General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW B 95, 075139 (2017) 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

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... Brillouin zone in La 2−x Sr x CuO 4 , spanning the doping phase diagram from the antiferromagnetic 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 antinodal 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.