A detailed analysis of the thermal expansion mechanism of graphite oxide to produce functionalized graphene sheets is provided. Exfoliation takes place when the decomposition rate of the epoxy and hydroxyl sites of graphite oxide exceeds the diffusion rate of the evolved gases, thus yielding pressures that exceed the van der Waals forces holding the graphene sheets together. A comparison of the Arrhenius dependence of the reaction rate against the calculated diffusion coefficient based on Knudsen diffusion suggests a critical temperature of 550 °C which must be exceeded for exfoliation to occur. As a result of their wrinkled nature, the functionalized and defective graphene sheets do not collapse back to graphite oxide but are highly agglomerated. After dispersion by ultrasonication in appropriate solvents, statistical analysis by atomic force microscopy shows that 80% of the observed flakes are single sheets.

We report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the YBa2Cu3O6+x high temperature superconductor: YBa2Cu3O6.5 (Tc = 52 K), YBa2Cu3O6.7 (Tc = 67 K), and YBa2Cu3O6.85 (Tc = 87 K). The spin susceptibility is determined in absolute units at excitation energies between 1 and 140 meV and temperatures between 1.5 and 300 K. Polarization analysis is used extensively at low energies. Transitional matrix elements, including those between spin states, in a bilayer system such as YBa2Cu3O6+x can be generally classified into even and odd, according to the sign change under a symmetry operation that exchanges the layers, and both even and odd excitations are detected in YBa2Cu3O6.5 and YBa2Cu3O6.7. While the even spin excitations show a true gap which depends on doping, the odd spectrum is characterized by a weakly dopingdependent pseudogap. Both even and odd components are substantially enhanced upon lowering the temperature from 300 K. The even excitations evolve smoothly through the superconducting transition temperature Tc, but the odd excitations develop a true gap below Tc. At the same time, the odd spin susceptibility is sharply enhanced below Tc around an energy that increases with doping. This anomaly in the magnetic spectrum is closely related to the magnetic resonance peak that appears at 40 meV in the superconducting state of the optimally doped compound (Tc = 93 K). From these data we extract the energy and the energy-integrated spectral weight of the resonance peak in absolute units as a function of doping level. Theoretical implications of these measurements are discussed, and a critique of recent attempts to relate the spin excitations to the thermodynamics of high temperature superconductors is given.

We report an extensive study of magnetic excitations in fully oxygenated YBa 2 Cu 3 O 7 , using neutron scattering with and without spin polarization analysis. By calibrating the measured magnetic intensity against calculated structure factors of optical phonons and against antiferromagnetic spin waves measured in the same crystal after deoxygenation to YBa 2 Cu 3 O 6.2 , we establish an absolute intensity scale for the dynamical spin susceptibility, Љ͑q,͒. The integrated spectral weight of the sharp magnetic resonance at បϭ40 meV and q ʈ ϭ(/a,/a) in the superconducting state is ͐d(ប) res Љ (q,)ϭ(0.52Ϯ0.1) at low temperatures. The energy and spectral weight of the resonance are measured up to Tϭ0.8T c . The resonance disappears in the normal state, and a conservative upper limit of 30 states/eV is established for the normal state dynamical susceptibility at q ʈ ϭ(/a,/a) and 10 meVрបр40 meV. Our results are compared to previous neutronscattering data on YBa 2 Cu 3 O 7 , theoretical interpretations of NMR data and current models of the 40 meV resonance.

Polarized and unpolarized neutron scattering has been used to determine the effect of superconductivity on the magnetic excitation spectra of YBa 2 Cu 3 O 6.5 (T c = 52K) and YBa 2 Cu 3 O 6.7 (T c = 67K). Pronounced enhancements of the spectral weight centered around 25 meV and 33 meV, respectively, are observed below T c in both crystals, compensated predominantly by a loss of spectral weight at higher energies. The data provide important clues to the origin of the 40 meV magnetic resonance peak in YBa 2 Cu 3 O 7 .