Systematic theoretical study of the spin and orbital magnetic moments of $4d$ and $5d$ interfaces with Fe films

Results of ab initio calculations using the relativistic local spin density theory are presented for the magnetic moments of periodic $5d$ and $4d$ transition metal interfaces with bcc Fe(001). In this systematic study we calculated the layer-resolved spin and orbital magnetic moments over the entire series. For the Fe/W(001) system, the Fe spin moment is reduced while its orbital moment is strongly enhanced. In the W layers a spin moment is induced, which is antiparallel to that of Fe in the first and fourth W layers but parallel to Fe in the second and third W layers. The W orbital moment does not follow the spin moment. It is aligned antiparallel to Fe in the first two W layers and changes sign in the third and fourth W layers. Therefore, Hund’s third rule is violated in the first and third W layers, but not in the second and fourth W layers. The trend in the spin and orbital moments over the $4d$ and $5d$ series for multilayers is quite similar to previous impurity calculations. These observations strongly suggest that these effects can be seen as a consequence of the hybridization between $5d$ $\mathrm{}\left(4d\right)\mathrm{}$ and Fe, which is mostly due to band filling, and to a lesser extent geometrical effects of either single impurity or interface.