Field-Induced Non-BEC Transitions in Frustrated Magnets.

Frustrated spin systems have traditionally proven challenging to understand, owing to a scarcity of controlled methods for their analyses. By contrast, under strong magnetic fields, certain aspects of spin systems admit simpler and universal description in terms of hardcore bosons. The bosonic formalism is anchored by the phenomenon of Bose-Einstein condensation (BEC), which has helped explain the behaviors of a wide range of magnetic compounds under applied magnetic fields. Here, we focus on the interplay between frustration and externally applied magnetic field to identify instances where the BEC paradigm is no longer applicable. As a representative example, we consider the antiferromagnetic J_{1}-J_{2}-J_{3} model on the square lattice in the presence of a uniform external magnetic field, and demonstrate that the frustration-driven suppression of the Néel order leads to a Lifshitz transition for the hardcore bosons. In the vicinity of the Lifshitz point, the physics becomes unmoored from the BEC paradigm, and the behavior of the system, both at and below the saturation field, is controlled by a Lifshitz multicritical point. We obtain the resultant universal scaling behaviors, and provide strong evidence for the existence of a frustration and magnetic-field driven correlated bosonic liquid state along the entire phase boundary separating the Néel phase from other magnetically ordered states.

Anisotropic Melting of Frustrated Ising Antiferromagnets.

Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition T_{N}. In this Letter, we use large-scale Monte Carlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gaslike paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range T_{N}

Diffusive excitonic bands from frustrated triangular sublattice in a singlet-ground-state system.

Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni2Mo3O8, where Ni2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.

Evidence for Topological Magnon-Phonon Hybridization in a 2D Antiferromagnet down to the Monolayer Limit.

Topological phonons and magnons potentially enable low-loss, quantum coherent, and chiral transport of information and energy at the atomic scale. Van der Waals magnetic materials are promising to realize such states due to their recently discovered strong interactions among the electronic, spin, and lattice degrees of freedom. Here, we report the first observation of coherent hybridization of magnons and phonons in monolayer antiferromagnet FePSe3 by cavity-enhanced magneto-Raman spectroscopy. The robust magnon-phonon cooperativity in the 2D limit occurs even in zero magnetic field, which enables nontrivial band inversion between longitudinal and transverse optical phonons caused by the strong coupling with magnons. The spin and lattice symmetry theoretically guarantee magnetic-field-controlled topological phase transition, verified by nonzero Chern numbers calculated from the coupled spin-lattice model. The 2D topological magnon-phonon hybridization potentially offers a new route toward quantum phononics and magnonics with an ultrasmall footprint.

Anisotropy-driven quantum criticality in an intermediate valence system.

Intermetallic compounds containing f-electron elements have been prototypical materials for investigating strong electron correlations and quantum criticality (QC). Their heavy fermion ground state evoked by the magnetic f-electrons is susceptible to the onset of quantum phases, such as magnetism or superconductivity, due to the enhanced effective mass (m*) and a corresponding decrease of the Fermi temperature. However, the presence of f-electron valence fluctuations to a non-magnetic state is regarded an anathema to QC, as it usually generates a paramagnetic Fermi-liquid state with quasiparticles of moderate m*. Such systems are typically isotropic, with a characteristic energy scale T0 of the order of hundreds of kelvins that require large magnetic fields or pressures to promote a valence or magnetic instability. Here we show the discovery of a quantum critical behaviour and a Lifshitz transition under low magnetic field in an intermediate valence compound α-YbAlB4. The QC origin is attributed to the anisotropic hybridization between the conduction and localized f-electrons. These findings suggest a new route to bypass the large valence energy scale in developing the QC.

Fractionalized Excitations Revealed by Entanglement Entropy.

Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of freedom, how to probe them and establish their existence is a long-standing challenge. We present a general procedure to reveal the fractionalized excitations using real-space entanglement entropy in critical spin liquids that are particularly relevant to experiments. Moreover, we show how to use the entanglement entropy to construct the corresponding spinon Fermi surface. Our work defines a new pathway to establish and characterize exotic excitations in novel quantum phases of matter.

Low-carrier density and fragile magnetism in a Kondo lattice system.

