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arXiv:1704.07707 · Physical Review Letters

Unified Description of Dynamics of a Repulsive Two-Component Fermi Gas

Piotr T. Grochowski, Tomasz Karpiuk, Mirosław Brewczyk, Kazimierz Rza̧żewski

Published Nov 21, 2017• 29 citations
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Abstract

We study a binary spin mixture of a zero-temperature repulsively interacting ^{6}Li atoms using both the atomic-orbital and density-functional approaches. The gas is initially prepared in a configuration of two magnetic domains and we determine the frequency of the spin-dipole oscillations which are emerging after the repulsive barrier, initially separating the domains, is removed. We find, in agreement with recent experiment [G. Valtolina et al., Nat. Phys. 13, 704 (2017)NPAHAX1745-247310.1038/nphys4108], the occurrence of a ferromagnetic instability in an atomic gas while the interaction strength between different spin states is increased, after which the system becomes ferromagnetic. The ferromagnetic instability is preceded by the softening of the spin-dipole mode.

DOI
10.1103/physrevlett.119.215303

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We study a binary spin mixture of a zero-temperature repulsively interacting ^{6}Li atoms using both the atomic-orbital and density-functional approaches. The gas is initially prepared in a configuration of two magnetic domains and we determine the frequency of the spin-dipole oscillations which are emerging after the repulsive barrier, initially separating the domains, is removed. We find, in agreement with recent experiment [G. Valtolina et al., Nat. Phys. 13, 704 (2017)NPAHAX1745-247310.1038/nphys4108], the occurrence of a ferromagnetic instability in an atomic gas while the interaction strength between different spin states is increased, after which the system becomes ferromagnetic. The ferromagnetic instability is preceded by the softening of the spin-dipole mode.
We develop a model of a binary fermionic mixture, consisting of a large number of atoms, applicable at nonzero temperatures, in the normal phase. We use this approach to study the dynamics of degenerate Fermi systems under various perturbations. For example, we analyze the spin-dipole oscillations of a two-component fermionic mixture, demonstrating that the ferromagnetic phase shows up at a stronger repulsion between components while the temperature rises. We study as well the radial oscillations of weakly interacting repulsive Fermi gases. We obtain a good agreement with experimental data when available. Otherwise, we compare our results with the outcome of the Hartree-Fock orbital calculations done for a system with a small number of fermions.
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.
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.
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.
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.