Ferromagnetism of the electron gas

A. K. Rajagopal, John C. Kimball, Mahadev Banerjee

A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.

R. A. Duine, Allan H. MacDonald

Markus Holzmann, Saverio Moroni

Do electrons become ferromagnetic just because of their repulsive Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetism of delocalized electrons without lattice and band structure, the most basic model considered by Stoner, is suppressed due to many-body correlations as speculated already by Wigner, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.

D. F. Wang

Alain Messager, J. C. Trotin

András Sütö

In a recent paper by Aizenman and Lieb [Phys. Rev. Lett. 65, 1470 (1990)], it was reported that the Nagaoka ferromagnet preserves its ferromagnetic character at temperatures T>0 in any finite volume. It is shown here that at any T>0 the Nagaoka ferromagnet becomes a perfect paramagnet in the thermodynamic limit. By using an inequality for the free energy, this result is extended to the general case when the number of electrons per site goes to 1. At any T>0 the spontaneous magnetization m(T,\ensuremath{\rho}) tends to zero as the electron density \ensuremath{\rho} tends to 1. Thus, a rigorous upper bound on m(T,\ensuremath{\rho}) is obtained. The results are independent of the statistics.