Spin-phonon coupling in the single-layer extended t-J model

We consider the implications of spin-phonon coupling within the slave-boson, mean-field treatment of the extended t-J model of a high-temperature superconductor. In materials such as YBaCuO, where the ${\mathrm{CuO}}_2$ plane is buckled, this interaction is linear in O displacement along the c axis, and the coupling constant is found to be large. We calculate the spin effects on phonon dynamics, finding at and below the spin singlet formation temperature changes in frequency shift and linewidth broadening for certain, key phonon modes which correspond well with experiment near the optimal doping level. Furthermore, the theory predicts that phonon anomalies in underdoped compounds should show evidence of spin-gap phenomena with the same characteristic temperature as that found in NMR studies; this is exactly as observed in YBaCuO systems, suggesting a possible unified understanding of the anomalies in magnetic and lattice properties. Finally, such a coupling affords the possibility of a small isotope effect, and our estimate is in good agreement with recent site-selective O-substitution experiments. © 1996 The American Physical Society.