13C NMR studies of the normal and superconducting states of the organic superconductor kappa -(ET)2Cu

Reducing the effects of weak homonuclear dipolar coupling with CPMG pulse sequences for static and spinning solids

The Carr-Purcell/Meiboom-Gill (CPMG) pulse sequence, initially introduced for measuring transverse relaxation time constants (T₂), can provide significant signal enhancements for solid-state NMR (SSNMR) spectra. The proper implementation of CPMG for acquiring spectra influenced by chemical shift anisotropies (CSAs), first and/or second order quadrupolar interactions, or paramagnetic broadening has been well documented to date, as have the effects of heteronuclear dipolar coupling on CPMG echo trains and T₂ lifetimes. Homonuclear dipolar coupling can also impact T₂ lifetimes and CPMG echo trains; these effects have been thoroughly investigated for spectra of homonuclear dipolar coupled spin-1/2 nuclei typically acquired under static conditions that are predominantly influenced by dipolar broadening (e.g., ¹H, ¹⁹F, etc.). In particular, it has been shown that short refocusing pulses with small flip angles can extend the effective T₂ (T₂^eff, the observed T₂ constant as impacted by experimental conditions) measured by CPMG sequences for strong homonuclear dipolar coupled spin-1/2 pairs under static conditions. To date, these effects have not been explored for (i) spin-1/2 nuclei that have significant CSAs and simultaneously feature weak homonuclear dipolar couplings, (ii) for quadrupolar nuclei that are also weakly homonuclear dipolar coupled, and (iii) for either of these cases under magic-angle spinning (MAS) conditions. Herein, we demonstrate that short refocusing pulses that cause small flip angles can reduce the attenuation of signal in CPMG echo trains resulting from dipolar dephasing caused by the weak homonuclear dipolar couplings. For both spin-1/2 and quadrupolar nuclei, this can lead to significant extensions in T₂^eff and signal enhancements of up to three times compared to conventional CPMG in favourable cases. These phenomena can occur under both static and magic-angle spinning (MAS) conditions, in the latter of which homonuclear couplings are reintroduced by rotational resonance (R²) recoupling. Experimental examples of ¹³C (I = 1/2), ²H (I = 1), ⁸⁷Rb (I = 3/2), ²³Na (I = 3/2), and ³⁵Cl (I = 3/2) NMR under static and MAS conditions, as well as simulations of these phenomena, are shown and discussed.

Spin Vortex Crystal Order in Organic Triangular Lattice Compound

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.

Competing Nodal d-Wave Superconductivity and Antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

Quantum Disordering of an Antiferromagnetic Order by Quenched Randomness in an Organic Mott Insulator

The behavior of interacting spins subject to randomness is a longstanding issue and the emergence of exotic quantum states is among intriguing theoretical predictions. We show how a quantum-disordered phase emerges from a classical antiferromagnet by controlled randomness. ^{1}H NMR of a successively x-ray-irradiated organic Mott insulator finds that the magnetic order collapses into a spin-glass-like state, immediately after a slight amount of disorder centers are created, and evolves to a gapless quantum-disordered state without spin freezing, spin gap, or critical slowing down, as reported by T. Furukawa et al. [Phys. Rev. Lett. 115, 077001 (2015)]PRLTAO0031-900710.1103/PhysRevLett.115.077001 through sequential reductions in the spin freezing temperature and moment.

Electronic Griffiths Phase in Disordered Mott-Transition Systems

Solid-state physics and soft-matter physics have been developed independently, with little mutual exchange of the underlying physical concepts. However, after many studies of correlated electron systems, it has been recognized that correlated electrons (especially in Mott-transition systems) in solid matter sometimes show behavior similar to "structured fluids" in soft matter; that is, the electrons exhibit long-length self-organization (but without long-range order) and slow dynamics, which is inevitable for the long-length structures. The essential question is this: what condition causes such behavior in solid matter? We focused on an organic Mott-transition system and demonstrated that the electrons of this system fluctuate very slowly only when the following two factors are met simultaneously: (i) the electronic system is on the metal and Mott-insulator boundary and (ii) the system is subject to quenched disorder. This electronic state with slow dynamics under this condition can be explained by the concept of the "(electronic) Griffiths phase." This concept will potentially be a key in connecting solid-state physics with soft-matter physics.

