  The magnetic correlations within the cuprates have undergone intense scrutiny
as part of efforts to understand high temperature superconductivity. We explore
the evolution of the magnetic correlations along the nodal direction of the
Brillouin zone in La2-xSrxCuO4, spanning the doping phase diagram from the
anti-ferromagnetic Mott insulator at x = 0 to the metallic phase at x = 0.26.
Magnetic excitations along this direction are found to be systematically
softened and broadened with doping, at a higher rate than the excitations along
the anti-nodal direction. This phenomenology is discussed in terms of the
nature of the magnetism in the doped cuprates. Survival of the high energy
magnetic excitations, even in the overdoped regime, indicates that these
excitations are marginal to pairing, while the influence of the low energy
excitations remains ambiguous.
