Bosons and Magnons in Ordered Magnets

In earlier experimental studies we have shown that in accordance with the principles of renormalization group theory the spin dynamics of ordered magnets is controlled by a boson guiding field instead by exchange interactions between nearest magnetic neighbors. In particular, thermal decrease of the magnetic order parameter is given by the heat capacity of the boson field. The typical signature of boson dynamics is that the critical power functions either at $T=T_{c}$ or at T=0 hold up to a considerable distance from critical temperature. The critical power functions of the atomistic models hold asymptotically at $T=T_{c}$ or at T=0 only. In contrast to the atomistic magnons field bosons cannot directly be observed using inelastic neutron scattering. However, for some classes of magnets the field bosons seem to have magnetic moment and thus are able to interact directly with magnons. This interaction, although weak in principle, leads to surprisingly strong functional modifications in the magnon dispersions at small q-values. In particular, the magnon excitation gap seems to be due to the magnon-boson interaction. In this communication we want to show that for small q-values the continuous part of the magnon dispersions can be fitted over a finite q-range by a power function of wave vector. The power function can be identified with the dispersion of the field bosons. It appears that for low q-values magnon dispersions get attracted by the boson dispersion and assume the dispersion of the bosons. This allows for an experimental evaluation of the boson dispersions from the known magnon dispersions. Exponent values of 1, 1.25, 1.5, and 2 have been identified. The boson dispersion relations and the associated power functions of temperature for the heat capacity of the boson fields are now empirically known for all dimensions of the field and for magnets with integer and half-integer spin quantum number. These are two 2× 3 exponent schemes