Thermal decay of magnons in MnF2

It is shown that for nearly all magnets only two types of magnon dispersions occur. For the first group of magnets, magnon dispersions are as for the linear spin chain (a sine-function of wave-vector for antiferromagnets but a sine-function squared for ferromagnets), quite independent of the lattice structure. Since the observed magnon dispersions are specific to the individual domain, the identical magnon dispersions show that the domains of all magnets are very similar in that all spins are perfectly aligned along the domain axis. The linear chain dispersion is explained by a strong coupling of the spins to the one-dimensionally ordered boson field in each domain. The bosons were identified as essentially magnetic dipole radiation generated essentially through stimulated emission by the precessing spins. In the ordered state of the boson field, the bosons are in a coherent and one-dimensional state, like the radiation field of a LASER. For the second group of magnets, magnon dispersions exhibit an analytical crossover from a power function of wave vector (∼q ^x) plus a gap to the dispersion of the linear spin chain. Occasionally it turns out to be necessary to add a phase shift in the argument of the sine function. The functionality of the local exchange interactions is restricted to determine the relative orientation of neighboring spins, i.e. to decide between the sine-function and the sine-function squared and to define the absolute values of the magnon energies. As a consequence, instead by exchange interactions, magnon dispersions have to be characterized by four parameters: the gap, the pre-factor of the ∼q ^x power function, the amplitude of the sine-function and the phase-shift in the argument of the sine function. For MnF ₂ the temperature dependence of these four parameters is evaluated, as far as experimental data are available. The exponent x is the only parameter that is characteristic of the dynamic dimensionality of the system and is temperature-independent. For MnF ₂ with a half-integer spin of S = 5/2 and a one-dimensional dynamic symmetry x = 3/2.