Derivation of effective spin models from a three band model for CuO2-planes
Institute of Theoretical Physics, University of Cologne, Zülpicher Str 77, 50937 Cologne, Germany
Corresponding author: a email@example.com
Revised: 28 May 2002
Published online: 19 July 2002
The derivation of effective spin models describing the low energy magnetic properties of undoped CuO2-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La2CuO4. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping tpd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Padé approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Padé approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor model is emphasized.
PACS: 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 75.30.Et – Exchange and superexchange interactions / 75.10.Jm – Quantized spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002