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Zeitschrift für Physik A Hadrons and Nuclei

Self-consistent approximations for itinerant ferromagnets above the phase transition point

U. Brandt, W. Pesch, Ludwig Tewordt

Published Apr 1, 1970• 24 citations
Publisher
DOI
10.1007/bf01399298

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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 is one of the most-studied quantum phase transitions, the transition point and the nature of this phase transition being widely discussed. In dilute Fermi liquids, this analysis has been carried out up to second order in the gas parameter, where the results for any spin degeneracy are universal in terms of only the s -wave scattering length a 0 . We extend this analysis to third order, where energies depend not only on a 0 , but also on the s -wave effective range r 0 and the p -wave scattering length a 1 . The introduction in the theory of these new parameters changes the transition point, with respect to the second-order estimation, and also can modify the nature of the phase transition itself. We analyze these interaction effects on the phase transition for different spin values. The emerging phase diagram shows that the type of ferromagnetic transition changes dramatically as a function of r 0 and a 1 and, importantly, that this classification is not solely determined by the spin value, as happens at second order.