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Domain wall dynamics in antiferromagnetically-coupled double-lattice systems

In ferromagnetic materials, the rich dynamics of magnetic domain walls (DWs) under magnetic field or current have been successfully described using the well-known q-ϕ analytical model. We demonstrate here that this simple unidimensional model holds for multiple-sublattice materials such as ferrimagnetic alloys or synthetic antiferromagnets (SAF) by using effective parameters, and is in excellent agreement with double-lattice micromagnetic simulations. We obtain analytical laws for the DW velocity and internal precession angle as a function of net magnetisation for different driving forces (magnetic field, spin transfer and spin-orbit torques) and different propagation regimes in ferrimagnetic alloys and SAFs. The model predicts that several distinctive dynamical features occur near or at the magnetic and the angular compensation points when the net magnetization or the net angular momentum of the system vanishes, and we discuss the experimental observations that have been reported for some of them. Using a higher degree-of-freedom analytical model that accounts for inter-sublattice distortions, we give analytical expressions for these distortions that agree with the micromagnetic simulations. This model shows that the DW velocity and precession rate are independent of the strength of the inter-sublattice exchange coupling, and justifies the use of the simpler effective parameters model.