5 - Ferromagnetism and exchange

Summary

Order, order, order!

Ferromagnetism and the Curie temperature were explained by Weiss in terms of a huge internal ‘molecular field’ proportional to the magnetization. The theory is applicable both to localized and delocalized electrons. No such magnetic field really exists, but it is a useful way of approximating the effect of the interatomic Coulomb interaction in quantum mechanics, which Heisenberg described by the Hamiltonian ℋ = −2JS₁ · S₂, where S₁ and S₂ are operators describing the localized spins on two adjacent atoms. When J > 0, ferromagnetic exchange leads to ferromagnetic order in three dimensions. Spin waves are the low-energy excitations of the exchange-coupled magnetic lattice. In the delocalized electron picture, a ferromagnet has spontaneously spin-split energy bands. The density of ↑ and ↓ states is calculated using spin-dependent density functional theory. Important physical phenomena associated with ferromagnetism are discussed in this chapter, including magnetic anisotropy and, magnetoelastic, magneto-optic and magnetotransport effects.

The characteristic feature of a ferromagnet is its spontaneous magnetization M_s, which is due to alignment of the magnetic moments located on an atomic lattice. The magnetization tends to lie along easy directions determined by crystal structure, atomic-scale texture or sample shape. Heating above a critical temperature known as the Curie point, which ranges from less than 1 K for magnetically dilute salts to almost 1400 K for cobalt, leads to a reversible collapse of the spontaneous magnetization.