Neutron scattering study of the magnetic phase diagram of underdoped YBa2Cu3O6+x

We present a neutron triple-axis and resonant spin-echo spectroscopy study of the spin correlations in untwinned YBa2Cu3O6+x single crystals with x = 0.3, 0.35 and 0.45 as a function of temperature and magnetic field. As the temperature T -> 0, all samples exhibit static incommensurate magnetic order with propagation vector along the a-direction in the CuO2 planes. The incommensurability delta increases monotonically with hole concentration, as it does in La2-xSrxCuO4 (LSCO). However, delta is generally smaller than in LSCO at the same doping level, and there is no sign of a reorientation of the magnetic propagation vector at the lowest doping levels. The intensity of the incommensurate Bragg reflections increases linearly with magnetic field for YBa2Cu3O6.45 (superconducting T-c = 35 K), whereas it is field independent for YBa2Cu3O6.35 (T-c = 10 K). These results fit well into a picture in which superconducting and spin-density wave order parameters coexist, and their ratio is controlled by the magnetic field. They also suggest that YBa2Cu3O6+x samples with x similar to 0.5 exhibit incommensurate magnetic order in the high fields used for the recent quantum oscillation experiments on this system, which likely induces a reconstruction of the Fermi surface. We present neutron resonant spin-echo measurements (with energy resolution similar to 1 mu eV) for T not equal 0 that demonstrate a continuous thermal broadening of the incommensurate magnetic Bragg reflections into a quasi-elastic peak centered at excitation energy E = 0, consistent with the zero-temperature transition expected for a two-dimensional spin system with full spin-rotation symmetry. Measurements on YBa2Cu3O6.45 with a conventional triple-axis spectrometer (with energy resolution similar to 100 mu eV) yield a characteristic crossover temperature T-SDW similar to 30 K for the onset of quasi-static magnetic order. Upon further heating, the wavevector characterizing low-energy spin excitations progressively approaches the commensurate antiferromagnetic wavevector, and the incommensurability vanishes in an order-parameter-like fashion at an 'electronic liquid crystal' onset temperature T-ELC similar to 150 K. Both T-SDW and T-ELC increase continuously as the Mott-insulating phase is approached with decreasing doping level. These findings are discussed in the context of current models of the interplay between magnetism and superconductivity in the cuprates.