R. J. Ragan

Castaing Instabilities in Longitudinal Spin-Diffusion Experiments

We analyze the anomalous long-lived NMR signals which have been observed in longitudinal spin-diffusion experiments with Fermi fluids. These signals have been attributed to the Castaing instability of the spin current in the Leggett equation. By considering an idealized experimental geometry in which diffusion occurs between two reservoirs of up and down spins connected via a thin tube, we are able to carry out a full stability analysis of the longitudinal spin current. We show that, in the absence of a field gradient, the instability of the spin current sets in when the spin-rotation parameter exceeds the critical value μM=π/2. In the unstable regime, we obtain spontaneous domain-wall structures as solutions to the steady-state Leggett equation, and discuss their formation from small perturbations. We find that the domain wall reduces the spin current through the tube, leading to an extraordinary increase of the lifetime of the magnetization in the reservoirs. We also show that a magnetic field gradient confines the instability, and that a large enough gradient stabilizes the longitudinal spin current.

Temperature Increase of Highly-Polarized Fermi Liquids in Spin-Echo Experiments

We show that there are restrictions on the maximum tipping angle that can be used without significantly raising the temperature of the 3He distribution in high B/T spin-echo experiments with pure liquid 3He and 3He-4He solutions. The temperature increase occurs during the diffusion process as quasiparticles in mixed-spin states are scattered and converted into thermal excitations at the spin-up and spin-down Fermi surfaces. This temperature increase can mimic the effects of zero temperature attenuation, leading to a higher values of the measured anisotropy temperature Ta. We analyze the dependence of the increase on polarization, initial temperature, 3He concentration, and tip angle, and estimate the size of the effect in recent experiments.

Leggett-rice systems in harmonic traps

We present two resugts concerning the spin (or pseudo spin) dynamics of trapped quantum gases in the hydrodynamic regime described by the Leggett equations. First, we apply perturbation theory to extend the “bounded diffusion” description to trapped systems for small field inhomogeneities. Second, we study the formation of long-lived domains with a numerical stability analysis of the lowest-lying longitudinal diffusive modes. We also use computer simulations of π/2-pulse experiments to determine the range of experimental parameters where the formation of domains can be observed.

Castaing Instabilities in Spin-Echo Experiments

The effects of spin-wave instabilities on θ−Δt−π spin-echo experiments in spin-polarized normal Fermi fluids are investigated. Using a linear stability analysis, the helical configuration of the magnetization density which occurs in such experiments is shown to be unstable against long-wavelength perturbations—an example of the Castaing instability of the Leggett equation. For large values of the spin rotation parameter, μM≫1, and large tip angles, perturbations develop into large amplitude oscillations which destroy the helix before the transverse magnetization decays by diffusion. This, of course, affects the interpretation of spin echo data. The nonlinear dynamics of the instabilities in spin echo experiments and their effects on spin-echo data are studied using computer simulations. The results are compared with the linear analysis and summarized in a μM−θ diagram which indicates when the standard Leggett–Rice spin-echo analysis breaks down.

Non‐Conservation of Transverse Magnetization in Spin Diffusion in Trapped Boltzmann Gases

Experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin‐1/2 system, including transverse spin waves and other familiar Leggett‐Rice‐type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral. We find that the hydrodynamic diffusive modes cease to exist because interactions with different scattering lengths for up‐up, up‐down, and down‐down spins lead to a spin‐spin relaxation, that causes non‐conservation of transverse magnetization. We give results for the quadrupole modes, the modes studied in experiments with equal scattering lengths. Instead of a linear dependence on relaxation time τ for the diffusive mode, we find a divergence at small τ. No such effect occurs in Fermi gases.

Spin-Current Relaxation Time in Spin-Polarized Heisenberg Paramagnets

No HeadingWe study the spatial Fourier transform of the spin correlation function Gq(L) 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 a the correlation function Gq(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 ∝ q2. 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 ansalz for the second derivative of the correlation function.

Anisotropic Spin Diffusion in Trapped Boltzmann Gases

No HeadingRecent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.

Landau Damping of Spin Waves in Trapped Boltzmann Gases

No HeadingA semiclassical method is used to study Landau damping of transverse pseudo-spin waves in harmonically trapped ultracold gases in the collisionless Boltzmann limit. In this approach, the time evolution of a spin is calculated numerically as it travels in a classical orbit through a spatially dependent mean field. This method reproduces the Landau damping results for spin-waves in unbounded systems obtained with a dielectric formalism. In trapped systems, the simulations indicate that Landan damping occurs for a given spin-wave mode because of resonant phase space trajectories in which spins are “kicked out” of the mode (in spin space). A perturbative analysis of the resonant and nearly resonant trajectories gives the Landau damping rate, which is calculated for the dipole and quadrupole modes as a function of the interaction strength. The results are compared to a numerical solution of the kinetic equation by Nikuni et al.

Spin-Wave Instabilities in Spin-Echo Experiments

The importance of Castaing instabilities in θ−Δt−π spin-echo experiments in spin-polarized normal Fermi fluids is investigated. For small tip angles and very large values of the spin rotation parameter μM, a previous stability analysis is extended to account for angular relaxation, an effect which tends to reduce the growth of unstable modes. The results are compared with computer simulations and are applied to currently planned experiments at NHMFL.

Instability and Self-Modulation of the Classical Heisenberg Ferromagnet

The helical solution of the one-dimensional classical Heisenberg chain is shown to be unstable against long-wavelength perturbations. Using the fact that the classical Heisenberg chain is exactly integrable, inverse scattering techniques are used to display the growth of the instabilities all the way to nonlinear saturation.