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The approximations leading to Eq. -the isotropic dispersion law and the predominance of the Fe-Fe exchange interaction over the Gd-Fe and Gd-Gd ones-do not appear explicitly in Ref., where Eq. was derived; rather, they are implicitly built into Eq. therein. The same result is obtainable as a special case of the more general expressions by neglecting the intersublattice and one of the intrasublattice exchange integrals therein.
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