John Chalker

Abstract:

We present detailed calculations of the magnetic ground state properties of Cs$_2$CuCl$_4$ in an applied magnetic field, and compare our results with recent experiments. The material is described by a spin Hamiltonian, determined with precision in high field measurements, in which the main interaction is antiferromagnetic Heisenberg exchange between neighboring spins on an anisotropic triangular lattice. An additional, weak Dzyaloshinkii-Moriya interaction introduces easy-plane anisotropy, so that behavior is different for transverse and longitudinal field directions. We determine the phase diagram as a function of field strength for both field directions at zero temperature, using a classical approximation as a first step. Building on this, we calculate the effect of quantum fluctuations on the ordering wavevector and components of the ordered moments, using both linear spinwave theory and a mapping to a Bose gas which gives exact results when the magnetization is almost saturated. Many aspects of the experimental data are well accounted for by this approach.

Abstract:

We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. We focus on the interpretation of recent experiments under these conditions (Phys. Rev. Lett. 86 (2001) 866; Phys. Rev. B 64 (2001) 121305), in which a large resistance anisotropy develops at low temperatures. Modelling the systems involved as Ising quantum Hall ferromagnets, we suggest that this transport anisotropy reflects domain formation induced by a random field arising from isotropic sample surface roughness. (C) 2003 Elsevier B.V. All rights reserved.

Abstract:

We consider classical normal modes and non-interacting bosonic excitations in disordered systems. We emphasise generic aspects of such problems and parallels with disordered, non-interacting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of non-interacting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low frequency limit, above a critical dimension $d_c$, which in different circumstances takes the values $d_c=2$ and $d_c=0$. For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\rho(\omega) \propto \omega^4$ is a universal feature in systems with ground states that depend on the disorder realisation. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.