Further investigations on magnets with pure spin moments are presented show
ing that the temperature dependence of the order parameter can accurately b
e described over a large temperature range by a single T-epsilon power term
. The exponent epsilon is found to be independent of the spin order type bu
t it depends on whether the spin quantum number is integral or half-integra
l and, of course, on the dimensionality of the magnetic interactions. The s
ix empirical spin wave exponents epsilon defined in this way are 9/2, 2 and
3 for isotropic, anisotropic and axial interactions and integral spin quan
tum number but 2, 3/2 and 5/2 for isotropic, anisotropic and axial interact
ions and half-integral spin quantum number. Thermodynamic crossover between
neighbouring exponents is frequently observed: antiferromagnetic NiO havin
g S = 1 is cubic above TN but undergoes a progressive trigonal lattice dist
ortion with decreasing temperature. For this material a crossover from isot
ropic (epsilon = 9/2) to anisotropic (epsilon = 2) interactions is observed
as a function of decreasing temperature (see Table I). The hexagonal ferro
magnet gadolinium having S = 7/2 exhibits a crossover from epsilon = 3/2 to
epsilon = 5/2 indicative for a gradual change from anisotropic to predomin
antly axial interactions with decreasing temperature. Also the itinerant fe
rromagnets Fe, Ni and Co show the same exponents e as insulators with S = 1
/2. While cubic Fe and Ni exhibit epsilon = 2 the same crossover from epsil
on = 3/2 to epsilon = 5/2 as for hexagonal Gd is observed for hcp cobalt.