Magnetic Domain Wall Motion

Domain wall dynamics in a ferromagnet are governed by the Landau–Lifshitz–Gilbert (LLG) equation. A Bloch wall separates domains with opposite magnetisation. Under an applied field H, the wall moves with velocity v = μ·H where μ is the wall mobility. Below a critical field H_W = α·H_K/2 (the Walker field), the wall moves steadily. Above H_W, the wall undergoes Walker breakdown: the magnetisation inside the wall precesses, causing the wall to oscillate. The time-averaged velocity actually decreases above H_W — a counterintuitive result. The top panel shows the magnetisation direction across the wire (arrows + colour = m_z component). The bottom panel tracks wall velocity over time; watch for oscillation onset.