Using the model of classical Heisenberg exchange and Dzyaloshinskii-Moriya (DM) interaction we show that the ground state of B20 FeGe chiral magnet is a superposition of twisted helical spin-density waves formed by different sublattices of the crystal. Such twisted spin-density waves propagate in the same direction but with different phases and different directions of the rotation axes. We derive an advanced micromagnetic expression describing the exchange and DM interaction for such magnetic structures. By employing first-principles calculations based on density functional theory and using our micromagnetic model we show that the magnitude of the spin-spiral twist in B20 FeGe is of the same order as global spiraling. While the energy difference between the ground state of twisted spirals and the FM state is in good agreement with the experimental results, for the spin spirals without a twist it is smaller by factor three. In addition, we verify our results by employing spin dynamics simulations. This calls for new experiments exploring the ground state properties of B20 chiral magnets.
FeGe in the B20 phase is an experimentally well-studied prototypical chiral magnet exhibiting helical spirals, skyrmion lattices and individual skyrmions with a robust length of 70~nm. While the helical spiral ground state can be verified by first-principles calculations based on density functional theory, this feature size could not be reproduced even approximately. To develop a coherent picture of the discrepancy between experiment and theory, we investigate in this work the magnetic properties of FeGe from first-principles using different electronic-structure methods. We study atomistic as …
Although chiral magnetic materials have emerged as a potential ingredient in future spintronic memory devices, there are few comprehensive studies of magnetic properties in scalably-grown thin films. We present growth, systematic physical and magnetic characterization, and microwave absorption spectroscopy of B20 FeGe thin films. We also perform micromagnetic simulations and analytical theory to understand the dynamical magnetic behavior of this material. We find magnetic resonance features in both the helical and field-polarized magnetic states that are well explained by micromagnetic simulat…
Chiral magnetic interactions induce complex spin textures including helical and conical spin waves, as well as particle-like objects such as magnetic skyrmions and merons. These spin textures are the basis for innovative device paradigms and give rise to exotic topological phenomena, thus being of interest for both applied and fundamental sciences. Present key questions address the dynamics of the spin system and emergent topological defects. Here we analyze the micromagnetic dynamics in the helimagnetic phase of FeGe. By combining magnetic force microscopy, single-spin magnetometry, and Landa…
The tensile strain is a promising tool for creation and manipulation of magnetic solitonic textures in the chiral helimagnets via tunable control of magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Here, by using the in-situ resonant small-angle x-ray scattering we demonstrate that the skyrmion and chiral soliton lattices can be achieved as metastable states in FeGe lamella as distinct states or even simultaneously by combining the tensile strain and magnetic fields in various orientations with respect to the deformation. The small-angle scattering data are discussed in the frame of …
Magnetic skyrmion lattice disclinations in pentagon- and heptagon-shaped FeGe crystals
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich（尤利希研究中心）；Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA（尤利希研究中心）；University of Luxembourg（卢森堡大学）
We report experimental and theoretical evidence for the formation of chiral bobbers - an interfacial topological spin texture - in FeGe films grown by molecular beam epitaxy (MBE). After establishing the presence of skyrmions in FeGe/Si(111) thin film samples through Lorentz transmission electron microscopy and topological Hall effect, we perform magnetization measurements that reveal an inverse relationship between film thickness and the slope of the susceptibility (d\c{hi}/dH). We present evidence for the evolution as a function of film thickness, L, from a skyrmion phase for L < LD/2 to a c…
We theoretically study the magnetic properties of iron germanium, known as one of canonical helimagnets. For this purpose we use the real-space spin Hamiltonian and micromagnetic model, derived in terms of Andersen's "local force theorem", to describe the low-lying magnetic excitations via spin-polarized Green's function, obtained from the first-principles calculations. The model was designed to numerically evaluate the spin stiffness constant in reciprocal space, in order for assessment of the contributing itinerant mechanisms. The calculated pairwise exchange interactions reveal the essentia…
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…
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…
