Spin-stripe density varies linearly with the hole content in single-layer Bi_2+xSr_2-xCuO_6+y cuprate superconductors

We have performed inelastic neutron scattering measurements on the single-layer cuprate Bi_2+xSr_2-xCuO_6+y (Bi2201) with x=0.2, 0.3, 0.4, and 0.5, a doping range that spans the spin-glass to superconducting phase boundary. The doping evolution of low energy spin fluctuations (11 meV) was found to be characterized by a change in the incommensurate modulation wave vector from the tetragonal [110] to [100]/[010] directions, while maintaining a linear relation between the incommensurability and the hole concentration, δ≈p. In the superconducting regime, the spectral weight is strongly suppressed below ∼4 meV. Similarities and differences in the spin correlations between Bi2201 and the prototypical single-layer system La_2-xSr_xCuO₄ are discussed.