Domain wall depinning from a single notch in a synthetic ferrimagnetic nanoribbon

Ferrimagnetic (FiM) materials have been receiving substantial attention in recent years for advanced spintronic applications, and their wall pinning/depinning exhibits fascinating but more complex behaviors than those of ferromagnetic and antiferromagnetic materials. Here, we develop an analytic theory on magnetic field-driven depinning for a FiM domain wall from a notch in a synthetic FiM nanoribbon. A clear correlation of the wall oscillation and depinning field over a broad damping regime is established. It is revealed that the damping constant and inter-layer coupling suppress wall oscillation and thus increase the depinning field up to a saturation value at strong damping and inter-layer coupling where no wall oscillation is allowed. On the other hand, the net angular momentum and thermal fluctuations are beneficial to wall oscillation and thus suppress the depinning field. Moreover, in the large damping regime, the dependences of the depinning field on intrinsic parameters and the notch dimension are theoretically derived, and the theoretical predictions show good consistency with numerical and experimental results. Therefore, this study offers a theoretical foundation of material selection in future studies of FiM domain wall depinning for both experiments and applications.