Atomic-Level Control of the Domain Wall Velocity in Ultrathin Magnets by Tuning of Exchange Interactions

We demonstrate that the propagation velocity of field driven magnetic domain walls in ultrathin $\mathrm{Au}/\mathrm{Co}/\mathrm{Au}$ films with perpendicular anisotropy on vicinal substrates is anisotropic and strongly depends on the step density of the substrate. The velocity of walls oriented perpendicular to the steps drastically increases with increasing local step density while being unchanged or only weakly decreased for the walls oriented parallel to the steps. We develop an analytical model revealing the step-modified exchange interactions as the main driving force for this anisotropic behavior. The enhancement of the domain wall velocity at low magnetic fields far below the Walker instability threshold makes this phenomenon interesting for magnetic nanodevices.

Figure 1

In situ STM topographs: (a) $40\times 40{\mathrm{nm}}^2$ image of the surface with single steps and (b) $180\times 180{\mathrm{nm}}^2$ image of the surface with step bunches. Insets show crystallographic orientations and the cross sections of steps.

Figure 2

DW displacement parallel and perpendicular to the $\mathrm{Si}[-110]$ direction for: (a) an atomically flat surface, (b) monatomic steps, and (c) an array of step bunches. Insets show the field dependence of DW velocity and a selection of remanent domain structure images ($220\times 170\mu {\mathrm{m}}^2$) recorded at different times.

Figure 3

Analytical model. (a) Side view of a continuous film, a monatomic step, and a step bunch consisting of three monatomic steps. The atoms belonging to the $A$-hcp planes are dark gray (blue), while those of $B$-hcp planes are light gray (red). The top views of bottom (3), middle (2), and top (1) atomic layers are shown at the bottom of the figure. Hatched circles denote missing atoms; dotted balls represent the atoms lying in the underlayer. Three typical unit cells with broken bonds are outlined by parallelograms. Solid and dashed lines denote intact and broken lines, respectively. (b) Schematic representation of a nucleated domain (white square) with domain walls (gray bars) and activation volume $V_A$ (hatched areas). (c) Schematic representation of the thermal energy barrier and corresponding orientation of magnetization in the activation volume.

Figure 4

(a) Theoretical prediction for $v_{\parallel }/v_{\perp }$ as a function of the number of steps $m$ belonging to the domain wall for three different film thicknesses and experimental data for 3 ML Co films. Vertical dashed lines show the width of domain walls. (b) Theoretically calculated exchange stiffness at the step as a function of film thickness.