  We study a microscopic derivation and the properties of the
Dzyaloshinskii-Moriya interaction (DMI) between local magnetic moments in
ferromagnet/heavy metal heterostructures. First, we derive DMI by
Ruderman-Kittel-Kasuya-Yosida interaction through electrons in a heavy metal
with Rashba spin orbit interaction (SOI). Next, we study the dependences of the
DMI on the Rashba SOI, lattice constant, and chemical potential. We find that
the DMI amplitude increases linearly when the Rashba SOI is small, has a
maximum when the Rashba SOI is comparable to the hopping integral, and
decreases when the Rashba SOI is large. The sign of the DMI not only changes
depending on the sign of the Rashba SOI but also the lattice constants and the
chemical potential of the heavy metal. The implications of the obtained results
for experiments are discussed.
