Criterion for the Ferromagnetism of Hard Sphere Fermi Liquid. II

Abstract

The spin polarization and the ensuring ferromagnetism of hard sphere Fermi liquid have been studied by several authors. In particular,. recent works correct to the second order in (b/ J.F) show that the system will become partially ferromagnetic if b/J.F>0.168. 0 • 2 > Here b is the diameter of the hard sphere and J.F is the Fermi wave length. It has now been possible to evaluate the energy of the system with arbitrary degree of spin polarization. This evaluation is also correct to order (b/ J.F) 2 and the result shows that the system will become fully ferromagnetic (saturated spontaneous magnetization) if b/ J.F>O.l78. The following is a brief account of this evaluation. The energy of the system correct to order b 2 is 3 > Here tJ is the volume of the system, the indices i, j and k specify momenta and spin projections, and the n's are quasi-particle occupation numbers. The factor Qi.J is the projection operator for the pair (i,j) with antiparallel spins. The ground state energy of the system consisting of N (1 + r) /2 quasi-particle with up spin and the N(l-r) /2 quasi-particles .. with down spin is E() _ 3NpF 2 [ 1 (5 5) r-10m 2 P+ +P