  The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic
$s$-$d$ spin impurities across a tunneling junction is studied when the system
is driven out of equilibrium through biasing the junction. The nonequilibrium
situation is handled with the Keldysh time-loop perturbation formalism in
conjunction with appropriate coupling methods for tunneling systems due to
Caroli and Feuchtwang. We find that the presence of a nonequilibrium bias
across the junction leads to an interference of several fundamental
oscillations, such that in this tunneling geometry, it is possible to tune the
interaction between ferromagnetic and antiferromagnetic coupling at a fixed
impurity configuration, simply by changing the bias across the junction.
Furthermore, it is shown that the range of the RKKY interaction is altered out
of equilibrium, such that in particular the interaction energy between two
slabs of spins scales extensively with the thickness of the slabs in the
presence of an applied bias.
