Extended Berry Curvature Tail in Ferromagnetic Weyl Semimetals NiMnSb and PtMnSb.

Heusler compounds belong to a large family of materials and exhibit numerous physical phenomena with promising applications, particularly ferromagnetic Weyl semimetals for their use in spintronics and memory devices. Here, anomalous Hall transport is reported in the room-temperature ferromagnets NiMnSb (half-metal with a Curie temperature (TC) of 660 K) and PtMnSb (pseudo half-metal with a TC of 560 K). They exhibit 4 µB/f.u. magnetic moments and non-trivial topological states. Moreover, NiMnSb and PtMnSb are the first half-Heusler ferromagnets to be reported as Weyl semimetals, and they exhibit anomalous Hall conductivity (AHC) due to the extended tail of the Berry curvature in these systems. The experimentally measured AHC values at 2 K are 1.8 × 102 Ω-1 cm-1 for NiMnSb and 2.2 × 103 Ω-1 cm-1 for PtMnSb. The comparatively large value between them can be explained in terms of the spin-orbit coupling strength. The combined approach of using ab initio calculations and a simple model shows that the Weyl nodes located far from the Fermi energy act as the driving mechanism for the intrinsic AHC. This contribution of topological features at higher energies can be generalized.

Weyl spin-momentum locking in a chiral topological semimetal.

Spin-orbit coupling in noncentrosymmetric crystals leads to spin-momentum locking - a directional relationship between an electron's spin angular momentum and its linear momentum. Isotropic orthogonal Rashba spin-momentum locking has been studied for decades, while its counterpart, isotropic parallel Weyl spin-momentum locking has remained elusive in experiments. Theory predicts that Weyl spin-momentum locking can only be realized in structurally chiral cubic crystals in the vicinity of Kramers-Weyl or multifold fermions. Here, we use spin- and angle-resolved photoemission spectroscopy to evidence Weyl spin-momentum locking of multifold fermions in the chiral topological semimetal PtGa. We find that the electron spin of the Fermi arc surface states is orthogonal to their Fermi surface contour for momenta close to the projection of the bulk multifold fermion at the Γ point, which is consistent with Weyl spin-momentum locking of the latter. The direct measurement of the bulk spin texture of the multifold fermion at the R point also displays Weyl spin-momentum locking. The discovery of Weyl spin-momentum locking may lead to energy-efficient memory devices and Josephson diodes based on chiral topological semimetals.

Interplay between Magnetism and Topology: Large Topological Hall Effect in an Antiferromagnetic Topological Insulator, EuCuAs.

Magnetic interactions in combination with nontrivial band structures can give rise to several exotic physical properties such as a large anomalous Hall effect, the anomalous Nernst effect, and the topological Hall effect (THE). Antiferromagnetic (AFM) materials exhibit the THE due to the presence of nontrivial spin structures. EuCuAs crystallizes in a hexagonal structure with an AFM ground state (Néel temperature ∼ 16 K). In this work, we observe a large topological Hall resistivity of ∼7.4 µΩ-cm at 13 K which is significantly higher than the giant topological Hall effect of Gd2PdSi3 (∼3 µΩ-cm). Neutron diffraction experiments reveal that the spins form a transverse conical structure during the metamagnetic transition, resulting in the large THE. In addition, by controlling the magnetic ordering structure of EuCuAs with an external magnetic field, several fascinating topological states such as Dirac and Weyl semimetals have been revealed. These results suggest the possibility of spintronic devices based on antiferromagnets with tailored noncoplanar spin configurations.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

Anomalous Hall Conductivity and Nernst Effect of the Ideal Weyl Semimetallic Ferromagnet EuCd2 As2.

