Quantifying the interfacial dzyaloshinskii-moriya interactions from spin-waves

We determined the magnitude of the Dzyaloshinskii-Moriya interaction for a thickness series of Ni₈₀Fe₂₀/Pt samples from Brillouin Light Scattering (BLS) measurements . The Dzyaloshinskii-Moriya interaction is an anti-symmetric exchange mechanism and is for two neighboring spins S_i and S_j given by HDMI=-D.(S_i×S_j), where D is the Dzyaloshinskii-Moriya interaction vector . In systems with interfacial Dzyaloshinskii-Moriya interaction D is perpendicular to the interface normal and the vector connecting S_i and S_j. The symmetric Heisenberg exchange is given by H=-J_ij(S_i.S_j), where J is the exchange integral . T . Moriya showed for magnetic oxides and A . Fert and P . Levy for metallic spin-glasses that the anti-symmetric Dzyaloshinskii-Moriya interaction and the symmetric Heisenberg exchange share the same underlying physics and are both proportional to each other .