Asymmetric magnetic domain-wall motion by the Dzyaloshinskii-Moriya interaction

We demonstrate here that ultrathin ferromagnetic Pt/Co/Pt films with perpendicular magnetic anisotropy exhibit a sizable Dzyaloshinskii-Moriya interaction (DMI) effect. Such a DMI effect modifies the domain-wall (DW) energy density and consequently, results in an asymmetric DW expansion driven by an out-of-plane magnetic field under an in-plane magnetic field bias. From an analysis of the asymmetry, the DMI effect is estimated to be strong enough for the DW to remain in the Néel-type configuration in contrast to the general expectations of these materials. Our findings emphasize the critical role of the DMI effect on the DW dynamics as the underlying physics of the asymmetries that are often observed in spin-transfer-related phenomena.

Figure 1

Circular DW expansion driven by an out-of-plane magnetic field $H_z$ (3 mT), (a) without an in-plane magnetic field and (b) with an in-plane magnetic field $H_x$ (50 mT). Each image is obtained by adding four sequential images with a fixed time step (0.4 s), which are captured using a magneto-optical Kerr effect microscope. The white arrow and the symbols indicate the directions of each magnetic field. The blue box in (b) designates where the DW displacement is measured. The dashed red circles in (b) show the calculation results based on Eq. (5) with an extension to arbitrary angles.

Figure 2

Two-dimensional equi-speed contour map of $V$ as a function of $H_x$ and $H_z$. The color corresponds to the magnitude of $V$ with the scale on the right. The symbols with error bars show the measured positions $(H_x,H_z)$ on several equi-speed contours. The black solid lines show the best fit using Eq. (2). The purple line indicates the symmetric axis $H_x=H_0$ for inversion.

Figure 3

(a) $H_z/H_z^{*}\left(V\right)$ and (b) ${\alpha }^{*}$ with respect to $H_x$. The solid lines show the best fit using Eq. (6). The inset shows $V$ vs. ${\alpha }^{*}{H}_z^{-\mu }$ for all experimental data. Each color of the symbols corresponds to a different $H_x$. The solid line shows the best linear fit.

Figure 4

${\alpha }^{*}$ vs. $H_x$ of the latter experiment with opposite magnetic polarities. The solid line is obtained using the best fitting values for Fig. 3, except the opposite polarity of $H_{\mathrm{DMI}}$. The inset shows the equi-speed contour map. The symbols and the lines are identical to those in Fig. 2.

Figure 5

The DMI-induced asymmetry in $V$ with respect to $H_x$ depending on the thickness of (a) the lower ($x$) and (b) the upper ($y$) Pt layers.

Figure 6

Almost symmetric $V$ with respect $H_x$ obtained from films with thick Pt layers. The black dotted line is shown as a reference of the asymmetric DW motion. The letters $a$, $b$, and $c$ indicate the thicknesses of Ta buffer layer, lower Pt layer, and upper Pt layer respectively.