Stability of the high-density ferromagnetic ground state of a chargeless, magnetic-dipolar, quantum Fermi liquid

We obtain the best upper bound for the ground-state energy of a system of chargeless fermions of mass m, spin s=1/2, and magnetic moment mu(s) over right arrow as a function of its density in the fully spin-polarized Hartree-Fock determinantal state, specified by a prolate spheroidal plane-wave single-particle occupation function n(up arrow)((k) over right arrow), by minimizing the total energy E at each density with respect to the variational spheroidal deformation parameter beta(2),0 <=beta(2)<= 1. We find that at high densities, this spheroidal ferromagnetic state is the most likely ground state of the system, but it is still unstable towards the infinite-density collapse. This optimized ferromagnetic state is shown to be a stable ground state of the dipolar system at high densities, if one has an additional repulsive short-range hardcore interaction of sufficient strength and nonvanishing range.