Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0504459 · Physical Review Letters

Itinerant Ferromagnetism in an Ultracold Atom Fermi Gas

R. A. Duine, Allan H. MacDonald

Published Nov 29, 2005• 147 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.95.230403

Related papers

Exchange interactions and itinerant ferromagnetism in ultracold Fermi gases

E. Vermeyen, Carlos A. R. Sá de Melo, Jacques Tempere

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.

arXiv:1511.04502•Physical Review A•Aug 31, 2018•8 citations

Mean-field study of itinerant ferromagnetism in trapped ultracold Fermi gases: Beyond the local-density approximation

Hang Dong, Hui Hu, Xia-Ji Liu +1 more

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.

arXiv:1004.5443•Physical Review A•Jul 21, 2010•12 citations

Itinerant ferromagnetism in dilute SU(N) Fermi gases

Jordi Pera, J. Casulleras, Jordi Boronat

We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of previous results that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.

arXiv:2205.13837•SciPost Physics•Mar 17, 2023•10 citations

Itinerant ferromagnetism in ultracold Fermi gases

H. Heiselberg

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.

arXiv:1012.4569•Physical Review A•May 31, 2011•22 citations

Itinerant ferromagnetism in SU(N)-symmetric fermi gases at finite temperature: first order phase transitions and time-reversal symmetry

Chen-How Huang, Miguel A. Cazalilla

Abstract At temperatures well below the Fermi temperature T F , the coupling of magnetic fluctuations to particle-hole excitations in a two-component Fermi gas leads to non-analytic corrections in the renormalized free energy and makes the transition to itinerant ferromagnetism first order. On the other hand, despite that larger symmetry often introduces larger degeneracies in the low-lying states, here we show that for a Fermi gas with SU(N > 2)-symmetry in three space dimensions the ferromagnetic phase transition is first order in agreement with the predictions of Landau’s mean-field theory in its minimal formulation, which contains a cubic term in the free-energy (Cazalilla et al 2009 New J. Phys. 11 103033). By performing unrestricted Hartree–Fock calculations for an SU(N > 2)-symmetric Fermi gas with short range interactions, we find the order parameter undergoes a finite jump across the transition. In addition, for SU(N > 2) we do not observe any tri-critical point up to temperatures T ≃ 0.5 T F , for which the thermal smearing of the Fermi surface and thermal fluctuations are substantial. Going beyond mean-field theory, we find that the coupling of magnetic fluctuations to particle-hole excitations makes the transition more abrupt and further enhances the tendency of the gas to become fully polarized for smaller values of N and the gas parameter k F a s . In our study, we also clarify the role of time reversal symmetry in the microscopic Hamiltonian and obtain the temperature dependence of Tan’s contact. For the latter, the presence of the tri-critical point for N = 2 leads to a more pronounced temperature dependence around the transition than for SU(N > 2)-symmetric gases. Although the results are obtained for a microscopic model relevant to ultracold atomic gases, they may also apply to models of solid state systems with SU(N > 2) symmetry provided Coulomb interactions are sufficiently well screened.

arXiv:2211.12882•New Journal of Physics•May 25, 2023•8 citations

Effect of three-body loss on itinerant ferromagnetism in an atomic Fermi gas

G. J. Conduit, Ehud Altman

A recent experiment has provided tentative evidence for itinerant ferromagnetism in an ultracold atomic gas. However, the interpretation of the results is complicated by significant atom losses. We argue that during the loss process the system gradually heats up but remains in local equilibrium.To quantify the consequences of atom loss on the putative ferromagnetic transition we adopt an extended Hertz-Millis theory. The losses damp quantum fluctuations, thus increasing the critical interaction strength needed to induce ferromagnetism and revert the transition from being first order to second order. This effect may resolve a discrepancy between the experiment and previous theoretical predictions. We further illuminate the impact of loss by studying the collective spin excitations in the ferromagnet. Even in the fully polarized state, where loss is completely suppressed, spin waves acquire a decay rate proportional to the three-body loss coefficient.

arXiv:0911.2839•Physical Review A•Apr 20, 2011•20 citations
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.
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.
We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of previous results that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.
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.
Abstract At temperatures well below the Fermi temperature T F , the coupling of magnetic fluctuations to particle-hole excitations in a two-component Fermi gas leads to non-analytic corrections in the renormalized free energy and makes the transition to itinerant ferromagnetism first order. On the other hand, despite that larger symmetry often introduces larger degeneracies in the low-lying states, here we show that for a Fermi gas with SU(N > 2)-symmetry in three space dimensions the ferromagnetic phase transition is first order in agreement with the predictions of Landau’s mean-field theory in its minimal formulation, which contains a cubic term in the free-energy (Cazalilla et al 2009 New J. Phys. 11 103033). By performing unrestricted Hartree–Fock calculations for an SU(N > 2)-symmetric Fermi gas with short range interactions, we find the order parameter undergoes a finite jump across the transition. In addition, for SU(N > 2) we do not observe any tri-critical point up to temperatures T ≃ 0.5 T F , for which the thermal smearing of the Fermi surface and thermal fluctuations are substantial. Going beyond mean-field theory, we find that the coupling of magnetic fluctuations to particle-hole excitations makes the transition more abrupt and further enhances the tendency of the gas to become fully polarized for smaller values of N and the gas parameter k F a s . In our study, we also clarify the role of time reversal symmetry in the microscopic Hamiltonian and obtain the temperature dependence of Tan’s contact. For the latter, the presence of the tri-critical point for N = 2 leads to a more pronounced temperature dependence around the transition than for SU(N > 2)-symmetric gases. Although the results are obtained for a microscopic model relevant to ultracold atomic gases, they may also apply to models of solid state systems with SU(N > 2) symmetry provided Coulomb interactions are sufficiently well screened.
A recent experiment has provided tentative evidence for itinerant ferromagnetism in an ultracold atomic gas. However, the interpretation of the results is complicated by significant atom losses. We argue that during the loss process the system gradually heats up but remains in local equilibrium.To quantify the consequences of atom loss on the putative ferromagnetic transition we adopt an extended Hertz-Millis theory. The losses damp quantum fluctuations, thus increasing the critical interaction strength needed to induce ferromagnetism and revert the transition from being first order to second order. This effect may resolve a discrepancy between the experiment and previous theoretical predictions. We further illuminate the impact of loss by studying the collective spin excitations in the ferromagnet. Even in the fully polarized state, where loss is completely suppressed, spin waves acquire a decay rate proportional to the three-body loss coefficient.