Ab initio determination of an extended Heisenberg Hamiltonian in CuO2 layers

Accurate ab initio calculations on embedded Cu4O12 square clusters, fragmen ts of the La2CuO4 lattice, confirm a value of the nearest neighbor antiferr omagnetic coupling (J = 124 meV) previously obtained from ab initio calcula tions on bicentric clusters and in good agreement with experiment. These ca lculations predict non negligible antiferromagnetic second-neighbor interac tion (J ' = 6.5 meV) and four spin cyclic exchange (K = 14 meV), which may affect the thermodynamic and spectroscopic properties of these materials. T he dependence of the magnetic coupling on local lattice distortions has als o been investigated. Among them the best candidate to induce a spin-phonon effect seems to be the movement of the Cu atoms, changing the Cu-Cu distanc e, for which the variation of the nearest neighbor magnetic coupling with t he Cu-O distance is DeltaJ/Delta dc(u-O) similar to 1700 cm(-1) Angstrom (- 1).