Theory of nuclear magnetic relaxation in Haldane gap materials: an illustration of the use of (1+1)-dimensional field theory techniques

A comprehensive theory of nuclear magnetic relaxation in S = 1 Haldane gap materials is developed using nonlinear-σ, boson and fermion models. We find that at temperatures much smaller than the lowest gap the dominant contribution to the relaxation rate comes from two magnon processes with T₁⁻¹ ∼ e[sup -Δm/T], where Δm is the smallest gap corresponding to a polarization direction perpendicular to the field direction. As the gap closes, we find that the dominant contribution comes from one magnon processes, and the result depends on the symmetry of the Hamiltonian. Overall the models agree qualitatively, except near the critical regime, where the fermion model is shown to be the best description. We include a thorough discussion of the effects of interchain-couplings, nearest neighbour hyperfine interactions and crystal structure, and introduce a new theory of impurities corresponding to broken chain ends weakly coupled to bulk magnons. The work is then applied to recent measurements on NENP. We find overall fair agreement between available T₁⁻¹ data and our calculations. We finish by suggesting further experimental tests of our conclusions.Science, Faculty ofPhysics and Astronomy, Department ofGraduat