Interfacial Dzyaloshinskii-Moriya Interaction in $\mathrm{Pt}/\mathrm{CoFeB}$ Films: Effect of the Heavy-Metal Thickness

We report the observation of a Pt layer thickness dependence on the induced interfacial Dzyaloshinskii-Moriya interaction in ultrathin $\mathrm{Pt}(d_{\mathrm{Pt}})/\mathrm{CoFeB}$ films. Taking advantage of the large spin-orbit coupling of the heavy metal, the interfacial Dzyaloshinskii-Moriya interaction is quantified by Brillouin light scattering measurements of the frequency nonreciprocity of spin waves in the ferromagnet. The magnitude of the induced Dzyaloshinskii-Moriya coupling is found to saturate to a value of $0.45\mathrm{mJ}/{\mathrm{m}}^2$ for Pt thicknesses larger than $\sim 2\mathrm{nm}$. The experimental results are explained by analytical calculations based on the three-site indirect exchange mechanism that predicts a Dzyaloshinskii-Moriya interaction at the interface between a ferromagnetic thin layer and a heavy metal. Our findings open up a way to control and optimize chiral effects in ferromagnetic thin films through the thickness of the heavy-metal layer.

Figure 1

(a) Schematic depiction of the system under study. The magnetization $\mathbf{M}$ is saturated along the $z$ axis by an external magnetic field $\mathbf{H}$. Spin waves propagate on the $xz$ plane and are characterized by a wave vector $\mathit{k}$ making an angle ${\varphi }_{\mathit{k}}$ with the saturation direction. Based on the three-site Fert-Levy model, the interfacial DMI is determined under the scheme (b), where brown dots represent a pair of CoFeB spins interacting through a third Pt atom (gray dot) at position ${\mathit{R}}_i^{\mathit{l}}$ with respect to spin $i$. (c) Illustration of a (100) plane of a fcc crystallite oriented at an angle $\beta$ with the $x$ axis, while the pair of spins is oriented at an angle $\delta$ with $x$. (d) The resulting DMI vector is distributed on the $xz$ plane and is perpendicular to the triangle in (b).

Figure 2

Brillouin light scattering spectra measured at $k=1.81\times 10^7\mathrm{rad}/\mathrm{m}$ under a magnetic field $H=3\mathrm{kOe}$ for samples having a Pt thickness of (a) 0.4 and (b) 1 nm.

Figure 3

Measured frequency shift for different Pt thicknesses. The samples are under a magnetic field $H=\pm 3\mathrm{kOe}$, with the corresponding theoretical fitting based on Eq. (2).

Figure 4

(a) Spin-wave frequency asymmetry in a $\mathrm{CoFeB}/\mathrm{Pt}$ as a function of Pt thickness at $k_{\max }=2.04\times 10^7\mathrm{rad}/\mathrm{m}$. The fit (red line) of the data, based on Eq. (2), is done with the parameters $a=0.25\mathrm{nm}$, $b=0.39\mathrm{nm}$, and $L_0=0.32\mathrm{nm}$, and $n=2.85$. The inset shows the in-plane angular dependence of $\mathrm{\Delta }f$ and its corresponding fit curve for a thickness $d_{\mathrm{Pt}}=5\mathrm{nm}$ at a wave vector $k=1.35\times 10^7\mathrm{rad}/\mathrm{m}$. (b) DMI strength as a function of $d_{\mathrm{Pt}}$ obtained from $\mathrm{\Delta }f(k_{\max },d_{\mathrm{Pt}})$ and for a gyromagnetic ratio $\gamma =187\mathrm{GHz}/\mathrm{T}$ [59].