Large off-diagonal magnetoelectricity in a triangular Co2+-based collinear antiferromagnet.

Magnetic toroidicity is an uncommon type of magnetic structure in solid-state materials. Here, we experimentally demonstrate that collinear spins in a material with R-3 lattice symmetry can host a significant magnetic toroidicity, even parallel to the ordered spins. Taking advantage of a single crystal sample of CoTe6O13 with an R-3 space group and a Co2+ triangular sublattice, temperature-dependent magnetic, thermodynamic, and neutron diffraction results reveal A-type antiferromagnetic order below 19.5 K, with magnetic point group -3' and k = (0,0,0). Our symmetry analysis suggests that the missing mirror symmetry in the lattice could lead to the local spin canting for a toroidal moment along the c axis. Experimentally, we observe a large off-diagonal magnetoelectric coefficient of 41.2 ps/m that evidences the magnetic toroidicity. In addition, the paramagnetic state exhibits a large effective moment per Co2+, indicating that the magnetic moment in CoTe6O13 has a significant orbital contribution. CoTe6O13 embodies an excellent opportunity for the study of next-generation functional magnetoelectric materials.

A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2.

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al-MoTe2-Al junctions.

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency ([Formula: see text]) based on the Dirac semimetal MoTe2, the MAR features are observed with exceptional resolution. By tuning the phase difference [Formula: see text] between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent [Formula: see text]. As we vary the junction voltage V, the supercurrent amplitude [Formula: see text] varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to [Formula: see text]. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe2 does not affect the MAR features.

Structural Diversity in Oxoiridates with 1D IrnO3(n+1) Chain Fragments and Flat Bands.

A previously unreported series of hexagonal-perovskite-based Rb-oxoiridates, Rb5Ir2O9, Rb7Ir3O12, and Rb12Ir7O24, have been synthesized and structurally analyzed via N2-protected single-crystal X-ray diffraction (SC-XRD). These materials exhibit different 1D IrnO3(n+1) chain fragments along their c axes. IrO6 octahedra and RbOx (x = 6, 8, and 10) polyhedra are their basic building blocks. The IrO6 octahedra are linked via face-sharing, forming Ir2O9 dimers, Ir3O12 trimers, and Ir7O24 heptamers. The nonmagnetic RbOx (x = 6, 8, and 10) polyhedra serve as both bridging units and spacers. Temperature-dependent SC-XRD shows all three to display positive thermal expansion and rules out structural transitions from their triangular symmetries down to 100 K. Density functional theory results suggest semiconducting-like behavior for the title compounds. The flatness of the electronic bands and our structural analysis are of potential interest for understanding and designing 1D quantum materials.

Unconventional supercurrent phase in Ising superconductor Josephson junction with atomically thin magnetic insulator.

In two-dimensional (2D) NbSe2 crystal, which lacks inversion symmetry, strong spin-orbit coupling aligns the spins of Cooper pairs to the orbital valleys, forming Ising Cooper pairs (ICPs). The unusual spin texture of ICPs can be further modulated by introducing magnetic exchange. Here, we report unconventional supercurrent phase in van der Waals heterostructure Josephson junctions (JJs) that couples NbSe2 ICPs across an atomically thin magnetic insulator (MI) Cr2Ge2Te6. By constructing a superconducting quantum interference device (SQUID), we measure the phase of the transferred Cooper pairs in the MI JJ. We demonstrate a doubly degenerate nontrivial JJ phase (ϕ), formed by momentum-conserving tunneling of ICPs across magnetic domains in the barrier. The doubly degenerate ground states in MI JJs provide a two-level quantum system that can be utilized as a new dissipationless component for superconducting quantum devices. Our work boosts the study of various superconducting states with spin-orbit coupling, opening up an avenue to designing new superconducting phase-controlled quantum electronic devices.

Low-temperature high-frequency dynamic magnetic susceptibility of classical spin-ice Dy2Ti2O7.

Radio-frequency (14.6 MHz) AC magnetic susceptibility,χAC', of Dy2Ti2O7was measured using self-oscillating tunnel-diode resonator. Measurements were made with the excitation AC field parallel to the superimposed DC magnetic field up to 5 T in a wide temperature range from 50 mK to 100 K. At 14.6 MHz, a known broad peak ofχAC'(T)from kHz-range audio-frequency measurements around 15 K for both [111] and [110] directions shifts to 45 K, continuing the Arrhenius activated behavior with the same activation energy barrier ofEa≈ 230 K. Magnetic field dependence ofχAC'along [111] reproduces previously reported low-temperature two-in-two-out to three-in-one-out spin configuration transition at about 1 T, and an intermediate phase between 1 and 1.5 T. The boundaries of the intermediate phase show reasonable overlap with the literature data and connect at a critical endpoint of the first order transition line, suggesting that these features are frequency independent. An unusual upturn of the magnetic susceptibility atT→ 0 was observed in magnetic fields between 1.5 T and 2 T for both magnetic field directions, before fully polarized configuration sets in above 2 T.

