Switching between Magnetic Bloch and Néel Domain Walls with Anisotropy Modulations

It has been shown previously that the presence of a Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films stabilizes Néel type domain walls. We demonstrate, using micromagnetic simulations and analytical modeling, that the presence of a uniaxial in plane magnetic anisotropy can also lead to the formation of Néel walls in the absence of a Dzyaloshinskii-Moriya interaction. It is possible to abruptly switch between Bloch and Néel walls via a small modulation of the in plane, but also the perpendicular, magnetic anisotropy. This opens up a route toward electric field control of the domain wall type with small applied voltages through electric field controlled anisotropies.

Figure 1

Left: sketch of the simulation geometry with definition of directions. Right: definition of in plane color wheel and domain wall magnetization angle $\varphi$ between the magnetization $\overrightarrow{M}$ at the center of the domain wall and the normal $\widehat{n}$ to the domain wall.

Figure 2

Domain wall images as a function of (a) DMI constant $D$ and (b) in plane anisotropy constant $K_{\mathrm{IP}}$ for a perpendicular anisotropy constant $K_{\mathrm{PP}}=1\times {10}^6\mathrm{J}/{\mathrm{m}}^3$. (c) Images as a function of $K_{\mathrm{PP}}$ for $K_{\mathrm{IP}}=3\times {10}^4\mathrm{J}/{\mathrm{m}}^3$. Corresponding domain wall magnetization angles $\varphi$ as a function of (d) $D$, (e) $K_{\mathrm{IP}}$, and (f) $K_{\mathrm{PP}}$.

Figure 3

(a) Phase diagram of the domain wall magnetization angle $\varphi$ as a function of perpendicular ($K_{\mathrm{PP}}$) and in plane ($K_{\mathrm{IP}}$) anisotropy constants. (b) Location of the transition between Bloch and Néel walls for a thin film (blue line), for a nanowire (orange dashed line), and according to the analytical model (black dotted line). (c) Widths $\delta$ of Bloch (green line) and Néel (red dashed line) domain walls just below and above the transition. The analytical expression $\delta =2\sqrt{A/K_{\mathrm{PP},\mathrm{eff}}}$ is shown as a black dotted line.

Figure 4

(a) Phase diagram of the domain wall magnetization angle $\varphi$ as a function of perpendicular magnetic anisotropy constant $K_{\mathrm{PP}}$ and nanowire width $w$. (b) Domain wall images as a function of $K_{\mathrm{PP}}$ for $w=32\mathrm{nm}$.

Figure 5

Phase diagram of the domain wall magnetization angle $\varphi$ as a function of DMI constant $D$ and in plane anisotropy constant $K_{\mathrm{IP}}$ for a fixed magnitude of the perpendicular anisotropy constant $K_{\mathrm{PP}}=1\times {10}^6\mathrm{J}/{\mathrm{m}}^3$. Solid blue lines are contour lines of the simulation data for given domain wall magnetization angles of 15°, 45°, and 75°. Dotted black lines are the contour lines expected from the analytical model.