N.22 The mechanism of ferromagnetism

It should be noted that in solids, not just spatial anti­symmetry, but also symmetry can give rise to spin alignment. In particular, in many ferrites, there is an opposite spin coupling between the iron atoms and the oxygen ones. If two iron atoms are opposite in spin to the same oxygen atom, it implies that they must have aligned spins even if their electrons do not interact directly.

It comes as somewhat a surprise to discover that in this time of high-temperature super­conductors, the mechanism of plain old ferro­magnetism is still not understood that well if the magnetic material is a conductor, such as a piece of iron.

For a conductor, the description of the exclusion effect should really be at least partly in terms of band theory, rather than electrons localized at atoms. More specifi­cally, Aharoni [2, p. 48] notes “There is thus no doubt in anybody’s mind that neither the itinerant electron theory nor the localized electron one can be considered to be a complete picture of the physical reality, and that they both should be combined into one theory.”

Sproull notes that in solid iron, most of the 4s electrons move to the 4d bands. That reduces the magnet­ization by reducing the number of unpaired electrons.

While Sproull [40, p. 282] in 1956 describes ferro­magnetism as an inter­action between electrons localized at neighboring atoms, Feynman [21, p. 37-2] in 1965 notes that calcul­ations using such a model produce the wrong sign for the inter­action. According to Feynman, the inter­action is thought to occur with [4s] conduction band electrons acting as inter­mediaries. More recently, Aharoni [2, p. 44] notes: “It used to be stated [...] that nobody has been able to compute a positive exchange integral for Fe, and a negative one for Cu [...]. More modern compu­tations [...] already have the right sign, but the magnitude of the computed exchange still differs considerably from the experi­mental value. Improving the techniques [...] keeps improving the results, but not sufficiently yet.”

Batista, Bona, and Gubernatis note that “After seven decades of intense effort we still do not know what is the minimal model of itinerant ferro­magnetism and, more importantly, the basic mechanism of ordering.” (Phys Rev Let 88, 2002, 187203-1) and “Even though the transition metals are the most well studied itinerant ferro­magnets, the ultimate reason for the stabil­ization of the FM phase is still unknown.” (Phys Rev B 68, 2003, 214430-11)