A new model for the ground-state spin determination in ferromagnetics: The influence of many-electron exchange effects on the ground-state total spin in titanium and nickel

A new approximate exchange interaction operator, derived from the exact atomic second quantization formalism, has been applied to the study of the magnetic properties of atoms with spin $\text{S =}\text{1}\text{2}$ and S = 1 which obey Hund's rule. The new operator involves the effects of one-pair and two-pair electron exchanges. The one-pair exchange effects are compared with the Heisenberg model. It is shown that our model comprises the symmetry properties of the atomic wavefunction and the interaction of all electrons in the unfilled shells of two atoms, which are not considered in the Heisenberg theory. The conditions under which the new one-pair exchange effect may be used to improve the old one are pointed out. The significance of the two-pair exchange effects is discussed. It is demonstrated that, owing to the simultaneous exchange of two electron pairs, the total ground-state spin of two atoms may have intermediate values in addition to those predicted by the Heisenberg model. The importance of the interrelation between the first- and second-order effects, with respect to both sign and magnitude, is pointed out. The existence of the intermediate values, even in the case where the first order exchange integral is negative, is taken as a conjecture by which one may explain the fact that the mean magnetic moment per atom in magnetic 3d metals is not equal to the spin magnetic moment of an individual atom and accounts for the existence of magnetic ordering when the first order exchange integral is negative.