Abstract
Spin-phonon coupling (SPC) has been shown to be compatible with many unusual properties of the high-${T}_{c}$ copper oxides. Parameters from ab initio band calculations for unit cells of ${\text{La}}_{2}{\text{CuO}}_{4}$ are used in a free-electron-like model in order to study the variation in coupling between spin waves and different phonons. Different SPC for different phonons can explain the ``hour-glass'' shape of the spin excitations. The model predicts larger $q$ vectors at less doping and rather complex isotope shifts. A link between the SPC parameters and the parameters for superconductivity is proposed. Also the pseudogap depends on the efficiency of SPC, and it will interfere with superconductivity at low doping. Different contributions to the coupling parameters $\ensuremath{\lambda}$ are discussed. It is argued that ${\ensuremath{\lambda}}_{\text{SPC}}$ coming from the interaction between spin waves and O phonons can be strong enough to explain high ${T}_{c}$.
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