Investigation of the superconducting gap structure in κ-(BEDT-TTF)2Cu(NCS)2 and κ-(BEDT-TTF)2Cu[N(CN)2]Br by means of thermal-conductivity measurements

We report temperature-dependent thermal-conductivity, κ, measurements on the layered quasi-two-dimensional organic superconductors κ-(BEDT-TTF)₂Cu(NCS)₂ and κ-(BEDT-TTF)₂Cu[N(CN)₂]Br down to 160 mK. The results for κ-(BEDT-TTF)₂Cu(NCS)₂ may be consistent with a nodal superconducting (SC) gap structure as indicated by a non-negligible remnant linear contribution when [Formula: see text] is extrapolated to [Formula: see text]. For κ-(BEDT-TTF)₂Cu[N(CN)₂]Br, contrary to expectations, higher κ values are observed in the superconducting regime as compared to the normal, high-field state evidencing a dominant phonon contribution to κ in the superconducting state. The strong increase of κ in the normal state below T _c for both samples indicates strong electron-phonon scattering. Our results highlight the need for thermal-conductivity measurements performed down to significantly lower temperatures to determine the symmetry of the SC gap.

Microscopic Study of the Fulde-Ferrell-Larkin-Ovchinnikov State in an All-Organic Superconductor

Quasi-two-dimensional superconductors with a sufficiently weak interlayer coupling allow magnetic flux to penetrate in the form of Josephson vortices for in-plane applied magnetic fields. A consequence is the dominance of the Zeeman interaction over orbital effects. In the clean limit, the normal state is favored over superconductivity for fields greater than the paramagnetic limiting field, unless an intermediate, inhomogeneous state is stabilized. Presented here are nuclear magnetic resonance (NMR) studies of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state for β''-(ET)2SF5CH2CF2SO3. The uniform superconductivity-FFLO transition is identified at an applied field value of 9.3(0.1) T at low temperature (T=130  mK), and evidence for a possible second transition between inhomogeneous states at ∼11  T is presented. The spin polarization distribution inferred from the NMR absorption spectrum compares favorably to a single-Q modulation of the superconducting order parameter.

Determination of the hyperfine coupling tensor in organic conductors κ-(BEDT-TTF)₂X (X=Cu[N(CN)₂]Br, Cu(NCS)₂) on central ¹³C sites

Although the organic superconductors κ-(BEDT-TTF)2X (X=Cu[N(CN)2]Br and Cu(NCS)2) have been studied by NMR spectroscopy, hyperfine coupling tensors are required to quantify NMR spectra. Angle dependences of NMR spectra were measured to determine hyperfine coupling tensors applicable to further NMR assessments of attractive physical phenomena on κ-salts. The tensors of κ-(BEDT-TTF)2X and β(')-(BEDT-TTF)2ICl2 salts were compared to determine the hyperfine coupling mechanism in organic metals, with the results indicating that off-site dimer contribution should be considered. We also report the electron correlation of these salts and further application of the tensors.

Thermodynamics of a bad metal-Mott insulator transition in the presence of frustration

Thermodynamic properties of the Hubbard model on the anisotropic triangular lattice at half filling are calculated by the finite-temperature Lanczos method. The charge susceptibility exhibits clear signatures of a Mott metal-insulator transition. The metallic phase is characterized by a small charge susceptibility, large entropy, large renormalized quasiparticle mass, and large spin susceptibility. The fluctuating local magnetic moment in the metallic phase is large and comparable to that in the insulating phase. These bad metallic characteristics occur above a relatively low coherence temperature, as seen in organic charge transfer salts.

Angle-dependent evolution of the Fulde-Ferrell-Larkin-Ovchinnikov state in an organic superconductor

We report magnetic-field and angular-dependent high-resolution specific-heat measurements of the organic superconductor β''-(BEDT-TTF)2SF5CH2CF2SO3. When the magnetic field is aligned precisely within the conducting BEDT-TTF layer, at low temperatures a clear upturn of the upper critical field beyond the Pauli limit of 9.73 T is observed, hinting at the emergence of a Fulde-Ferrell-Larkin-Ovchinnikov state. This upturn disappears when the field is oriented out of plane by more than ∼0.5  deg. For smaller out-of-plane angles, the specific-heat anomaly at T(c) sharpens and a second peaky phase transition appears within the superconducting state.

