Cooper-Pair Localization in the Magnetic Dynamics of a Cuprate Ladder

Doped spin ladders are expected to form unconventional electronic states driven by charge and spin pairing. To date, their study has been hampered by the difficulty in connecting theoretical models and experiment together. Here, we revisit this outstanding problem by combining inelastic neutron scattering measurements of Sr2.5Ca11.5Cu24O41 - a prototypical doped spin ladder which shows both charge density wave formation and superconductivity under pressure - with density matrix renormalization group calculations of the dynamical spin structure factor of an extended Hubbard model. Calculations on both doped and undoped Hubbard models are compared to experiment showing that the magnetic dynamics remains remarkably unchanged except for the appearance of sub-gap states in the doped charge ordered phase. Effects of charge fluctuations are observed in the spin spectrum consistent with hole-pair localization induced by a combination of disorder and a charge density wave that preempts the Luther-Emery liquid state expected for a Hubbard ladder away from half-filling.