The revisited theoretical phase diagrams for thin films of cubic helimagnets with the easy-plane anisotropy are shown to have different topology as previously reported [Phys. Rev. B 85, 094429 (2012)]. For both in-plane and out-of-plane directions of an applied magnetic field, the phase diagrams exhibit extensive areas of stable skyrmions, which overlap for a wide range of anisotropy parameters. Although the existence of the out-of-plane skyrmions was contradicted within the previous theoretical models, we prove that additional surface twists lead to their stability, while the moderate easy-plane anisotropy increases the stability range of in-plane skyrmions. Moreover, the interplay between the anisotropy and the surface twists gives rise to a stable spiral state canted with respect to the surfaces. Being absent in bulk helimagnets, this oblique spiral occupies vast areas at the phase diagrams in thin-film nanosystems and serves as a connecting-link between cones and helicoids. Our theory gives clear directions for renewed experimental studies of in-plane and out-of-plane skyrmions in epitaxial MnSi(111)/Si(111) thin films.
We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data was analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in smal…
Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future ultra-dense memory and logic devices1-4. To enable such applications, particular attention has been focused on the skyrmions properties in highly confined geometry such as one dimensional nanowires5-8. Hitherto it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here we report the experimental demonstration of such scheme, where magnetic field-driven skyrmion cluster (SC) states with small num…
Skyrmions, novel topologically stable spin vortices, hold promise for next-generation magnetic storage due to their nanoscale domains to enable high information storage density and their low threshold for current-driven motion to enable ultralow energy consumption. One-dimensional (1D) nanowires are ideal hosts for skyrmions since they not only serve as a natural platform for magnetic racetrack memory devices but also can potentially stabilize skyrmions. Here we use the topological Hall effect (THE) to study the phase stability and current-driven dynamics of the skyrmions in MnSi nanowires. Th…
This paper reports on magnetometry and magnetoresistance measurements of MnSi epilayers performed in out-of-plane magnetic fields. We present a theoretical analysis of the chiral modulations that arise in confined cubic helimagnets where the uniaxial anisotropy axis and magnetic field are both out-of-plane. In contrast to in-plane field measurements (Wilson et al., Phys. Rev. B 86, 144420 (2012)), the hard-axis uniaxial anisotropy in MnSi/Si(111) increases the energy of (111)-oriented skyrmions and in-plane helicoids relative to the cone phase, and makes the cone phase the only stable magnetic…
The magnetic structure of the in-plane skyrmions in epitaxial MnSi/Si(111) thin films is probed in three dimensions by the combination of polarized neutron reflectometry (PNR) and small angle neutron scattering (SANS). We demonstrate that skyrmions exist in a region of the phase diagram above at temperature of 10 K. PNR shows the skyrmions are confined to the middle of the film due to the potential well formed by the surface twists. However, SANS shows that there is considerable disorder within the plane indicating that the magnetic structure is a 2D skyrmion glass.
A detailed investigation of the magnetization processes in epitaxial MnSi thin film reveals the existence of elliptically distorted skyrmion strings that lie in the plane of the film. We provide proof that the uniaxial anisotropy stabilizes this state over extended regions of the magnetic phase diagram. Theoretical analysis of an observed cascade of first-order phase transitions is based on rig- orous numerical calculations of competing chiral modulations, which shows the existence of helicoids, elliptic skyrmions, and cone phases.
Magneto-transport properties have been investigated for epitaxial thin films of B20-type MnSi grown on Si(111) substrates. Both Lorentz transmission electron microscopy (TEM) images and topological Hall effect (THE) clearly point to the robust formation of skyrmions over a wide temperature-magnetic field region. New features distinct from those of bulk MnSi are observed for epitaxial MnSi films: a shorter (nearly half) period of the spin helix and skyrmions, and an opposite sign of THE. These observations suggest versatile features of skyrmion-induced THE beyond the current understanding.
We present a comprehensive analysis of high resolution neutron scattering data involving Neutron Spin Echo spectroscopy and Spherical Polarimetry which confirm the first order nature of the helical transition and reveal the existence of a new spin liquid skyrmion phase. Similar to the blue phases of liquid crystals this phase appears in a very narrow temperature range between the low temperature helical and the high temperature paramagnetic phases.