Magnetic materials without structural inversion symmetry can display the Dzyaloshinskii-Moriya interaction, which manifests itself as chiral magnetic ground states. These chiral states can interact in complex ways with applied fields and boundary conditions provided by finite sample sizes that are of the order of the lengthscale of the chiral states. Here we study epitaxial thin films of FeGe with a thickness close to the helix pitch of the helimagnetic ground state, which is about 70 nm, by conventional magnetometry and polarized neutron reflectometry. We show that the helix in an FeGe film r…
Charge order in kagome metals is of extensive current interest. Recently, a charge density wave was discovered in the magnetic binary kagome metal FeGe. In analogy to its predecessor, the non-magnetic $A$V$_3$Sb$_5$ ($A$=K, Cs, Rb), the in-plane ordering occurs at the $M$ point. In contrast, however, the system manifestly shows effects of substantial correlations. Here we identify the topological bands crossing the Fermi energy (E$_F$) in FeGe and characterize the correlation-induced renormalization of these bands. We then derive a charge order from an effective model comprising topological ka…
We studied metastable $α$-FeGe$_2$, a novel layered tetragonal material, embedded as a spacer layer in spin valve structures with ferromagnetic Fe$_3$Si and Co$_2$FeSi electrodes. For both types of electrodes, spin valve operation is demonstrated with a metallic transport behavior of the $α$-FeGe$_2$ spacer layer. The spin valve signals are found to increase both with temperature and spacer thickness, which is discussed in terms of a decreasing magnetic coupling strength between the ferromagnetic bottom and top electrodes. The temperature-dependent resistances of the spin valve structures exhi…
Nature of magnetic exchange interactions in kagome antiferromagnets FeGe and FeSn
Institute of High Pressure Physics, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院高压物理研究所）；College of Science, Nanjing University of Aeronautics and Astronautics（南京航空航天大学理学院）
The study of nanoscale chiral magnetic order in polycrystalline materials with a strong Dzyaloshinkii-Moriya interaction (DMI) is interesting for the observation of magnetic phenomena at grain boundaries and interfaces. One such material is sputter-deposited B20 FeGe on Si, which has been actively investigated as the basis for low-power, high-density magnetic memory technology in a scalable material platform. Although conventional Lorentz electron microscopy provides the requisite spatial resolution to probe chiral magnetic textures in single-crystal FeGe, probing the magnetism of sputtered B2…
In this work, we theoretically study the charge order and orbital magnetic properties of a new type of antiferromagnetic kagome metal FeGe. Based on first principles density functional theory (DFT) calculations, we have studied the electronic structures, Fermi-surface quantum fluctuations, as well as phonon properties of the antiferromagnetic kagome metal FeGe. We find that charge density wave emerges in such a system due to a subtle cooperation between electron-electron ($e$-$e$) interactions and electron-phonon couplings, which gives rise to an unusual scenario of interaction-triggered phono…
We report on detailed polarized small-angle neutron scattering on cubic FeGe in magnetic fields applied either along (transverse) the scattering vector or parallel (longitudinal)to the neutron beam. The ($H,T$) phase diagrams for all principal axes contain a segmented $A$-phase region just below the onset of magnetic order. Hexagonal Bragg-spot patterns were observed across the entire $A$-phase region for the longitudinal geometry. Scattering intensity was observed in parts of the A phase for both scattering configurations. Only in a distinct pocket ($A_1$) vanishing scattering intensity was f…
Skyrmions are localized magnetic spin textures whose stability has been shown theoretically to depend on material parameters including bulk Dresselhaus spin orbit coupling (SOC), interfacial Rashba SOC, and magnetic anisotropy. Here, we establish the growth of a new class of artificial skyrmion materials, namely B20 superlattices, where these parameters could be systematically tuned. Specifically, we report the successful growth of B20 superlattices comprised of single crystal thin films of FeGe, MnGe, and CrGe on Si(111) substrates. Thin films and superlattices are grown by molecular beam epi…
The diversity of three-dimensional magnetic states in a FeGe nanocylinder is studied using micromagnetic simulations and off-axis electron holography in the transmission electron microscope. In particular, we report the observation of a dipole string -- a spin texture composed of two coupled Bloch points -- which becomes stable under geometrical confinement. Quantitative agreement is obtained between experimental and theoretical phase shift images by taking into account the presence of a damaged layer on the surface of the nanocylinder. The theoretical model is based on the assumption that the…
We report strong unidirectional anisotropy in bulk polycrystalline B20 FeGe measured by ferromagnetic resonance spectroscopy. Bulk and micron-sized samples were produced and analytically characterized. FeGe is a B20 compound with inherent Dzyaloshinskii-Moriya interaction. Lorenz microscopy confirms a skyrmion lattice at $190 \; \text{K}$ in a magnetic field of 150 mT. Ferromagnetic resonance was measured at $276 \; \text{K} \pm 1 \; \text{K}$, near the Curie temperature. Two resonance modes were observed, both exhibit a unidirectional anisotropy of $K=1153 \; \text{J/m}^3 \pm 10 \; \text{J/m}…
