  It is well known that the kinetic exchange interaction between
single-occupied magnetic orbitals (s-s) is always antiferromagnetic, while
between single- and double-occupied orbitals (s-d) is always ferromagnetic and
much weaker. Here we show that the exchange interaction between strongly
anisotropic doublets of lanthanides, actinides and transition metal ions with
unquenched orbital momentum contains a new s-d kinetic contribution equal in
strength with the s-s one. In non-collinear magnetic systems, this s-d kinetic
mechanism can cause an overall ferromagnetic exchange interaction which can
become very strong for transition metal ions. These findings are fully
confirmed by DFT based analysis of exchange interaction in several Ln$^{3+}$
complexes.
