Raman Response of Magnetic Excitations in Cuprate Ladders and Planes

Abstract

An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J_parallel and J_perp plus an additional four-spin interaction J_cyc. Within this model Sr123 and Sr14 can be described by x:=J_parallel/J_perp=1.5, x_cyc:=J_cyc/J_perp=0.2, J_perp^Sr123=1130 cm^-1 and J_perp^Sr14=1080 cm^-1. The couplings found for La6Ca8 are x=1.2, x_cyc=0.2, and J_perp^La6Ca8=1130 cm^-1. The unexpected sharp two-triplon peak in the ladder materials compared to the undoped two-dimensional cuprates can be traced back to the anisotropy of the magnetic exchange in rung and leg direction. With the results obtained for the isotropic ladder we calculate the Raman line-shape of a two-dimensional square lattice using a toy model consisting of a vertical and a horizontal ladder. A direct comparison of these results with Raman experiments for the two-dimensional cuprates R2CuO4 (R=La,Nd), Sr2CuO2Cl2, and YBa2Cu3O(6+delta) yields a good agreement for the dominating two-triplon peak. We conclude that short range quantum fluctuations are dominating the magnetic Raman response in both, ladders and planes. We discuss possible scenarios responsible for the high-energy spectral weight of the Raman line-shape, i.e. phonons, the triple-resonance and multi-particle contributions.

10 pages, 6 figures

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• One- and Two-Triplon Spectra of a Cuprate Ladder
• Collective spin excitations in a quantum spin ladder probed by high-resolution Resonant Inelastic X-ray Scattering
• Spectral Properties of Magnetic Excitations in Cuprate Two-Leg Ladder Systems
• Magnetic nature of the 500 meV peak in $\mathrm{L}{\mathrm{a}}_{2-\mathrm{x}}\mathrm{S}{\mathrm{r}}_{\mathrm{x}}\mathrm{Cu}{\mathrm{O}}_4$ observed with resonant inelastic x-ray scattering at the Cu $K$-edge
• Effects of ring exchange interaction on the Neel phase of two-dimensional, spatially anisotropic, frustrated Heisenberg quantum antiferromagnet
• Evidence for Dimer Crystal Melting in the Frustrated Spin-Ladder BiCu2PO6
• Competing phases in spin ladders with ring exchange and frustration
• Excitation Spectrum of One-dimensional Extended Ionic Hubbard Model
• Antiferromagnetic ordering of energy levels for spin ladder with four-spin cyclic exchange: Generalization of the Lieb-Mattis theorem
• Breathers and Raman scattering in a two-leg ladder with staggered Dzialoshinskii-Moriya interaction
• Dynamics in two-leg spin ladder with a four-spin cyclic interaction
• Vertex corrections in the dynamic structure factor in spin ladders
• Theory of L-edge resonant inelastic x-ray scattering for magnetic excitations in two-leg spin ladder
• Linked Cluster Expansions via Hypergraph Decompositions
• Raman study of spin excitations in the tunable quantum spin ladder Cu(Qnx)(Cl${}_{1-x}$Br${}_x$)${}_2$
• Two-Dimensionality of Magnetic Excitations on the Trellis Lattice: (La,Sr,Ca)${}_{14}$Cu${}_{24}$O${}_{41}$ and SrCu${}_2$O${}_3$
• $K$ -edge and $L_3$ -edge RIXS study of columnar and staggered quantum dimer phases of the square lattice Heisenberg model