Measurement of the magnetic octupole susceptibility of PrV2Al20

In the electromagnetic multipole expansion, magnetic octupoles are the subsequent order of magnetic multipoles allowed in centrosymmetric systems, following the more commonly observed magnetic dipoles. As order parameters in condensed matter systems, magnetic octupoles have been experimentally elusive. In particular, the lack of simple external fields that directly couple to them makes their experimental detection challenging. Here, we demonstrate a methodology for probing the magnetic octupole susceptibility using a product of magnetic field $H_i$ and shear strain $\epsilon_{jk}$ to couple to the octupolar fluctuations, while using an adiabatic elastocaloric effect to probe the response to this composite effective field. We observe a Curie-Weiss behavior in the obtained octupolar susceptibility of \ce{PrV2Al20} up to temperatures approximately forty times the putative octupole ordering temperature. Our results demonstrate the presence of magnetic octupole fluctuations in the particular material system, and more broadly highlight how anisotropic strain can be combined with magnetic fields to formulate a versatile probe to observe otherwise elusive emergent `hidden' electronic orders.Comment: 7 pages, 3 figure

Quantum limit transport and destruction of the Weyl nodes in TaAs

Weyl fermions are a new ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. We use magnetic fields up to 95 tesla to drive the Weyl semimetal TaAs far into its quantum limit (QL), where only the purely chiral 0th Landau levels (LLs) of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 tesla: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 tesla we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral LLs. Above 80 tesla we observe strong ultrasonic attenuation below 2 kelvin, suggesting a mesoscopically-textured state of matter. These results point the way to inducing new correlated states of matter in the QL of Weyl semimetals

Scale-invariant magnetic anisotropy in RuCl3_3 at high magnetic fields

In RuCl$_3$, inelastic neutron scattering and Raman spectroscopy reveal a continuum of non-spin-wave excitations that persists to high temperature, suggesting the presence of a spin liquid state on a honeycomb lattice. In the context of the Kitaev model, magnetic fields introduce finite interactions between the elementary excitations, and thus the effects of high magnetic fields - comparable to the spin exchange energy scale - must be explored. Here we report measurements of the magnetotropic coefficient - the second derivative of the free energy with respect to magnetic field orientation - over a wide range of magnetic fields and temperatures. We find that magnetic field and temperature compete to determine the magnetic response in a way that is independent of the large intrinsic exchange interaction energy. This emergent scale-invariant magnetic anisotropy provides evidence for a high degree of exchange frustration that favors the formation of a spin liquid state in RuCl$_3$.Comment: arXiv admin note: substantial text overlap with arXiv:1901.09245. Nature Physic

Inducing superconductivity in Weyl semimetal microstructures by selective ion sputtering

Work by N.N. and J.G.A. is partly supported by the Office of Naval Research under the Electrical Sensors and Network Research Division, Award No. N00014-15-1-2674, and by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4374. M.D.B. and P.J.W.M. acknowledge funding through the Max Planck Society. M.D.B. acknowledges studentship funding from the EPSRC under grant no. EP/I007002/1. N.N. is supported by the NSF Graduate Research Fellowship Program under grant no. DGE 1106400. F.F. acknowledges support from a Lindemann Trust Fellowship of the English Speaking Union. R.I. is funded by the Air Force Office of Scientific Research Multidisciplinary University Research Initiative. T.M. is funded by Deutsche Forschungsgemeinschaft through GRK 1621 and SFB 1143. N.J.G. and E.D.B. were supported under the auspices of the U.S. Department of Energy, Office of Science. F.R. was supported by the Los Alamos National Laboratory Laboratory Directed Research and Development program. Data underpinning this publication can be accessed at http://dx.doi.org/10.17630/04280577-35c4-44e7-97d2-5c827ace7a4e.By introducing a superconducting gap in Weyl or Dirac semimetals, the superconducting state inherits the nontrivial topology of their electronic structure. As a result, Weyl superconductors are expected to host exotic phenomena, such as nonzero-momentum pairing due to their chiral node structure, or zero-energy Majorana modes at the surface. These are of fundamental interest to improve our understanding of correlated topological systems, and, moreover, practical applications in phase-coherent devices and quantum applications have been proposed. Proximity-induced superconductivity promises to allow these experiments on nonsuperconducting Weyl semimetals. We show a new route to reliably fabricate superconducting microstructures from the nonsuperconducting Weyl semimetal NbAs under ion irradiation. The significant difference in the surface binding energy of Nb and As leads to a natural enrichment of Nb at the surface during ion milling, forming a superconducting surface layer (Tc ~ 3.5 K). Being formed from the target crystal itself, the ideal contact between the superconductor and the bulk may enable an effective gapping of the Weyl nodes in the bulk because of the proximity effect. Simple ion irradiation may thus serve as a powerful tool for the fabrication of topological quantum devices from monoarsenides, even on an industrial scale.Publisher PDFPeer reviewe

