Functional crossover in the dispersion relations of magnons and phonons

Abstract

Experimental data are presented showing that the dispersion relations of magnons and acoustic phonons can consist of two sections with different functions of wave vector. In the low wave vector range a power function of wave vector often holds over a finite q-range while dispersions for larger wave vector values better approach the atomistic model predictions. In the magnon spectra ∼⃒qx power functions with exponents x=1.25, 1.5 and 2 are identified. The dispersion of the acoustic phonons can be a linear function of wave vector over a surprisingly large range of energy. Since the slope of the linear section agrees with the known sound velocities it can be concluded that the dispersion of the acoustic phonons has got attracted by the linear dispersion of the mass less Debye bosons (sound waves). Due to the different (translational) symmetries of bosons and atomistic excitations (magnons, phonons) the associated dispersions can attract each other. In the same way the different ∼⃒qx power functions in the magnon dispersions indicate that magnon dispersions are attracted by the dispersion of the bosons of the magnetic continuum (Goldstone bosons). This allows evaluation of the otherwise difficult to obtain dispersions of the Goldstone bosons from the known magnon dispersions. Interestingly, the dispersions of Goldstone bosons (Debye bosons) attract magnon dispersions (phonon dispersions) and not vice versa.