  Many recently discovered advanced materials, such as high-Tc cuprates, iron
pnictides and several heavy-fermions, exhibit a rich phase diagram suggesting
the presence of different competing interactions that would lead to various
types of ordering. Nevertheless, there is not yet a clear unifying picture
allowing the understanding of the detailed mechanisms that generate such
competing interactions. Having such a picture, however, could quite well be at
the very roots of the requirements for understanding high-Tc superconductivity
in cuprates and pnictides, for instance. In this work we consider the
antiferromagnetic (AF) Heisenberg-Kondo lattice, consisting of localized spins
with AF exchange interactions between nearest neighbors on a square lattice and
itinerant electrons, which undergo a magnetic Kondo interaction with the
localized spins, but are otherwise non-interacting. Using the Schwinger-boson
(CP$^1$) formalism and assuming the electrons are Dirac-like, we integrate on
the localized degrees of freedom thereby obtaining the effective interaction
among the itinerant electrons. This contains a BCS-like superconducting term, a
Nambu-Jona-Lasinio-like, charge gap term and a Ising and Heisenberg-like
magnetic terms. All these four competing interactions, therefore are generated
by the original Kondo magnetic interaction.
