Properties of undoped and doped spin-1/2 ladders at finite temperature

Abstract

Antiferromagnetic spin-1/2 ladders have been studied in theoretical and experimental physics for several years. The spin ladder is a good model to bridge between theory and experiment, because it is realized in the copper oxide family Sr14-x(La,Ca)xCu24O41. These copper oxides consist of alternating layers of edge-sharing chains and ladders. The insulating mother compound Sr14Cu24O41 is hole doped in the chains as well as slightly in the ladders. The hole content in the Sr14Cu24O41 ladders is reduced, if La3+ is substituted for Sr2+ resulting in a pure antiferromagnetic spin ladder given by La4Sr10Cu24O41. In this thesis such spin ladders are studied by an amalgamated approach of theoretical work and experiments. For the La4Sr10Cu24O41 ladder the temperature development is investigated using scattering techniques as well as computer modelling. At zero temperature the spin ladder has already been well described by effective models computed via perturbative continuous unitary transformations (PCUTs). These PCUT results are now combined with a mean field approach allowing for incorporation of temperature induced conditional excitations via vertex corrections. The vertex correction results in a decreasing one-triplon spectral weight upon increasing temperature. This effect is studied by inelastic neutron scattering (INS) on La4Sr10Cu24O41 crystals by measuring the scattering amplitude at various temperatures. Convincing agreement is found within the experimental and theoretical error bars. Additionally the coupling constants found in Ref. [1] could be confirmed. The importance of an inter-ladder coupling Jinter between isolated ladders in the plane is investigated by combination of the PCUT with a mean field approach. This calculation is undertaken for the square and the trellis lattice. The difference to the existing calculations [2], [3] and [4] is the partial inclusion of the hardcore interaction for neighbouring ladders. At zero temperature we reveal the effect of quantum fluctuations on the spin gap. In the case of the square lattice we find the closure of the spin gap at a critical inter-ladder coupling enlarged by 3 - 4%. In the case of the trellis lattice, the spin gap decreases also as a function of inter-ladder coupling. In this case we find an enlarged critical inter-ladder coupling up to 21%. In additon, the theoretically predicted shift of the spectral weight by Uhrig and Schmidt could experimentally be confirmed. Substituting Ca2+ for Sr2+ results in hole doped ladders, such as Sr2.5Ca11.5Cu24O41 and Sr8Ca6Cu24O41, where the hole doping depends on the substituted Ca2+ content. The magnetic spectra of these two doped ladders are measured by INS and compared with the undoped ladder La4Sr10Cu24O41. The comparison reveals new features tracing back to the presence of holes. At low temperature in both compounds scattering below the gap of the undoped ladder is found resulting in a subgap1 state at about 8meV. The subgap broadens at high temperature so much that the closing of the subgap results. Additionally for…