The spin-polarized ferromagnetic state of a cold Fermi gas is investigated for interacting and noninteracting charge-neutral and $\ensuremath{\beta}$-equilibrated gases. The standard minimal couplings between the magnetic field and the fermions' charges and magnetic dipole moments define the fermions' interaction with the magnetic field. Assuming a variable coupling strength between the magnetic field and the fermion (baryon) dipole moments, it is shown that a ferromagnetized state can be achieved that corresponds to a lower energy spin-polarized state with a magnetic field entirely due to the gas's magnetic response. We find that, depending on the density, a very large increase in the baryon dipole moments is needed to achieve this ferromagnetized state. While the required increase seems unlikely, the induced magnetic field is of the order $\ensuremath{\approx}{10}^{17}$ gauss. Furthermore, while externally magnetized Fermi gases have an anisotropic pressure, the pressure of the ferromagnetized gas is completely isotropic and in the thermodynamically preferred magnetized state.
An interacting electron liquid in two (2D) and three (3D) dimensions may undergo a paramagnetic-to-ferromagnetic quantum spin polarization transition at zero applied magnetic field, driven entirely by exchange interactions, as the system density (
n) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field (
B), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, $B\ensuremath{\sim}{n}^{p}$. For
p<pc, with
pc=1(2/3) in
2(3)D, the system remains either fully spin polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin polarized or fully spin polarized. However, for
p>pc, the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second-order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first-order transition back to the fully spin-polarized phase again with a single Fermi surface.
We investigate the ground-state properties of a one-dimensional spin-1/2 fermionic atoms interacting through the attractive δ-function potential in an external magnetic field. By the thermal Bethe ansatz method, the integral equations for the dressed energies are formulated. Those integral equations at zero-temperature are solved in the power series forms of rapidity and momentum for both strong and weak coupling cases. The magnetization as a function of the coupling constant and the external field is also obtained explicitly. Based on the analytic results, quantum phase transitions are identified among three phases, an unpolarized fully paired state, a fully polarized normal ferromagnetic state and a mixed state of paired and unpaired atoms.
We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.
We examine the superfluid and collapse instabilities of a quasi-two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipole-dipole interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii-Kosterlitz-Thouless temperature as a function of the dipole angle.
We study the spinor properties of S = 3 (52)Cr condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.