Competing orders in a magnetic field: spin and charge order in the cuprate superconductors

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large N theory provide detailed information on the phase diagram and on the spatial structure of the dynamic spin spectrum. Our results apply to phases with and without long-range spin density wave order and to the magnetic quantum critical point separating these phases. We discuss the relationship of our results to a number of recent neutron scattering measurements on the cuprate superconductors in the presence of an applied field. We compute the pinning of static charge order by the vortex cores in the `spin gap' phase where the spin order remains dynamically fluctuating, and argue that these results apply to recent scanning tunnelling microscopy (STM) measurements. We show that with a single typical set of values for the coupling constants, our model describes the field dependence of the elastic neutron scattering intensities, the absence of satellite Bragg peaks associated with the vortex lattice in existing neutron scattering observations, and the spatial extent of charge order in STM observations. We mention implications of our theory for NMR experiments. We also present a theoretical discussion of more exotic states that can be built out of the spin and charge order parameters, including spin nematics and phases with `exciton fractionalization'.Comment: 36 pages, 33 figures; for a popular introduction, see http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new work of Chen and Ting; (v3) reorganized presentation for improved clarity, and added new appendix on microscopic origin; (v4) final published version with minor change

Spin dynamics in the stripe phase of high-T c cuprates with the modulation of superconducting order

Possible superconducting order modulation and its effect on the spin susceptibility in the coexisting phase of the stripe and superconducting orders are investigated. It is shown that the superconducting order modulation is mainly caused by the spin-domain-derived scattering, while the charge-domain-derived scattering tends to suppress it in a wide parameter region. The modulation leads to a two-peak structure in the spin excitation spectrum, which is qualitatively consistent with the recent experimental observations in La2-xSrxCuO4. This result suggests the importance of the superconducting order modulation for the understanding of the multiform spin excitations in these cuprate superconductors