Cyclic spin exchange in cuprate spin ladders

Abstract

We investigate the influence of a cyclic spin exchange Jcyc on the one-and two-triplet excitations of an undoped two-leg S=1/2 ladder, using the density matrix renormalization group (DMRG). The dispersion of the S=0 two-triplet bound state is dramatically reduced by Jcyc due to a repulsion between triplets on neighboring rungs. In (La,Ca)14Cu24O41 a consistent description of both the spin gap and the S=0 bound state requires Jcyc/J ⊥ ≈ 0.20-0.27 and J/J ⊥ ≈ 1.25-1.35. With these coupling ratios the recently developed dynamical DMRG yields an excellent description of the entire S=0 excitation spectrum observed in the optical conductivity, including the continuum contribution.PACS numbers: 75.10. Jm, 75.40.Gb, 75.40.Mg, 74.72.Jt, 75.30.Et The antiferromagnetic parent compounds of the high-T c cuprates are thought to be the best representatives of the two-dimensional S=1/2 square-lattice Heisenberg model. Understanding their magnetic properties is of utmost importance due to the intimate relationship of magnetic correlations and high-T c superconductivity. Recently, the question how to set up a minimal model which accounts for these magnetic properties has been readdressed. High-resolution inelastic neutron scattering experiments performed on the two-dimensional S=1/2 antiferromagnet La 2 CuO 4 [1] exhibit a magnon dispersion at the zone boundary which cannot be obtained within a nearest-neighbor Heisenberg model. It has been argued that the inclusion of a cyclic spin exchange term of about 20% would reproduce this dispersion [2]. This cyclic spin exchange emerges as a correction to the nearestneighbor Heisenberg Hamiltonian in order t 4 /U 3 from a t/U -expansion of the one-band Hubbard model [3]. It is expected to be the dominant correction within a more realistic three-band description of the CuO 2 -planes because there the cyclic permutation of 4 spins on a plaquette can take place without double occupancy [4,5]. Similar cyclic spin exchange processes have proven to be significant in other systems, e.g. in cuprate spin chains a ferromagnetic 2-spin cyclic exchange is responsible for the unusually strong exchange anisotropy [6].Cuprate spin ladders offer an alternative approach to decide about the existence and potential implications of a cyclic spin exchange term. They are composed of the same corner-sharing Cu-O plaquettes as the 2D cuprates, thus similar exchange couplings are expected for all spin products. In fact the inclusion of a cyclic spin exchange has been suggested in order to explain the smallness of the ladder spin gap observed in (La,Ca) 14 Cu 24 O 41 [7][8][9]. However, it is impossible to extract a unique set of coupling parameters or even to settle the existence of a cyclic spin exchange term from an analysis of the spin gap only. Here, the optical conductivity σ(ω) [10,11] can provide the missing information. Magnetic excitations can be observed in σ(ω) via the simultaneous excitation of a phonon [12,13]. In (La,Ca) 14 Cu 24 O 41 , two peaks in σ(ω) were identified as S=0 bound states of tw...

Raman response of magnetic excitations in cuprate ladders and planes

“…This order of magnitude was previously obtained for cuprate ladders by inelastic neutron scattering 57,58 , by infrared absoption 27,28 , Raman response 19,32 and theoretical works deriving extended low-energy Heisenberg models 35,74 . In order to account for the FWHM and the two-triplon peak position we determine x = 1.5 and global energy scales J ⊥ = 1130 cm −1 for Sr123 and J ⊥ = 1080 cm −1 for Sr14.…”

“…In case of inconclusive extrapolants the bare truncated series are used. We will estimate the overall accuracy below by comparing with DMRG results 27 . The Raman line shape is finally calculated as continued fraction by tridiagonalization of the effective two-triplon Hamiltonian.…”

“…In the last years theoretical developments in the field of quasi one-dimensional systems, namely the quantitative calculation of spectral densities 25,26,27,28,29,30,31 , has led to a deeper understanding of magnetic contributions to the Raman response of undoped cuprate ladders. Besides the usual Heisenberg exchange terms the minimal magnetic model includes four-spin interactions which are 4-5 times smaller than the leading Heisenberg couplings 19,27,28,32,33 .…”

“…Besides the usual Heisenberg exchange terms the minimal magnetic model includes four-spin interactions which are 4-5 times smaller than the leading Heisenberg couplings 19,27,28,32,33 . The existence and the size of the four-spin interactions are consistent with theoretical derivations of generalized t-J models from one-band or three-band Hubbard models 34,35,36,37,38,39,40 .…”

Spin-liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice

“…Since the early studies by Thouless [36], single monolayers of solid 3 He have been absorbed on graphite [37,38] and several studies were performed to develop a theoretical understanding of the experiments in terms of multiple spin-exchange models [39][40][41][42][43][44][45][46][47]. Additionally, multiple spin-exchange models have gained interest in frustrated spin systems, in particular the parent cuprate high-temperature superconductors [48][49][50].…”