long-range order and dynamical response of magnetic materials. We study the relaxation mechanisms at the conical-to-helical phase transition in the chiral magnet FeGe. By combining ac susceptibility, magnetic force microscopy measurements and micromagnetic simulations, we demonstrate how the motion of magnetic topological defects, here edge dislocations, impacts the local formation of a stable helimagnetic spin structure. Although the simulations show that the edge dislocations move with a velocity of a…
Small-angle neutron scattering (SANS) profiles revealed the existence of magnetic textures like liquid crystals in the low-temperature helical phase of Fe0.7Co0.3Si, isomorphous of MnSi.
The structure of domain walls determines to a large extent the properties of magnetic materials, in particular their hardness and switching behavior, it represents an essential ingredient of spintronics. Common domain walls are of Bloch and Neel types in which the magnetization rotates around a fixed axis, giving rise to a one-dimensional magnetization profile. Domain walls in helical magnets, most relevant in multiferroics, were never studied systematically. Here we show that domain walls in helical magnets are fundamentally different from Bloch and Neel walls. They are generically characteri…
We present long-wavelength neutron diffraction data measured on both single crystal and polycrystalline samples of the skyrmion host material Cu$_{2}$OSeO$_{3}$. We observe magnetic satellites around the $(0\bar{1}1)$ diffraction peak not accessible to other techniques, and distinguish helical from conical spin textures in reciprocal space. We confirm successive transitions from helical to conical to field polarised ordered spin textures as the external magnetic field is increased. The formation of a skyrmion lattice with propagation vectors perpendicular to the field direction is observed in …
A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There is an analogy with the classical problem of an electric field applied to a cholesteric liquid crystal, but with important differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between director anchoring to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding th…
Helical-to-Fan Transitions under Magnetic Fields in the Noncentrosymmetric Tetragonal Magnet EuRhGe$_3$
Hiroshima University（广岛大学）；Institute of Materials Structure Science, High Energy Accelerator Research Organization（高能加速器研究机构材料结构科学研究所）；University of the Ryukyus（琉球大学）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
The lack of inversion symmetry in the crystal lattice of magnetic materials gives rise to complex non-collinear spin orders through interactions of relativistic nature, resulting in interesting physical phenomena, such as emergent electromagnetism. Studies of cubic chiral magnets revealed a universal magnetic phase diagram, composed of helical spiral, conical spiral and skyrmion crystal phases. Here, we report a remarkable deviation from this universal behavior. By combining neutron diffraction with magnetization measurements we observe a new multi-domain state in Cu2OSeO3. Just below the uppe…
3D topological solitons are marvels of mathematical physics that arise in theoretical models in elementary particle and nuclear physics, condensed matter, and cosmology. A particularly interesting type of them is described by the mathematical Hopf map from a hypersphere to an ordinary sphere, which in the physical 3D space exhibits inter-linked circle-like or knotted localized regions of constant order parameter values. Despite their prevalence in models, such solitons remained experimentally elusive until recently, when hopfions were discovered in colloids and chiral liquid crystals, whereas …
Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity / vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd3Ru4Al12, which materializes a breathing kagomé lattice of Gadolinium moments. The …
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 …
We present a systematic study of the ac susceptibility of the chiral magnet Fe$_{1-x}$Co$_x$Si with $x$ = 0.30 covering four orders of magnitude in frequencies from 0.1 Hz to 1 kHz, with particular emphasis to the pronounced history dependence. Characteristic relaxation times ranging from a few milliseconds to tens of seconds are observed around the skyrmion lattice A-phase, the helical-to-conical transition and in a region above $T_C$. The distribution of relaxation frequencies around the A-phase is broad, asymmetric and originates from multiple coexisting relaxation processes. The pronounced…
Understanding spin-wave dynamics in chiral magnets is a key step for the development of high-speed, spin-wave based spintronic devices that take advantage of chiral and topological spin textures for their operation. Here we present an experimental and theoretical study of spin-wave dynamics in a cubic B20 FeGe single crystal. Using the combination of waveguide microwave absorption spectroscopy (MAS), micromagnetic simulations, and analytical theory, we identify the resonance dynamics in all magnetic phases (field polarized, conical, helical, and skyrmion phases). Because the resonance frequenc…
By employing resonant X-ray microdiffraction, we image the magnetisation and magnetic polarity domains of the Y-type hexaferrite Ba$_{0.5}$Sr$_{1.5}$Mg$_2$Fe$_{12}$O$_{22}$. We show that the magnetic polarity domain structure can be controlled by both magnetic and electric fields, and that full inversion of these domains can be achieved simply by reversal of an applied magnetic field in the absence of an electric field bias. Furthermore, we demonstrate that the diffraction intensity measured in different X-ray polarisation channels cannot be reproduced by the accepted model for the polar magne…
We present a comprehensive and systematic magnetization and ac susceptibility study of Mn$_{1-x}$Fe$_{x}$Si over an extensive range of ten Fe concentrations between $x$ = 0 - 0.32. With increasing Fe substitution, the critical temperature decreases but the magnetic phase diagrams remain qualitatively unaltered for $x$ $\leq$ $x^*$ $\approx$ 0.11 with clear boundaries between the helical, conical, and skyrmion lattice phase as well as an enhanced precursor phase. A notably different behavior sets in for $x$ $=$ 0.11, 0.13 and 0.14, where certain characteristics of helimagnetic correlations pers…
Non-collinear spin textures in ferromagnetic ultrathin films are attracting a renewed interest fueled by possible fine engineering of several magnetic interactions, notably the interfacial Dzyaloshinskii-Moriya interaction. This allows the stabilization of complex chiral spin textures such as chiral magnetic domain walls (DWs), spin spirals, and magnetic skyrmions. We report here on the ultrafast behavior of chiral DWs after optical pumping in perpendicularly magnetized asymmetric multilayers, probed using time-resolved circular dichroism in x-ray resonant magnetic scattering (CD-XRMS). We obs…
Quasi-1D Spin Textures: From Chiral Soliton Lattice to Fan State
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Dresden Center for Nanoanalysis, cfaed, Technical University Dresden（德累斯顿纳米分析中心，cfaed，德累斯顿工业大学）；Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg（奥格斯堡大学电子关联与磁学中心实验物理学第六系）；Diamond Light Source（钻石光源）；Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen（杜伊斯堡-埃森大学物理学院及杜伊斯堡-埃森纳米集成中心（CENIDE））；Department of Physics, Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室物理系）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源研究中心）