Hexagonal Perovskites as Quantum Materials.

Hexagonal perovskites, in contrast to the more familiar perovskites, when oxides, allow for face-sharing of metal-oxygen octahedra or trigonal prisms within their structural frameworks. This results in dimers, trimers, tetramers, or longer fragments of chains of face-sharing octahedra in the crystal structures, and consequently in much shorter metal-metal distances and lower metal-oxygen-metal bond angles than are seen in the more familiar perovskites. The presence of the face-sharing octahedra can have a dramatic impact on magnetic properties of these compounds, and dimer-based materials, in particular, have been the subjects of many quantum-materials-directed studies in materials physics. Hexagonal oxide perovskites are also of contemporary interest due to their potential for geometrical frustration of the ordering of magnetic moments or orbital occupancies at low temperatures, which is especially relevant to their significance as quantum materials. As such, several hexagonal oxide perovskites have been identified as potential candidates for hosting the quantum-spin-liquid state at low temperatures. In our view, hexagonal oxide perovskites are fertile ground for finding new quantum materials. This review briefly describes the solid state chemistry of many of these materials.

Superconductivity on a Bi Square Net in LiBi.

We present the crystallographic analysis, superconducting characterization and theoretical modeling of LiBi, that contains the lightest and the heaviest nonradioactive metal. The compound crystallizes in a tetragonal (CuAu-type) crystal structure with Bi square nets separated by Li planes (parameters a = 3.3636(1) Å and c = 4.2459(2) Å, c/a = 1.26). Superconducting state was studied in detail by magnetic susceptibility and heat capacity measurements. The results reveal that LiBi is a moderately coupled type-I superconductor (λe-p = 0.66) with T c = 2.48 K and a thermodynamic critical field Hc(0) = 157 Oe. Theoretical studies show that bismuth square net is responsible for superconductivity in this compound, but the coupling between the Li planes and Bi planes makes a significant contribution to the superconductivity.

Synthesis, structure, and magnetism of BCC KIrO3.

KIrO3 in the body-centered cubic variant of the KSbO3-type structure is reported. Black cube-shaped single crystals, obtained from the solid-state reaction in a half-closed silver capsule in a sealed quartz tube, were used for the structural characterization by single-crystal X-ray diffraction. The material, space group Im3[combining macron] (no. 204), exhibits a disordered K array and a three-dimensional (3D) IrO6-based tunnel-like framework. Temperature-dependent magnetization and heat capacity measurements suggest a paramagnetic state for KIrO3, with significant contribution of temperature independent paramagnetism and without any sign of long-range magnetic ordering (down to 1.8 K). The 3D motif of this material, based on the 5d Ir5+ ion, is of interest for investigating unconventional magnetism.

Evidence for an edge supercurrent in the Weyl superconductor MoTe2.

Edge supercurrents in superconductors have long been an elusive target. Interest in them has reappeared in the context of topological superconductivity. We report evidence for the existence of a robust edge supercurrent in the Weyl superconductor molybdenum ditelluride (MoTe2). In a magnetic field B, fluxoid quantization generates a periodic modulation of the edge condensate observable as a "fast-mode" oscillation of the critical current I c versus B The fast-mode frequency is distinct from the conventional Fraunhofer oscillation displayed by the bulk supercurrent. We confirm that the fast-mode frequency increases with crystal area as expected for an edge supercurrent. In addition, weak excitation branches are resolved that display an unusual broken symmetry.

K3Ir2O6 and K16.3Ir8O30, Low-Dimensional Iridates with Infinite IrO6 Chains.

A previously unreported 1D iridate, K3Ir2O6, has been grown by a flux method in O2-rich environment, and its crystal structure was determined via single crystal structural analysis. It exhibits straight chains of face-sharing [IrO6] octahedra, which are arranged along the crystallographic c axis, separated by nonmagnetic K ions. No magnetic transitions are observed during measured range, and the material is electrically insulating. Potentially interesting electronic behavior for K3Ir2O6 is supported by electronic structure calculations. A structurally related material, K16.3Ir8O30, which displays similar fundamental geometric units but in a different spatial arrangement-zigzag chains-based on edge and face sharing [IrO6] octahedra, is also reported. Both materials are of interest for probing the properties of a 1D system with strong spin-orbit coupling.

Quantum spin liquids.

Spin liquids are quantum phases of matter with a variety of unusual features arising from their topological character, including "fractionalization"-elementary excitations that behave as fractions of an electron. Although there is not yet universally accepted experimental evidence that establishes that any single material has a spin liquid ground state, in the past few years a number of materials have been shown to exhibit distinctive properties that are expected of a quantum spin liquid. Here, we review theoretical and experimental progress in this area.

