We study transport in the presence of magnetic domain walls (DWs) in a lattice model of ferromagnetic type-I Weyl metals. We compute the diagonal and Hall conductivities in the presence of a DW, using both Kubo and Landauer formalisms, and uncover the effect of DW scattering. When the Fermi level lies near Weyl points, we find a strong skew scattering at the DW which leads to a significant additional Hall effect. We estimate the average Hall resistivity for multi-domain configurations and identify the limit where the DW scattering contribution becomes significant. We show that a continuum model obtained by linearizing the lattice dispersion around the Weyl points does not correctly capture this DW physics. Going beyond the linearized theory, and incorporating leading curvature terms, leads to a semi-quantitative agreement with our lattice model results. Our results are relevant for experiments on the Hall resistivity of spin-orbit coupled ferromagnets, which can have Weyl points near the Fermi energy.
The anomalous Hall effect in ferromagnetic metals is classified into two based on the mechanism. The first one is the intrinsic Hall effect due to the Berry curvature in momentum space; this is a Hall effect that solely arises from the band structure of solids. On the other hand, another contribution to the Hall effect, so-called extrinsic mechanism, comes from impurity scatterings such as skew scattering and side jump; for the extrinsic mechanism, the spin-orbit interaction of the impurity ions is often required. These two mechanisms are often discussed separately; the intrinsic Hall effect i…
Magnetic Weyl semimetals are predicted to host emergent electromagnetic fields at heterogeneous strained phases or at the magnetic domain walls. Tunability and control of the topological and magnetic properties is crucial for revealing these phenomena, which are not well understood or fully realized yet. Here, we use a scanning SQUID microscope to image spontaneous magnetization and magnetic susceptibility of CeAlSi, a noncentrosymmetric ferromagnetic Weyl semimetal candidate. We observe large metastable domains alongside stable ferromagnetic domains. The metastable domains most likely embody …
The magnetotransport properties of disordered ferromagnetic Weyl semimetals are investigated numerically. We found an extraordinarily stable and huge magnetoresistance effect in domain walls of Weyl semimetals. This effect originates from the helicity mismatch of Weyl fermions and is a specific property of Weyl semimetals. Although conventional magnetoresistance effects are strongly suppressed in domain walls where local magnetization varies gradually, the helicity-protected magnetoresistance in Weyl semimetals maintains almost $100\%$ of the magnetoresistance ratio for any kind of thick domai…
We experimentally compare two types of interface structures with magnetic and non-magnetic Weyl semimetals. They are the junctions between a gold normal layer and magnetic Weyl semimetal Ti$_2$MnAl, and a ferromagnetic nickel layer and non-magnetic Weyl semimetal WTe$_2$, respectively. Due to the ferromagnetic side of the junction, we investigate spin-polarized transport through the Weyl semimetal surface. For both structures, we demonstrate similar current-voltage characteristics, with hysteresis at low currents and sharp peaks in differential resistance at high ones. Despite this behavior re…
Co$_2$MnGa is a ferromagnetic semimetal with Weyl nodal lines identified by ARPES. We studied electrical transport in thin Co$_2$MnGa lamellae (10 $\times$ 10 $\times$ 0.4-5 microns) cut from single-crystals using a focused ion beam. These crystals exhibit an unexpected and highly unusual planar resistance anisotropy ($\sim$10 times) with principal axes that rotate by 90 degrees between the upper and lower faces. Using symmetry arguments and simulations, we find that the observed resistance anisotropy resembles that of an isotropic conductor with anisotropic surface states that are impeded fro…
We propose that the topological semimetal features can co-exist with ferromagnetic ground state in vanadium-phosphorous-oxide $β$-V$_2$OPO$_4$ compound from first-principles calculations. In this magnetic system with inversion symmetry, the direction of magnetization is able to manipulate the symmetric protected band structures from a node-line type to a Weyl one in the presence of spin-orbital-coupling. The node-line semimetal phase is protected by the mirror symmetry with the reflection-invariant plane perpendicular to magnetic order. Within mirror symmetry breaking due to the magnetization …
Co$_3$Sn$_2$S$_2$ has recently emerged as a ferromagnetic Weyl semi-metal. Theoretical investigation of the spin-split bands predicted half metalicity in the compound. Here, we report the detection of a spin polarized supercurrent through a Nb/Co$_3$Sn$_2$S$_2$ point contact where Andreev reflection is seen to be large indicating a large deviation from half metallicity. In fact, analysis of the Andreev reflection spectra reveals only 50\% spin polarization at the Fermi level of Co$_3$Sn$_2$S$_2$. Our theoretical calculations of electronic Density of States (DOS) reveal a spin depolarizing effe…
