Properties of undoped and doped spin-1/2 ladders at finite temperature
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Date
2011-01-18
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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 both dopings and at low and high temperature a hole-pair captured by
triplons is found with a fixed energy gap at 23meV. The new features are qualitatively
explained in terms of resonant valence bond theory (RVB) as well as stripe ordering
theory.
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Keywords
Continuous unitary transformation, Mean field approach, Neutron scattering, Undoped and doped cuprates, Finite temperature, Triplon