1. SPIN EXCITATIONS IN La 2 CuO 4 : CONSISTENT DESCRIPTION BY INCLUSION OF RING EXCHANGE A.A.Katanin a,b and A.P.Kampf a a Institut für Physik, Universität Augsburg, Augsburg, Germany b Institute of Metal Physics, Ekaterinburg, Russia

2. Magnetic structure of La 2 CuO 4 Heisenberg model Ring-exchange term i j kl i j Appears in next-to-leading order in t/U expansion of Hubbard model First introduced in connection with 3 He (see, e.g., M.Roger et al, Rev.Mod.Phys 55 1 (1983))

3. La 2 CuO 4 Experimental spin-wave dispersion at T=10K (R.Coldea et al, Phys. Rev. Lett. 86, 5377 (2001))

4. The Heisenberg model with ring exchange Previously estimated values of parameters [1]: J=146 meV; J´=J´´=0.02J; J  <10 -3 J, J [] /J=0.41 The derivation of effective spin model from three-band Hubbard model [2] led to estimate J [] /J=0.11 [1] R.Coldea et al, Phys. Rev. Lett. 86, 5377 (2001) [2] E. Müller-Hartmann and A. Reischl, cond-mat/0105392.

5. Calculational steps The Dyson-Maleev representation for spin operators Calculation of renormalized spin-wave spectrum The factors {   } are the renormalization factors Solution of the self-consistent equations

6. La 2 CuO 4

7. The results of fitting of experimental data Parameters of the model J = 151.9 meV, J = J  = 0.025J, J [] = 0.24J Groud-state magnetization Spin stiffness and the perpendicular susceptibility  s = 23.8 meV, c = 206meV,   = 4.8·10 -5 K -1  Earlier estimate from fitting the spin-spin correlation length  (T) at T>T N is  s = 23.9 meV Renormalization factors Z c = 0.96, Z  = 0.63, Z  = 0.68 Interlayer coupling J  /J = 1.0 ·10 -3 The Neel temperature T N = 328 K  T N exp = 325 K

8. Conclusions The exchange parameters of La 2 CuO 4 are determined with account of quantum fluctuations from the best fit to magnon spectrum The values of exchange parameters are in good agreement with other experimental data on La 2 CuO 4.