First-principles investigation of chiral magnetic structures in multilayers: {Rh|Co|Pt} and {Pd|Co|Pt}

In the search and formation of chiral magnetic skyrmions in magnetic multilayers, the antisymmetric exchange interaction, known as Dzyaloshinskii-Moriya interaction (DMI), created at the surfaces and interfaces of metallic multilayers plays a determining role.
Here, we determine the symmetric and antisymmetric magnetic interaction parameters of the magnetic multilayers {Rh|Co|Pt} and {Pd|Co|Pt} using first-principles calculations based on the relativistic full-potential linearized augmented plane-wave (FLAPW) method, as implemented in the FLEUR code (www.flapw.de). We find that the 4d (i.e. Rh and Pd) elements induce a DMI that partly cancels the large DMI produced by the heavy-metal Pt layer. Upon variation of the thickness of the Pt layer between one and five atomic layers, we investigate the interlayer exchange coupling between the magnetic Co layers. For the {Pd|Co|Pt} system, a RKKY-type oscillatory behavior between ferromagnetic and antiferromagnetic interactions is observed. The {Rh|Co|Pt} system has a qualitatively different behavior, where frustrations in between the Co layers lead to a non-collinear order along the c axis.