Spin-deviation theory of ferromagnetism I general theory

Abstract

Synopsis A theory is developed of the properties of a ferromagnetic spin system of the Heisenberg exchange type for spins 1/2, in which the spin deviations (wrong spins) rather than the spin waves constitute the basic elements of the theory. It is shown that because of an inherent difficulty in the usual spin-wave formalism, this formalism cannot be used if one wants to go beyond the Bloch spin-wave approximation. The spin-deviation theory is therefore derived directly from the Hamiltonian of the spin system by introducing the wave functions describing the motion of the spin deviations through the lattice. The wave equations satisfied by these wave functions admit of a simple interpretation in terms of kinetic and potential energy operators, and this enables one to introduce the concept of a gas of spin deviations interacting according to a simple, additive potential. A general relation is derived between the partition function of this spin-deviation gas and the spin system. The ideal-gas law which is obtained by neglecting the interaction between the spin deviations, leads to the Bloch spin-wave approximation. The interaction between the spin deviations can be investigated by applying the standard methods used in the theory of ordinary gases and liquids to the spin-deviation gas. The application of the virial expansion is discussed in detail, and it is shown what this expansion implies for the spin system. Some other applications of the spin-deviation theory are also discussed.