Kondo-based semimetals and semiconductors are of extensive current interest as a viable platform for strongly correlated states in the dilute carrier limit. It is thus important to explore the routes to understand such systems. One established pathway is through the Kondo effect in metallic nonmagnetic analogs, in the so called half-filling case of one conduction electron and one 4f electron per site. Here, we demonstrate that Kondo-based semimetals develop out of conduction electrons with a low-carrier density in the presence of an even number of rare-earth sites. We do so by studying the Kondo material Yb3Ir4Ge13 along with its closed-4f -shell counterpart, Lu3Ir4Ge13. Through magnetotransport, optical conductivity, and thermodynamic measurements, we establish that the correlated semimetallic state of Yb3Ir4Ge13 below its Kondo temperature originates from the Kondo effect of a low-carrier conduction-electron background. In addition, it displays fragile magnetism at very low temperatures, which in turn, can be tuned to a Griffiths-phase-like regime through Lu-for-Yb substitution. These findings are connected with recent theoretical studies in simplified models. Our results can pave the way to exploring strong correlation physics in a semimetallic environment.

Local orthorhombic lattice distortions in the paramagnetic tetragonal phase of superconducting NaFe1-xNixAs.

Understanding the interplay between nematicity, magnetism and superconductivity is pivotal for elucidating the physics of iron-based superconductors. Here we use neutron scattering to probe magnetic and nematic orders throughout the phase diagram of NaFe1-xNixAs, finding that while both static antiferromagnetic and nematic orders compete with superconductivity, the onset temperatures for these two orders remain well separated approaching the putative quantum critical points. We uncover local orthorhombic distortions that persist well above the tetragonal-to-orthorhombic structural transition temperature Ts in underdoped samples and extend well into the overdoped regime that exhibits neither magnetic nor structural phase transitions. These unexpected local orthorhombic distortions display Curie-Weiss temperature dependence and become suppressed below the superconducting transition temperature Tc, suggesting that they result from the large nematic susceptibility near optimal superconductivity. Our results account for observations of rotational symmetry breaking above Ts, and attest to the presence of significant nematic fluctuations near optimal superconductivity.

Erratum: Spin Ferroquadrupolar Order in the Nematic Phase of FeSe [Phys. Rev. Lett. 116, 247203 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.247203.

A Mott insulator continuously connected to iron pnictide superconductors.

Iron-based superconductivity develops near an antiferromagnetic order and out of a bad-metal normal state, which has been interpreted as originating from a proximate Mott transition. Whether an actual Mott insulator can be realized in the phase diagram of the iron pnictides remains an open question. Here we use transport, transmission electron microscopy, X-ray absorption spectroscopy, resonant inelastic X-ray scattering and neutron scattering to demonstrate that NaFe1-xCuxAs near x≈0.5 exhibits real space Fe and Cu ordering, and are antiferromagnetic insulators with the insulating behaviour persisting above the Néel temperature, indicative of a Mott insulator. On decreasing x from 0.5, the antiferromagnetic-ordered moment continuously decreases, yielding to superconductivity ∼x=0.05. Our discovery of a Mott-insulating state in NaFe1-xCuxAs thus makes it the only known Fe-based material, in which superconductivity can be smoothly connected to the Mott-insulating state, highlighting the important role of electron correlations in the high-Tc superconductivity.

Competing superconducting channels in iron pnictides from the strong coupling theory with biquadratic spin interactions.

We study the symmetry and strength of the superconducting pairing in a two-orbital [Formula: see text] model for iron pnictides using the slave boson strong coupling approach. We show that the nearest-neighbor biquadratic interaction [Formula: see text] strongly affects the superconducting pairing phase diagram by promoting the [Formula: see text] B 1g and the [Formula: see text] A 1g channels. The resulting phase diagram consists of several competing pairing channels, including the isotropic [Formula: see text] A 1g channel, an anisotropic [Formula: see text] B 1g channel, and two [Formula: see text] pairing channels. We have investigated the evolution of superconducting states with electron doping, and find that the biquadratic interaction plays a crucial role in stabilizing the [Formula: see text] and even pure d-wave pairing in the heavily electron- and hole-doped regimes. In addition, we identify a novel orbital-B 1g pairing channel, which has a s-wave form factor but a B 1g symmetry. This channel has a comparable pairing amplitude to the d-wave pairing, and may strongly influence the superconducting gap anisotropy of the system in the overdoped regime. These findings are crucial in understanding the doping evolution of the superconducting gap anisotropy observed by angle resolved photoemission spectroscopy in the iron pnictides and iron chalcogenides, including the heavily K-doped BaFe2As2 and K-doped FeSe films.