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB2C2

The adiabatic elastocaloric effect measures the temperature change of given systems with strain and probes the entropic landscape in the temperature-strain space. In this study we demonstrate that the DC bias strain-dependence of AC elastocaloric effect can be used to decompose the latter into contributions from symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strains, using a tetragonal f-electron system DyB2C2--whose antiferroquadrupolar order locally breaks four-fold rotational site symmetries while globally remaining tetragonal--as a showcase example. We capture the strain evolution of the quadrupolar and magnetic phase transitions in the system using both singularities in the elastocaloric coefficient and its jump at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a bi-quadratic manner in the antiferroquadrupolar (AFQ) phase but in a linear-quadratic manner in the canted antiferromagnetic (CAFM) phase; the contrast is attributed to a preserved (broken) tetragonal symmetry in the AFQ (CAFM) phase, respectively. The broken tetragonal symmetry in the CAFM phase is further supported by elastocaloric strain-hysteresis and observation of two sets of domains with mutually perpendicular principal axes in optical birefringence. Additionally, when the quadrupolar moments are ordered in a staggered fashion, we uncover an elastocaloric response that reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnets by promoting pseudospin flips. Our results show that AC elastocaloric effect is a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain, which can potentially be applied to broader classes of quantum materials.Comment: 10 pages, 7 figure

Directional ballistic transport in the two-dimensional metal PdCoO2

In an idealized infinite crystal, the material properties are constrained by the symmetries of its unit cell. Naturally, the point-group symmetry is broken by the sample shape of any finite crystal, yet this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from anisotropic Fermi surfaces are needed. Here we show how strongly facetted Fermi surfaces and long quasiparticle mean free paths present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. Bar shaped transport devices narrower than the mean free path are carved from single crystals using focused ion beam (FIB) milling, such that the ballistic charge carriers at low temperatures frequently collide with both sidewalls defining a channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and transverse voltages appear in zero magnetic field. We robustly identify the channel direction as the source of symmetry breaking via ballistic Monte- Carlo simulations and numerical solution of the Boltzmann equation

h/e oscillations in interlayer transport of delafossites

Funding: This project was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant no. 715730, MiTopMat) and also was supported by the Max Planck Society. A.P.M. and R.M. acknowledge support from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147). M.D.B., P.M., and V.S. acknowledge studentship funding from the EPSRC under grant no. EP/L015110/1. A.S. was supported by the Israel Science Foundation, the European Research Council (Project LEGOTOP), and the DFG through projectno.CRC-183. M.K. acknowledges support from the SIRIUS irradiation facility through project no. EMIR 2019 18-7099.Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO2 and PtCoO2 The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck's constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T > 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.PostprintPeer reviewe

Resonant torsion magnetometry in anisotropic quantum materials

Unusual behavior of quantum materials commonly arises from their effective low-dimensional physics, which reflects the underlying anisotropy in the spin and charge degrees of freedom. Torque magnetometry is a highly sensitive technique to directly quantify the anisotropy in quantum materials, such as the layered high-T$_c$ superconductors, anisotropic quantum spin-liquids, and the surface states of topological insulators. Here we introduce the magnetotropic coefficient $k=\partial^2 F/\partial \theta^2$, the second derivative of the free energy F with respect to the angle $\theta$ between the sample and the applied magnetic field, and report a simple and effective method to experimentally detect it. A sub-$\mu$g crystallite is placed at the tip of a commercially available atomic force microscopy cantilever, and we show that $k$ can be quantitatively inferred from a shift in the resonant frequency under magnetic field. While related to the magnetic torque $\tau=\partial F/\partial \theta$, $k$ takes the role of torque susceptibility, and thus provides distinct insights into anisotropic materials akin to the difference between magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is discontinuous at second-order phase transitions and subject to Ehrenfest relations with the specific heat and magnetic susceptibility. We apply this simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP and the spin-liquid candidate RuCl$_3$, yet it is broadly applicable in quantum materials research.Comment: 7 pages including 6 figures and methods sectio