Antiferromagnetism

Abstract

The familiar Heisenberg theory of ferromagnetism in the 3d transition metals iron, cobalt and nickel, rests on the assumption of a positive exchange integral between neighbouring ions, since ferromagnetism is not possible in cases where this integral is negative (` antiferromagnetic '). The idea that the remaining non-ferromagnetic members of the 3d series (Sc, Ti, V, Cr, Mn) therefore have negative exchange integrals led to a theoretical study of the properties of antiferromagnetic systems. Néel was the first to show that such a system has a critical temperature, T_c, below which the atomic moments are arranged alternately parallel and antiparallel. Above T_c the moments are disordered, as in a ferromagnetic above its Curie temperature. The theory was later extended by Van Vleck and it then became apparent that the antiferromagnetic model closely fitted a number of simple compounds of the transition metals (e.g. CrSb, MnO, MnF₂). These early developments, which had occurred by the first years of the war, are described in § § 1 and 2. Particular attention is given to Van Vleck's theory, as this forms a starting point for much subsequent work. In § 3 later experimental studies of antiferromagnetic compounds are reviewed, especial attention being paid to the results obtained by the methods of neutron diffraction. Measurements of magnetic anisotropy and of the slight distortions which occur in many antiferromagnetic lattices on ordering, are also described in detail, and the theoretical significance of the observations is discussed incidentally. The theoretical attempts to improve the Van Vleck theory, both by extending the model and by using more accurate statistics, are considered in § 4. This section also includes a discussion of the superexchange mechanism, which accounts for the observation that the strongest interactions in, say, MnO are between next nearest neighbouring Mn ions and not between nearest neighbours as one might expect. The final section (§ 5) contains a brief survey of the present status of the non-ferromagnetic transition metals themselves; it is shown how the recent neutron diffraction studies by Shull and Wilkinson favour a collective electron description, rather than the sort of description which is successful for the antiferromagnetic compounds. The way to extend the present collective electron theory so that it may give antiferromagnetic ordering has recently been indicated by Slater. The Report concludes with a table listing experimental papers on antiferromagnetism by compound and by the property studied. This should be useful since it is often difficult to trace the experimental work on a particular compound of interest.