ONE of the long-standing mysteries associated with the high-temperature copper oxide superconductors concerns the anomalous suppression1 of superconductivity in La2-xBaxCuO4 (and certain related compounds) when the hole concentration x is near . Here we examine the possibility that this effect is related to dynamical two-dimensional spin correlations, incommensurate with the crystal lattice, that have been observed in La2-xSrxCuO4 by neutron scattering2–4. A possible explanation for the incommensurability involves a coupled, dynamical modulation of spin and charge in which antiferromagnetic 'stripes' of copper spins are separated by periodically spaced domain walls to which the holes segregate5–9. An ordered stripe phase of this type has recently been observed in hole-doped La2NiO4 (refs 10–12). We present evidence from neutron diffraction that in the copper oxide material La1.6-xNd0.4SrxCuO4, with x = 0.12, a static analogue of the dynamical stripe phase is present, and is associated with an anomalous suppression of superconductivity13,14. Our results thus provide an explanation of the '
 ' conundrum, and also support the suggestion15 that spatial modulations of spin and charge density are related to superconductivity in the copper oxides.

Evidence for stripe correlations of spins and holes in copper oxide superconductors

This article discusses fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies are derived for extracting information concerning such local order from experiments, with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems---an exactly solvable one-dimensional (1D) electron gas with an impurity, and a weakly interacting 2D electron gas. Experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies are extensively reviewed. The authors adduce evidence that stripe correlations are widespread in the cuprates. They compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi-liquid state, and strong coupling, in which the magnetism is associated with well-defined localized spins, and stripes are viewed as a form of micro phase separation. The authors present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

How to detect fluctuating stripes in the high-temperature superconductors

Methods that fix atmospheric nitrogen to ammonia under mild conditions could offer a more environmentally benign alternative to the Haber–Bosch process. Now, a Ru-loaded electride, [Ca24Al28O64]4+(e−)4, is reported that acts as an efficient electron donor and reversible hydrogen store, and is demonstrated to function as an efficient catalyst for ammonia synthesis.

Ammonia synthesis using a stable electride as an electron donor and reversible hydrogen store

The character of the ground state of an antiferromagnetic insulator is fundamentally altered following addition of even a small amount of charge1. The added charge is concentrated into domain walls across which a π phase shift in the spin correlations of the host material is induced. In two dimensions, these domain walls are ‘stripes’ which can be insulating2,3 or conducting4,5,6 — that is, metallic ‘rivers’ with their own low-energy degrees of freedom. However, in arrays of one-dimensional metals, which occur in materials such as organic conductors7, interactions between stripes typically drive a transition to an insulating ordered charge-density-wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large compared tothe CDW coupling between stripes. As a consequence, there should exist electronic quantum liquid-crystal phases, which constitute new states of matter, and which can be either high-temperature superconductors or two-dimensional anisotropic ‘metallic’ non-Fermi liquids. Neutron scattering and other experiments in the copper oxide superconductor La1.6−xNd0.4SrxCuO4 already provide evidence for the existence of these phases in at least one class of materials.

Electronic liquid-crystal phases of a doped Mott insulator

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

We removed approximately 100% of clathrated oxygen ions from the crystallographic cages in a single crystal of 12CaO.7Al2O3, leading to the formation of high-density (approximately 2 x 10(21) cm-3) electrons highly localized in the cages. The resulting electron forms a structure that we interpret as an F+ center and migrates throughout the crystal by hopping to a neighboring cage with conductivity approximately 100 siemens per centimeter, demonstrating that the encaged electron behaves as an anion. The electron anions couple antiferromagnetically with each other, forming a diamagnetic pair or singlet bipolaron. The resulting [Ca24Al28O64]4+(4e-) may be regarded as a thermally and chemically stable single crystalline "electride."

https://science.sciencemag.org/content/sci/301/5633/626.full.pdf

High-density electron anions in a nanoporous single crystal: [Ca24Al28O64]4+(4e-).

Superconducting single crystals

The dimerization of the Cu ions in the spin-Peierls state of ${\mathrm{CuGeO}}_{3}$ below 14 K has been determined by neutron-diffraction measurements. In addition to superlattice reflections with indices $\frac{h}{\frac{2kl}{2}}$ ($h$, $k$, $l$, all odd) recently observed in electron and x-ray diffraction studies, we also found peaks for which $k=5$ = even. Oxygen displacements in the $a\ensuremath{-}b$ plane of about 0.01 \AA{}, accompanied by comparable shifts of the Cu ions along the chain direction $c$, can be related to the dimerized spin state in a natural fashion.

Dimerization of CuGeO3 in the spin-Peierls state

Magnetic relaxation and hysteresis studies have been performed for a c-axis-oriented single crystal of ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_{4}$. We demonstrate that the effective activation energy for flux creep, ${\mathit{U}}_{\mathrm{eff}}$, is a strongly nonlinear function of the current density J (as given by the irreversible magnetization). For fixed fields of 0.5, 1.0, 2.0, and 3.0 T and temperatures between 4 and 15 K (as consistent with full field penetration of the sample), ${\mathit{U}}_{\mathrm{eff}}$(J) is seen to vary approximately logarithmically with J. A scaling relationship, ${\mathit{U}}_{\mathrm{eff}}$(J)=[-${\mathit{U}}_{1}$g(T)/${\mathit{H}}^{\mathit{n}}$]ln(J/${\mathit{J}}_{\mathit{c}}$), is shown to be obeyed for this crystal with n\ensuremath{\simeq}0.9 (H in T), ${\mathit{U}}_{1}$\ensuremath{\simeq}180${\mathit{k}}_{\mathit{B}}$, and ${\mathit{J}}_{\mathit{c}}$(1 T)\ensuremath{\simeq}3.2\ifmmode\times\else\texttimes\fi{}${10}^{5}$ A/${\mathrm{cm}}^{2}$. Several functional forms of g(T) have been explored and shown to give reasonable fits if monotonically decreasing in temperature over the range where flux creep is observed. We also explore the ramifications of this functional dependence in explaining an observed exponential temperature dependence of the hysterically determined critical current density. Finally, we show that comparison of the temperature dependence of logarithmic relaxation rate A=dM/d ln(t) and the derivative of the magnetization with respect to ln(T) at fixed time, ${\mathit{dM}}_{0}$/d ln(T), can be used to set a scale of the attempt frequency for flux motion consistent with the other measurements.

Dependence of the flux-creep activation energy on the magnetization current for a La1.86Sr0.14CuO4 single crystal

Using neutron-scattering techniques, we have studied the temperature dependence of the magnetic excitations at varied energies in a high-quality single crystal of ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_{4}$. This crystal exhibits a sharp superconducting transition at 33 K with nearly 100% flux exclusion. For magnetic excitation energies of 9 meV and lower, the intensity drops dramatically with decreasing temperature for temperatures below \ensuremath{\sim}150 K. However, at 12 MeV the intensity is independent of temperature between 300 and 5 K.

Isao Tanaka

Papers

High-density electron anions in a nanoporous single crystal: [Ca24Al28O64]4+(4e-).

Superconducting single crystals

Dimerization of CuGeO3 in the spin-Peierls state

Dependence of the flux-creep activation energy on the magnetization current for a La1.86Sr0.14CuO4 single crystal

Temperature dependence of the magnetic excitations in La 1.85 Sr 0.15 CuO 4 (T c =33 K)