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arXiv:cond-mat/0307063 · Physical Review A

Ferromagnetic phase transition and Bose-Einstein condensation in spinor Bose gases

Qiang Gu, Richard A. Klemm

Published Sep 25, 2003• 40 citations
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Abstract

Phase transitions in spinor Bose gases with ferromagnetic (FM) couplings are studied via mean-field theory. We show that an infinitesimal value of the coupling can induce a FM phase transition at a finite temperature always above the critical temperature of Bose-Einstein condensation. This contrasts sharply with the case of Fermi gases, in which the Stoner coupling ${I}_{s}$ cannot lead to a FM phase transition unless it is larger than a threshold value ${I}_{0}.$ The FM coupling also increases the critical temperatures of both the ferromagnetic transition and the Bose-Einstein condensation.

DOI
10.1103/physreva.68.031604

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It is shown that the ferromagnetic transition takes place always above Bose-Einstein condensation in ferromagnetically coupled spinor Bose gases. We describe the Bose ferromagnet within Ginzburg-Landau theory by a ``two-fluid'' model below Bose-Einstein condensation. Both the Bose condensate and the normal component are spontaneously magnetized. As a main result we show that spin waves in the two fluids are coupled together so as to produce only one mixed spin-wave mode in the coexisting state. The spin-wave stiffness coefficient of the mixed mode, cs{c}_{s}cs​, includes contributions from both the two phases, implying the ``two-fluid'' feature of the system. cs{c}_{s}cs​ can show a sharp bend at the Bose-Einstein condensation temperature.
The achievement in cooling alkali atomic gases, such as 87^{87}87Rb, 23^{23}23Na and 7^{7}7Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic transition occurs always above Bose-Einstein condensation and the Bose condensate is fully polarized. The low-lying collective excitations of the spinor condensate, including spin and density modes, are discussed. The spectrum of the density mode is of the Bogliubov form and the spin wave spectrum has a k2k^2k2-formed dispersion relation at long wavelengths. The spin-wave stiffness coefficient contains contribut
The properties of spin-1 Bose gases with ferromagnetic interactions in the presence of a nonzero magnetic field are studied. The equation of state and thermodynamic quantities are worked out with the help of a mean-field approximation. The phase diagram besides Bose-Einstein condensation contains a first-order transition where two values of the magnetization coexist. The dynamics is investigated with the help of the random phase approximation. The soft mode corresponding to the critical point of the magnetic phase transition is found to behave like in conventional theory.
We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature Tc{T}_{c}Tc​. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below Tc{T}_{c}Tc​ the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.