Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii-Moriya interaction in metal films

Proposals for novel spin-orbitronic logic(1) and memory devices(2) are often predicated on assumptions as to how materials with large spin-orbit coupling interact with ferromagnets when in contact. Such interactions give rise to a host of novel phenomena, such as spin-orbit torques(3,4), chiral spin structures(5,6) and chiral spin torques(7,8). These chiral properties are related to the antisymmetric exchange, also referred to as the interfacial Dzyaloshinskii-Moriya interaction (DMI; refs 9,10). For numerous phenomena, the relative strengths of the symmetric Heisenberg exchange and the DMI are of great importance. Here, we use optical spin-wave spectroscopy (Brillouin light scattering) to directly determine the volume-averaged DMI vector D for a series of Ni80Fe20/Pt thin films, and then compare the nearest-neighbour DMI coupling energy with an independently measured value of the Heisenberg exchange for each sample. We show that the dependence on Ni80Fe20 thickness of both the microscopic symmetric and antisymmetric exchange are nearly identical, consistent with the notion that the fundamentals of the DMI and Heisenberg exchange essentially share the same underlying physics, albeit with different symmetries, as was originally proposed by Moriya(11) for superexchange in magnetic oxides, and by Fert and Levy(12) for RKKY coupling in metallic spin glasses. Indeed, our result demonstrates the generality of the original DMI theory, insofar as the proportionality of the symmetric and antisymmetric exchange is robust with regard to the details of spin coupling for the material system in question. Although of significant fundamental importance, this result also leads us to a deeper understanding of DMI and how it could be optimized for spin-orbitronic applications.