Classification of Magnetic Forces on Antiferromagnetic Domain Wall

A major challenge in spintronics is to find an efficient means to manipulate antiferromagnet (AFM) states, which are inert relative to a uniform magnetic field, due to the vanishingly-small net magnetization. The question is, how does an AFM response to an inhomogeneous field? Here we address the problem through a complete classification of the magnetic forces on an AFM domain wall (DW), revealing the following physical properties: (i) the tiny net magnetization still responses to the field gradient. (ii) the N\'{e}el order is sensitive to the field difference between two sublattices. (iii) DW energy has a quadratic dependence on the magnetic field due to its noncollinear structure. Remarkably, the first two factors drive DW to the opposite directions in a nanowire, but the third effect tends to push the DW to the high field region. Consequently, the competition among these three forces can be applied to understand the seemingly-contradictory results on AFM motion in literature. Additionally, our results provide a new route for a speedy manipulating AFM DW; our numerical simulation indicated that for a synthetic antiferromagnet, the DW propagating speed can reach tens of kilometers per second, an order of magnitude higher than that driven by an electric current.