A gap-protected zero-Hall effect state in the quantum limit of the non-symmorphic metal KHgSb.

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2 topological insulators by time-reversal symmetry1-3. Recently, interest has turned to unusual surface states in the large class of non-symmorphic materials4-12. In particular, KHgSb is predicted to exhibit double quantum spin Hall states10. Here we report measurements of the Hall conductivity in KHgSb in a strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We theoretically propose that, in this quantum limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right- and left-moving quantum spin Hall surface modes to produce the zero-Hall state. The zero-Hall state illustrates how topological protection in a non-symmorphic material with glide symmetry may lead to highly unusual transport phenomena.

Author Correction: Layer-dependent quantum cooperation of electron and hole states in the anomalous semimetal WTe2.

This Article contains an error in the spelling of the author A. Yazdani, which is incorrectly given as A. Yadzani. The error has not been fixed in the original PDF and HTML versions of the Article.

Interacting multi-channel topological boundary modes in a quantum Hall valley system.

Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3-8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires. QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.

Triangular Rare-Earth Lattice Materials RbBa R(BO3)2 ( R = Y, Gd-Yb) and Comparison to the KBa R(BO3)2 Analogs.

A previously unreported family of electrically insulating rare-earth borates, RbBa R(BO3)2 ( R = Y, Gd-Yb), was designed and then successfully obtained by traditional solid-state reaction. They crystallize in a monoclinic crystal system space group P21 /m (No. 11). They feature triangular planar rare-earth ( R) lattices, which are part of, for example, [Yb(BO3)2]3- infinite 2D layers. These R-based triangular lattices are stacked with layers of crystallographically ordered Rb and Ba atoms to build the 3D structures. Polycrystalline samples of RbBa R(BO3)2 were used to study the elementary magnetic properties, and millimeter-size RbBaYb(BO3)2 single crystals were grown by spontaneous nucleation for further anisotropic magnetic characterization. Antiferromagnetic spin interactions are observed for all magnetic compounds, and no long-range magnetic ordering is found down to 1.8 K. Our results suggest that this RbBa R(BO3)2 ( R = Gd-Yb) family may be of further interest both experimentally and theoretically as highly geometrically frustrated magnets.

Homogeneous reduced moment in a gapful scalar chiral kagome antiferromagnet.

We present a quantitative experimental investigation of the scalar chiral magnetic order with in Nd3Sb3Mg2O14. Static magnetization reveals a net ferromagnetic ground state, and inelastic neutron scattering from the hyperfine coupled nuclear spin reveals a local ordered moment of 1.76(6) µB, just 61(2)% of the saturated moment size. The experiments exclude static disorder as the source of the reduced moment. A 38(1) µeV gap in the magnetic excitation spectrum inferred from heat capacity rules out thermal fluctuations and suggests a multipolar explanation for the moment reduction. We compare Nd3Sb3Mg2O14 to Nd pyrochlores and show that Nd2Zr2O7 is in a spin fragmented state using nuclear Schottky heat capacity.

µSR study of spin freezing and persistent spin dynamics in NaCaNi2F7.

A new pyrochlore compound, NaCaNi2F7, was recently synthesized and has a single magnetic site with spin-1 Ni2+ . We present zero field and longitudinal field muon spin rotation (µSR) measurements on this pyrochlore. Density functional theory calculations show that the most likely muon site is located between two fluorine ions, but off-centre. A characteristic F-µ-F muon spin polarization function is observed at high temperatures where Ni spin fluctuations are sufficiently rapid. The Ni2+ spins undergo spin freezing into a disordered ground state below 4 K, with a characteristic internal field strength of 140 G. Persistent Ni spin dynamics are present to our lowest temperatures (75 mK), a feature characteristic of many geometrically frustrated magnetic systems.

Band Structure of the IV-VI Black Phosphorus Analog and Thermoelectric SnSe.

The success of black phosphorus in fast electronic and photonic devices is hindered by its rapid degradation in the presence of oxygen. Orthorhombic tin selenide is a representative of group IV-VI binary compounds that are robust and isoelectronic and share the same structure with black phosphorus. We measure the band structure of SnSe and find highly anisotropic valence bands that form several valleys having fast dispersion within the layers and negligible dispersion across. This is exactly the band structure desired for efficient thermoelectric generation where SnSe has shown great promise.

Author Correction: Signatures of the topological s+- superconducting order parameter in the type-II Weyl semimetal T d -MoTe2.

The original version of this article omitted the following from the Acknowledgements: "CAM and AL were supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). Additionally, this research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under 'Contract No. DE-AC02-05CH11231'." This has now been corrected in both the PDF and HTML versions of the article.