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arXiv:0909.4917 · Physical Review A

Correlated versus ferromagnetic state in repulsively interacting two-component Fermi gases

Hui Zhai

Published Nov 30, 2009• 52 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.80.051605

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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.
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.
A degenerate Fermi gas is rapidly quenched into the regime of strong effective repulsion near a Feshbach resonance. The spin fluctuations are monitored using speckle imaging and, contrary to several theoretical predictions, the samples remain in the paramagnetic phase for an arbitrarily large scattering length. Over a wide range of interaction strengths a rapid decay into bound pairs is observed over times on the order of 10ℏ/E[subscript F], preventing the study of equilibrium phases of strongly repulsive fermions. Our work suggests that a Fermi gas with strong short-range repulsive interactions does not undergo a ferromagnetic phase transition.
Ho claims in his comment that our experiment is direct evidence that itinerant ferromagnetism does not exist in ultracold Fermi gases. This claim is incorrect and based on an invalid estimate of relaxation times and an erroneous interpretation of the detectability of ferromagnetic domains. We point out that the experimental evidence is consistent with the existence of ferromagnetism, but further experiments are needed to distinguish a ferromagnetic ground state from a non-magnetic ground state with ferromagnetic correlations.
A degenerate Fermi gas is rapidly quenched into the regime of strong effective repulsion near a Feshbach resonance. The spin fluctuations are monitored using speckle imaging and, contrary to several theoretical predictions, the samples remain in the paramagnetic phase for an arbitrarily large scattering length. Over a wide range of interaction strengths a rapid decay into bound pairs is observed over times on the order of 10ℏ/E(F), preventing the study of equilibrium phases of strongly repulsive fermions. Our work suggests that a Fermi gas with strong short-range repulsive interactions does not undergo a ferromagnetic phase transition.
Ultracold atomic Fermi gases close to Feshbach resonances represent the ideal platform to study strongly correlated fermionic states [1]. Up to now, most of the experimental efforts have been dedicated to the study of the famous BEC-BCS crossover, i.e. the transition from a Bose-Einstein condensate of tightly bound molecules to a BCS superfluid of long-range fermion pairs. However, such fermionic gases are the ideal environment to explore also the effects of strong, repulsive interactions. The interest in studying repulsive Fermi gases is manifold, since many phase transitions are driven by the strong repulsion between electrons in solids. One notable example is represented by the onset of itinerant ferromagnetism in metals, as envisioned by Stoner almost ninety years ago.
We study ferromagnetism in a repulsively interacting two-component Fermi gas in a harmonic trap. Within a local density approximation, the two components phase separate beyond a critical interaction strength, with one species having a higher density at the trap center. We discuss several easily observable experimental signatures of this transition. The mean-field release energy, its separate kinetic and interaction contributions, as well as the potential energy all depend on the interaction strength and contain a sharp signature of this transition. In addition, the conversion rate of atoms to molecules, arising from three-body collisions, peaks at an interaction strength just beyond the ferromagnetic transition point. We then go beyond the local density approximation and derive an energy functional that includes a term that depends on the local magnetization gradient and acts as a ``surface tension.'' Using this energy functional, we numerically study the energetics of some candidate spin textures that may be stabilized in a harmonic trapping potential at zero net magnetization. We find that a hedgehog state has a lower energy than an ``in-out'' domain-wall state in an isotropic trap. Upon inclusion of trap anisotropy we find that the hedgehog magnetization profile gets distorted due to the surface tension term, this distortion being more apparent for small atom numbers. We estimate that the magnetic dipole interaction does not play a significant role in this system. We consider possible implications for experiments on trapped 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K gases.