Abstract
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 CuO2 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.
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