Ordering Phenomena in Transition Metal Oxides

Coupled spin ladders, stripes and the neutron resonance mode   

The dynamic spin susceptibility measured in inelastic neutron scattering experiments is one of the most widely discussed issues in the field of high-temperature superconductivity. Two features have been in the focus of interest: the resonance peak appearing in the superconducting phase and stripe order which manifests itself in superstructure satellites. For many years, these two features were regarded as separate issues, each of them apparent in only one of the two families of cuprates on which most neutron studies have focused: LSCO and YBCO. However, recent experimental results show that the resonance peak in YBCO is accompanied at lower energies by incommensurate reflections, and that stripe order appears also in YBCO. Very recently, Tranquada et al. [1] observed a resonance peak also in stripe-ordered La_15/8Ba_1/8CuO₄ (for T>T_c). The resonance peak is a prominent feature of many different theoretical scenarios. Its interpretation ranges from a particle-hole bound state to a particle-particle bound state in SO(5) theory. The magnetic excitations of the stripe-ordered phase, on the other hand, have not been analyzed in great detail and are often discussed as simple 'vertical rods' in momentum space. Based on a two-dimensional model of coupled two-leg ladders, we calculate the dispersion and the magnetic structure factor for the case of static stripe order [2]. We derive a unified description of the low-energy superstructure modes, of the resonance peak and of the high-energy excitations observed by Tranquada et al. [1]. The superstructure modes arise from a ferromagnetic coupling between neighboring ladders, whereas the resonance peak in the stripe-ordered phase corresponds to a saddle point of the triplon dispersion. The central result is that we arrive at a quantitative agreement with the neutron data of Ref. [1] for realistic values of the exchange parameters. In particular a cyclic exchange of J_cyc/J ≈ 0.2-0.25 is required to match the resonance peak position and the spectral intensity. It is very intriguing that a spin-only model of coupled ladders generically shows the effects observed in the superconducting phase: a resonance mode and excitation branches dispersing to both higher and lower energies.

[1] J. M. Tranquada et al., cond-mat/0401621, to be published in Nature.
[2] G. S. Uhrig, K. P. Schmidt and M. Grüninger, cond-mat/0402659.