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arXiv:0810.1094 · Physical Review B

Thermodynamic properties of the itinerant-boson ferromagnet

Chengjun Tao, Peilin Wang, Jihong Qin, Qiang Gu

Published Oct 3, 2008• 12 citations
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Abstract

Thermodynamics of a spin-1 Bose gas with ferromagnetic interactions is investigated via the mean-field theory. It is apparently shown in the specific-heat curve that the system undergoes two phase transitions, the ferromagnetic transition and Bose-Einstein condensation, with the Curie point above the condensation temperature. Above the Curie point, the susceptibility fits the Curie-Weiss law perfectly. At a fixed temperature, the reciprocal susceptibility is also in a good linear relationship with the ferromagnetic interaction.

DOI
10.1103/physrevb.78.134403

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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 investigate the low-temperature behavior of the integrable one-dimensional two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility, and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat ${c}_{v}\ensuremath{\sim}{T}^{1∕2}$ and the susceptibility $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.
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On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and δ-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like T at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.
We investigate the thermodynamics of a spin-1 Bose gas with fixed magnetization including the quadratic Zeeman energy shift. Our calculations are based on the grand canonical description for the ideal gas and the classical field approximation for atoms with ferromagnetic and antiferromagnetic interactions. We confirm the occurrence of a double phase transition in the system that takes place due to two global constraints. We show analytically for the ideal gas how critical temperatures and condensed fractions are changed by a nonzero magnetic field. The interaction strongly affects the condensate scenario below the second critical temperature. The effect imposed by interaction energies becomes diminished in high magnetic fields where condensation of both ferromagnetic and antiferromagnetic atoms agrees with the ideal gas results.