Quasi-one-dimensional magnetism in TiOCl and a theory of a lightly doped dimerized insulator

Abstract

Transition metal oxides with low dimensional geometry have displayed fascinating new phenomena such as high temperature superconductivity and unconventional magnetism. The first part of this thesis is related to this rich and diverse subject, where TiOCl is studied as an example of an S = 1/2 layered Mott insulator. Earlier experiments on this material indicating two-dimensional spin-liquid behavior are reviewed critically and are compared to new susceptibility data. The latter suggest a new picture, where band structure effects produce quasi-one-dimensional spin chains formed by t2g orbitals. Based on these findings, TiOC1 is proposed to be a new example of Heisenberg-chains which undergo a spin-Peierls transition. Within this picture, the effect of doping with non-magnetic Sc impurities can be explained in good agreement with the experiment. The magnetic energy scale of J - 660K and the frustration of the interchain geometry render TiOC1 unique among materials with a spin-Peierls transition. This unusual geometry is interpreted as the main reason for the failure of conventional mean-field theory to describe the details of the transition such as its first order character. It will be shown that a simple Ginzburg-Landau theory which takes proper account of interchain-frustration is capable of explaining this unconventional behavior.

(cont.) In the second part of the thesis, the problem of a doped dimerized spin chain is studied in the context of the tJJ'-model one dimension. The focus is on the regime J'/J - .5 where a spin gap is present at small doping and the undoped spin chain is strongly dimerized, and on the limit of small hole doping x as well as small J/t, J'/t. In this regime, earlier numerical calculations have not been able to yield conclusive results. Using a perturbative approach and Luttinger liquid arguments, it will be demonstrated for this non-integrable class of models that the charge degrees of freedom behave as non-interacting spinless solitons in the dilute hole limit. These results are verified up to third order in perturbation theory. The same approach is also used to evaluate the energy and mass renormalization of a single hole, where non-analytic corrections in powers of [the square root of] J/t are obtained. At J'/J = .5 a variational spin-polaron wave function for the hole is constructed and good agreement with the perturbative results is found.