Classification of magnetic forces acting on an antiferromagnetic domain wall

A major challenge in antiferromagnetic (AFM) spintronics is to find an efficient way to manipulate AFM states, which are inert to a uniform magnetic field due to a vanishingly small net magnetization. The question is, how does an AFM respond to an inhomogeneous field? Here, we present a complete classification of the magnetic forces on an AFM domain wall (DW): (i) The tiny net magnetization can respond to the field gradient. (ii) The staggered magnetization is sensitive to the field difference of two sublattices. (iii) DW energy has a quadratic dependence on the magnetic field due to its noncollinear structure. Interestingly, the first two forces drive the DW to propagate to the opposite directions in a nanowire, but the third effect tends to push the DW to the high-field region. Consequently, the competition between these three forces can be used to understand the seemingly contradictory results on AFM-DW motion reported in the literature. Additionally, our results provide a route for a speedy manipulating AFM-DW; our numerical simulation indicated that, for antiferromagnetically coupled ferromagnetic layers, the DW propagating speed can reach tens of kilometers per second, an order of magnitude higher than that driven by an electric current.