NaFe_{0.56}Cu_{0.44}As: A Pnictide Insulating Phase Induced by On-Site Coulomb Interaction.

In the studies of iron pnictides, a key question is whether their bad-metal state from which the superconductivity emerges lies in close proximity with a magnetically ordered insulating phase. Recently, it was found that at low temperatures, the heavily Cu-doped NaFe_{1-x}Cu_{x}As (x>0.3) iron pnictide is an insulator with long-range antiferromagnetic order, similar to the parent compound of cuprates but distinct from all other iron pnictides. Using angle-resolved photoemission spectroscopy, we determined the momentum-resolved electronic structure of NaFe_{1-x}Cu_{x}As (x=0.44) and identified that its ground state is a narrow-gap insulator. Combining the experimental results with density functional theory (DFT) and DFT+U calculations, our analysis reveals that the on-site Coulombic (Hubbard) and Hund's coupling energies play crucial roles in the formation of the band gap about the chemical potential. We propose that at finite temperatures, charge carriers are thermally excited from the Cu-As-like valence band into the conduction band, which is of Fe 3d-like character. With increasing temperature, the number of electrons in the conduction band becomes larger and the hopping energy between Fe sites increases, and finally the long-range antiferromagnetic order is destroyed at T>T_{N}. Our study provides a basis for investigating the evolution of the electronic structure of a Mott insulator transforming into a bad metallic phase and eventually forming a superconducting state in iron pnictides.

Spin Ferroquadrupolar Order in the Nematic Phase of FeSe.

We provide evidence that spin ferroquadrupolar (FQ) order is the likely ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By studying the variational mean-field phase diagram of a bilinear-biquadratic Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close proximity to the columnar antiferromagnet commonly realized in iron-based superconductors; the stability of the FQ phase is further verified by the density matrix renormalization group. The dynamical spin structure factor in the FQ state is calculated with flavor-wave theory, which yields a qualitatively consistent result with inelastic neutron scattering experiments on FeSe at both low and high energies. We verify that FQ can coexist with C_{4} breaking environments in the mean-field calculation, and further discuss the possibility that quantum fluctuations in FQ act as a source of nematicity.

Three-Dimensional Crystallization of Vortex Strings in Frustrated Quantum Magnets.

We demonstrate that frustrated exchange interactions can produce exotic 3D crystals of vortex strings near the saturation field (H=H(sat)) of body- and face-centered cubic Mott insulators. The combination of cubic symmetry and frustration leads to a magnon spectrum of the fully polarized spin state (H>H(sat)) with degenerate minima at multiple noncoplanar Q vectors. This spectrum becomes gapless at the quantum critical point H=H(sat) and the magnetic ordering below H(sat) can be formally described as a condensate of a dilute gas of bosons. By expanding in the lattice gas parameter, we find that different vortex crystals span sizable regions of the phase diagrams for isotropic exchange and are further stabilized by symmetric exchange anisotropy.

An itinerant antiferromagnetic metal without magnetic constituents.

The origin of magnetism in metals has been traditionally discussed in two diametrically opposite limits: itinerant and local moments. Surprisingly, there are very few known examples of materials that are close to the itinerant limit, and their properties are not universally understood. In the case of the two such examples discovered several decades ago, the itinerant ferromagnets ZrZn2 and Sc3In, the understanding of their magnetic ground states draws on the existence of 3d electrons subject to strong spin fluctuations. Similarly, in Cr, an elemental itinerant antiferromagnet with a spin density wave ground state, its 3d electron character has been deemed crucial to it being magnetic. Here, we report evidence for an itinerant antiferromagnetic metal with no magnetic constituents: TiAu. Antiferromagnetic order occurs below a Néel temperature of 36 K, about an order of magnitude smaller than in Cr, rendering the spin fluctuations in TiAu more important at low temperatures. This itinerant antiferromagnet challenges the currently limited understanding of weak itinerant antiferromagnetism, while providing insights into the effects of spin fluctuations in itinerant-electron systems.

Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model.

