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

Abstract

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La 2 CuO 4 , the paradigm of high-T c superconductor parent compounds, and for the SrCu 2 O 3 ladder compound are reported. For La 2 CuO 4 , present results support experimental evidence by Toader et al. [Phys. Rev. Lett. 94, 197202 (2005)]. For SrCu 2 O 3 even larger four-body spin amplitudes are found together with J l =J r 1 and non-negligible ferromagnetic interladder exchange. DOI: 10.1103/PhysRevLett.97.087003 PACS numbers: 74.20.Mn, 71.15.ÿm, 74.25.Jb, 75.30.Et The strong antiferromagnetic interactions observed in lamellar cuprates are fundamental ingredients of the high-T c (HTC) superconductivity microscopic mechanism [1,2]. Magnetic interactions arise from the particular crystal and electronic structure of these cuprates with Cu 2 ions arranged in edge sharing Cu 4 O 4 plaquettes. The electronic ground state involves a single d x2ÿy2 -type hole in each Cu3d shell leading to a network of effective spin S 1=2 particles. Nevertheless, these systems are strongly correlated in nature, making standard band theory techniques unable to accurately describe either their valence or low energy spectrum [3,4]. The low energy spectrum and collective properties of these compounds are assumed to be governed by a Heisenberg Hamiltonian as in the first term of Eq. (1) accounting for the magnetic coupling J ij between nearestneighbor (NN) centers i and j only. This is in agreement with the widely accepted general picture for HTC superconductivity involving a ''Heisenberg sea'' where holes are introduced by doping the perfect structures. 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. Notwithstanding, previous estimates of J ring for 2D and spin ladder cuprates, obtained from either indirect measurements or numerical simulations with an extended Heisenberg model, propose substantially smaller amplitudes with J ring 0:30J [7,9,10,12,19] Clearly, a bottom-up accurate and independent determination of all important terms in the spin Hamiltonian in Eq. (1) for La 2 CuO 4 -or any other similar system-is PRL 97,

Two dimensionality of magnetic excitations on the trellis lattice:(La,Sr,Ca)14Cu24Schmidt1, Uhrig2 2007Phys. Rev. B4030View full textAdd to dashboardCite

“…8 It is argued that the magnetic exchanges along the legs J ʈ and the rungs J Ќ are almost equal but a strong ferromagnetic interladder coupling x int Ϸ −0.2 is present ͑the calculations were done for the compound SrCu 2 O 3 ͒. We want to point out that this scenario of an iso-tropic exchange x Ϸ 1 is not consistent with our results.…”

“…8 It is therefore an important issue to clarify the impact of the two dimensionality of these systems on their magnetic properties. Theoretically, this question has been treated by mean-field theory using the bond-operator approach which is reliable when the rung-coupling J Ќ dominates.…”

“…8 is an interesting new aspect of the physics in these materials. It will be interesting to see if the analysis of inelasticneutron-scattering data using the results obtained in this work will yield values of the magnetic exchange J int which are consistent with the quantum chemistry calculations.…”

Heisenberg behavior of some carbon‐beryllium compounds: How well truncated‐CI approaches work

“…Similar behavior has been observed for magnetic 2D and spin ladder cuprates from DDCI calculations [23][24][25]28,29 and finite and periodic DFT-based calculations. 25,26,30 For those systems, the J 4 /J ratio is about 0.1-0.25, which can be rationalized on the basis of the perturbative expressions of J and J 4 . 28,29,31,32 These expressions are based on the superexchange model of the magnetic coupling, governed by through-ligand interactions, assuming a negligible direct exchange (K ab ) among magnetic centers:…”

“…3). The importance of this term has been discussed in the recent past in the field of 2D and spin ladder magnetic cuprates [23][24][25][26] and in solid 3 He. 27 The four body operator has the following form for tetrahedral clusters:…”