Spin waves in La 2 CuO 4 : band structure and correlation effects

We calculate the antiferromagnetic spin wave dispersion in the half-filled (electronic density n = 1) Hubbard model for a two-dimensional square lattice, using the random phase approximation (RPA) in a broken symmetry (spin density wave) ground state. Our results for the spin wave dispersion, ω(q), are compared with high-resolution inelastic neutron scattering performed on La 2 CuO 4. The effects of different band structures and different values of the on-site Coulomb interaction on the spin wave spectrum is studied. Particular attention is put on the high energy dispersion values ω(π/2, π/2) and ω(0, π). Introduction: In two recent papers, [1, 2] high-resolution inelastic neutron scattering measurements have been performed on two different two-dimensional spin 1/2 quantum antifer-romagnets. These are copper deuteroformate tetradeuterate (CFTD) and La2CuO4. Surprisingly , the dispersion at the zone boundary that has been observed in the two materials, does not agree with spin-wave theory predictions [3]. Moreover the amount of dispersion is not the same for both materials. In CFTD the dispersion is about 6% from ω(π/2, π/2) to ω(π, 0), whereas in La2CuO4 it is about-13% along the same direction. In the case of CFTD the dispersion at the zone boundary can be explained using the nearest-neighbor Heisenberg model alone, [2] and high precision quantum Monte Carlo simulations have confirmed that it is so.[4] On the other hand, an explanation for the observed dispersion in La2CuO4 has been proposed [1] using an extended Heisenberg model [5, 6] involving first-, second-, and third-nearest-neighbor interactions as well as interactions among four spins. In a previous paper [7], we have shown that it possible to obtain the observed dispersion difference of-13% for La2CuO4 using the single band Hubbard model at half filling, with nearest neighbor hopping. In our formulation the extended Heisenberg model used in ref. [1] is incorporated by means of the virtual excursions of the electrons on the lattice. Fitting our results to the experimental data the obtained values of U and t agree well with those of ref. [1] and where confirmed by Quantum Monte Carlo calculations in the Hubbard model [8]. In this paper we generalize our previous study incorporating in the calculations the effect of a second nearest neighbor hopping t ′ in the electronic spectrum (in high-Tc materials the ratio |t ′ /t| ranges roughly from 0.1 to 0.5). The effect of U on the spin wave dispersion at the special points ω(π/2, …