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arXiv:0911.2839 · Physical Review A

Effect of three-body loss on itinerant ferromagnetism in an atomic Fermi gas

G. J. Conduit, Ehud Altman

Published Apr 20, 2011• 20 citations
arXivHTMLPDF

Abstract

A recent experiment has provided tentative evidence for itinerant ferromagnetism in an ultracold atomic gas. However, the interpretation of the results is complicated by significant atom losses. We argue that during the loss process the system gradually heats up but remains in local equilibrium.To quantify the consequences of atom loss on the putative ferromagnetic transition we adopt an extended Hertz-Millis theory. The losses damp quantum fluctuations, thus increasing the critical interaction strength needed to induce ferromagnetism and revert the transition from being first order to second order. This effect may resolve a discrepancy between the experiment and previous theoretical predictions. We further illuminate the impact of loss by studying the collective spin excitations in the ferromagnet. Even in the fully polarized state, where loss is completely suppressed, spin waves acquire a decay rate proportional to the three-body loss coefficient.

DOI
10.1103/physreva.83.043618

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A recent experiment has provided tentative evidence for itinerant ferromagnetism in an ultracold atomic gas. However, the interpretation of the results is complicated by significant atom losses. We argue that during the loss process the system gradually heats up but remains in local equilibrium.To quantify the consequences of atom loss on the putative ferromagnetic transition we adopt an extended Hertz-Millis theory. The losses damp quantum fluctuations, thus increasing the critical interaction strength needed to induce ferromagnetism and revert the transition from being first order to second order. This effect may resolve a discrepancy between the experiment and previous theoretical predictions. We further illuminate the impact of loss by studying the collective spin excitations in the ferromagnet. Even in the fully polarized state, where loss is completely suppressed, spin waves acquire a decay rate proportional to the three-body loss coefficient.
We address the possible occurrence of ultracold atom ferromagnetism by evaluating the free energy of a spin polarized Fermi gas to second order in its interaction parameter. We find that Hartree-Fock theory underestimates the tendency toward ferromagnetism, predict that the ferromagnetic transition is first order at low temperatures, and point out that the spin coherence time of gases prepared in a ferromagnetic state is strongly enhanced as the transition is approached. We relate our results to recent experiments.
We study the emergence of itinerant ferromagnetism in an ultracold atomic gas with a variable mass ratio between the up- and down-spin species. Mass imbalance breaks the SU(2) spin symmetry, leading to a modified Stoner criterion. We first elucidate the phase behavior in both the grand canonical and canonical ensembles. Second, we apply the formalism to a harmonic trap to demonstrate how a mass imbalance delivers unique experimental signatures of ferromagnetism. These could help future experiments to better identify the putative ferromagnetic state. Furthermore, we highlight how a mass imbalance suppresses the three-body loss processes that handicap the formation of a ferromagnetic state. Finally, we study the time-dependent formation of the ferromagnetic phase following a quench in the interaction strength.
Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the most well-characterized phases of correlated Fermi systems. A recent experiment has reported the first evidence for novel phase behavior on the repulsive side of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting recent theoretical studies to the atomic trap geometry, we show that an adiabatic ferromagnetic transition would take place at a weaker interaction strength than is observed in experiment. This discrepancy motivates a simple nonequilibrium theory that takes account of the dynamics of magnetic defects and three-body losses. The formalism developed displays good quantitative agreement with experiment.
Itinerant ferromagnetism in cold Fermi gases with repulsive interactions is studied applying the Jastrow-Slater approximation generalized to finite polarization and temperature. For two components at zero temperature, a second-order transition is found at ${\mathit{ak}}_{F}\ensuremath{\simeq}0.90$ compatible with results of quantum-Monte-Carlo (QMC) calculations. Thermodynamic functions and observables, such as the compressibility and spin susceptibility and the resulting fluctuations in number and spin, are calculated. For trapped gases, the resulting cloud radii and kinetic energies are calculated and compared to recent experiments. Spin-polarized systems are recommended for effective separation of large ferromagnetic domains. Collective modes are predicted and tricritical points are calculated for multicomponent systems.
In the 1930s, two main paradigms for the theoretical description of ferromagnetism were developed: Heisenberg ferromagnetism of localized fermions (e.g., in a lattice), and Bloch or Stoner ferromagnetism of nonlocalized fermions (i.e., in a gas), also called itinerant ferromagnetism. Despite many theoretical predictions, itinerant ferromagnetism has remained elusive in experiments. This ferromagnetic state is predicted to occur for strong repulsive interactions, corresponding to a regime that is very challenging to describe theoretically because there are multiple competing physical effects, including superfluid pairing. In this paper, we point out that the problem of itinerant ferromagnetism for atomic Fermi gases is different from that of electron gases in metals due to the short-range nature of the interatomic interactions. We also show that the standard saddle point used to describe itinerant ferromagnetism of the electron gas in metals does not apply, because in the short-range limit of this approximation the Pauli exclusion principle is violated. As a remedy, we introduce a modified interaction pseudopotential for ultracold gases which includes both local (Hartree) and nonlocal (Fock) terms while preserving the Pauli exclusion principle in the short-range regime. Furthermore, we demonstrate the usefulness of this method to study the existence and stability of itinerant ferromagnetism in ultracold atomic gases. Lastly, we obtain the critical temperature for the ferromagnetic transition as a function of the opposite-spin interaction strength and find a rather good agreement with recent experimental results.
We theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local-density approximation. We demonstrate that, while the local-density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase transition by monitoring the shape change of the free-energy curve with increasing the polarization at various interaction strengths.