Zeeman-driven phase transition within the superconducting state of κ-(BEDT-TTF)2Cu(NCS)2

(13)C nuclear magnetic resonance measurements were performed on κ-(BEDT-TTF)(2)Cu(NCS)(2), with the external field placed parallel to the quasi-2D conducting layers. The absorption spectrum is used to determine the electronic spin polarization M(s) as a function of external field H at a temperature T=0.35 K. A discontinuity in the derivative dM(s)/dH at an applied field of H(s)=213±3 kOe is taken as evidence for a Zeeman-driven transition within the superconducting state and stabilization of inhomogeneous superconductivity.

On the practical aspects of recording wideline QCPMG NMR spectra

The practical aspects of applying CPMG for acquisition of wideline powder patterns are examined. It is shown that most distortions/modulations of spikelet spectra can be traced to the incoherent signal averaging from multiple coherence transfer pathways. A strategy for minimizing these distortions/modulations is described. Also, a few interesting observations regarding the implementation of the wideline WURST-QCPMG experiment are presented, namely the accumulation of second-order signal phase and the effects of varying the sweep rate and rf field of chirp pulses.

Scanning tunnelling spectroscopy study of paramagnetic superconducting β''-ET(4)[(H(3)O)Fe(C(2)O(4))(3)]·C(6)H(5)Br crystals

Scanning tunnelling spectroscopy (STS) and microscopy (STM) were performed on the paramagnetic molecular superconductor β''-ET(4)[(H(3)O)Fe(C(2)O(4))(3)]·C(6)H(5)Br. Under ambient pressure, this compound is located near the boundary separating superconducting and insulating phases of the phase diagram. In spite of a strongly reduced critical temperature T(c) (T(c) = 4.0 K at the onset, zero resistance at T(c) = 0.5 K), the low temperature STS spectra taken in the superconducting regions show strong similarities with the higher T(c) ET κ-derivatives series. We exploited different models for the density of states (DOS), with conventional and unconventional order parameters to take into account the role played by possible magnetic and non-magnetic disorder in the superconducting order parameter. The values of the superconducting order parameter obtained by the fitting procedure are close to the ones obtained on more metallic and higher T(c) organic crystals and far above the BCS values, suggesting an intrinsic role of disorder in the superconductivity of organic superconductors and a further confirmation of the non-conventional superconductivity in such compounds.

Antiferromagnetic fluctuations in the organic superconductor kappa-(BEDT-TTF)2Cu(NCS)_{2} under pressure

We measured the 13C-NMR spectrum and T1 of the quasi-two-dimensional organic superconductor kappa-(BEDT-TTF)2Cu(NCS)_{2} under pressure. This material was thought to show a relationship between T_{c} and the effective cyclotron mass m_{c};{*}, obtained from the Shubnikov-de Haas (SdH) effect. We found that kappa-(BEDT-TTF)2Cu(NCS)_{2} behaved as a Fermi liquid at low temperature under all pressures, and antiferromagnetic fluctuations were expected. The pressure dependence of the Korringa factor is similar to that of the effective cyclotron mass m_{c};{*}, suggesting that antiferromagnetic fluctuations contribute to the superconductivity of this material. We also found that, under pressure, T;{*} was shifted to 150 K, the temperature characteristic of the shift from bad metal to good metal.

Vertex corrections and the Korringa ratio in strongly correlated electron materials

We show that the Korringa ratio, associated with nuclear magnetic resonance in metals, is unity if vertex corrections to the dynamic spin susceptibility are negligible, the hyperfine coupling is momentum independent, and there exists an energy scale below which the density of states is constant. In the absence of vertex corrections we also find a Korringa behaviour for T(1), the nuclear spin relaxation rate, i.e., [Formula: see text], and a temperature independent Knight shift. These results are independent of the form and magnitude of the self-energy (so far as is consistent with neglecting vertex corrections) and of the dimensionality of the system.

Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors

We study the Mott transition, antiferromagnetism, and superconductivity in layered organic conductors using the cellular dynamical mean-field theory for the frustrated Hubbard model. A d-wave superconducting phase appears between an antiferromagnetic insulator and a metal for t'/t=0.3-0.7 or between a nonmagnetic Mott insulator (spin liquid) and a metal for t'/t>or=0.8, in agreement with experiments on layered organic conductors including kappa-(ET)2Cu2(CN)3. These phases are separated by a strong first-order transition. The phase diagram gives much insight into the mechanism for -wave superconductivity. Two predictions are made.

Unconventional critical behaviour in a quasi-two-dimensional organic conductor

Changing the interactions between particles in an ensemble--by varying the temperature or pressure, for example--can lead to phase transitions whose critical behaviour depends on the collective nature of the many-body system. Despite the diversity of ingredients, which include atoms, molecules, electrons and their spins, the collective behaviour can be grouped into several families (called 'universality classes') represented by canonical spin models. One kind of transition, the Mott transition, occurs when the repulsive Coulomb interaction between electrons is increased, causing wave-like electrons to behave as particles. In two dimensions, the attractive behaviour responsible for the superconductivity in high-transition temperature copper oxide and organic compounds appears near the Mott transition, but the universality class to which two-dimensional, repulsive electronic systems belongs remains unknown. Here we present an observation of the critical phenomena at the pressure-induced Mott transition in a quasi-two-dimensional organic conductor using conductance measurements as a probe. We find that the Mott transition in two dimensions is not consistent with known universality classes, as the observed collective behaviour has previously not been seen. This peculiarity must be involved in any emergent behaviour near the Mott transition in two dimensions.

Pairing and superconductivity driven by strong quasiparticle renormalization in two-dimensional organic charge transfer salts

We introduce and analyze a variational wave function for quasi-two-dimensional kappa-(ET)(2) organic salts containing strong local and nonlocal correlation effects. We find an unconventional superconducting ground state for intermediate charge carrier interaction, sandwiched between a conventional metal at weak coupling and a spin liquid at larger coupling. Most remarkably, the excitation spectrum is dramatically renormalized and is found to be the driving force for the formation of the unusual superconducting state.

Gossamer superconductivity near antiferromagnetic Mott insulator in layered organic conductors

Layered organic superconductors are on the verge of the Mott insulator. We use the Gutzwiller variational method to study a two-dimensional Hubbard model including a spin exchange coupling term as a minimal model for the compounds. The ground state is found to be a Gossamer superconductor at small on-site Coulomb repulsion U and an antiferromagnetic Mott insulator at large U, separated by a first order phase transition. Our theory is qualitatively consistent with major experiments reported in organic superconductors.

Precise determination of the orientation of the Dzialoshinskii-Moriya vector in kappa-(BEDT-TTF)2Cu[N(CN)(2)]Cl

A novel electron spin-reorientation transition is discovered by 13C NMR in the quasi-two-dimensional organic antiferromagnet kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. The spin reorientation occurs as an external field is swept through the orientation of the characteristic vector of the Dzialoshinskii-Moriya (DM) interaction, thus providing a precise determination of the orientation of the DM vector. Such a spin reorientation could help to characterize the DM interaction in other antiferromagnetic systems.

Test for pairing symmetry based on spin fluctuations in the organic superconductor kappa-(BEDT-TTF)2X

We propose that the superconducting pairing symmetry of organic superconductors kappa-(BEDT-TTF)2X can be determined by measuring the position in momentum space of the incommensurate peaks of the spin susceptibility. Using the weak coupling BCS theory and including the many-body effects via the random-phase approximation for the Hubbard model on an anisotropic triangular lattice, we show that the position of these peaks is uniquely determined by the pairing symmetry of the superconducting state and the geometry of the Fermi surface. We demonstrate the different incommensurate patterns of spin responses for d(x(2)-y(2-)) and d(xy)-like pairing states. In addition, we find that there is no spin resonance mode in the reasonable range of parameters discussed.

