A magnetic domain wall separates two regions of opposite magnetization. Apply a current, and the wall moves — this is the basis of spintronic memory devices. The current exerts a torque, the torque drives the wall, and the direction of the wall’s motion follows the direction of the current. Reverse the current, reverse the wall.

In ferrimagnets near the angular momentum compensation point, this breaks. The wall can move forward or backward under the same direct current. The direction is determined not by the current’s sign but by its magnitude. Below a threshold, the wall moves one way. Above it, the wall reverses. Same current direction, opposite wall motion.

The mechanism is inertial. Domain walls have internal collective coordinates — the wall center position and an internal angle. Near angular momentum compensation, the effective mass of these coordinates is large, and the internal dynamics create a current-dependent double-well potential. At low current, the system sits in one well, and the wall moves in the expected direction. At high current, the system hops to the other well, and the direction reverses. The transition is smooth and reversible — reduce the current, and the wall switches back.

The structural point: the response reverses not because the drive reverses but because the nonlinear potential landscape has two minima whose relative depth changes with driving strength. The same input, at different amplitudes, accesses different dynamical states. This is fundamentally different from the linear picture where output direction follows input direction. The wall’s internal degrees of freedom act as a hidden variable that inverts the response when the driving is strong enough.

(arXiv:2603.18722)