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturing symmetry broken magnetic and orbitally ordered phases. Both approaches show that the electron and hole doping affect the two orders differently. While hole doping tends to suppress both magnetism and orbital ordering, the electron doping suppresses magnetism faster. Crucially, we find a realistic parameter regime for moderate electron doping that stabilizes orbital nematicity in the absence of long-range antiferromagnetic order. This is reminiscent of the non-magnetic orbital nematic phase observed recently in FeSe and a number of iron pnictide materials and raises the possibility that at least in some cases, the observed electronic nematicity may be primarily due to orbital rather than magnetic fluctuations.

Superconductivity. Nematic spin correlations in the tetragonal state of uniaxial-strained BaFe(2-x)Ni(x)As2.

Understanding the microscopic origins of electronic phases in high-transition temperature (high-T(c)) superconductors is important for elucidating the mechanism of superconductivity. In the paramagnetic tetragonal phase of BaFe(2-x)T(x)As2 (where T is Co or Ni) iron pnictides, an in-plane resistivity anisotropy has been observed. Here, we use inelastic neutron scattering to show that low-energy spin excitations in these materials change from fourfold symmetric to twofold symmetric at temperatures corresponding to the onset of the in-plane resistivity anisotropy. Because resistivity and spin excitation anisotropies both vanish near optimal superconductivity, we conclude that they are likely intimately connected.

Hydrogen diffusion and stabilization in single-crystal VO2 micro/nanobeams by direct atomic hydrogenation.

We report measurements of the diffusion of atomic hydrogen in single crystalline VO2 micro/nanobeams by direct exposure to atomic hydrogen, without catalyst. The atomic hydrogen is generated by a hot filament, and the doping process takes place at moderate temperature (373 K). Undoped VO2 has a metal-to-insulator phase transition at ∼340 K between a high-temperature, rutile, metallic phase and a low-temperature, monoclinic, insulating phase with a resistance exhibiting a semiconductor-like temperature dependence. Atomic hydrogenation results in stabilization of the metallic phase of VO2 micro/nanobeams down to 2 K, the lowest point we could reach in our measurement setup. Optical characterization shows that hydrogen atoms prefer to diffuse along the c axis of rutile (a axis of monoclinic) VO2, along the oxygen "channels". Based on observing the movement of the hydrogen diffusion front in single crystalline VO2 beams, we estimate the diffusion constant for hydrogen along the c axis of the rutile phase to be 6.7 × 10(-10) cm(2)/s at approximately 373 K, exceeding the value in isostructural TiO2 by ∼38×. Moreover, we find that the diffusion constant along the c axis of the rutile phase exceeds that along the equivalent a axis of the monoclinic phase by at least 3 orders of magnitude. This remarkable change in kinetics must originate from the distortion of the "channels" when the unit cell doubles along this direction upon cooling into the monoclinic structure. Ab initio calculation results are in good agreement with the experimental trends in the relative kinetics of the two phases. This raises the possibility of a switchable membrane for hydrogen transport.

In situ diffraction study of catalytic hydrogenation of VO2: stable phases and origins of metallicity.

Controlling electronic population through chemical doping is one way to tip the balance between competing phases in materials with strong electronic correlations. Vanadium dioxide exhibits a first-order phase transition at around 338 K between a high-temperature, tetragonal, metallic state (T) and a low-temperature, monoclinic, insulating state (M1), driven by electron-electron and electron-lattice interactions. Intercalation of VO2 with atomic hydrogen has been demonstrated, with evidence that this doping suppresses the transition. However, the detailed effects of intercalated H on the crystal and electronic structure of the resulting hydride have not been previously reported. Here we present synchrotron and neutron diffraction studies of this material system, mapping out the structural phase diagram as a function of temperature and hydrogen content. In addition to the original T and M1 phases, we find two orthorhombic phases, O1 and O2, which are stabilized at higher hydrogen content. We present density functional calculations that confirm the metallicity of these states and discuss the physical basis by which hydrogen stabilizes conducting phases, in the context of the metal-insulator transition.

ß-YbAlB4: a critical nodal metal.

We propose a model for the intrinsic quantum criticality of ß-YbAlB(4), in which a vortex in momentum space gives rise to a new type of Fermi surface singularity. The unquenched angular momentum of the |J=7/2,m(J)=±5/2> Yb 4f states generates a momentum-space line defect in the hybridization between 4f and conduction electrons, leading to a quasi-two-dimensional Fermi surface with a k(⊥)(4) dispersion and a singular density of states proportional to E(-1/2). We discuss the implications of this line node in momentum space for our current understanding of quantum criticality and its interplay with topology.