Oscillatory behavior of interlayer Dzyaloshinskii-Moriya interaction by spacer thickness variation

The interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) has recently emerged as an ingredient promoting chiral orthogonal coupling between adjacent magnetic layers in multilayered systems. IL-DMI offers an additional tuning knob to engineer the magnetic behavior in spintronic devices, which could be useful for nonvolatile logic and memory technologies. Here, we systematically study, via first-principles calculations and the three-site Fert-Lévy model, the spacer thickness dependence of the IL-DMI between an out-of-plane ferrimagnet TbCo and an in-plane ferromagnet Co through Pt, Ir, Pd, and Ru. We observed a damped oscillatory behavior with increasing spacer thickness in all cases with characteristic amplitude and periodicity. Furthermore, we established a direct correlation between the IL-DMI and density of states of bottom and top Co atoms, dominated by the spacer thickness, which is attributed to a hybridization of electronic orbitals. Based on this compelling evidence, we propose that the electronic orbital hybridization contributes to the microscopic origin of the IL-DMI metallic magnetic multilayers. We anticipate that our results will provide insights into the understanding and precise control of IL-DMI in a wide range of materials and spintronic device concepts.