C. J. Peters

We report elastic, quasielastic (F dE), and inelastic neutron-scattering studies of the instantaneous and dynamic spin fluctuations in as-grown and doped ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. Four samples have been studied: (A) as-grown ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ with ${T}_{N}$=195 K, (B) oxygenated ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ with ${\mathit{T}}_{\mathit{N}}$\ensuremath{\simeq}100 K, (C) ${\mathrm{La}}_{2}$${\mathrm{Cu}}_{0.95}$${\mathrm{Li}}_{0.05}$${\mathrm{O}}_{4}$, and (D) ${\mathrm{La}}_{1.97}$${\mathrm{Sr}}_{0.03}$${\mathrm{Cu}}_{0.95}$${\mathrm{Li}}_{0.05}$${\mathrm{O}}_{4}$. All crystals exhibit variable-range-hopping conductivity behavior. At room temperature each sample exhibits two-dimensional (2D) antiferromagnetic instantaneous correlations in the ${\mathrm{CuO}}_{2}$ sheets with correlation length varying from \ensuremath{\sim}200 A\r{} in crystal A to \ensuremath{\sim}14 A\r{} in crystal D. The integrated intensity and therefore the effective moment is, however, constant to within the experimental error. In samples A and B the 2D correlation length becomes sufficiently large with decreasing temperature that the interplanar coupling is able to drive a transition to 3D long-range order. The spin dynamics have been studied in detail in crystals A and B and quite unusual behavior is observed. In contrast to previously studied planar antiferromagnets, there is no significant E\ensuremath{\simeq}0 component for temperatures \ensuremath{\ge}${T}_{N}$ and instead the 2D response function is highly inelastic. The effective dispersion of the spin excitations is \ensuremath{\ge}0.4 eV A\r{}. This large energy scale for the spin fluctuations gives credence to models of the superconductivity in doped ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ in which the pairing is magnetic in origin.

Using a flux technique we have grown sizable single crystals of ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Sr}}_{\mathrm{x}}$${\mathrm{CuO}}_{4}$. With x rays and neutrons we have studied both the static and dynamic aspects of the tetragonal to orthorhombic structural phase transition; classic soft-phonon behavior is observed at the ((1/2, 1) / 2 , 0) zone boundary involving rotations of ${\mathrm{CuO}}_{6}$ octahedra. The pure and lightly-doped single crystals show hopping conductivity, ln\ensuremath{\rho}\ensuremath{\sim}(${T}_{0}$/T${)}^{1/4}$, indicating that the electronic states at the Fermi energy are localized.

The dispersion of the low-lying phonon branches of several doped and undoped single crystals of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ has been investigated by using inelastic-neutron-scattering techniques. The zone-center modes are in reasonable agreement with Raman measurements. The reported peaks in the phonon density of states show up at energies that correspond to extrema in the dispersion curves of the transverse and longitudinal acoustic branches near the zone boundary. The tetragonal-to-orthorhombic phase transition is caused by a softening of a transverse-optic-phonon mode at the $X$ point. The rotational nature of the soft mode leads to moderate electron-phonon coupling and the mode is unlikely to enhance significantly conventional phonon mediated superconductivity. We did not observe any evidence for the predicted breathing-mode instability near the zone boundary.

The resistivity of nonmetallic ${\mathrm{La}}_{2\ensuremath{-}y}{\mathrm{Sr}}_{y}{\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x}{\mathrm{O}}_{4\ensuremath{-}\ensuremath{\delta}}$ single crystals and ceramics accurately follows the functional form $\mathrm{exp}({(\frac{{T}_{0}}{T})}^{\frac{1}{4}})$, characteristic of variable-range hopping. For each of the crystals grown from Li-containing flux and CuO flux, pure reduced ceramics, and ceramics containing 0.025 to 0.2 mole% Li, the values of ${T}_{0}$ are in the range 0.3-7 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ K. The hopping conductivity shows that the crystals, which also manifest the two-dimensional quantum spin fluid state, antiferromagnetism, and the tetragonal-to-orthorhombic transition, are nonmetallic because the electronic states at the Fermi energy are localized. No evidence of a large gap is observed, and all samples, including the reduced ceramic, are $p$ type, leading to the suggestion that in the nonmetallic state as well as the superconductor, the Fermi energy lies near the top of the band of singly occupied states (lower Hubbard band). The suppression of superconductivity by Li impurities is discussed.

We have studied the spin-wave excitations near the two-dimensional zone center at 80 K in a single crystal of ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$ which orders at ${T}_{N}=195$ K. In-plane and out-of-plane modes are observed at energies of 1.0\ifmmode\pm\else\textpm\fi{}0.25 meV and 2.5\ifmmode\pm\else\textpm\fi{}0.5 meV, respectively, The in-plane mode energy is determined primarily by the antisymmetric exchange and it measures this term directly. The out-of-plane mode energy corresponds to a planar anisotropy energy of \ensuremath{\sim}0.016 meV. We observe, in addition, the appearance of significant $E\ensuremath{\simeq}0$ scattering below 30 K.