Weyl semimetal is a unique topological phase with topologically protected band crossings in the bulk and robust surface states called Fermi arcs. Weyl nodes always appear in pairs with opposite chiralities, and they need to have either time-reversal or inversion symmetry broken. When the time-reversal symmetry is broken the minimum number of Weyl points (WPs) is two. If these WPs are located at the Fermi level, they form an ideal Weyl semimetal (WSM). In this study, intrinsic ferromagnetic (FM) EuCd2 As2 are grown, predicted to be an ideal WSM and studied its electronic structure by angle-resolved photoemission spectroscopy, and scanning tunneling microscopy which agrees closely with the first principles calculations. Moreover, anomalous Hall conductivity and Nernst effect are observed, resulting from the non-zero Berry curvature, and the topological Hall effect arising from changes in the band structure caused by spin canting produced by magnetic fields. These findings can help realize several exotic quantum phenomena in inorganic topological materials that are otherwise difficult to assess because of the presence of multiple pairs of Weyl nodes.

Ruthenium-Alloyed Iron Phosphide Single Crystal with Increased Fermi Level for Efficient Hydrogen Evolution.

Transition metal phosphide alloying is an effective approach for optimizing the electronic structure and improving the intrinsic performance of the hydrogen evolution reaction (HER). However, obtaining 3d transition metal phosphides alloyed with noble metals is still a challenge owing to their difference in electronegativity, and the influence of their electronic structure modulated by noble metals on the HER reaction also remains unclear. In this study, we successfully incorporated Ru into an Fe2P single crystal via the Bridgeman method and used it as a model catalyst, which effectively promoted HER. Hall transport measurements combined with first-principles calculations revealed that Ru acted as an electron dopant in the structure and increased the Fermi level, leading to a decreased water dissociation barrier and an improved electron-transfer Volmer step at low overpotentials. Additionally, the (21̅1) facet of Ru-Fe2P was found to be more active than its (001) facet, mainly due to the lower H desorption barrier at high overpotentials. The synergistic effect of Ru and Fe sites was also revealed to facilitate H* and OH* desorption compared with Fe2P. Therefore, this study elucidates the boosting effect of Ru-alloyed iron phosphides and offers new understanding about the relationship between their electronic structure and HER performance.

Giant Topological Hall Effect in the Noncollinear Phase of Two-Dimensional Antiferromagnetic Topological Insulator MnBi4Te7.

Magnetic topological insulators provide an important platform for realizing several exotic quantum phenomena, such as the axion insulating state and the quantum anomalous Hall effect, owing to the interplay between topology and magnetism. MnBi4Te7 is a two-dimensional Z2 antiferromagnetic (AFM) topological insulator with a Néel temperature of ∼13 K. In AFM materials, the topological Hall effect (THE) is observed owing to the existence of nontrivial spin structures. A material with noncollinearity that develops in the AFM phase rather than at the onset of the AFM order is particularly important. In this study, we observed that such an unanticipated THE starts to develop in a MnBi4Te7 single crystal when the magnetic field is rotated away from the easy axis (c-axis) of the system. Furthermore, the THE resistivity reaches a giant value of ∼7 µΩ-cm at 2 K when the angle between the magnetic field and the c-axis is 75°. This value is significantly higher than the values for previously reported systems with noncoplanar structures. The THE can be ascribed to the noncoplanar spin structure resulting from the canted state during the spin-flip transition in the ground AFM state of MnBi4Te7. The large THE at a relatively low applied field makes the MnBi4Te7 system a potential candidate for spintronic applications.

Direct Measurement of Helicoid Surface States in RhSi Using Nonlinear Optics.

Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction G. Chang et al., Phys. Rev. Lett. 124, 166404 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.166404, we have measured the linear and circular photogalvanic effect currents deriving from the Fermi arcs of the nonsymmorphic, chiral Weyl semimetal RhSi over the 0.45-1.1 eV incident photon energy range. Our data are in good agreement with the predicted spectral shape of the circular photogalvanic effect as a function of photon energy, although the direction of the surface photocurrent departed from the theoretical expectation over the energy range studied. Surface currents arising from the linear photogalvanic effect were observed as well, with the unexpected result that only two of the six allowed tensor element were required to describe the measurements, suggesting an approximate emergent mirror symmetry inconsistent with the space group of the crystal.

Sondheimer oscillations as a probe of non-ohmic flow in WP2 crystals.

