Exchange stiffness of Ca-doped YIG

Abstract

An effective medium theory for the zero-temperature exchange stiffness of uncompensated Ca-doped YIG is presented. The theory is based on the assumption that the effect of the Ca impurities is to produce strong, random ferromagnetic interactions between spins on the a and d sublattices. In the simplest version of the theory, a fraction, x, of the ad exchange integrals are large and positive, x being related to the Ca concentration. The stiffness is calculated as function of x for arbitrary perturbed ad exchange integral, Jxad. For Jxad≳(1/5)‖8Jaa+3Jdd‖, with Jaa and Jdd denoting the aa and dd exchange integrals, respectively, there is a critical concentration, Xc, such that when x≳Xc, the stiffness is complex. It is suggested that Xc delineates the region where there are significant departures from colinearity in the ground state of the Fe spins. Extension of the theory to a model where the Ca doping is assumed to generate Fe4+ ions on the tetrahedral sites is discussed. Possible experimental tests of the theory are mentioned.