  We study a spin-ice Kondo lattice model on a breathing pyrochlore lattice
with classical localized spins. The highly efficient kernel polynomial
expansion method, together with a classical Monte Carlo method, is employed in
order to study the magnetic phase diagram at four representative values of the
number density of itinerant electrons. We tune the breathing mode by varying
the hopping ratio -- the ratio of hopping parameters for itinerant electrons
along inequivalent paths. Several interesting magnetic phases are stabilized in
the phase diagram parameterized by the hopping ratio, Kondo coupling, and
electronic filling fraction, including an "all-in/all-out" ordered spin
configuration phase, spin-ice, ordered phases containing $16$ and $32$ spin
sites in the magnetic unit cell, as well as a disordered phase at small values
of the hopping ratio.
