  Fourth-order strong-coupling degenerate perturbation theory is used to derive
an effective low-energy Hamiltonian for the Kondo-lattice model with a depleted
system of localized spins. In the strong-J limit, completely local Kondo
singlets are formed at the spinful sites which bind a fraction of conduction
electrons. The low-energy theory describes the scattering of the excess
conduction electrons at the Kondo singlets as well as their effective
interactions generated by virtual excitations of the singlets. Besides the
Hubbard term, already discussed by Nozieres, we find a ferromagnetic Heisenberg
interaction, an antiferromagnetic isospin interaction, a correlated hopping
and, in more than one dimensions, three- and four-site interactions. The
interaction term can be cast into highly symmetric and formally simple
spin-only form using the spin of the bonding orbital symmetrically centered
around the Kondo singlet. This spin is non-local. We show that, depending on
the geometry of the depleted lattice, spatial overlap of the non-local spins
around different Kondo singlets may cause ferromagnetic order. This is
sustained by a rigorous argument, applicable to the half-filled model, by a
variational analysis of the stability of the fully polarized Fermi sea of
excess conduction electrons as well as by exact diagonalization of the
effective model. A similar fourth-order perturbative analysis is performed for
the depleted Anderson lattice in the limit of strong hybridization. Even in a
parameter regime where the Schrieffer-Wolff transformation does not apply, this
yields the same effective theory albeit with a different coupling constant.