A developing frontier in condensed matter physics is the emergence of novel electromagnetic responses, such as topological and anomalous Hall effect (AHE), in ferromagnetic Weyl semimetals (FM-WSMs). Candidates of FM-WSM are limited to materials that preserve inversion symmetry and generate Weyl crossings by breaking time-reversal symmetry. These materials share three common features: a centrosymmetric lattice, a collinear FM ordering, and a large AHE observed when the field is parallel to the magnetic easy-axis. Here, we present CeAlSi as a new type of FM-WSM, where the Weyl nodes are stabili…
The propagation of light in Weyl semimetal films is analyzed. The magnetic family of these materials is known by anomalous Hall effect, which, being enhanced by the large Berry curvature, allows one to create strong gyrotropic and nonreciprocity effects without external magnetic field. The existence of nonreciprocal waveguide electromagnetic modes in ferromagnetic Weyl semimetal films in the Voigt configuration is predicted. Thanks to the strong dielectric response caused by the gapless Weyl spectrum and the large Berry curvature, ferromagnetic Weyl semimetals combine the best waveguide proper…
We propose a new scaling law for anomalous Hall effect in ferromagnetic thin films by distinguishing three scattering sources, namely, bulk impurity, phonon, and more importantly a rough surface. This new scaling law fits the recent experimental data excellently with constant coefficients that are independent of temperature and film thickness. This is in stark constrast with previous scaling laws that use temperature/thickness dependent fitting coefficients, and is a strong indicator that this law captures the essential physics. By intepretating the experiments for Fe, Co, and Ni with this new…
We introduce and investigate material junctions as a generic and tuneable electronic platform for the realization of exotic non-Hermitian (NH) topological states of matter, where the NH character is induced by the surface self-energy of a thermal reservoir. As a conceptually rich and immediately experimentally realizable example, we consider a three-dimensional topological insulator (TI) coupled to a ferromagnetic lead. Remarkably, the symmetry protected TI is promoted in a dissipative fashion to a non-symmetry protected NH Weyl phase with no direct Hermitian counterpart and which exhibits rob…
Weyl semimetal phase in solid-solution narrow-gap semiconductors
本文从理论上研究了具有强自旋-轨道相互作用的磁掺杂固溶体窄隙半导体如Cr掺杂Bi $_2$（Se $_x$ Te $_{1-x}$）$_3$中的铁磁有序。我们计算了杂质和巡游电子的自发磁化强度，并估计了临界温度作为磁性掺杂剂浓度和自旋轨道相互作用强度的函数。发现临界温度与掺杂浓度成正比，且随自旋轨道相互作用的增强而提高。铁磁相变可以使系统转变为具有动量空间中分离的一对外尔点的外尔半金属。
We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to linear response Nernst effect in ferromagnetic Dirac materials such as Fe$_3$Sn$_2$, Weyl semimetal Co$_3$Sn$_2$S$_2$ and to second order response of monolayer graphene on hBN with trigonal warping. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and used to explain an enhanced thermoelectric response.
Observation of the Magnus Nonlinear Hall effect from Chiral Weyl Monopoles
Max Planck Institute for Chemical Physics of Solids（德国德累斯顿固体化学物理马克斯·普朗克研究所）；Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA（美国田纳西大学）；Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA（美国橡树岭国家实验室）；Department of Physics, National University of Singapore, 117551, Singapore（新加坡国立大学）
We study the intrinsic and extrinsic Hall effects in disordered magnetic Weyl semimetals numerically. We show that in Weyl metals, where the Fermi energy deviates from the Weyl point, the Hall and longitudinal conductances exhibit a specific relation, which is distinguished from the well-known relation in integer quantum Hall systems. Around the Weyl point, the Hall conductance increases with increasing longitudinal conductance. This increasing behavior indicates the existence of additional contributions to the Hall conductance from the subbands of Weyl cones besides that from the bulk Berry c…
We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields, and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was recently observed in…
Quantum oscillations in resistivity and magnetization at high magnetic fields are a macroscopic fingerprint of the energy quantization due to the cyclotron motion of quasiparticles. In a thin Weyl semimetal, a unique thickness dependent Weyl-orbit quantum oscillation was proposed to exist, originating from a nonlocal cyclotron orbit via the electron tunneling between the top and bottom Fermi-arc surface states. Here, untwinned and high crystalline Weyl metal SrRuO$_3$ thin films with different thicknesses were grown on miscut SrTiO$_3$ (001) substrates. Magneto-transport measurements were carr…
We theoretically study the anisotropic magnetotransport in Dirac-Weyl magnetic junctions where a doped ferromagnetic Weyl semimetal is sandwiched between doped Dirac semimetals. We calculate the conductance using the Landauer formula and find that the system exhibits extraordinarily large anisotropic magnetoresistance (AMR). The AMR depends on the ratio of the Fermi energy and the strength of the exchange interaction. The origin of the AMR is the shift of the Fermi surface in the Weyl semimetal and the mechanism is completely different from the conventional AMR originating from the spin depend…
In this paper we present spin-to-charge current conversion properties in the Weyl semimetal TaP by means of the inverse Rashba-Edelstein effect (IREE) with the integration of this quantum material with the ferromagnetic metal Permalloy $(Py=Ni_{81}Fe_{19})$. The spin currents are generated in the Py layer by the spin pumping effect (SPE) from microwave-driven ferromagnetic resonance and are detected by a dc voltage along the TaP crystal, at room temperature. We observe a field-symmetric voltage signal without the contamination of asymmetrical lines due to spin rectification effects observed in…
