  Anisotropic exchange couplings, such as the Dzyaloshinskii-Moriya interaction
(DMI), have played a vital role in the formation and dynamics of spin textures.
This work predicts an anisotropic conduction electron spin density in metals
with heavy magnetic impurities. The polarization of this
$Dzyaloshinskii$-$Moriya$ $spin$ $density$ (DM-SD) is not collinear to the
localized magnetic moments but rotated by the spin-dependent skew scattering of
heavy atoms. The DM-SD induces the DMI between magnetic moments in metals and,
therefore, it is the anisotropic extension of the
Rutherman-Kittel-Kasuya-Yoshida spin density. Our model consists of two
localized magnetic moments, one with a large spin-orbit coupling (a lanthanide
or rare earth), in a free electron gas. The lanthanide spin controls the DM-SD
strength and polarization, promising a flexible control mechanism for
anisotropic couplings.
