On the temperature dependence of the magnetic excitations

We compare experimental data for temperature dependence of the magnetic order parameter and the magnetic excitations (spin waves) in materials with a quenched orbital moment and a well-defined spin quantum number. It is observed that the thermal decrease of the two quantities proceeds according to the same analytical function of the type y(T)=1-cTε with an identical exponent ε. This power function applies not only asymptotically for T→0 but holds over a wide temperature range. The exponent ε is universal, i.e. independent of spin order type and lattice symmetry and depends only on the dimensionality of the relevant interactions and on whether the spin quantum number is integer or half-integer. The different Tε functions are identified as representations of stable universality classes. The fact that order parameter and magnetic excitations follow the same Tε function shows that the two quantities belong to the same universality class. The (geometrical) details of the magnetic excitation spectrum are not important for the thermodynamic of the order parameter. Most interesting is the observation of a significant magnetic excitation gap in isotropic magnets with an integer spin. Also in these materials the thermal decrease of gap and sublattice magnetization proceeds according to the same cTε function with ε=92. However, the coefficient c is much larger for the gap than for the magnetization. Arguments will be given that the gap in the isotropic magnets with an integer spin is an independent order parameter.