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 δ increases monotonically with hole concentration, as it does in La2−xSrxCuO4 (LSCO). However, δ 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 Tc=35 K), whereas it is field independent for YBa2Cu3O6.35 (Tc=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~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 ~1 μeV) for T≠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 ~100 μeV) yield a characteristic crossover temperature TSDW~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 TELC~150 K. Both TSDW and TELC 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.