Antiferromagnetism

Marshall, W (1954). Antiferromagnetism. University of Birmingham. Ph.D.

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Abstract

After a brief description of antiferromagnetism the spin wave theory of Kubo (1952) and Ziman (1952 I, II. 1955), which is the most important trestment of the problem to date, is shown to be open to many criticisms. Following this, the ground state of a lattice with one electron per atom and antiferromagnetic interactions between nearest neighbours only is examined by a variational method. The calculation involves a statistical problem which is shown to be exactly equivalent to the Ising ferromagnetic problem with a magnetic field applied. This cannot be solved exactly, except in the one-dimensional case, and so the ’first shell’ Bethe-Peierls method is used to solve it approximately.

In complete contradiction with the Kubo (1953) variational calculation, which starts from the spin wave theory, it is concluded that all lattices have disordered ground states when only nearest neighbour interactions are present. However, for two and three dimensional lattices the energy difference between some ordered and the best disordered state is so small that this conclusion might be changed if a better solution of the statistical problem than can be given by the ’first shell’ Bethe-Peierls method, were obtained. It seems more probable, however, that this better calculation will confirm our conclusion and this suggests that a necessary condition for antiferromagnetism is that the next nearest neighbour interactions be ferromagnetic, and that when both the nearest and next nearest interactions are antiferromagnetic, weak paramagnetism will result.

The attached reprint, ‘Inelastic magnetic Scattering of neutrons from a Ferromagnetic Crystal’ consists of a calculation following Moorhouse (1951) but assuming two electrons (instead of one) per atom as is more appropriate for iron, which has a meon number of 2.2 electrons per atom.

Type of Work:	Thesis (Doctorates > Ph.D.)
Award Type:	Doctorates > Ph.D.
College/Faculty:	Faculties (to 1997) > Faculty of Science
School or Department:	Department of Mathematical Physics
Funders:	Other
Other Funders:	Department of Scientific and Industrial Research
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
URI:	http://etheses.bham.ac.uk/id/eprint/17388

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