Exchange anisotropy provides a direction dependent mechanism for the stability of the skyrmion lattice phase in noncentrosymmetric bulk chiral magnets. Based on the Fourier representation of the skyrmion lattice, we explain the direction dependence of the temperature-magnetic field phase diagram for bulk MnSi through a phenomenological mean-field model incorporating exchange anisotropy. Through quantitative comparison with experimental results, we clarify that the stability of the skyrmion lattice phase in bulk MnSi is determined by a combined effect of negative exchange anisotropy and thermal…
Using small-angle neutron scattering (SANS), we investigate the deformation of the magnetic skyrmion lattice in bulk single-crystalline MnSi under electric current flow. A significant broadening of the skyrmion-lattice-reflection peaks was observed in the SANS pattern for current densities greater than a threshold value j_t ~ 1 MA/m^2 (10^6 A/m^2). We show this peak broadening to originate from a spatially inhomogeneous rotation of the skyrmion lattice, with an inverse rotation sense observed for opposite sample edges aligned with the direction of current flow. The peak broadening (and the cor…
Recent small angle neutron scattering suggests, that the spin structure in the A-phase of MnSi is a so-called triple-$Q$ state, i.e., a superposition of three helices under 120 degrees. Model calculations suggest that this structure in fact is a lattice of so-called skyrmions, i.e., a lattice of topologically stable knots in the spin structure. We report a distinct additional contribution to the Hall effect in the temperature and magnetic field range of the proposed skyrmion lattice, where such a contribution is neither seen nor expected for a normal helical state. Our Hall effect measurements…
We report grazing incidence small angle neutron scattering (GISANS) and complementary off-specular neutron reflectometry (OSR) of the magnetic order in a single-crystalline epitaxial MnSi film on Si(111) in the thick film limit. Providing a means of direct reciprocal space mapping, GISANS and OSR reveal a magnetic modulation perpendicular to the films under magnetic fields parallel and perpendicular to the film, where additional polarized neutron reflectometry (PNR) and magnetization measurements are in excellent agreement with the literature. Regardless of field orientation, our data does not…
We present a comparative study of the (magneto)transport properties, including Hall effect, of bulk, thin film and nanostructured MnSi. In order to set our results in relation to published data we extensively characterize our materials, this way establishing a comparatively good sample quality. Our analysis reveals that in particular for thin film and nanostructured material, there are extrinsic and intrinsic contributions to the electronic transport properties, which by modeling the data we separate out. Finally, we discuss our Hall effect data of nanostructured MnSi under consideration of th…
In epitaxial MnSi/Si(111) films, the in-plane magnetization saturation is never reached due to the formation of specific surface chiral modulations with the propagation direction perpendicular to the film surfaces [Wilson et al. Phys. Rev. B 88, 214420 (2013)]. In this paper we show that the occurrence of such chiral surface twists is a general effect attributed to all bulk and con- fined magnetic crystals lacking inversion symmetry. We present experimental investigations of this phenomenon in nanolayers of MnSi/Si(111) supported by detailed theoretical analysis within the standard phenomenolo…
Magnetic skyrmions are particle-like topological excitations that recently generated much interest as candidates for future spintronic devices based on skyrmion small size, enhanced topological stability, and/or mutual interaction. Here we examine the properties of isolated skyrmions in a frustrated chiral magnet with competing Dzyaloshinskii-Moriya and frustrated exchange interactions. We show that the skyrmion size drastically decreases even for small values of competing stabilization mechanisms. Skyrmion mutual interaction remains attracting as is inherent for frustrated skyrmions, but the …
Skyrmions represent topologically stable field configurations with particle-like properties. We used neutron scattering to observe the spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Our study experimentally establishes magnetic materials lacking inversion symmetry as an…
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 …
We report the critical role of La doping in the topological Hall effect observed in LaxEu1-xO thin films (~ 50 nm) grown by molecular beam epitaxy. When the La doping exceeds 0.036, topological Hall effect emerges, which we attribute to the formation of magnetic skyrmions. Besides, the La doping is found to play a critical role in determining the phases, densities, and sizes of the skyrmions in the LaxEu1-xO thin films. The maximum region of the skyrmion phase diagram is observed on the La0.1Eu0.9O thin film. As the La doping increases, the skyrmion density increases while the skyrmion size de…
We studied the symmetry of magnetic properties and the resulting magnetic textures in ultra-thin epitaxial Au$_{0.67}$Pt$_{0.33}$/Co/W, a model system exhibiting perpendicular magnetic anisotropy and interface Dzyaloshinskii-Moriya interaction (DMI). As a peculiar feature, the C$_\mathrm{2v}$ crystal symmetry induced by the Co/W interface results in an additional uniaxial in-plane magnetic anisotropy in the cobalt layer. Photoemission electron microscopy with magnetic sensitivity reveals the formation of self-organized magnetic stripe domains oriented parallel to the hard in-plane magnetizatio…
In non-centrosymmetric crystals such as MnSi, magnetic order can take the form of a skyrmion crystal (SkX) . In this phase, conduction electrons coupled to the local magnetic moments acquire a Berry's phase, leading to an emergent electromagnetism. Motivated by experimental reports of a non-Fermi liquid phase in MnSi, in which resistivity is observed to scale as $Δρ\sim T^{3/2}$, here we examine the effect of coupling phonons of an incommensurate SkX to electrons. Despite the formal similarity to a system consisting of a Fermi surface coupled to an electromagnetic field, the Berry phase fluctu…
