An effective medium theory for the zero-temperature exchange stiffness
of uncompensated Ca-doped YIG is presented. The theory is based on th
e assumption that the effect of the Ca impurities is to produce strong
, random ferromagnetic interactions between spins on the a and d subla
ttices. In the simplest version of the theory, a fraction, x, of the a
d exchange integrals are large and positive, x being related to the Ca
concentration. The stiffness is calculated as function of x for arbit
rary perturbed ad exchange integral, J(ad)x. For J(ad)x > (1/5)18J(aa)
+ 3J(dd)\, with J(aa) and J(dd) denoting the aa and dd exchange integ
rals, respectively, there is a critical concentration, X(c), such that
when x>X(c), the stiffness is complex. It is suggested that X, deline
ates the region where there are significant departures from colinearit
y in the ground state of the Fe spins. Extension of the theory to a mo
del where the Ca doping is assumed to generate Fe4+ ions on the tetrah
edral sites is discussed. Possible experimental tests of the theory ar
e mentioned.