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.
Third parties have the same rights to reuse articles in NJP as described in the Creative Commons Attribution-Non-Commercial-ShareAlike 3.0 license. These open-access rights allow third-party users to copy, distribute and display the published version of articles in NJP, and create derivative works, subject to appropriate attribution and non-commercial exploitation.