Collective ferromagnetism in two-component Fermi-degenerate gas trapped in a finite potential

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.