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arXiv:1001.5139 · Physical Review A

Stability of a fully magnetized ferromagnetic state in repulsively interacting ultracold Fermi gases

Xiaoling Cui, Hui Zhai

Published Apr 13, 2010• 133 citations
arXivHTMLPDF

Abstract

We construct a variational wave function to study whether a fully polarized Fermi sea of ultracold atoms is energetically stable against a single spin flip. Our variational wave function contains short-range correlations at least to the same level as Gutzwiller's projected wave function. For the Hubbard lattice model and the continuum model with pure repulsive interaction, we show that a fully polarized Fermi sea is generally unstable even for infinite repulsive strength. By contrast, for a resonance model, the ferromagnetic state is possible if the $s$-wave scattering length is positive and sufficiently large and the system is prepared to be orthogonal to the molecular bound state. However, we cannot rule out the possibility that more exotic correlations can destabilize the ferromagnetic state.

DOI
10.1103/physreva.81.041602

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We construct a variational wave function to study whether a fully polarized Fermi sea of ultracold atoms is energetically stable against a single spin flip. Our variational wave function contains short-range correlations at least to the same level as Gutzwiller's projected wave function. For the Hubbard lattice model and the continuum model with pure repulsive interaction, we show that a fully polarized Fermi sea is generally unstable even for infinite repulsive strength. By contrast, for a resonance model, the ferromagnetic state is possible if the sss-wave scattering length is positive and sufficiently large and the system is prepared to be orthogonal to the molecular bound state. However, we cannot rule out the possibility that more exotic correlations can destabilize the ferromagnetic state.
We obtain the best upper bound for the ground-state energy of a system of chargeless fermions of mass m, spin s=1/2 , and magnetic moment mus[over ] as a function of its density in the fully spin-polarized Hartree-Fock determinantal state, specified by a prolate spheroidal plane-wave single-particle occupation function n_(k[over ]) , by minimizing the total energy E at each density with respect to the variational spheroidal deformation parameter beta(2),0< or =beta(2)< or =1 . We find that at high densities, this spheroidal ferromagnetic state is the most likely ground state of the system, but it is still unstable towards the infinite-density collapse. This optimized ferromagnetic state is shown to be a stable ground state of the dipolar system at high densities, if one has an additional repulsive short-range hardcore interaction of sufficient strength and nonvanishing range.
We address the phase of a highly polarized Fermi gases across a narrow Feshbach resonance starting from the problem of a single down-spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron-to-pairing transition will take place on the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For the pairing phase, we find the critical strength of the repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with sss-wave BCS superfluidity at large Zeeman fields, which is a remarkable property absent in conventional BCS superconductors (or fermion-pair superfluids).
Using continuous-space quantum Monte Carlo methods, we investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of periodic potentials that describe the effect of a simple-cubic optical lattice. Simulations are performed with balanced and with imbalanced components, including the case of a single impurity immersed in a polarized Fermi sea (repulsive polaron). For an intermediate density below half filling, we locate the transitions between the paramagnetic, and the partially and fully ferromagnetic phases. As the intensity of the optical lattice increases, the ferromagnetic instability takes place at weaker interactions, indicating a possible route to observe ferromagnetism in experiments performed with ultracold atoms. We compare our findings with previous predictions based on the standard computational method used in material science, namely density functional theory, and with results based on tight-binding models.
The two- and three-body correlation functions of the ground state of an optically trapped ultracold spin-12\frac{1}{2}21​ Fermi gas (SFG) in a tight waveguide [one-dimensional (1D) regime] are calculated in the plane of even- and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D ppp-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D sss-wave scattering. The calculations are based on the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg'' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas, a spin-aligned 1D Fermi gas with infinitely attractive ppp-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.
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.
We investigate the phase diagram of a two-component repulsive Fermi gas at T=0 by means of quantum Monte Carlo simulations. Both purely repulsive and resonant attractive model potentials are considered in order to analyze the limits of the universal regime where the details of interatomic forces can be neglected. The equation of state of both balanced and unbalanced systems is calculated as a function of the interaction strength and the critical density for the onset of ferromagnetism is determined. The energy of the strongly polarized gas is calculated and parametrized in terms of the physical properties of repulsive polarons, which are relevant for the stability of the fully ferromagnetic state. Finally, we analyze the phase diagram in the interaction-polarization plane under the assumption that only phases with homogeneous magnetization can be produced.