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arXiv:0907.2888 · Science

Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms

Gyu-Boong Jo, Ye-Ryoung Lee, Jae-Hoon Choi, Caleb A. Christensen, Tony Hyun Kim, Joseph H. Thywissen, David E. Pritchard, Wolfgang Ketterle

Published Sep 18, 2009• 311 citations
arXivHTMLPDF

Abstract

Cold Atom Magnetism Magnetic ordering arises from the strong interactions between atoms, with its origins deeply rooted in quantum mechanics. How the ordering comes about, however, has long been a topic of debate because most condensed-matter systems are limited by a somewhat fixed parameter space. Cold atom systems, by comparison, provide the ability to tune the magnitude and sign of the atom-atom interaction, as well as the density. Jo et al. (p. 1521 ; see the Perspective by Zwerger ) exploit this flexibility to use an ensemble of ultracold fermionic atoms as a “quantum simulator” to explore the possibility of magnetic ordering. As the repulsive interaction between atoms is increased, an instability occurs in the free two-component Fermi gas (or jellium), which results in a phase transition and the ferromagnetic ordering of the atoms.

DOI
10.1126/science.1177112

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Cold Atom Magnetism Magnetic ordering arises from the strong interactions between atoms, with its origins deeply rooted in quantum mechanics. How the ordering comes about, however, has long been a topic of debate because most condensed-matter systems are limited by a somewhat fixed parameter space. Cold atom systems, by comparison, provide the ability to tune the magnitude and sign of the atom-atom interaction, as well as the density. Jo et al. (p. 1521 ; see the Perspective by Zwerger ) exploit this flexibility to use an ensemble of ultracold fermionic atoms as a “quantum simulator” to explore the possibility of magnetic ordering. As the repulsive interaction between atoms is increased, an instability occurs in the free two-component Fermi gas (or jellium), which results in a phase transition and the ferromagnetic ordering of the atoms.
We investigate ferromagnetic ordering in an itinerant ultracold atomic Fermi gas with repulsive interactions and population imbalance. In a spatially uniform system, we show that at zero temperature the transition to the itinerant magnetic phase transforms from first to second order with increasing population imbalance. Drawing on these results, we elucidate the phases present in a trapped geometry, finding three characteristic types of behavior with changing population imbalance. Finally, we outline the potential experimental implications of the findings.
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.
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.
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.
Ferromagnetism is a pure quantum correlation phenomenon, and yet it is responsible for most magnetic phenomena that we encounter in everyday life. Metallic magnets, such as iron and nickel, owe their magnetic behavior to mobile conduction electrons, whose spins can align with one another giving rise to non-zero magnetization. In the 1930s, Edmund C. Stoner first devised a simple and minimal model, where a ferromagnetic instability of the homogeneous Fermi gas is afforded only through short-range repulsive interactions. While his model captures the fundamental physics behind itinerant ferromagnetism, various additional effects in solid materials, such as orbital couplings and peculiar band dispersions, make it difficult to isolate the Stoner mechanism. Here we present our experimental investigation performed on an ultracold Fermi mixture of 6Li atoms where only genuine short-range repulsive interactions are present. Studying the stability of an artificially created ferromagnetic state, we provide a signature of a Stoner-like instability in a metastable system.
The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the N\'eel antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional ppp-wave interactions. In this strong-coupling limit, the 1D trapped Fermi gas exhibits an effective Heisenberg spin XXZXXZXXZ chain in the anisotropic ppp-wave scattering channels. For a particular ppp-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the antiferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of 40K^{40}\mathrm{K}40K atoms with very close sss-wave and ppp-wave Feshbach resonances.