The nature of spin wave modes excited by spin-polarized direct current in a spin-torque auto-oscillator based on a magnetic nanocontact was studied by a micromagnetic simulation in the case when the external bias magnetic field was rotated from the in-plane to perpendicular-to-plane orientation. In qualitative agreement with the weakly-nonlinear analytical theory it was found, that at a certain critical angle, an abrupt switching from the self-localized nonlinear "bullet" mode to a propagating quasi-linear Slonczewski mode takes place, and is accompanied by an upward jump in generated microwav…
Spin relaxation in the ultrathin metallic films of stacked microelectronic devices is investigated on the basis of a modified Landau-Lifshitz equation of micromagnetic dynamics in which the damping torque is treated as originating from the coupling between precessing magnetization-vector and the introduced stress-tensors of intrinsic and extrinsic magnetic anisotropy. Particular attention is given to the time of exponential relaxation and ferromagnetic resonance linewidth which are derived in analytic form from the equation of magnetization energy loss and Gabor uncertainty relation between th…
This paper is devoted to numerical simulations of the magnetization dynamics driven by a spin-polarized current in extended ferromagnetic multilayers when a point-contact setup is used. We present (i) detailed analysis of methodological problems arising by such simulations and (ii) physical results obtained on a system similar to that studied in Rippard et al., Phys. Rev. Lett., v. 92, 027201 (2004). We demonstrate that the usage of a standard Slonczewski formalism for the phenomenological treatment of a spin-induced torque leads to a qualitative disagreement between simulation results and exp…
B20-type compounds, such as MnSi and FeGe, host helimagnetic and skyrmion phases at the mesoscale, which are canonically explained by the combination of ferromagnetic isotropic interactions with weaker chiral Dzyaloshinskii-Moriya ones. Mysteriously, MnGe evades this paradigm as it displays a noncollinear magnetic state at a much shorter nanometer scale. Here we show that the length scale and volume-dependent magnetic properties of MnGe stem from purely isotropic exchange interactions, generally obtained in the paramagnetic state. Our approach is validated by comparing MnGe with the canonical …
We investigate the spin transfer torque (STT) in the magnetic multilayer structures with micromagnetic simulations. We implement the STT contribution for the magnetic multilayer structures in addition to the Landau-Lifshitz-Gilbert (LLG) micromagnetic simulators. Not only the Sloncewski STT term, the zero, first, and second order field- like terms are also considered, and the effects of the Oersted field by the current are addressed. We determine the switching current densities of the free layer with the exchange biased synthetic ferrimagnetic reference layers for various cases.
The development of permanent magnets containing less or no rare-earth elements is linked to profound knowledge of the coercivity mechanism. Prerequisites for a promising permanent magnet material are a high spontaneous magnetization and a sufficiently high magnetic anisotropy. In addition to the intrinsic magnetic properties the microstructure of the magnet plays a significant role in establishing coercivity. The influence of the microstructure on coercivity, remanence, and energy density product can be understood by {using} micromagnetic simulations. With advances in computer hardware and num…
Perpendicular MgO-based Magnetic Tunnel Junctions are optimal candidates as building block of Spin Transfer Torque (STT) magnetoresistive memories. However, up to now, the only STT is not enough to achieve switching current density below 106 A/cm2. A recent work [Wang et al., Nature Mater., vol. 11, pp 64-68, Jan. 2012] has experimentally demonstrated the possibility to perform magnetization switching assisted by an electric-field at ultra-low current density. Theoretically, this switching has been studied by using a macrospin approach only. Here, we show a full micromagnetic study. We found t…
A numerical model of single-domain nanoscale iron magnets fabricated using scanning-microscope-assisted chemical vapor deposition is simulated using finite-temperature micromagnetics. A Projective-dynamics method is used to determine the magnetization at the saddle point as a function of temperature. This magnetization is found to decrease linearly as the temperature is raised.
We studied magnetic vortex oscillations associated with vortex gyrotropic motion driven by spin-polarized out-of-plane dc current by analytical and micromagnetic numerical calculations. Reliable controls of the tunable eigenfrequency and orbital amplitude of persistent vortex oscillations were demonstrated. This work provides an advanced step towards the practical application of vortex oscillations to persistent vortex oscillators in a wide frequency (f) range of 10 to 2000 MHz and with high values of f/(delta f).
