Spin-Current Relaxation Time in Spin-Polarized Heisenberg Paramagnets

Abstract

We study the spatial Fourier transform of the spin correlation function G q (t) in paramagnetic quantum crystals by direct simulation of a 1d lattice of atoms interacting via a nearest-neighbor Heisenberg exchange Hamiltonian. Since it is not practical to diagonalize the s = 1/2 exchange Hamiltonian for a lattice which is of sufficient size to study long-wavelength (hydrodynamic) fluctuations, we instead study the s → ∞ limit and treat each spin as a vector with a classical equation of motion. The simulations give a detailed picture of the correlation function G q (t) and its time derivatives. At high polarization, there seems to be a hierarchy of frequency scales: the local exchange frequency, a wavelength-independent relaxation rate 1/τ that vanishes at large polarization P → 1, and a wavelength-dependent spin-wave frequency ∝ q 2 . This suggests a form for the correlation function which modifies the spin diffusion coefficients obtained in a moments calculation by Cowan and Mullin, who used a standard Gaussian ansatz for the second derivative of the correlation function.The Heisenberg spin chain continues to be of the focus of much experimental and theoretical study (See Ref.1 and references therein). A number of new materials has been synthesized which appear to be nearly perfect experimental realizations of the spin-1/2 chain. These experiments have also pointed to the need for detailed theroeticals studies of the spin dynamics of the Heisenberg chain. In its simplest form the model is defined by the Hamiltonianwhere B is the external magnetic field, J is the nearest neighbor exchange integral, the second sum is over nearest neighbors. Its low temperature (T ≪