Spin Correlations in the Paramagnetic Phase and Ring Exchange inLa2CuO4

Abstract

Spin correlations in the paramagnetic phase of La2CuO4 have been studied using polarized neutron scattering, with two important results. First, the temperature dependence of the characteristic energy scale of the fluctuations and the amplitude of the neutron structure factor are shown to be in quantitative agreement with the predictions of the quantum non-linear sigma model. Secondly, comparison of a high-temperature series expansion of the equal-time spin correlations with the diffuse neutron intensity provides definitive experimental evidence for ring exchange.Heisenberg was the first to realize that strong effective spin interactions arise from the principle of the indistinguishability of the particles [1]. Dirac generalized this concept, in the context of Group Theory, to include higher order interactions[2]. Multi-particle exchange dominates the physics of the quantum solid 3 He[3] but, surprisingly, is generally not taken into account for electronic magnetic materials. The most powerful technique for exploring exchange interactions is the study of excitations from the ordered phase using inelastic neutron scattering. However, ambiguities in the interpretation of magnon dispersion curves sometimes mean that higher order terms remain hidden. By employing the independent approach of studying the instantaneous spin correlations in the paramagnetic phase, we obtain complementary information that enables a better understanding of the exchange mechanism. In this letter we describe studies of the diffuse magnetic scattering from La 2 CuO 4 which provide compelling, quantitative evidence for the existence of four-particle cyclic exchange.La 2 CuO 4 is of great intrinsic interest both as the parent compound of a canonical high-temperature superconductor, and as a very good realization of a two-dimensional quantum Heisenberg antiferromagnet (2DQHAF). Magnetic Raman experiments [4], infrared absorption studies [5,6] and inelastic neutron scattering measurements [7] show definitively the inadequacy of the nearest-neighbour Heisenberg model, and suggest the possibility that four-particle exchange may be significant.In an important series of experiments to study the diffuse magnetic scattering from La 2 CuO 4 using unpolarized neutrons[8] the temperature dependence of the magnetic correlation length was found to agree with the predictions of the quantum non-linear sigma model (QNLσM) [9]. However, the observed amplitude shows dramatic deviations from the predictions of this theory [8]. The QNLσM is the simplest possible effective action for a 2DQHAF that is compatible with the long-wavelength spin waves and that does not assume a spontaneously broken symmetry. Moreover, its predictions should hold even in the presence of four-spin exchange, as discussed below. Here we study the dynamical spin correlations above the Néel temperature using polarized neutrons, and find complete agreement of the observed 2D critical fluctuations with the predictions of the QNLσM.Dirac's approach provides the most transparent theoretical fram...

First-Principles Periodic Calculation of Four-Body Spin Terms in High-TcCuprate Superconductors

“…Second, the present estimate of [19]. Notice, however, that the J ring =J 0:25 ratio predicted here is smaller than that reported by Toader et al [18], which is of 0.5, but in excellent agreement with a more generally accepted ratio J ring =J 0:3 [9,10,19] for this compound. Also, the Fock-35 method predicts an antiferromagnetic J d 8:8 meV, again consistent with the values provided by embedded cluster calculations.…”

“…However, to fully understand the magnetic excitations and the infrared and neutron scattering spectra of 2D [5][6][7][8][9][10][11] and spin ladder cuprates [12,13], it has been necessary to extend the spin Hamiltonian as in Eq. (1), [18] provided definitive evidence of its existence in La 2 CuO 4 . They suggest J ring 0:5J, comparable to the pairing energies, and propose that the resulting circulating currents could have an important role in the mechanism of superconductivity.…”

“…Also, the Fock-35 method predicts an antiferromagnetic J d 8:8 meV, again consistent with the values provided by embedded cluster calculations. Hence, it will be of great interest to repeat the fit in the experiments by Toader et al [18] by using the present estimate of both J and J d . For Sr 2 CuO 2 Cl 2 , there are no previous values for the amplitude of the four-body exchange terms.…”

“…Similar four-body terms are crucial to describe the ground state properties of 3 He [17]. Although there is a general agreement about the role of J ring in determining the properties of cuprates [9][10][11][12], only very recently Toader et al [18] provided definitive evidence of its existence in La 2 CuO 4 . They suggest J ring 0:5J, comparable to the pairing energies, and propose that the resulting circulating currents could have an important role in the mechanism of superconductivity.…”

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

“…These corrections alter the low-energy excitations and theoretically they may, if large enough, produce exotic ground states 5 . At the present time, there are still many experiments designed to search for evidence of ring exchange terms in materials such as parent high-temperature superconductors 6 .…”