Temperature-dependent crystal field effects in the spin-wave spectrum of terbium

A variational principle for the free energy is applied to the Hamiltonian for terbium in the ferromagnetic region to study the effect of interactions among spin waves having their origin in the strong crystalline electric fields. At high temperatures this `crystal field renormalization' has the effect of multiplying the crystal field parameters appearing in the spin-wave energies of the non-interacting theory by powers of the reduced …