Nonreciprocal Dzyaloshinskii–Moriya Magnetoacoustic Waves

We study the interaction of surface acoustic waves with spin waves in ultrathin $\mathrm{CoFeB}/\mathrm{Pt}$ bilayers. Because of the interfacial Dzyaloshinskii–Moriya interaction (DMI), the spin wave dispersion is nondegenerate for oppositely propagating spin waves in $\mathrm{CoFeB}/\mathrm{Pt}$. In combination with the additional nonreciprocity of the magnetoacoustic coupling itself, which is independent of the DMI, highly nonreciprocal acoustic wave transmission through the magnetic film is observed. We systematically characterize the magnetoacoustic wave propagation in a thickness series of $\mathrm{CoFeB}(d)/\mathrm{Pt}$ samples as a function of magnetic field magnitude and direction, and at frequencies up to 7 GHz. We quantitatively model our results to extract the strength of the DMI and magnetoacoustic driving fields.

Figure 1

(a) Schematic illustration of the experimental setup and the coordinate system. A scaled drawing is shown in the Supplemental Material [22]. Nonreciprocal MASWs are characterized by different transmission amplitudes $\mathrm{\Delta }{S}_{21}$ and $\mathrm{\Delta }{S}_{12}$ for oppositely propagating SAWs $k_{S21}$ and $k_{S12}$. The SAW transmission curves of (b) CoFeB(2) and (c) $\mathrm{CoFeB}(2)/\mathrm{Pt}$ are obtained at 6.90 GHz, 6.88 GHz, and ${\varphi }_H=64.8°$. Only $\mathrm{CoFeB}(2)/\mathrm{Pt}$ reveals a nonreciprocity in both transmission amplitude at resonance and resonant magnetic field.

Figure 2

Change of the SAW transmission $\mathrm{\Delta }{S}_{ij}$ as a function of the orientation and magnitude of the external magnetic field. The experimental $\mathrm{\Delta }{S}_{21}$ and $\mathrm{\Delta }{S}_{12}$ of the (a) CoFeB(2) single layer and (b) $\mathrm{CoFeB}(2)/\mathrm{Pt}$ bilayer (upper row) are measured at the resonance frequencies of the SAW delay lines at 6.90 and 6.88 GHz, respectively. Both samples reveal nonreciprocal behavior with respect to the transmission magnitude. An additional nonreciprocal shift of the resonance fields is induced by DMI in the $\mathrm{CoFeB}(2)/\mathrm{Pt}$ sample. Numerical fits (lower row).

Figure 3

(a) Angular dependence of the resonance fields of the $\mathrm{CoFeB}(2)/\mathrm{Pt}$ sample in Fig. 2. Dots denote the experimental data, solid curves the fit. (b) The magnitude of the effective DMI constant as a function of the inverse of the film thickness agrees with the expected linear behavior, revealing the interface character of the underlying interaction. (c) The driving field fit parameters $b_{xx}$ and $b_{xz}$ for the $\mathrm{CoFeB}(d)/\mathrm{Pt}$ thickness series (dots) and the CoFeB(2) sample (stars). The error bars in (b) and (c) are smaller than the symbol size. (d) Summary of the highest attained transmission nonreciprocity $\mathrm{\Delta }S$ and the corresponding attenuation in the acoustic diode forward direction $IL$.

Figure 4

(a) Nonreciprocal MASW detected in a continuous frequency range of 3 to 7 GHz. The results are shown for $\mathrm{CoFeB}(2)/\mathrm{Pt}$ and ${\varphi }_H=45°$. The blue line indicates the position of the resonance fields from the simulation in (b), carried out with the parameters in the Supplemental Material, Table SIII [22].