Source and origin of the interfacial Dzyaloshinskii-Moriya interaction in a heavy-metal|magnetic-insulator bilayer

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) was observed in the bilayer consisting of a heavy metal and a ferromagnetic insulator such as $\mathrm{Pt}|{\mathrm{Tm}}₃{\mathrm{Fe}}₅{\mathrm{O}}₁₂$ (TIG), but the source and origin are still controversial. Here, we quantitatively investigate the iDMI strength in Pt|TIG by inserting a thin ${\mathrm{Y}}₃{\mathrm{Fe}}₅{\mathrm{O}}₁₂$ layer and/or a thin Cu layer between Pt and TIG. Our results suggest the iDMI contributed by both the Pt|TIG and the TIG|substrate interfaces. At the Pt|TIG interface, we find that Pt is essential for the strong iDMI. The disentangled iDMIs for Fe-Fe and Tm-Fe pairs are comparable, revealing that the Tm ions provide not only an additional Tm-Fe iDMI, but also the spin-orbit coupling to enhance the iDMI. At the TIG|substrate interface, the iDMI is attributed to the lattice-mismatch-induced deformation of the electron cloud for the ferromagnetic ions.