Chasing the spin gap through the phase diagram of a frustrated Mott insulator.

The quest for entangled spin excitations has stimulated intense research on frustrated magnetic systems. For almost two decades, the triangular-lattice Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 has been one of the hottest candidates for a gapless quantum spin liquid with itinerant spinons. Very recently, however, this scenario was overturned as electron-spin-resonance (ESR) studies unveiled a spin gap, calling for reevaluation of the magnetic ground state. Here we achieve a precise mapping of this spin-gapped phase through the Mott transition by ultrahigh-resolution strain tuning. Our transport experiments reveal a reentrance of charge localization below T⋆ = 6 K associated with a gap size of 30-50 K. The negative slope of the insulator-metal boundary, dT⋆/dp < 0, evidences the low-entropy nature of the spin-singlet ground state. By tuning the enigmatic '6K anomaly' through the phase diagram of κ-(BEDT-TTF)2Cu2(CN)3, we identify it as the transition to a valence-bond-solid phase, in agreement with previous thermal expansion and magnetic resonance studies. This spin-gapped insulating state persists at T → 0 until unconventional superconductivity and metallic transport proliferate.

Controlled Frustration Release on the Kagome Lattice by Uniaxial-Strain Tuning.

It is predicted that strongly interacting spins on a frustrated lattice may lead to a quantum disordered ground state or even form a quantum spin liquid with exotic low-energy excitations. However, a controlled tuning of the frustration strength, separating its effects from those of disorder and other factors, is pending. Here, we perform comprehensive ^{1}H NMR measurements on Y_{3}Cu_{9}(OH)_{19}Cl_{8} single crystals revealing an unusual Q[over →]=(1/3×1/3) antiferromagnetic state below T_{N}=2.2 K. By applying in situ uniaxial stress, we break the symmetry of this disorder-free, frustrated kagome system in a controlled manner yielding a linear increase of T_{N} with strain, in line with theoretical predictions for a distorted kagome lattice. In-plane strain of ≈1% triggers a sizable enhancement ΔT_{N}/T_{N}≈10% due to a release of frustration, demonstrating its pivotal role for magnetic order.

Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance.

Phases of matter are usually identified through spontaneous symmetry breaking, especially regarding unconventional superconductivity and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analogue to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected 'split' transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temperature were observed3,4. Here we use nuclear magnetic resonance (NMR) spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of superconductivity in Sr2RuO4 and its evolution under strain. A reduction of the Knight shift is observed for all strain values and at temperatures below the critical temperature, consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theoretical interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its superconductivity emerges from a strongly correlated Fermi liquid, and our work imposes tight constraints on the order parameter symmetry of this archetypal system.

Internal strain tunes electronic correlations on the nanoscale.

In conventional metals, charge carriers basically move freely. In correlated electron materials, however, the electrons may become localized because of strong Coulomb interactions, resulting in an insulating state. Despite considerable progress in the last decades, elucidating the driving mechanisms that suppress metallic charge transport, the spatial evolution of this phase transition remains poorly understood on a microscopic scale. Here, we use cryogenic scanning near-field optical microscopy to study the metal-to-insulator transition in an electronically driven charge-ordered system with a 20-nm spatial resolution. In contrast to common mean-field considerations, we observe pronounced phase segregation with a sharp boundary between metallic and insulating regions evidencing its first-order nature. Considerable strain in the crystal spatially modulates the effective electronic correlations within a few micrometers, leading to an extended "zebra" pattern of metallic and insulating stripes. We can directly monitor the spatial strain distribution via a gradual enhancement of the optical conductivity as the energy gap is depressed. Our observations shed new light on previous analyses of correlation-driven metal-insulator transitions.

Low-Energy Excitations in Quantum Spin Liquids Identified by Optical Spectroscopy.

The electrodynamic response of organic spin liquids with highly frustrated triangular lattices has been measured in a wide energy range. While the overall optical spectra of these Mott insulators are governed by transitions between the Hubbard bands, distinct in-gap excitations can be identified at low temperatures and frequencies, which we attribute to the quantum-spin-liquid state. For the strongly correlated ß^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, we discover enhanced conductivity below 175 cm^{-1}, comparable to the energy of the magnetic coupling J≈250 K. For ω→0, these low-frequency excitations vanish faster than the charge-carrier response subject to Mott-Hubbard correlations, resulting in a dome-shaped band peaked at 100 cm^{-1}. Possible relations to spinons, magnons, and disorder are discussed.

Quantum spin liquids unveil the genuine Mott state.

The localization of charge carriers by electronic repulsion was suggested by Mott in the 1930s to explain the insulating state observed in supposedly metallic NiO. The Mott metal-insulator transition has been subject of intense investigations ever since1-3-not least for its relation to high-temperature superconductivity4. A detailed comparison to real materials, however, is lacking because the pristine Mott state is commonly obscured by antiferromagnetism and a complicated band structure. Here we study organic quantum spin liquids, prototype realizations of the single-band Hubbard model in the absence of magnetic order. Mapping the Hubbard bands by optical spectroscopy provides an absolute measure of the interaction strength and bandwidth-the crucial parameters that enter calculations. In this way, we advance beyond conventional temperature-pressure plots and quantitatively compose a generic phase diagram for all genuine Mott insulators based on the absolute strength of the electronic correlations. We also identify metallic quantum fluctuations as a precursor of the Mott insulator-metal transition, previously predicted but never observed. Our results suggest that all relevant phenomena in the phase diagram scale with the Coulomb repulsion U, which provides a direct link to unconventional superconductivity in cuprates and other strongly correlated materials.