Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in presence of a hard core potential:A stable ferromagnetic state

TL;DR

This paper uses Hartree-Fock variational methods to demonstrate the possibility of a stable high-density ferromagnetic state in a system of chargeless fermions with magnetic moments, stabilized by short-range repulsion.

Contribution

It introduces a new Hartree-Fock variational bound showing a stable ferromagnetic state at high densities with spheroidal occupation, considering hard core interactions.

Findings

Ferromagnetic state has lower energy than paramagnetic state at high densities.

Hard core repulsion can prevent collapse and stabilize the system.

Stable ferromagnetic state exists when hard core and dipole interactions are sufficiently balanced.

Abstract

We use different types of determinantal Hartree-Fock (HF) wave functions to calculate variational bounds for the ground state energy of spin-half fermions in volume V_0, with mass m, electric charge zero, and magnetic moment mu, which are interacting through long range magnetic dipole-dipole interaction. We find that at high densities when the average inter particle distance r_0 becomes small compared to the magnetic length r_m, a ferromagnetic state with spheroidal occupation function, involving quadrupolar deformation, gives a lower energy compared to the variational energy for the uniform paramagnetic state. This HF variational bound to the ground state energy turns out to have a lower energy than our earlier calculation in which instead of a determinantal wavefunction we had used a positive semi-definite single particle density matrix operator whose eigenvalues, having quadrupolar deformation, were allowed to take any value from 0 to 1. This system is of course still unstable towards infinite density collapse, but we show here explicitly that a suitable short range repulsive (hard core) interaction of strength U_0 and range a can stop this collapse.The existence of a stable high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of hard-core and magnetic dipole coupling constants is not very small compared to 1.