Spin incommensurability varies linearly with hole content in single-layer Bi2201 cuprate

We have performed inelastic neutron scattering measurements on the single-layer cuprate Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+y}$ (Bi2201) with $x=0.2$, 0.3, 0.4 and 0.5, a doping range that spans the spin-glass (SG) to superconducting (SC) phase boundary [1]. The doping evolution of low energy spin fluctuations ($\la 11$~meV) was found to be characterized by a change of incommensurate modulation wave vector from the tetragonal [110] to [100]/[010] directions, while maintaining a linear relation between the incommensurability and the hole concentration, $\delta\approx p$. In the SC regime, the spectral weight is strongly suppressed below $\sim4$~meV. Similarities and differences in the spin correlations between Bi2201 and the prototypical single-layer system La$_{2-x}$Sr$_x$CuO$_4$ will be discussed.\\[4pt] [1] M. Enoki {\it et al.}, arXiv:1205.3301.