Field-Theoretical Studies of a doped Mott Insulator

Abstract

In this thesis, the magnetic and the transport properties of La(2-x)Sr(x)CuO(4) in the undoped and lightly doped regime are investigated.

In Chapter 2, we consider the role of the Dzyaloshinskii-Moriya (DM) and the pseudodipolar (XY) interactions in determining the magnetic properties of the undoped material, La(2)CuO(4), motivated by recent experiments, which show a complete anisotropy in the magnetic susceptibility response. We start with the microscopic spin model, which, besides the Heisenberg superexchange interaction, contains the anisotropic DM and the XY interactions. We map this microscopic model into a corresponding field theory, which turns out to be a generalized nonlinear sigma model. The effect of the anisotropies is to introduce gaps for the spin excitations, which are responsible for the ground-state properties of the material. When a magnetic field is applied, the DM anisotropy leads to an unexpected linear coupling of the staggered magnetization to the magnetic field, which is responsible for a completely anisotropic magnetic susceptibility, in agreement with experiments.

In Chapter 3, we investigate the effect of the DM and the XY anisotropies on the magnetism when Sr doping is introduced in La(2)CuO(4). Our starting point is the nonlinear sigma model, which includes these anisotropies, and also the dopant holes, represented via an effective dipole field which couples to the background magnetization current. In the antiferromagnetic phase, x<2%, the dipole-magnetization current coupling leads to a decrease of the spin gaps, in good agreement with recent experiments. The DM gap gives rise to the stability of the antiferromagnetic state up to the doping level x=2%, at which the dipole field acquires a nonzero expectation value, causing a change in the magnetic ground state of the system. Beyond this doping concentration, the spins rearrange to form an incommensurate helicoidal state, which gives rise to two incommensurate peaks in the spin-glass phase of La(2-x)Sr(x)CuO(4), as observed by neutron scattering experiments. The incommensurability is related to the doping and the XY gap in a way that allows us to explain the linear doping dependence of the incommensurability at higher doping, as well as the deviation from the linear behavior at the onset of the spin-glass phase. We propose a measurement of the doping dependence of the incommensurability in the magnetic field as a "smoking-gun" experiment that would discriminate between the helicoidal and the stripe scenarios in the spin-glass phase of La(2-x)Sr(x)CuO(4).

In Chapter 4, we study the dynamics of topological defects of a frustrated spin system displaying helicoidal order. As a starting point we consider the SO(3) nonlinear sigma model to describe long-wavelength fluctuations around the noncollinear spin state. This model allows for vortex-like topological defects, associated with the change of chirality of the noncollinear state. We consider single vortices and vortex-antivortex pairs, and quantize them using the collective coordinate method, which allows us to represent the defect as a particle coupled to a bath of harmonic oscillators. As a result, the defect motion is damped due to the scattering by the magnons. Finally, motivated by recent experiments, we consider an application of the model for describing the transport in lightly doped La(2-x)Sr(x)CuO(4).