Scaling of magnetic domain walls in systems with perpendicular magnetic anisotropy

Magnetic domain walls play a critical role in the nanoscale evolution of magnetic devices. Despite the early efforts, a complete understanding of the micromagnetic evolution of the width and the type of magnetic domain walls has still remained missing. Here, we report a combined analytical and micromagnetic simulation study and establish the scaling of the magnetic domains as a function of the exchange stiffness (A), uniaxial perpendicular magnetic anisotropy (Ku), saturation magnetization (Ms), and Dzyaloshinskii-Moriya interaction (DMI), and shape anisotropy of the magnetic device. We find that the width of both Bloch and Neel walls scales excellently with the analytical prediction. The DMI is found to have little influence on the domain wall width but strongly affect the type of the domain wall. The domain wall has a Bloch configuration at zero DMI and gradually transitions to Neel configuration upon increase of the DMI. The shape anisotropy of the magnetic domain wall also affects the domain wall width. These results have established a comprehensive, conclusive understanding of the magnetic domain walls within spintronics devices.