Heisenberg's model of ferro- and antiferromagnetism

Author links open overlay panelRyoichiKikuchi12‡

a

Massachusetts Institute of Technology, Cambridge, Massachusetts USA

b

Armour Research Foundation of Illinois Institute of Technology, Chicago, Illinois USA

Received 30 December 1957, Available online 24 September 2004.

Abstract

Heisenberg's model of ferromagnetism, which is better than the Ising model in taking account of the exchange coupling of electrons, is treated for various lattices, extending the author's treatment of the Ising model reported previously. The first approximation using a pair of orbitals as the fundamental cluster gives the same results as those obtained by Yvon, Nakamura, and Kastelein and van Kranendonk based on different approaches. In the second approximations, ferromagnetic states appear only for the three-dimensional lattices. The anti-Curie point does not appear, but difficulties still remain for low temperatures. It is shown that the same technique can be applied to the case of spin one and also to antiferromagnetism.

https://sci-hub.tw/https://doi.org/10.1016/0003-4916(58)90035-6