Spin-wave dispersion inLa2CuO4

Abstract

We calculate the antiferromagnetic spin-wave dispersion in a half-filled Hubbard model for a two-dimensional square lattice, and find it to be in excellent agreement with recent high-resolution inelastic neutron scattering performed on La2CuO4 [Phys. Rev. Lett. 86, 5377 (2001)].PACS numbers: 75.30. Ds, 71.10.Fd, 75.40.Gb After over a decade of intense research on the microscopic origin of high-temperature superconductivity in cuprates, there is no general consensus on the microscopic Hamiltonian suitable for describing these materials. Nevertheless, it appears that magnetic fluctuations must play an important role. Therefore, the study of magnetic fluctuations in the high-temperature superconductor parent compounds, such as La 2 CuO 4 , is an important field of research, both theoretical and experimental.In two recent papers, 1,2 high-resolution inelastic neutron-scattering measurements were 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 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 La 2 CuO 4 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 highprecision quantum Monte Carlo simulations have confirmed that this is so. 4 On the other hand, an explanation for the observed dispersion in La 2 CuO 4 was proposed, 1 using an extended Heisenberg model 5,6 involving first-, second-, and third-nearest-neighbor interactions as well as interactions among four spins. This extended model was obtained from the Hubbard model, using perturbation theory, and is diagonalized afterward using classical (large-S) linear spin-wave theory. 1 The La 2 CuO 4 results clearly show that the usual Heisenberg model is insufficient to explain the experimental data, and that the Hubbard model is the correct Hamiltonian for describing the magnetic interactions in the cuprates. 7 In this work we do not use perturbation theory for deriving an effective magnetic Hamiltonian. Instead we work directly with the Hubbard model. We consider a half-filled Hubbard model in a spin-densitywave (SDW)-broken symmetry ground state and, by summing up all ladder diagrams, we compute the transverse spin susceptibility and from this obtain the spinwave dispersion.The Hubbard model for a square lattice of N sites is defined as

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

“…As mentioned above, for the original electrons the problem is highly correlated and involves an infinite set of ladder diagrams and no simple analytical expression was found for the spin-wave energy spectrum 41 . In contrast, for the s1 fermion description it is effectively non interacting and described by simple analytical expressions.…”

“…Fortunately, there are reliable results on that particular problem obtained by controlled approximations of the standard formalism of many-electron physics: within such approximations its solution requires summing up an infinite set of ladder diagrams, to find the spin-wave dispersion of the half-filled Hubbard model on the square lattice in a spin-density-wave-broken symmetry ground state 41 . In turn, within our description the spin spectrum is that of Eq.…”

“…Within the description of the quantum problem used here, for 1/k B T → ∞ the coherent spin-spectral-weight distribution derived in Ref. 41 corresponds to a surface of energy and momentum given by, …”

“…9 , the spin excitations generate the emergence of two holes in the s1 momentum band but phase-space, exclusion-principle, and energy and momentum conservation restrictions prevent inelastic collisions between the two emerging s1 fermion holes. In contrast, in terms of the original electrons it is a complex many-electron problem whose solution requires summing up an infinite number of diagrams 41 . The excellent agreement reached in Section VI between the spin spectrum as expressed in terms of the s1 fermion dispersions and as obtained by the usual many-electron machinery then confirms the validity of the c and s1 fermion description associated with the square-lattice quantum liquid.…”

“…Also concerning the limitation (ii), in Subsection VI-B we consider one of the few physical limits where there are reliable and controlled studies of the Hubbard model on the square lattice by means of the standard formalism of many-electron physics 41 : The spin excitations at half filling. The results of that section reveal an excellent quantitative agreement between the results obtained within the square-lattice quantum liquid and those of Ref.…”