Critical Behaviour of Heisenberg Ferromagnets with Dipolar Interactions and Uniaxial Anisotropy

Abstract

In any real magnetic system, weak anisotropic long-range dipole-dipole interactions are invariably present besides crystal-field interactions and dominant isotropic short-range Heisenberg interactions (in insulating systems) or isotropic long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions (in metallic systems) that couple the localized magnetic moments. In many magnetic systems, the dominant interactions normally sustain long-range magnetic order and govern the ground state and finite-temperature magnetic properties. Crystal-field interactions lead to magnetocrystalline anisotropy, which constrains the domain magnetizations to lie along the "easy directions". Even in such systems, the magnetic behaviour in the critical region is significantly altered by the dipolar interactions so much so that the interplay between crystal-field, dipolar and Heisenberg or RKKY interactions gives rise to a complex scenario of crossovers between different critical regimes. A thorough study of critical behaviour of these systems has yielded rich dividends in that their magnetic properties are now much better understood. We will make only a few passing remarks about such systems. However, there are certain exceptional cases where dipolar interactions, despite their weak strength, play a very important role in deciding the nature of magnetic order. That gadolinium metal belongs to this rare category of magnetic systems is demonstrated by the latest advances in understanding its complex magnetic behaviour in the critical region. We present recent experimental results on the critical behaviour of gadolinium and the relevant theoretical background so as to bring out these latest developments clearly.