Proximity of pseudogapped superconductor and commensurate antiferromagnet in a quasi-two-dimensional organic system

We performed the single-crystal 13C NMR studies on a quasi-two-dimensional system, deuterated kappa-(BEDT-TTF)2Cu[N(CN)(2)]Br, which is just on the border of the Mott transition. The NMR spectra are separated into two parts coming from the metallic (superconducting) and insulating phases due to the phase separation at low temperature. The examination of the separated spectra revealed that the Mott transition in this system is characterized by the first-order transition between the pseudogapped superconductor and the simplest commensurate antiferromagnet with a moment of 0.26 mu(B)/dimer.

Small-q phonon-mediated superconductivity in organic kappa-BEDT-TTF compounds

We propose a new picture for superconductivity in kappa-(BEDT-TTF)2X salts arguing that small- q electron-phonon scattering dominates the pairing. We reproduce the distinct X-shaped d-wave gap reported recently by magneto-optic measurements and we argue that the softness of the momentum structure of the gap and the near degeneracy of s- and d-wave gap states may be at the origin of the experimental controversy about the gap symmetry. We show that a magnetic field applied parallel to the planes may induce extended gapless regions on the Fermi surface accounting for the experimental signatures of a Fulde-Ferrel-Larkin-Ovchinikov state and it may induce gap symmetry transitions as well.

Superconducting gap structure of kappa-(BEDT-TTF)2Cu(NCS)2 probed by thermal conductivity tensor

The thermal conductivity of organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2 (Tc = 10.4 K) has been studied in a magnetic field rotating within the 2D superconducting planes with high alignment precision. At low temperatures ( T < or = 0.5 K), a clear fourfold symmetry in the angular variation, which is characteristic of a d-wave superconducting gap with nodes along the directions rotated 45 degrees relative to the b and c axes of the crystal, was resolved. The determined nodal structure is inconsistent with recent theoretical predictions of superconductivity induced by the antiferromagnetic spin fluctuation.

Triplet superconductivity in an organic superconductor probed by NMR Knight shift

The nature of the superconducting state in quasi-one-dimensional organic conductors has remained controversial since its discovery. Here we present results of (77)Se NMR Knight shift (K(s)) experiments in (TMTSF)(2)PF(6) under 7 kbar of pressure with a magnetic field aligned along the most conducting a axis. We find no noticeable shift in K(s) upon cooling through the superconducting transition. Since K(s) directly probes the spin susceptibility chi(s), the fact that chi(s) remains unchanged through the superconducting transition strongly suggests spin-triplet superconductivity.

Superconductivity mediated by charge fluctuations in layered molecular crystals

We consider the competition between superconducting, charge ordered, and metallic phases in layered molecular crystals with the theta and beta(") structures. Applying slave-boson theory to the relevant extended Hubbard model, we show that the superconductivity is mediated by charge fluctuations and the Cooper pairs have d(xy) symmetry. This is in contrast to the kappa-(BEDT-TTF)(2)X family, for which theoretical calculations give superconductivity mediated by spin fluctuations and with d(x(2)-y(2)) symmetry. We predict several materials that should become superconducting under pressure.

Relaxation of polarized nuclei in superconducting rhodium

Nuclear spin lattice relaxation rates were measured in normal and superconducting (sc) rhodium with nuclear polarizations up to p = 0. 55. This was sufficient to influence the sc state of Rh, whose T(c) and B(c) are exceptionally low. Because B(c)<<B(loc) and the short-range spin-spin interaction is unchanged, the nuclear spin entropy was fully sustained across the sc transition. The relaxation in the sc state was slower at all temperatures without the coherence enhancement close to T(c). Nonzero nuclear polarization strongly reduced the difference between the relaxation rates in the sc and normal states.

kappa-(BEDT-TTF)2Cu[N(CN)(2)]Br: a fully gapped strong-coupling superconductor

High-resolution specific-heat measurements of the organic superconductor kappa-(BEDT-TTF)(2)-Cu[N(CN)(2)]Br in the superconducting ( B = 0) and normal ( B = 14 T) states show a clearly resolvable anomaly at T(c) = 11.5 K and an electronic contribution, C(es), which can be reasonably well described by strong-coupling BCS theory. Most importantly, C(es) vanishes exponentially in the superconducting state which gives evidence for a fully gapped order parameter.