Magnetic properties and field-driven dynamics of chiral domain walls in epitaxial ${\mathrm{Pt}\text{/}\mathrm{Co}\text{/}\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ trilayers

Chiral domain walls in ultrathin perpendicularly magnetized layers have a Néel structure stabilized by a Dzyaloshinskii-Moriya interaction (DMI) that is generated at the interface between the ferromagnet and a heavy metal. Different interface materials or properties are required above and below a ferromagnetic film in order to generate the structural inversion asymmetry needed to ensure that the DMI arising at the two interfaces does not cancel. Here we report on the magnetic properties of epitaxial Pt/Co/${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ trilayers grown by sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0 to 1, a structural inversion asymmetry is progressively generated. We characterize the epilayer structure with x-ray diffraction and cross-sectional transmission electron microscopy, revealing (111) stacking. The saturation magnetization falls as the proximity magnetization in Pt is reduced, whilst the perpendicular magnetic anisotropy $K_{\mathrm{u}}$ rises. The micromagnetic DMI strength $D$ was determined using the bubble expansion technique and also rises from a negligible value when $x=0$ to $\sim 1$ mJ/${\mathrm{m}}^2$ for $x=1$. The depinning field at which field-driven domain wall motion crosses from the creep to the depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater spatial fluctuations of the domain wall energy with increasing Au concentration. Meanwhile, the increase in DMI causes the Walker field to rise from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x=1$ sample is the steady flow regime accessible. The full dependence of domain wall velocity on driving field bears little resemblance to the prediction of a simple one-dimensional model, but can be described very well using micromagnetic simulations with a realistic model of disorder. These reveal a rise in Gilbert damping as $x$ increases.

Figure 1

Structural characterization of Pt/Co/${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ trilayers. (a) X-ray diffraction spectra confirming the fcc (111) orientation of the samples. (b) Dark field HRTEM cross-section images. (c) EDX spectra showing distinguishable layers with possible intermixing at the interfaces.

Figure 2

Magnetic characterization of Pt/Co/${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ trilayers. (a) Polar MOKE loops. (b) Anisotropy field, $H_{\mathrm{K}}$, and effective anisotropy energy, $K_{\mathrm{eff}}$ both increase with Au concentration. (c) Saturation magnetization $M_{\mathrm{s}}$ supposing that all the magnetic moment is confined in the Co layer (black dots), extracted proximity-induced magnetism in Pt layers (red) and corrected Co layer values $M_{\mathrm{Co}}$ (blue). (d) Variation of relative saturation magnetization with temperature for Pt/Co/Pt. The solid red line is a fit of the Bloch law.

Figure 3

Asymmetric bubble expansion measurements. (a) Effective DMI field ${\mu }_0{H}_{\mathrm{DMI}}$ and effective DMI constant $D_{\mathrm{eff}}$ as a function of Au concentration $x$ in Pt/Co(6 Å)/${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ epilayers. An example of a Kerr difference image of the bubble expansion in Pt/Co/Au is shown as an inset. The values plotted were derived from the data in (b)–(d), which show DW velocity as a function of in-plane magnetic field ${\mu }_0{H}_x$ in case of Pt, ${\mathrm{Pt}}_{50}{\mathrm{Au}}_{50}$, and Au capping layers, respectively, for ${\mu }_0{H}_z=7$, 8, and 10.5 mT.

Figure 4

OoP-only field-driven DW motion for Pt/Co/${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ epilayers. (a) Fits to the data by universal models for creep (dashed-dotted curve) and depinning regimes (solid curve) on a linear-linear plot. The dotted lines are linear fits to the viscous flow regime. (b) Semilogarithmic plot of the same velocity data as a function of ${\left({\mu }_{0}H\right)}^{-1/4}$ to show fitting to the creep regime more clearly. Data are shifted to the right respectively for clarity of presentation. In each case, the solid stars show the depinning field $H_{\mathrm{d}}$. (c)–(f) Changes of derived parameters with concentration of gold $x$: depinning field $H_{\mathrm{d}}$, depinning temperature $T_{\mathrm{d}}$, DW velocity in a film with pinning $v_T$, and DW mobility $m$, respectively.

Figure 5

Field-induced DW motion in Pt/Co/${\mathrm{Au}}_x{\mathrm{Pt}}_{1-x}$ epilayers. (a) and (b) Visualizations of the micromagnetic simulations for Pt/Co/Au with $\delta =8.5\%,\alpha =0.35$ at $t=0\mathrm{ns}$. (c) Field-dependent velocity curves along with the simulation from micromagnetic simulations and 1D model calculations. It is shown that 1D model calculations cannot reproduce the data while the micromagnetic simulations can follow change in velocity precisely.