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arXiv:1301.3163 · Physical Review Letters

Itinerant Ferromagnetism in a Polarized Two-Component Fermi Gas

Pietro Massignan, Zhenhua Yu, Georg M. Bruun

Published Jun 4, 2013• 52 citations
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Abstract

We analyze when a repulsively interacting two-component Fermi gas becomes thermodynamically unstable against phase separation. We focus on the strongly polarized limit, where the free energy of the homogeneous mixture can be calculated accurately in terms of well-defined quasiparticles, the repulsive polarons. Phase diagrams as a function of polarization, temperature, mass imbalance, and repulsive polaron energy, as well as scattering length and range parameter, are provided. We show that the lifetime of the repulsive polaron increases significantly with the interaction range and the mass of the minority atoms, raising the prospects of detecting the transition to the elusive itinerant ferromagnetic state with ultracold atoms.

DOI
10.1103/physrevlett.110.230401

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We analyze when a repulsively interacting two-component Fermi gas becomes thermodynamically unstable against phase separation. We focus on the strongly polarized limit, where the free energy of the homogeneous mixture can be calculated accurately in terms of well-defined quasiparticles, the repulsive polarons. Phase diagrams as a function of polarization, temperature, mass imbalance, and repulsive polaron energy, as well as scattering length and range parameter, are provided. We show that the lifetime of the repulsive polaron increases significantly with the interaction range and the mass of the minority atoms, raising the prospects of detecting the transition to the elusive itinerant ferromagnetic state with ultracold atoms.
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.
We employ radio-frequency spectroscopy to investigate a polarized spin mixture of ultracold ^{6}Li atoms close to a broad Feshbach scattering resonance. Focusing on the regime of strong repulsive interactions, we observe well-defined coherent quasiparticles even for unitarity-limited interactions. We characterize the many-body system by extracting the key properties of repulsive Fermi polarons: the energy E_{+}, the effective mass m^{*}, the residue Z, and the decay rate Γ. Above a critical interaction, E_{+} is found to exceed the Fermi energy of the bath, while m^{*} diverges and even turns negative, thereby indicating that the repulsive Fermi liquid state becomes energetically and thermodynamically unstable.
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.
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.
We report a fully analytical description of zero-temperature itinerant ferromagnetism in repulsive SU(N) Fermi gases with arbitrary mass imbalance among components. Using perturbation theory in the gas parameter x = kFa0, with kF the Fermi momentum and a0 the s-wave scattering length, we derive the second-order energy for arbitrary spin polarization and arbitrary mass ratio. Our main result is a closed analytic expression for the beyond-mean-field correction in mixtures with unequal masses. This analytical result extends the theory of dilute Fermi gases beyond the mass-balanced case and provides a compact equation of state for multicomponent mixtures. We show that mass imbalance breaks the paramagnetic symmetry already in the non-interacting limit, favors the occu pation of heavier components, and lowers the interaction strength required to reach a fully polarized state. For S = 1/2, the system evolves continuously from a mass-induced partially polarized state to full ferromagnetism. For larger spins, distinct mass distributions generate qualitatively differ ent polarization paths, including smooth and discontinuous sequences. Our results identify mass imbalance as a powerful control tool for magnetic ordering in ultracold Fermi mixtures.
We study the extremely polarized two-component Fermi gas with a mass imbalance in the strongly interacting regime. Specifically we focus on the experimentally available mixture of 6{}^{6}6Li and 40{}^{40}40K atoms. In this regime spin polarons, i.e., dressed minority atoms, form. We consider the spectral function for the minority atoms, from which the lifetime and the effective mass of the spin polaron can be determined. Moreover, we predict the radio-frequency (rf) spectrum and the momentum distribution for the spin polarons for experiments with 6{}^{6}6Li and 40{}^{40}40K atoms. Subsequently we study the relaxation of the motion of the Fermi polaron due to spin drag.