Complex critical magnetic behaviour in three dimensions

Experimental results on the critical magnetic behaviour of magnets with a three-dimensional (3D) spin and isotropic 3D interactions are presented. It is observed that the critical behaviour can be rather complicated. This is because two magnetic order parameters can occur even in magnets with only one magnetic lattice site. The two order parameters must be attributed to an ordered longitudinal and transverse spin component meaning that the spin precession is elliptic rather than circular. Usually, one of the two order parameters is discontinuous at Tc. Characteristic for this type of first-order phase transition is that the continuous part in the rise of the order parameter follows critical power law with exponent β and that the paramagnetic susceptibility diverges. The exponent γ belongs not necessarily to the same universality class as β meaning that the scaling hypothesis can be violated. It appears necessary to distinguish between magnets with integer and half-integer spin. For magnets with integer spin, the critical exponent β is close to the Heisenberg value but for magnets with half-integer spin β is close to the Landau (mean field) value. The different critical behaviour seems to be associated with the opening of a magnetic excitation gap at Tc for integer spin values while for half-integer spins the magnetic excitation spectrum is essentially continuous. The magnon gap of the magnets with integer spin is identified as a second-order parameter. The origin of the gap is a mystery. Discontinuous phase transitions and the appearance of a second-order parameter can be considered as signatures of higher order interactions such as four-spin interactions. Higher order interactions seem to be especially important in three dimensions.