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arXiv:cond-mat/9612041

Antiferromagnetic systems with spin gap: exact results

Indrani Bose

Published Dec 3, 1996• 0 citations
arXivHTMLPDF

Abstract

We describe some antiferromagnetic systems which exhibit spin gaps. We also discuss the effect of doping one such system, namely, the spin-ladders, with holes. Some model antiferromagnetic systems with spin gap are reviewed for which exact results are available. Exact results for a doped spin-ladder model are also mentioned.
DOI
10.48550/arxiv.cond-mat/9612041

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The low-energy charge excitations of a doped antiferromagnetic ladder are modeled by a system of interacting spinless fermions that live on the same ladder. A relatively large spin gap is assumed to ``freeze out'' all spin fluctuations. We find that the formation of rung hole pairs coincides with the opening of a single-particle gap for charge excitations along chains and with the absence of coherent tunneling in between chains. We also find that such hole pairs condense into either a crystalline or superconducting state as a function of the binding energy.
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.
Effects of nonmagnetic impurity doping in a spin ladder system with a spin gap are investigated by the exact diagonalization as well as by the variational Monte Carlo calculations. Substantial changes in macroscopic properties such as enhancements in spin correlations and magnetic susceptibilities are observed in the low impurity concentration region, which are caused by the increase of low-energy states. These results suggest that small but finite amount of nonmagnetic impurity doping relevantly causes the reduction or the vanishment of the spin gap. This qualitatively explains the experimental result of Zn-doped SrCu2_{2}2​O3_{3}3​ where small doping induces gapless nature. We propose a possible scenario for this drastic change as a quantum phase transition in a spin gapped ladder system due to spinon doping effects.
We study low-energy magnetic excitations of doped spin-ladders, based on an effective Hamiltonian describing interactions of mobile spin and background spins. The helicity modulus against fluctuations in the ladder plane as well as out-of-the-plane are calculated in terms of the doping concentration, the leg number and interaction strengths in the ladder. The doping range for spiral phase is computed and its relation to spin gap structure is discussed. The spiral order can enhance existing antiferromagnetic order at certain doping or reduce it at very low density of holes. For odd-legged ladders, formation of spin gap at certain narrow doping range becomes possible via coupling of spirals and background spins. Our results of the doping range for gapped mode in odd-ladders agree well with those existing numerical studies.