Theoretical analysis of magnetic Raman scattering inLa2CuO4:Two-magnon intensity with the inclusion of ring exchange

Abstract

We evaluate the Raman light scattering intensity for the square lattice Heisenberg antiferromagnet with plaquette ring exchange J✷. With the exchange couplings as fixed before from an accurate fit to the spin wave dispersion in La2CuO4, leading in particular to J✷ = 0.24J, we demonstrate in a parameter free calculation that the inclusion of the plaquette exchange contribution to the dispersion and the magnon-magnon interaction vertex gives a peak position in B1g scattering geometry Emax = 2.71J which is in excellent agreement with the experimental data. Yet, the intrinsic width and the lineshape of the two-magnon remain beyond a descriptions in terms of a spin-only Hamiltonian.PACS Numbers: 75.40.Gb, 75.10.Jm, 76.60.Es The magnetic properties of La 2 CuO 4 have been the subject of many detailed investigations over the last decade. Understanding this undoped parent compound of high temperature superconducting cuprates is a precondition for the many theories which describe metallic cuprates by doping carriers into a layered antiferromagnet. The conventional starting point for undoped cuprates is the two-dimensional (2D) spin-1/2 Heisenberg model with nearest-neighbor (nn) exchange interaction J [1]. Despite the substantial progress on the theory of the 2D Heisenberg antiferromagnet [2], some of the experimental facts for La 2 CuO 4 have clearly demonstrated that a complete description of the magnetic excitations requires additional physics not contained in the 2D Heisenberg model with J only. Examples include the asymmetric lineshape of the two-magnon Raman intensity [3] or the infrared optical absorption [4].The importance of an additional ring (plaquette) exchange coupling for La 2 CuO 4 recently found direct experimental support from the observed dispersion of the spin-waves along the magnetic Brillouin zone boundary [5]. A fit of the experimental results [5] using the theoretical spin-wave dispersion, which consistently includes quantum renormalization effects [6], has provided accurate values for the nn exchange integral J = 1720K and the ring-exchange coupling J ✷ = 0.24J. The new estimate for J corrects previous values which have been used in past years and which were consistently 10 to 15% lower. Also the value for J ✷ must be considered surprisingly large, but the spin stiffness and the Néel temperature calculated with the new parameter set obtained in Ref. [6] were in excellent agreement with the experimental data and thereby confirmed the deduced exchange coupling parameters. The value of the ring exchange J ✷ also agreed with the strong-coupling expansion studies of the three-band Hubbard model in the parameter range relevant for CuO 2 planes [7].The Heisenberg model with J only was previously found insufficient to describe the experimentally observed asymmetry and width of the Raman spectra of undoped cuprate compounds [3]. The Raman spectrum of the Heisenberg model was investigated within the ladder approximation for the magnon-magnon scattering vertex many years ago [8,9] and gave an almost symme...

Variational ground states of the two-dimensional Hubbard model

“…Experiments on layered cuprates indicate that U is neither small enough for a perturbative treatment nor large enough for the mapping to the t − J model. Thus, neutron scattering experiments on undoped cuprates [22] can be very well interpreted in terms of the 2D Hubbard model with U between 8 t and 10 t (depending on the approximation used for the magnon spectrum [23,24]), in agreement both with an analysis of Raman data [25] and with a comparison between theoretical and experimental optical absorption spectra [26]. As to the 'kinetic' termĤ 0 , angularresolved photoemission experiments [27,28] give evidence for a hole-like Fermi surface, which can be described by taking both nearest-neighbour and next-nearest-neighbour hopping terms into account [29,30]; the experiments are consistent with t ′ ≈ −0.3t.…”

Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice

“…The REM thus provides an intermediate step between the two limiting cases of the Heisenberg Hamiltonian and the Hubbard Hamiltonian. La 2 CuO 4 , the parent compound of the cuprates La 2−x Ba x CuO 4 and La 2−x Sr x CuO 4 , falls into this category [4][5][6][7][8] . It is essentially two-dimensional, with a quantum spin s = 1/2 on each site placed in a square geometry, where quantum effects are expected to play a dominant role.…”

Magnetic Phase Diagram of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchanges

“…2,[6][7][8] Ring exchanges were also found to be relevant to some strongly correlated electron systems such as the two-leg spin ladder compound La x Ca 14−x Cu 24 O 41 [9][10][11][12][13] and two-dimensional antiferromagnet La 2 CuO 4 . [14][15][16][17][18][19] It has been suggested recently that ring exchanges can be dominant in quantum wires with a shallow confining potential. 20,21) In contrast to two-and three-spin exchange processes, the ring exchanges involving more than three spins take a very complicated form in terms of spin operators including bilinear, biquadratic, and higher-order couplings in general, which compete with each other.…”