As conductors in electronic applications shrink, microscopic conduction processes lead to strong deviations from Ohm's law. Depending on the length scales of momentum conserving (lMC) and relaxing (lMR) electron scattering, and the device size (d), current flows may shift from ohmic to ballistic to hydrodynamic regimes. So far, an in situ methodology to obtain these parameters within a micro/nanodevice is critically lacking. In this context, we exploit Sondheimer oscillations, semi-classical magnetoresistance oscillations due to helical electronic motion, as a method to obtain lMR even when lMR ≫ d. We extract lMR from the Sondheimer amplitude in WP2, at temperatures up to T ~ 40 K, a range most relevant for hydrodynamic transport phenomena. Our data on µm-sized devices are in excellent agreement with experimental reports of the bulk lMR and confirm that WP2 can be microfabricated without degradation. These results conclusively establish Sondheimer oscillations as a quantitative probe of lMR in micro-devices.

Assignment of enantiomorphs for the chiral allotrope ß-Mn by diffraction methods.

The assignment of enantiomorphs by diffraction methods shows fundamental differences for x-rays and electrons. This is particularly evident for the chiral allotrope of ß-Mn. While it is not possible to determine the sense of chirality of ß-Mn with established x-ray diffraction methods, Kikuchi pattern simulation of the enantiomorphs reveals differences, if dynamical electron diffraction is considered. Quantitative comparison between experimental and simulated Kikuchi patterns allows the spatially resolved assignment of the enantiomorph in polycrystalline materials of ß-Mn, as well as the structurally strongly related phase Pt2Cu3B. On the basis of enantiomorph distribution maps, crystals were extracted from enantiopure domains by micropreparation techniques. The x-ray diffraction analyses confirm the assignment of the Kikuchi pattern evaluations for Pt2Cu3B and do not allow to distinguish between the enantiomorphs of ß-Mn.

Crystal Structures of AlCr2 and MoSi2 : Same Structure Type vs. Different Bonding Pattern.

In a joint effort utilizing modified sample preparation, microscopy, X-ray diffraction and micro-fabrication, it became possible to prepare single crystals of the "hidden" phase AlCr2 . High-resolution X-ray diffraction analysis is described in detail for two crystals with the similar overall composition, but different degree of disorder, which seems to be the main cause for the differing unit cell parameters. Chemical bonding analysis of AlCr2 in comparison to prototypical MoSi2 shows pronounced differences reflecting the interchange of main group element vs. transition metal as majority component.

The impact of boron atoms on clathrate-I silicides: composition range of the borosilicide K8-xBySi46-y.

The clathrate-I borosilicide K8-xBySi46-y (0.8 ≤x≤ 1.2 and 6.4 ≤y≤ 7.2; space group Pm3[combining macron]n) was prepared in sealed tantalum ampoules between 900 °C and 1000 °C. By high-pressure preparation at 8 GPa and 1000 °C, a higher boron content is achieved (x = 0.2, y = 7.8). Crystal structure and composition were established from X-ray diffraction data, chemical analysis, WDX spectroscopy, and confirmed by 11B and 29Si NMR, and magnetic susceptibility measurements. The compositions are electron-balanced according to the Zintl rule within one estimated standard deviation. The lattice parameter varies with composition from a = 9.905 Å for K7.85(2)B7.8(1)Si38.2(1) to a = 9.968(1) Å for K6.80(2)B6.4(5)Si39.6(5).

Thermoelectric Properties of Novel Semimetals: A Case Study of YbMnSb2.

