Magnetic domain walls play a critical role in the nanoscale evolution of magnetic devices. Despite early efforts, complete understanding of the micromagnetic evolution of the width $\mathrm{\Delta }$ and the type of magnetic domain walls has still remained lacking. 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 $K_{\mathrm{u}}$, saturation magnetization $M_{\mathrm{s}}$, Dzyaloshinskii-Moriya interaction (DMI), and shape anisotropy of the magnetic device. We find that $\mathrm{\Delta }$ of both Bloch and Néel walls scales excellently with the analytical prediction of $\mathrm{\Delta }=C\sqrt{A/\left[K_{\text{u}}-{\mu }_0{M}_{\text{s}}^2(N_z-N_x{cos}^2\phi )/2\right]}$ (where $C$ is a constant depending on the definition of $\mathrm{\Delta }, \phi$ is the azimuth angle of the magnetic moment at the domain wall center, and $N_x$ and $N_z$ are the longitudinal and perpendicular demagnetization factors). 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 the Néel configuration upon an increase of the DMI. The shape anisotropy of the magnetic domain wall also affects the domain wall width. These results establish a comprehensive, conclusive understanding of the magnetic domain walls within spintronic devices.

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• Demagnetization
• Domain walls
• Dzyaloshinskii-Moriya interaction
• Magnetic anisotropy