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

Recent experiments [Jo et al., 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.

Figure 1

Spin drag relaxation rate $1/{\tau }_{\mathrm{sd}}(T)$ as a function of temperature $T$, for various values of the interaction parameter $k_{\mathrm{F}}a$. The Fermi energy is denoted by ${\epsilon }_{\mathrm{F}}=k_B{T}_{\mathrm{F}}={\hslash }^2{k}_{\mathrm{F}}^2/2m$. Note that for $k_{\mathrm{F}}a>\pi /2$, the spin drag relaxation rate shows a distinctive upturn when the critical temperatures, indicated by thin vertical lines, are approached from above. In particular, we have $T_c\simeq 0.43T_{\mathrm{F}}$ for $k_{\mathrm{F}}a=1.9$, $T_c\simeq 0.36T_{\mathrm{F}}$ for $k_{\mathrm{F}}a=1.8$, and $T_c\simeq 0.27T_{\mathrm{F}}$ for $k_{\mathrm{F}}a=1.7$. For $k_{\mathrm{F}}a<\pi /2$ no ferromagnetism occurs within mean-field theory. In that case $1/{\tau }_{\mathrm{sd}}(T)$ is smooth throughout the temperature range and exhibits the standard Fermi-liquid behavior $1/{\tau }_{\mathrm{sd}}(T)\propto T^2$ for $T\to 0$.

Figure 2

Spin drag relaxation rate $1/{\tau }_{\mathrm{sd}}$ as a function of $k_{\mathrm{F}}a$ for various temperatures. The thin vertical lines indicate the critical values of the interaction parameter $k_{\mathrm{F}}a$ at which ferromagnetism occurs.

Figure 3

Panel (a): spin diffusion constant $D_s$ as a function of temperature $T$ for various interaction strengths $k_{\mathrm{F}}a>\pi /2$. Panel (b): spin diffusion constant for $k_{\mathrm{F}}a=1.2<\pi /2$.