Improved method for calculating the effect of a local perturbation in a uniform or random system using the recursion method: Application to the magnetic excitation in iron

Abstract

A new and efficient method for calculating the total change in the structural energy of a uniform or random system due to a local perturbation is described. The method makes use of an exact algebraic cancellation between terms unchanged by the perturbation and a Green's-function "poles and zeros" method to calculate the changed contributions. The technique is particularly convenient as it uses a continued-fraction formulation which is amenable to well-developed numerical algorithms developed for the recursion programs in Cambridge. The method is applied to two outstanding problems in the theory of magnetism: the excitations in ferromagnetic iron at high temperatures and a direct evaluation of the Heisenberg exchange parameters ${J}_{\mathrm{ij}}$ out to fifth-nearest neighbor. The calculations support the concept of smoothly varying excitations in iron with a large amount of short-range order above ${T}_{c}$. They also indicate that the Heisenberg ${J}_{s}$ becomes negative beyond second-nearest neighbor in iron.