The emerging class of topological materials provides a platform to engineer exotic electronic structures for a variety of applications. As complex band structures and Fermi surfaces can directly benefit thermoelectric performance it is important to identify the role of featured topological bands in thermoelectrics particularly when there are coexisting classic regular bands. In this work, the contribution of Dirac bands to thermoelectric performance and their ability to concurrently achieve large thermopower and low resistivity in novel semimetals is investigated. By examining the YbMnSb2 nodal line semimetal as an example, the Dirac bands appear to provide a low resistivity along the direction in which they are highly dispersive. Moreover, because of the regular-band-provided density of states, a large Seebeck coefficient over 160 µV K-1 at 300 K is achieved in both directions, which is very high for a semimetal with high carrier concentration. The combined highly dispersive Dirac and regular bands lead to ten times increase in power factor, reaching a value of 2.1 mW m-1 K-2 at 300 K. The present work highlights the potential of such novel semimetals for unusual electronic transport properties and guides strategies towards high thermoelectric performance.

A New Highly Anisotropic Rh-Based Heusler Compound for Magnetic Recording.

The development of high-density magnetic recording media is limited by superparamagnetism in very small ferromagnetic crystals. Hard magnetic materials with strong perpendicular anisotropy offer stability and high recording density. To overcome the difficulty of writing media with a large coercivity, heat-assisted magnetic recording was developed, rapidly heating the media to the Curie temperature Tc before writing, followed by rapid cooling. Requirements are a suitable Tc , coupled with anisotropic thermal conductivity and hard magnetic properties. Here, Rh2 CoSb is introduced as a new hard magnet with potential for thin-film magnetic recording. A magnetocrystalline anisotropy of 3.6 MJ m-3 is combined with a saturation magnetization of µ0 Ms  = 0.52 T at 2 K (2.2 MJ m-3 and 0.44 T at room temperature). The magnetic hardness parameter of 3.7 at room temperature is the highest observed for any rare-earth-free hard magnet. The anisotropy is related to an unquenched orbital moment of 0.42 µB on Co, which is hybridized with neighboring Rh atoms with a large spin-orbit interaction. Moreover, the pronounced temperature dependence of the anisotropy that follows from its Tc of 450 K, together with a thermal conductivity of 20 W m-1 K-1 , make Rh2 CoSb a candidate for the development of heat-assisted writing with a recording density in excess of 10 Tb in.-2 .

Health-Enabling Technologies for Telerehabilitation of the Shoulder: A Feasibility and User Acceptance Study.

BACKGROUND: After discharge from a rehabilitation center the continuation of therapy is necessary to secure already achieved healing progress and sustain (re-)integration into working life. To this end, home-based exercise programs are frequently prescribed. However, many patients do not perform their exercises as frequently as prescribed or even with incorrect movements. The telerehabilitation system AGT-Reha was developed to support patients with shoulder diseases during their home-based aftercare rehabilitation. OBJECTIVES: The presented pilot study AGT-Reha-P2 evaluates the technical feasibility and user acceptance of the home-based telerehabilitation system AGT-Reha. METHODS: A nonblinded, nonrandomized exploratory feasibility study was conducted over a 2-year period in patients' homes. Twelve patients completed a 3-month telerehabilitation exercise program with AGT-Reha. Primary outcome measures are the satisfying technical functionality and user acceptance assessed by technical parameters, structured interviews, and a four-dimensional questionnaire. Secondary endpoints are the medical rehabilitation success measured by the active range of motion and the shoulder function (pain and disability) assessed by employing the Neutral-0 Method and the standardized questionnaire "Shoulder Pain and Disability Index" (SPADI), respectively. To prepare an efficacy trial, various standardized questionnaires were included in the study to measure ability to work, capacity to work, and subjective prognosis of work capacity. The participants have been assessed at three measurement points: prebaseline (admission to rehabilitation center), baseline (discharge from rehabilitation center), and posttherapy. RESULTS: Six participants used the first version of AGT-Reha, while six other patients used an improved version. Despite minor technical problems, all participants successfully trained on their own with AGT-Reha at home. On average, participants trained at least once per day during their training period. Five of the 12 participants showed clinically relevant improvements of shoulder function (improved SPADI score > 11). The work-related parameters suggested a positive impact. All participants would recommend the system, ten participants would likely reuse it, and seven participants would have wanted to continue their use after 3 months. CONCLUSION: The findings show that home-based training with AGT-Reha is feasible and well accepted. Outcomes of SPADI indicate the effectiveness of aftercare with AGT-Reha. A controlled clinical trial to test this hypothesis will be conducted with a larger number of participants.

Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi.

Weyl semimetals are crystals in which electron bands cross at isolated points in momentum space. Associated with each crossing point (or Weyl node) is a topological invariant known as the Berry monopole charge. The circular photogalvanic effect (CPGE), whereby circular polarized light generates a helicity-dependent photocurrent, is a notable example of a macroscopic property that emerges directly from the topology of the Weyl semimetal band structure. Recently, it was predicted that the amplitude of the CPGE associated with optical transitions near a Weyl node is proportional to its monopole charge. In chiral Weyl systems, nodes of opposite charge are nondegenerate, opening a window of wavelengths where the CPGE resulting from uncompensated Berry charge can emerge. Here, we report measurements of CPGE in the chiral Weyl semimetal RhSi, revealing a CPGE response in an energy window that closes at 0.65 eV, in agreement with the predictions of density functional theory.

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa.

It has recently been proposed that combining chirality with topological band theory results in a totally new class of fermions. Understanding how these unconventional quasiparticles propagate and interact remains largely unexplored so far. Here, we use scanning tunneling microscopy to visualize the electronic properties of the prototypical chiral topological semimetal PdGa. We reveal chiral quantum interference patterns of opposite spiraling directions for the two PdGa enantiomers, a direct manifestation of the change of sign of their Chern number. Additionally, we demonstrate that PdGa remains topologically non-trivial over a large energy range, experimentally detecting Fermi arcs in an energy window of more than 1.6 eV that is symmetrically centered around the Fermi level. These results are a consequence of the deep connection between chirality in real and reciprocal space in this class of materials, and, thereby, establish PdGa as an ideal topological chiral semimetal.

Observation and control of maximal Chern numbers in a chiral topological semimetal.

Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (C). Nodal band crossings with linear dispersion are expected to have at most [Formula: see text], which sets an upper limit to the magnitude of many topological phenomena in these materials. Here, we show that the chiral crystal palladium gallium (PdGa) displays multifold band crossings, which are connected by exactly four surface Fermi arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.

Observation of giant spin-split Fermi-arc with maximal Chern number in the chiral topological semimetal PtGa.

Non-symmorphic chiral topological crystals host exotic multifold fermions, and their associated Fermi arcs helically wrap around and expand throughout the Brillouin zone between the high-symmetry center and surface-corner momenta. However, Fermi-arc splitting and realization of the theoretically proposed maximal Chern number rely heavily on the spin-orbit coupling (SOC) strength. In the present work, we investigate the topological states of a new chiral crystal, PtGa, which has the strongest SOC among all chiral crystals reported to date. With a comprehensive investigation using high-resolution angle-resolved photoemission spectroscopy, quantum-oscillation measurements, and state-of-the-art ab initio calculations, we report a giant SOC-induced splitting of both Fermi arcs and bulk states. Consequently, this study experimentally confirms the realization of a maximal Chern number equal to ±4 in multifold fermionic systems, thereby providing a platform to observe large-quantized photogalvanic currents in optical experiments.

Absolute Structure from Scanning Electron Microscopy.

The absence of centrosymmetry in chiral and polar crystal structures is the reason for many technical relevant physical properties like optical birefringence or ferroelectricity. Other chirality related properties that are actually intensively investigated are unconventional superconductivity or unusual magnetic ordering like skyrmions in materials with B20 structure. Despite the often close crystal structure - property relation, its detection is often challenging due to superposition of domains with different absolute structure e.g. chirality. Our investigations of high quality CoSi crystals with B20 structure by both complementary methods X- ray (volume sensitive) and electron backscatter diffraction (EBSD) (surface sensitive) results the consistent assignment of the chirality and reveal fundamental differences in their sensitivity to chirality. The analysis of the surface of a CoSi crystal with domains of different chirality show the high spatial resolution of this method which opens the possibility to analyze the chirality in microstructures of technical relevant materials like thin films and catalysts.