Neutron scattering studies of two-dimensional antiferromagnetic spin fluctuations in insulating and superconducting S = ½ systems

In this thesis, neutron scattering techniques are used to study the magnetic excitations in two materials which derive from two-dimensional square lattices of S = 1/2 spins. Within these planes, nearest neighbor spins are known to interact predominantly via antiferromagnetic Heisenberg exchange interactions. By contrast, interactions between spins in neighboring planes are negligible small for most purposes. In particular, the magnetic fluctuation spectra of these systems are twodimensional, and this makes them well suited for time-of-flight neutron scattering experiments designed to shed light on important outstanding questions concerning − at the most fundamental level − the nature of the respective ground states.

• Cu(DCOO)₂·4D₂O is a two-dimensional S = 1/2 Heisenberg antiferromagnet on a square lattice. Theoretically, the ground state has long range order at T = 0 K, but quantum fluctuations are strong and lead to a large reduction in the ordered sublattice moment relative to classical expectations. This thesis reports on experiments designed to clarify the fate of the disordered part of the moment. Combining time-of-flight and polarized triple axis neutron scattering it is shown that despite the strongly quantum fluctuating nature of the system, the low-energy excitations are excellently described by linear spin wave theory. In particular, a continuum of longitudinally polarized multimagnon excitations existing above a dispersion cone of transversely polarized single-magnon excitations is identified. Such a multimagnon continuum has never before been observed in the square lattice S = 1/2 Heisenberg model. Its experimental verification proves that a substantial fraction of the disordered moment is associated with excitations involving more than one magnon. At higher energies, the intensities of the single-magnon excitations have been discovered to be characterized by a non-uniform renormalization away from the simplest model predictions. The momentum dependence of this intensity renormalization tracks that of a non-uniform renormalization of the single-magnon energies. Using polarization analysis, it is shown that the high-energy spin fluctuation spectrum consists of renormalized, transversely polarized single-magnon excitations and weak but finite continua of longitudinally and transversely polarized multimagnon excitations. The intensities and characteristic energy scales of all components of the high-energy excitation spectrum agree with state-of-the-art Quantum Monte Carlo computations to very high degree of accuracy.

• The La_2−xSr_xCuO₄ crystals studied in the second part of this thesis are members of the class of materials known as high-temperature superconductors. In these systems, superconductivity is achieved by doping holes into the two-dimensional, square lattice S = 1/2 Heisenberg antiferromagnet La₂CuO₄. In the process, static antiferromagnetism is destroyed but strong, two-dimensional antiferromagnetic fluctuations persist into the superconducting phase. The cause of superconductivity is unknown, but it is a commonly held belief that the antiferromagnetic fluctuations play an important role. The central contribution made by this thesis is the identification of a dispersion in the excitation spectrum of the dominant incommensurate magnetic fluctuations. This discovery points to the existence of a common spin fluctuation spectrum in all superconducting cuprates. It is further shown that the existence of dispersing excitations does not require phase coherent superconductivity and that the dispersion persist to 100 K in underdoped La_2−xSr_xCuO₄. Studies of the temperature dependence of the intensities associated with the dispersive magnetic fluctuations in optimally doped La_2−xSr_xCuO₄ have in addition revealed a spectral weight shift which displays qualitative and quantitative similarities to the widely studied resonance mode in other families of high-temperature superconductors, with the important difference that it occurs at incommensurate rather than commensurate wavevectors. These discoveries put strong constraints on theories for the magnetic excitations in high-temperature superconductors.