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arXiv:1002.2371 · Physical Review Letters

Spin Drag in an Ultracold Fermi Gas on the Verge of Ferromagnetic Instability

R. A. Duine, Marco Polini, Henk T. C. Stoof, Giovanni Vignale

Published Jun 1, 2010• 44 citations
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Abstract

Recent experiments [Jo, Science 325, 1521 (2009)] have presented evidence of ferromagnetic correlations in a two-component ultracold Fermi gas with strong repulsive interactions. Motivated by these experiments we consider spin drag, i.e., frictional drag due to scattering of particles with opposite spin, in such systems. We show that when the ferromagnetic state is approached from the normal side, the spin drag relaxation rate is strongly enhanced near the critical point. We also determine the temperature dependence of the spin diffusion constant. In a trapped gas the spin drag relaxation rate determines the damping of the spin dipole mode, which therefore provides a precursor signal of the ferromagnetic phase transition that may be used to experimentally determine the proximity to the ferromagnetic phase.

DOI
10.1103/physrevlett.104.220403

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Recent experiments [Jo, Science 325, 1521 (2009)] have presented evidence of ferromagnetic correlations in a two-component ultracold Fermi gas with strong repulsive interactions. Motivated by these experiments we consider spin drag, i.e., frictional drag due to scattering of particles with opposite spin, in such systems. We show that when the ferromagnetic state is approached from the normal side, the spin drag relaxation rate is strongly enhanced near the critical point. We also determine the temperature dependence of the spin diffusion constant. In a trapped gas the spin drag relaxation rate determines the damping of the spin dipole mode, which therefore provides a precursor signal of the ferromagnetic phase transition that may be used to experimentally determine the proximity to the ferromagnetic phase.
We calculate the spin-drag relaxation rate for a two-component ultracold atomic Fermi gas with positive scattering length between the two-spin components. In one dimension, we find that it vanishes linearly with temperature. In three dimensions, the spin-drag relaxation rate vanishes quadratically with temperature for sufficiently weak interactions. This quadratic temperature dependence is present, up to logarithmic corrections, in the two-dimensional (2D) case as well. For stronger interaction, the system exhibits a Stoner ferromagnetic phase transition in two and three dimensions. We show that the spin-drag relaxation rate is enhanced by spin fluctuations as the temperature approaches the critical temperature of this transition from above.
Spin drag, the friction between interacting atoms of opposite spin, is the single relaxation mechanism of spin currents in cold atomic gases. Experiments are ongoing and one of the quantities of interest is the spin drag relaxation rate in a two-component atomic Fermi gas. Motivated by these experiments, we use the Kubo formalism to obtain an expression for the spin drag conductivity. The sunset approximation to the selfenergy is considered and a T 2 dependence of the relaxation rate is found. The effect of the BCS phase transition is studied by taking into account pair correlations with a ladder summation. Preliminary results indicate a sudden increase of the spin drag relaxation rate close to but above the critical temperature.
Whether a spin-1/2 Fermi gas will become ferromagnetic as the strength of repulsive interaction increases is a long-standing controversial issue. Recently this problem has been studied experimentally by Jo et al. [Science 325, 1521 (2009)] in which the authors claim a ferromagnetic transition is observed. This work is to point out the results of this experiment cannot distinguish whether the system is in a ferromagnetic state or in a nonmagnetic but strongly short-range correlated state. A conclusive experimental demonstration of ferromagnetism relies on the observation of ferromagnetic domains.
In this Thesis, we show that in a rotating two-component Bose mixture, the spin drag between the two different spin species shows a Hall effect. This spin drag Hall effect can be observed experimentally by studying the out-of-phase dipole mode of the mixture. We determine the damping of this mode due to spin drag as a function of temperature. We find that due to Bose stimulation there is a strong enhancement of the damping for temperatures close to the critical temperature for Bose-Einstein condensation. We also show the difference between spin drag in Bose gases, Fermi gases and Bose-Fermi mixtures. Furthermore, we investigate coupled spin and heat transport in Bose gases, and calculate the associated coefficients. Finally, we calculate the power spectrum resulting from spin current fluctuations in a Bose gas.
We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose-Einstein condensation. In these systems the spin conductivity is determined by spin drag, i.e., frictional drag between the two spin components due to interactions. We find that in the critical region the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed experimentally.
Part of Focus on Bose Condensation Phenomena in Atomic and Solid State Physics We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose–Einstein condensation. In these systems, the spin conductivity is determined by spin drag, i.e. frictional drag between the two spin components due to interactions. We find that in the critical region, the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed experimentally.