We formulated a technique which combines the first-principles, micromagnetic and microstructural calculations and allows us to study the nature of hysteretic phenomena in hard magnets. Two distinct sources of coercivity in polytwinned CoPt type magnets, domain wall pinning at antiphase boundaries and splitting at twin boundaries, are illustrated for a realistic microstructure. Methodology of multiscale modelling of hysteretic phenomena in nanoscale magnets is discussed.
Control of helix orientation in chiral magnets via lateral confinement
Norwegian University of Science and Technology (NTNU)（挪威科技大学）；University of Stuttgart（斯图加特大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论固体物理研究所）；University of Tokyo（东京大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Department of Applied Physics, University of Tokyo（东京大学应用物理系）；Tokyo College, University of Tokyo（东京大学东京学院）
It was shown by micromagnetic simulation that a current-driven in-plane magnetized magnetic nano-contact, besides a quasi-linear propagating ("Slonczewski") spin wave mode, can also support a nonlinear self-localized spin wave "bullet" mode that exists in a much wider range of bias currents. The frequency of the "bullet" mode lies below the spectrum of linear propagating spin waves, which makes this mode evanescent and determines its spatial localization. The threshold current for the excitation of the self-localized "bullet" is substantially lower than for the linear propagating mode, but fin…
Conjugate gradient methods for energy minimization in micromagnetics are compared. When the step length in the line search is controlled, conjugate gradient techniques are a fast and reliable way to compute the hysteresis properties of permanent magnets. The method is applied to investigate demagnetizing effects in NdFe12 based permanent magnets. The reduction of the coercive field by demagnetizing effects is 1.4 T at 450 K.
The exchange interaction between nanostructured components is an effective way to enhance the magnetic properties of materials. This effect is used in exchange-coupled magnetic composites, which properties are governed by synergetic impact of constituent phases. Texturing is one of the problems that needs to be solved in order for such composites to be used in industry. In this work, we performed experimental and micromagnetic investigation of the exchange-bias properties in Co/Co3O4 nanocomposites based on nanorods array. Specifically, we investigated how the resulting properties will change …
In this work we investigate the potential of tetragonal L1$_0$ ordered FeNi as candidate phase for rare earth free permanent magnets taking into account anisotropy values from recently synthesized, partially ordered FeNi thin films. In particular, we estimate the maximum energy product ($BH$)$_\mathrm{max}$ of L1$_0$-FeNi nanostructures using micromagnetic simulations. The maximum energy product is limited due to the small coercive field of partially ordered L1$_0$-FeNi. Nano-structured magnets consisting of 128 equi-axed, platelet-like and columnar-shaped grains show a theoretical maximum ene…
Antiferromagnets (AFMs) are strong candidates for the future spintronic and memory applications largely because of their inherently fast dynamics and lack of stray fields, with Mn2Au being one of the most promising. For the numerical modelling of magnetic material properties, it is common to use ab-initio methods, atomistic models and micromagnetics. However, each method alone describes the physics within certain limits. Multiscale methods bridging the gap between these three approaches have been already proposed for ferromagnetic materials. Here, we present a complete multiscale model of the …
The magnetic properties of ferromagnetic thin films down to the nanoscale are ruled by the exchange stiffness, anisotropies and the effects of magnetic fields. As surfaces break inversion symmetry, an additional effective chiral exchange is omnipresent in any magnetic nanostructure. These so-called Dzyaloshinskii-Moriya interactions (DMI) affect all inhomogeneous magnetic states either subtly or spectacularly. E.g., DMIs cause a chirality selection of the rotation sense and can fix the local rotation axis for the magnetization in domain walls (DW). But, they can stabilize also entirely differe…
We present a general approach to the derivation of the effective anisotropy field which determines the dynamical behaviour of magnetic spins according to the Landau-Lifshitz-Gilbert equation. The approach is based on the gradient in spherical polar coordinates with the final results being expressed in Cartesian coordinates as usually applied in atomistic and micromagnetic model calculations. The approach is generally valid for all orders of anisotropies including higher order combinations of azimuthal and rotational anisotropies often found in functional magnetic materials such as permanent ma…
Ferri-/ferromagnetic exchange coupled composites are promising candidates for bit patterned media because of the ability to control the magnetic properties of the ferrimagnet by its composition. A micromagnetic model for the bilayer system is presented where we also incorporate the microstructural features of both layers. Micromagnetic finite element simulations are performed to investigate the magnetization reversal behaviour of such media. By adding the exchange coupled ferrimagnet to the ferromagnet, the switching field could be reduced by up to $40\,\%$ and also the switching field distrib…
