  The static and dynamic properties of spin-polarons in La-doped $CaMnO_3$ are
explored theoretically, by means of an effective low energy Hamiltonian. All
parameters from the Hamiltoniain are evaluated from first principles theory,
without adjustable parameters. %We compare different geometries, like
spin-polarons in bulk, surface and as single two-dimensional layers. The
Hamiltonian is used to investigate the temperature stability as well as the
response to an external applied electric field, for spin-polarons in bulk,
surface and as single two-dimensional layers. Technically this involves
atomistic spin-dynamics simulations in combination with kinetic Monte Carlo
simulations. Where a comparison can be made, our simulations exhibit an
excellent agreement with available experimental data and previous theory.
Remarkably, we find that excellent control of the mobility of spin-polarons in
this material can be achieved, and that the critical parameters deciding this
is the temperature and strength of the applied electrical field. We outline
different technological implications of spin-polarons, and point to
spin-polaronics as an emerging sub-field of nano-technology. In particular, we
demonstrate that it is feasible to write and erase information on atomic scale,
by use of spin-polarons in $CaMnO_3$.