We report a comprehensive small angle neutron scattering study (SANS) of the magnetic phase diagram of the doped semiconductor Fe_{1-x}Co_{x}Si for x=0.2 and 0.25. For magnetic field parallel to the neutron beam we observe a six-fold intensity pattern under field-cooling, which identifies the A-phase of Fe_{1-x}Co_{x}Si as a skyrmion lattice. The regime of the skyrmion lattice is highly hysteretic and extents over a wide temperature range, consistent with the site disorder of the Fe and Co atoms. Our study identifies Fe_{1-x}Co_{x}Si is a second material after MnSi in which a skyrmion lattice …
Recent advances on the stabilization and manipulation of chiral magnetization configurations in systems consisting in alternating atomic layers of ferromagnetic and non-magnetic materials hold promise of innovation in spintronics technology. The low dimensionality of the systems promotes spin orbit driven interfacial effects like antisymmetric Dzyaloshinskii-Moriya interactions (DMI) and surface magnetic anisotropy, whose relative strengths may be tuned to achieve stable nanometer sized magnetic objects with fixed chirality. While in most of the cases this is obtained by engineering complex mu…
Skyrmions, topologically protected vortex-like nanometric spin textures in magnets, have been attracting increasing attention for emergent electromagnetic responses and possible technological applications for spintronics. In particular, metallic magnets with chiral and cubic/tetragonal crystal structure may have high potential to host skyrmions that can be driven by low electrical current excitation. However, experimental observations of skyrmions have so far been limited to below room temperature for the metallic chiral magnets, specifically for the MnSi-type B20 compounds. Toward technologic…
Magnetic skyrmions in chiral-lattice ferromagnets are currently attracting enormous research interest because of their potential applications in spintronic devices. However, they emerge in bulk specimens only in a narrow window of temperature and magnetic field. This limited stability regime is recognized as an obstacle to technical applications. Recent experiments demonstrated that the thermodynamic stability of magnetic skyrmions is enhanced or suppressed by the application of a uniaxial strain depending on its axial direction in bulk chiral-lattice ferromagnets MnSi [Y. Nii et al., Nat. Com…
Here we derive the linear constitutive equations governing the emergent elastic behavior of skX under applied mechanical forces as well as other effective fields. The linear coefficients appearing in the equations are expressed analytically in terms of the thermodynamic parameters describing the magnetoelastic interaction of the underlying chiral magnet. Through the deduction of equations, we clarify that two types of coupled deformation may occur for skX, that is the internal deformation, described by variation of the Fourier magnitudes, and the lattice deformation, described by the emergent …
Magnetic skyrmions are topological spin configurations in materials with chiral Dzyaloshinskii-Moriya interaction (DMI), that are potentially useful for storing or processing information. To date, DMI has been found in few bulk materials, but can also be induced in atomically thin magnetic films in contact with surfaces with large spin-orbit interactions. Recent experiments have reported that isolated magnetic skyrmions can be stabilized even near room temperature in few-atom thick magnetic layers sandwiched between materials that provide asymmetric spin-orbit coupling. Here we present the min…
A magnetic skyrmion is a spin whirl with topological protection and high mobility to electric current. Intrinsic magnetoelastic coupling in chiral magnets permits manipulation of magnetic skyrmions and their lattice using mechanical loads, which is essential for developing future spintronics devices. It is found in experiments that the stability and deformation of skyrmions are sensitive to stresses, while the appearance of magnetic skyrmions in turn has a significant effect on the mechanical properties of the underlying material. However, a theory which explains these related phenomena within…
Spin-polarized scanning tunneling microscopy (SPSTM) was used to directly image nanoscale Néel skyrmions in a SrIrO3 / SrRuO3 bilayer system that are among the smallest reported to date in any system. Off-axis magnetron sputtering was used to cap epitaxial films of the oxide ferromagnet SRO with 2 unit cells of SrIrO3, intended to provide interfacial spin orbit coupling. Atomic resolution STM imaging and tunneling spectroscopy were used to identify island-like SrIrO3 grains and small regions of bare SrRuO3. Isolated skyrmions were only observed in SrIrO3-covered regions of the film, and exhibi…
Magnetic materials hosting topological spin textures like magnetic skyrmion exhibit nontrivial Hall effect, namely, topological Hall effect (THE). In this study, we demonstrate the emergence of THE in thin films of half-metallic perovskite manganites. To stabilize magnetic skyrmions, we control the perpendicular magnetic anisotropy by imposing a compressive epitaxial strain as well as by introducing a small Ru doping. When the perpendicular magnetic anisotropy is tuned so that it is balanced with the magnetic dipolar interaction, the film exhibits a sizable THE in a magnetization reversal proc…
A major challenge for future spintronics is to develop suitable spin transport channels with long spin lifetime and propagation length. Graphene can meet these requirements, even at room temperature. On the other side, taking advantage of the fast motion of chiral textures, i.e., Néel-type domain walls and magnetic skyrmions, can satisfy the demands for high-density data storage, low power consumption and high processing speed. We have engineered epitaxial structures where an epitaxial ferromagnetic Co layer is sandwiched between an epitaxial Pt(111) buffer grown in turn onto MgO(111) substrat…
Disorder-broadened topological Hall phase and anomalous Hall scaling in FeGe
University of Washington（华盛顿大学）；Cornell University（康奈尔大学）；Sandia National Laboratories（桑迪亚国家实验室）；University of Oklahoma（俄克拉荷马大学）；University of Nebraska-Lincoln（内布拉斯加大学林肯分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Colorado School of Mines（科罗拉多矿业学院）
