Fe magnon dispersion curve calculated with the frozen spin-wave method

Since Niu and Kleinman's recent derivation of the frozen spin-wave procedure for calculating magnon dispersion curves, two calculations have appeared which differ by about a factor of 2 in their Fe magnon frequencies at small wave vector. Because the frozen spin-wave state relaxes back to the ferromagnetic state upon iterating to self-consistency, those calculations included a constraining term. in the Hamiltonian. Here we describe a quasi-self-consistent method of imposing the frozen spin wave and compare our computational results with those we obtain using a constraining term. We demonstrate that the constrained results converge to the quasi-self-consistent results in the limit that the coefficient of the constraining term approaches zero.