Phase Diagram of a Spin-Orbit Coupled Dipolar Fermi Gas at T = 0 K^*

Abstract

We study a homogeneous two-component dipolar Fermi gas with 1D spin-orbit coupling (SOC) at zero temperature and find that the system undergoes a transition from the paramagnetic phase to the ferromagnetic phase under suitable dipolar interaction constant λ d, SOC constant λ SOC and contact interaction constant λ s. This phase transition can be of either 1st order or 2nd order, depending on the parameters. Near the 2nd-order phase transition, the system is partially magnetized in the ferromagnetic phase. With SOC, the ferromagnetic phase can even exist in the absence of the contact interaction. The increase in dipolar interaction, SOC strength, and contact interaction are all helpful to stabilize the ferromagnetic state. The critical dipolar interaction strength at the phase transition can be reduced by the increase in SOC strength or contact interaction. Phase diagrams of these systems are obtained.

Itinerant ferromagnetism of a dipolar Fermi gas with Raman-induced spin-orbit coupling

“…The energy of Raman coupling part takes the form of ΩV k 3 F t whose second derivative to n is zero thus also making no contribution to compressibility. As for the intermediate region, Raman coupling term equals to an x-direction exerted magnetic field and doesn't influence the intrinsic unstable properties as we have argued in my previous paper [51] that a momentumdependent magnetic field in z direction doesn't change the unstable region.…”

“…Itinerant ferromagnetism induced by long-range and anisotropic dipole-dipole interaction (DDI) has been less investigated, by contrast, many unconventional quantum phases such as the supersolidity [39], charge and spin density waves [40,41] were predicted in polar molecules 40 K 87 Rb [42][43][44][45], 23 Na 40 K [46] and magnetic dipolar 161 Dy [47]. Apart from giving rise to the exhibition of exotic quantum phases, dipolar interaction also changed the shape of a spherical Fermi surface into a distorted one [48][49][50][51][52] and caused a structural second-order ferromagnetism transition [50,51].…”

Ferromagnetic transition of a spin–orbit coupled dipolar Fermi gas at finite temperature*

“…[36] When 1D SOC is added to a two-component dipolar Fermi gas it shows in our previous work that the system undergoes a 1st-order and 2nd-order transition from a paramagnetic state to a ferromagnetic state at zero temperature. [37] In this paper we investigate the spin-orbit coupled dipolar Fermi system at finite temperature using the self-consistent Hartree-Fock approximation to determine the ferromagnetic transition temperature and finitetemperature phase diagram.…”

“…The Hamiltonian in the Hartree-Fock approximation can only be diagonalized self-consistently when the magnetization appears in the SOC direction. The SOC enhances ferromagnetism in the presence of the dipolar interaction, [37] which can be seen from the energy difference between the fully magnetized state and the paramagnetic state. With and without SOC, the dipolar interaction energy is the same in the fully magnetized state.…”

“…In a single component dipolar Fermi system at zero temperature, Fermi surface can be elongated along the polarization direction [38,39] and in a two-component system, Fermi surfaces of spin-up and spin-down can be one elongated and one stretched or both elongated. [36,37] To characterize Fermi surfaces at finite temperature, we introduce deformation parameters α In the experimental system of dipolar 161 Dy with SOC, [24] the experimental parameters are given by λ SOC ≈ 0.6, λ d ≈ 0.02 with density of 10 14 cm −3 , and λ T ranges from 0.1 to 0.4. In the absence of the s-wave contact interaction, the system is in the normal state at zero temperature according to our results.…”