Spin waves in La₂CuO₄: band structure and correlation effects

Abstract

We calculate the antiferromagnetic spin wave dispersion in the half-filled (electronic density n ¼ 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, wðqÞ, 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 are studied. Particular attention is put on the high energy dispersion values wðp=2; p=2Þ and wð0; pÞ.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 antiferromagnets. These are copper deuteroformate tetradeuterate (CFTD) and La 2 CuO 4 . 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 wðp=2; p=2Þ to wðp; 0Þ, whereas in La 2 CuO 4 it is about À13% 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 La 2 CuO 4 has been proposed [1] using an extended Heisenberg model [5,6] involving first-, second-, and thirdnearest-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 À13% for La 2 CuO 4 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 0 in the electronic spectrum (in high-T c materials the ratio jt 0 =tj ranges roughly from 0.1 to 0.5). The effect of U on the spin wave dispersion at the special points wðp=2; p=2Þ and wð0; pÞ is also studied.

Evolution of Midgap States and Residual Three Dimensionality inLa2−xSrxCuO4

“…3. Our parameter values are consistent with earlier data from insulating cuprates based on ARPES [23] and spin wave spectra [24]. (ii) TB calculations (white lines) with the same parameters as those used in the preceding case, except that the Hubbard parameter U is replaced by a d-wavelike pseudogap with 0 220 meV at M, which accounts for the presence of such a gap in the experimental spectra at x 0:03.…”

Phase diagram and magnetic collective excitations of the Hubbard model for graphene sheets and layers

“…This is in qualitative agreement with the Holstein-Primakoff result for the S = 1/2 Heisenberg model in the honeycomb lattice, which predicts a ground state magnetization of 48%. We should remark, however, that the spin wave spectrum calculated within RPA theory has shown much better agreement with experimental results for Mott-Hubbard antiferromagnetic insulators than the Holstein-Primakoff theory [16,17].…”

“…We should remark, however, that the spin wave spectrum calculated within RPA theory has shown much better agreement with experimental results for Mott-Hubbard antiferromagnetic insulators than the Holstein-Primakoff theory. 16,17 In Fig. 12 we show the imaginary part of the electron's Green's function at negative frequencies, on both sublattices, for two different values of U.…”

“…It is known that the Hartree-Fock-RPA theory of the halffilled Hubbard model is correct in both weak and strongly interacting limits: at strong coupling, the spin wave dispersion obtained in RPA agrees with the Holstein-Primakoff theory for the Heisenberg model; at intermediate interactions ͑U / t ϳ 6͒, the RPA dispersion shows excellent agreement with experiment. 16,17 The Hartree-Fock-RPA theory should, therefore, be considered as a useful starting point to study the intermediate coupling regime. Starting from the spin wave spectrum obtained in RPA theory, we calculate the quantum fluctuation correction to the ground state magnetization arising from virtual emission/reabsorption of spin waves.…”

Hubbard-model description of the high-energy spin-weight distribution in La2CuO4

“…Furthermore, the results of Refs. 8,9 reveal that as far as the LCO inelastic neutron scattering is concerned the inclusion of t ′ and t ′′ does not lead to a better quantitative fit. Accordingly, the studies of this paper consider the half-filled Hubbard model on the square lattice with only two independent effective parameters, t and U .…”