  Using relativistic first-principles calculations, we show that the chemical
trend of Dzyaloshinskii-Moriya interaction (DMI) in 3d-5d ultrathin films
follows Hund's first rule with a tendency similar to their magnetic moments in
either the unsupported 3d monolayers or 3d-5d interfaces. We demonstrate that,
besides the spin-orbit coupling (SOC) effect in inversion asymmetric
noncollinear magnetic systems, the driving force is the 3d orbital occupation
and their spin flip/mixing processes with the spin-orbit active 5d states
control directly the sign and magnitude of the DMI. The magnetic chirality
changes are discussed in the light of the interplay between SOC, Hund's first
rule, and the crystal field splitting of d orbitals.
