Nonreciprocal spin-wave dynamics in Pt/Co/W/Co/Pt multilayers

We present a detailed study of the spin-wave dynamics in single Pt/Co/W and double Pt/Co/W/Co/Pt ferromagnetic layer systems. The dispersion of spin waves was measured by wave-vector-resolved Brillouin light scattering spectroscopy while the in-plane and out-of-plane magnetization curves were measured by alternating gradient field magnetometry. The interfacial Dzyaloshinskii-Moriya interaction induced nonreciprocal dispersion relation was demonstrated for both single and double ferromagnetic layers and explicated by numerical simulations and theoretical formulas. The results indicate the crucial role of the order of layers deposition on the magnetic parameters. A significant difference between the perpendicular magnetic anisotropy constant in double ferromagnetic layer systems conduces to the decline of the interlayer interactions and different dispersion relations for the spin-wave modes. Our study provides a significant contribution to the realization of the multifunctional nonreciprocal magnonic devices based on ultrathin ferromagnetic/heavy-metal layer systems.

Figure 1

Schematic drawing of the BLS scattering geometry in the Damon-Eshbach configuration. The incident light makes an angle $\theta$ with respect to the sample normal. Measurements are performed in the backscattering configuration, where the same camera objective is used to focus laser light upon the sample surface and to collect scattered light sent to the interferometer for the frequency analysis. A magnetic field $H$ is applied in the sample plane and perpendicular to the incidence plane of light.

Figure 2

AGFM hysteresis loops measured in the in-plane configuration and out-of-plane configuration. The purple dashed lines represent the fitting using the numerical simulations. In the inset plots, the zoom to low external fields is shown. On top of the figure, the schematic representation of the samples is shown.

Figure 3

(a)–(d) The sequence of BLS spectra measured at $k=0$ ($\theta =0^{\circ }$) and different magnitudes of the externally applied field for all the investigated samples. (e)–(h) The spin-wave frequency measured by BLS in the function of the external field $H$ and fitting with the theoretical formula in Eqs. (8) and (9).

Figure 4

(a)–(d) Measured BLS spectra at $k=18.1\mathrm{rad}/\mu \mathrm{m}$ ($\theta ={50}^{\circ }$) and for two different orientations of the external field: $H=+5.5$ and $-5.5$ kOe. Black points represent the measured spectra, while red curves are the Lorentzian fitting of the peaks. (e)–(h) Dispersion relations measured by the BLS spectroscopy in the external field of $\pm 5.5$ kOe and fitted using finite-element method simulations. (i)–(l) Frequency asymmetry plots measured by the BLS spectroscopy with the linear regression fitting based on Eq. (7).