On the relationship between orbital moment anisotropy, magnetocrystalline anisotropy, and Dzyaloshinskii-Moriya interaction in W/Co/Pt trilayers

We have studied the Co layer thickness dependences of magnetocrystalline anisotropy (MCA), Dzyaloshinskii-Moriya interaction (DMI), and orbital moment anisotropy (OMA) in W/Co/Pt trilayers, in order to clarify their correlations with each other. We find that the MCA favors magnetization along the film normal and monotonically increases with decreasing effective magnetic layer thickness ($t_\mathrm{eff}$). The magnitude of the Dzyaloshinskii-Moriya exchange constant ($|D|$) increases with decreasing $t_\mathrm{eff}$ until $t_\mathrm{eff} \sim$1 nm, below which $|D|$ decreases. The MCA and $|D|$ scale with $1/t_\mathrm{eff}$ for $t_\mathrm{eff}$ larger than $\sim$1 nm, indicating an interfacial origin. The increase of MCA with decreasing $t_\mathrm{eff}$ continues below $t_\mathrm{eff}$ $\sim$ 1 nm, but with a slower rate. To clarify the cause of the $t_\mathrm{eff}$ dependences of MCA and DMI, the OMA of Co in W/Co/Pt trilayers is studied using x-ray magnetic circular dichroism (XMCD). We find non-zero OMA when $t_\mathrm{eff}$ is smaller than $\sim$0.8 nm. The OMA increases with decreasing $t_\mathrm{eff}$ more rapidly than what is expected from the MCA, indicating that factors other than OMA contribute to the MCA at small $t_\mathrm{eff}$. The $t_\mathrm{eff}$ dependence of the OMA also suggests that $|D|$ at $t_\mathrm{eff}$ smaller than $\sim$1 nm is not related to the OMA at the interface. We propose that the growth of Co on W results in a strain and/or texture that reduces the interfacial DMI, and, to some extent, MCA at small $t_\mathrm{eff}$.