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 YBa₂Cu₃O 6+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 La 2-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 ∼1μeV) 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 YBa ₂Cu₃O6.45 with a conventional triple-axis spectrometer (with energy resolution ∼ 100μeV) yield a characteristic crossover temperature TSDW ∼ 30K for the onset of quasistatic magnetic order. Upon further heating, the wavevector characterizing low-energy spin excitations progressively approaches the commensurate antiferromagnetic wavevector, and the incommensurability vanishes in an orderparameter- 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.