Collective electron ferronmagnetism

Abstract

I n t r o d u c t i o nThe essential contribution of Heisenberg to the theory of ferromagnetism was in showing th a t those effects which had been correlated by means of the formal molecular field hypothesis of Weiss could be interpreted as arising from interchange interaction between electrons in atoms, of the same type as th a t involved in the form ation of homopolar molecules. The Heisenberg m ethod of approach has, however, proved in m any ways less convenient in the detailed tre a tm e n t of ferrom agnetism th a n the method initiated by Bloch for the theory of m etallic properties generally, in which possible energy states are derived for electrons treated as waves travelling through the whole crystal. The first approxim ation in this collective electron treatm en t is th a t of free electrons, for which the energy is purely kinetic, the num ber of states per un it energy range then being proportional to the square root of the energy. The effect of the periodic field of the lattice is to modify the distribution of states, giving rise to a series of energy bands, separate or overlapping. E laborate calculation is necessary to determ ine the form of these bands w ith any precision, though in general near the bottom of a band the energy density of states depends on the energy in the same way as for free electrons, b u t w ith a different pro portionality factor; this holds also near the top of a band, the energy being m easured downwards from th a t limit. The salient characteristics of metals depend on the electrons in unfilled bands. In particular, in the ferro m agnetic m etals, iron, cobalt and nickel, the ferromagnetism may be a ttrib u te d to the electrons in the partially filled band corresponding to the d electron states in the free atom s. The exchange interaction is such th a t, a t low tem peratures, instead of the electrons occupying the lowest states in balanced pairs, there is an excess of electrons w ith spins pointing in one direction, giving rise to a spontaneous m agnetization. The d,ecrease of energy due to the exchange effect w ith increase in the num ber of excess parallel spins is accompanied by an increase due to the electrons moving to states of higher energy in the band. The equilibrium magnetization [ 372 ] on May 12, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from

Tunneling magnetothermopower in magnetic tunnel junctions

“…For this purpose we use Slonczewski's model [32,36], which describes the ferromagnetic electrodes using the Stoner model [37], and the tunneling barrier by means of a rectangular potential. This model also assumes that the energy and transverse modes of the electrons are conserved.…”

Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

“…For instance, for a strongly repulsively in-teracting Fermi gas, itinerant ferromagnetic transition is expected at low temperatures [25][26][27][28][29][30]. However, the critical transition temperature is yet to be determined.…”

Magnetic ordering of itinerant systems: the role of kinetic interactions

“…The largest interaction in this model is the on-site Coulomb repulsion, U = (i, i|1/r|i, i) , where i is the lattice site index. In the mean-field approximation, the Hubbard model leads to the well-known Stoner model for magnetism [2]. The Coulomb constant U coming out of the Stoner condition for creating ferromagnetism is large, i.e.…”