Exchange and Dzyaloshinskii-Moriya interaction in Rh/Co/Fe/Ir multilayers: Towards skyrmions in exchange-frustrated multilayers

Abstract

We study the magnetic interactions in transition-metal multilayers composed of Co layers and Co/Fe bilayers sandwiched between Ir and Rh layers based on density functional theory (DFT). By mapping our total energy DFT calculations of collinear and noncollinear spin states including spin-orbit coupling to an atomistic spin model we extract the intra- and interlayer exchange constants, the intra- and interlayer Dzyaloshinskii-Moriya interaction constants and the magnetocrystalline anisotropy energies of several multilayers. We demonstrate that the exchange frustration, which stabilizes zero-field sub-10 nm magnetic skyrmions in Rh/Co films on the Ir(111) surface [S. Meyer et al., Nat. Commun. 10, 3823 (2019)], can be transferred to multilayers formed by a repetition of Rh/Co/Ir trilayers. Increasing the number of Co layers reduces the exchange frustration whereas with adding Fe, a sufficient exchange frustration and strength of the Dzyaloshinskii-Moriya interaction can be obtained to stabilize topological spin structures such as skyrmions in Rh/Co/Fe/Ir multilayers. We show that the exchange interaction in Rh/Co/Fe/Ir multilayers results from the interplay of strong frustration of intralayer exchange in the Fe layer, weak ferromagnetic intralayer exchange in the Co layer, and ferromagnetic interlayer Fe-Co exchange. We analyze the Dzyaloshinskii-Moriya interaction in terms of inter- and intralayer contributions as well as its sign based on the electronic structure of Co/Fe based multilayers with different stacking sequences.