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Journal of Physics B Atomic Molecular and Optical Physics

Ferromagnetic transition in harmonically trapped Fermi gas with higher partial-wave interactions

Zongli Sun, Qiang Gu

Published Dec 16, 2016• 3 citations
Publisher

Abstract

Abstract Spontaneous ferromagnetic transition in trapped Fermi gas is studied in the presence of a higher partial-wave interaction. At the mean-field level, the ground-state energy contribution from an arbitrary partial wave is derived, with which the equilibrium density profile of each spin component can be calculated. Our results show that, in the spin- 1 2 Fermi gas, the individual repulsive d -wave interaction can induce ferromagnetic transition; while the individual repulsive or attractive p - and f -wave interactions fail. In addition, the higher partial waves can have a remarkable influence on the ferromagnetic phase induced by the s -wave interaction. The repulsive d -wave interaction and attractive p - or f -wave interactions lower the s -wave Stoner point and critical particle number, while the attractive d -wave interaction and repulsive p - or f -wave interactions increase them. In addition, our results also show that both repulsive d -wave interaction and attractive p - or f -wave interactions can enhance the ferromagnetic state induced by s -wave interaction.

DOI
10.1088/1361-6455/50/1/015302

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Abstract Spontaneous ferromagnetic transition in trapped Fermi gas is studied in the presence of a higher partial-wave interaction. At the mean-field level, the ground-state energy contribution from an arbitrary partial wave is derived, with which the equilibrium density profile of each spin component can be calculated. Our results show that, in the spin- 1 2 Fermi gas, the individual repulsive d -wave interaction can induce ferromagnetic transition; while the individual repulsive or attractive p - and f -wave interactions fail. In addition, the higher partial waves can have a remarkable influence on the ferromagnetic phase induced by the s -wave interaction. The repulsive d -wave interaction and attractive p - or f -wave interactions lower the s -wave Stoner point and critical particle number, while the attractive d -wave interaction and repulsive p - or f -wave interactions increase them. In addition, our results also show that both repulsive d -wave interaction and attractive p - or f -wave interactions can enhance the ferromagnetic state induced by s -wave interaction.
We study ferromagnetism in a repulsively interacting two-component Fermi gas in a harmonic trap. Within a local density approximation, the two components phase separate beyond a critical interaction strength, with one species having a higher density at the trap center. We discuss several easily observable experimental signatures of this transition. The mean-field release energy, its separate kinetic and interaction contributions, as well as the potential energy all depend on the interaction strength and contain a sharp signature of this transition. In addition, the conversion rate of atoms to molecules, arising from three-body collisions, peaks at an interaction strength just beyond the ferromagnetic transition point. We then go beyond the local density approximation and derive an energy functional that includes a term that depends on the local magnetization gradient and acts as a ``surface tension.'' Using this energy functional, we numerically study the energetics of some candidate spin textures that may be stabilized in a harmonic trapping potential at zero net magnetization. We find that a hedgehog state has a lower energy than an ``in-out'' domain-wall state in an isotropic trap. Upon inclusion of trap anisotropy we find that the hedgehog magnetization profile gets distorted due to the surface tension term, this distortion being more apparent for small atom numbers. We estimate that the magnetic dipole interaction does not play a significant role in this system. We consider possible implications for experiments on trapped 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K gases.
The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an effective contact interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multicomponent Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.
Spin asymmetry of ground states is studied in trapped spin-degenerate (two-component) gases of fermionic atoms with repulsive interaction between different components; and, for a large particle number, the asymmetric (collective ferromagnetic) states are shown to be stable because it can be energetically favorable to increase the Fermi energy of one component rather than increase the interaction energy between up-down components. We formulate the Thomas-Fermi equations and give algebraic methods to solve them. From the Thomas-Fermi solutions, we find three kinds of ground states in the finite system: (1) paramagnetic (spin-symmetric), (2) ferromagnetic (equilibrium), and (3) ferromagnetic (nonequilibrium) states. We present the density profiles and the critical atom numbers for these states obtained analytically, and, in ferromagnetic states, the spin asymmetries are shown to occur in the central region of the trapped gas, and increase with increasing particle number. Based on the obtained results, we discuss the experimental conditions and current difficulties in realizing the ferromagnetic states of the trapped atom gas, which should be overcome.
We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions toward ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree–Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the bare contact interaction energy and especially to the Thomas–Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a plethora of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general.
The influence of s- and p-wave interactions on trapped degenerate one- and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation, including the s- and p-wave terms of an effective contact interaction. On this basis the stability of the dilute gas against mean-field induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave scattering lengths are derived. Furthermore, the spatial separation in a two-component Fermi gas is discussed, explicit conditions for the onset of component demixing are given, and the density distributions in the separated phase are calculated. The findings are summarized in a zero-temperature phase diagram for the degenerate two-component Fermi gas. It is shown that the p-wave interaction has a significant influence on the phase diagram of the degenerate Fermi gas and causes new phenomena such as absolute stabilization against collapse and component separation. It may therefore be useful in the context of the envisioned BCS transition in trapped atomic Fermi gases.
We study spin asymmetry of the ground states for the trapped spin-degenerate (two-component) gases of the fermionic atoms in case that interparticle interaction between different spin components is repulsive. Density distributions are algebraically obtained from the Thomas–Fermi equation. We show that, for the system with a larger particle number than a critical value, the asymmetric (ferromagnetic) states are more stable than the spin-symmetric (paramagnetic) ones. The density profiles show that the spin-asymmetry occurs in the central regions of the trapped gas, and grows up with increasing particle number. We also discuss the realization of these ferromagnetic states in atom gases trapped in the optical potentials and suggest experimental conditions to perform it.