Interfacial Dzyaloshinskii-Moriya interaction and dampinglike spin-orbit torque in ${\left[\mathrm{Co}/\mathrm{Gd}/\mathrm{Pt}\right]}_N$ magnetic multilayers

Recently, magnetic multilayer systems have received again a great attention owing to their suitability for the generation of magnetic chiral spin structure. In this study, we experimentally investigated the interfacial Dzyaloshisnkii-Moriaya interaction (DMI) and the spin-Hall angle (SHA) of magnetic Co/Gd/Pt multilayers with respect to the repetition number $N$ of the multilayers. The DMI and SHA are important variables that govern the stability and mobility of a homochiral spin structure, respectively. The experimental results show that the ratio between the DMI and the dipole energy from the domain wall gradually decreases as $N$ increases, which is expected to be hard to achieve homochiral spin structure for larger $N$ and the values of SHA remain constant irrespective of $N$. The observed SHA invariance indicates that the Pt layers in repetition have a negligible effect on the SHA.

Figure 1

(a) Schematic diagram of sample structure. (b) Captured charge-coupled device (CCD) image of micropatterned device. Yellow arrow indicates current flow along the Au wire for DW writing. Orange dot presents laser-beam spot for the MOKE measurements. The inset presents up and down magnetic domains and a magnetic domain wall, where $\psi$ is the azimuthal angle of the DW center magnetization. (c) Plots of MOKE signal as a function of ${\mu }_0{H}_z$ with positive (blue), negative (red) current bias, and without current bias (inset). The purple arrow presents effective field induced by the current bias. (d) Plot of ${\mu }_0{H}_z^{\mathrm{eff}}$ as a function of $J$. The red dotted line indicates the best linear fitting. (e) Schematics of the DW types and ${\mu }_0{H}_x$ dependent of the azimuthal angle $\psi$ of the DW center magnetization. (f) Damping-like SOT efficiency ${\varepsilon }_{\mathrm{SOT}}={\varepsilon }_{\mathrm{SOT},\mathrm{sat}}cos\psi \left({\mu }_0{H}_x\right)$ under ${\mu }_0{H}_x$, where ${\varepsilon }_{\mathrm{SOT},\mathrm{sat}}$ is the SOT efficiency of the Néel-type DWs.

Figure 2

Plots of ${\varepsilon }_{\mathrm{SOT}}$ as a function of ${\mu }_0{H}_x$ for the present sample series. Red dotted lines guide the antisymmetric behavior of ${\varepsilon }_{\mathrm{SOT}}$. Blue arrows indicate ${\mu }_0{H}_x$, which completely compensates the DMI-induced effective field.

Figure 3

(a) Plot of ${\mu }_0{H}_{\mathrm{DMI}}$ and ${\mu }_0{H}_{\mathrm{S}}$ as a function of $N$. (b) $|H_{\mathrm{DMI}}/H_{\mathrm{S}}|$ as a function of $N$.

Figure 4

Plots of (a) ${\varepsilon }_{\mathrm{SOT},\mathrm{sat}}$ as a function of $N$. Purple curve in Fig. 3 indicates the inverse proportionality between ${\varepsilon }_{\mathrm{SOT},\mathrm{sat}}$ and $N$. (b) Plots of $M_{\mathrm{S}}$ (red) and $K_{\mathrm{eff}}$ (blue) as a function of $N$. The black solid line in Fig. 4 represents the best fitting based on Eq. (3). (c) Plot of ${\theta }_{\mathrm{SH}}$ as a function of $N$. The blue dotted line represents constant behavior of ${\theta }_{\mathrm{SH}}$. (d) Illustration describing the action of the spin-Hall effect in the present multilayer system. The blue and orange boxes correspond to the heavy-metal and ferrimagnet layer, respectively. The purple and green dashed box denotes top- and bottom-most stack and repetition stack, respectively.