We study the topological properties of magnon excitations in a wide class of three dimensional (3D) honeycomb lattices with ferromagnetic ground states. It is found that they host nodal ring magnon excitations. These rings locate on the same plane in the momentum space. The rings can be gapped by Dzyaloshinskii-Moriya (DM) interactions to form two Weyl points with opposite charges. We explicitly discuss these physics in the simplest 3D honeycomb lattice, the hyperhoneycomb lattice and show drumhead and arc surface states in the nodal ring and Weyl phases, respectively, due to the bulk-boundary…
The "Hydrogen atom" of magnetic Weyl semimetals, with the minimum number of Weyl points, have received growing attention recently due to the possible presence of Weyl-related phenomena. Here, we report a nontrivial electronic structure of the ferromagnetic alluaudite-type compound K$_{2}$Mn$_3$(AsO$_{4}$)$_3$. It exhibits only a pair of Weyl points constrained in the $z$-direction by the two-fold rotation symmetry, leading to extremely long Fermi arc surface states. In addition, the study of its low-energy effective model results in the discovery of various topological superconducting states, …
We start closing a gap in the comparison of experimental and theoretical data associated with the spin Hall effect. Based on a first-principles characterization of electronic structure and a semiclassical description of electron transport, we compute the skew-scattering contribution to the transverse spin and charge currents generated by spin and anomalous Hall effect in a Co/Cu multilayer system doped with Bi impurities. The fact that the created currents cross the interface between the two materials strongly influences the efficiency of charge to spin current conversion, as demonstrated by o…
In this work, we study the spin Hall effect and Rashba-Edelstein effect of a 2D Weyl fermion system in the clean limit using the Kubo formalism. Spin transport is solely due to the spin-torque current in this strongly spin-orbit coupled (SOC) system, and chiral spin-flip scattering off non-SOC scalar impurities, with potential strength $V$ and size $a$, gives rise to a skew-scattering mechanism for the spin Hall effect. The key result is that the resultant spin-Hall angle has a fixed sign, with $θ^{SH} \sim O \left(\tfrac{V^2}{v_F^2/a^2} (k_F a)^4 \right)$ being a strongly-dependent function o…
We construct a two-orbital effective model for a ferromagnetic Kagome-lattice shandite, $\rm{{Co}_3{Sn}_2{S}_2}$, a candidate material of magnetic Weyl semimetals, by considering one $d$ orbital from Co, and one $p$ orbital from interlayer Sn. The energy spectrum near the Fermi level, and the configurations of the Weyl points, computed by using our model, are similar to those obtained by first principle calculations. We show also that nodal rings appear even with spin-orbit coupling when the magnetization points in-plane direction. Additionally, magnetic properties of $\rm{{Co}_3{Sn}_2{S}_2}$ …
Bulk-surface correspondence in Weyl semimetals assures the formation of topological "Fermi-arc" surface bands whose existence is guaranteed by bulk Weyl nodes. By investigating three distinct surface terminations of the ferromagnetic semimetal Co3Sn2S2 we verify spectroscopically its classification as a time reversal symmetry broken Weyl semimetal. We show that the distinct surface potentials imposed by three different terminations modify the Fermi-arc contour and Weyl node connectivity. On the Sn surface we identify intra-Brillouin zone Weyl node connectivity of Fermi-arcs, while on Co termin…
Weyl semimetals are crystalline solids that host emergent relativistic Weyl fermions and have characteristic surface Fermi-arcs in their electronic structure. Weyl semimetals with broken time reversal symmetry are difficult to identify unambiguously. In this work, using angle-resolved photoemission spectroscopy, we visualized the electronic structure of the ferromagnetic crystal Co3Sn2S2 and discovered its characteristic surface Fermi-arcs and linear bulk band dispersions across the Weyl points. These results establish Co3Sn2S2 as a magnetic Weyl semimetal that may serve as a platform for real…
In this paper we argue that the electron skew-scattering on paramagnetic impurities in non-magnetic systems, such as bulk semiconductors, possesses a remarkable fingerprint allowing to differentiate it directly from other microscopic mechanisms of the emergent Hall response. We demonstrate theoretically that the exchange interaction between the impurity magnetic moment and mobile electrons leads to the emergence of an electric Hall current persisting even at zero electron spin polarization. We describe two microscopic mechanisms behind this effect, namely the exchange interaction assisted skew…
We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in 3$d$ ferromagnetic metals (Fe, Co, permalloy (Ni$_{81}$Fe$_{19}$; Py), and Ni) by varying their resistivities and temperature. At low temperatures where the phonon scattering is negligible, the skew scattering coefficients of the SHE and AHE in Py are related to its spin polarization. However, this simple relation breaks down for Py at higher temperatures as well as for the other ferromagnetic metals at any temperature. We find that, in general, the relation between the SHE and AHE is more complex, with th…
