High-wave-vector spin waves in ultrathin Co films on W(110)

We present an experimental study of high-wave-vector spin waves in 8 monolayer (ML) thick hexagonal closed-packed (hcp) Co films performed by spin-polarized electron energy loss spectroscopy (SPEELS). Using inelastic electron scattering, we were able to follow the spin wave dispersion up to the surface Brillouin zone boundary $\left(\overline{K}\right)$, i.e., up to a wave-vector transfer of $1.64{\mathrm{\AA }}^{-1}$. The spin wave dispersion was found to agree surprisingly well with the dispersion relation of a surface spin wave calculated by a nearest-neighbor Heisenberg model. From this description, we obtain a value for the product of the exchange coupling constant $\left(J\right)$ and the magnetic moment $\left(S\right)$ of $JS=14.8\pm 1\mathrm{meV}$. This value, within the error bar, is identical to our results obtained on thin fcc Co films on Cu(001). We also find that the spin wave features measured by SPEELS at high-wave-vectors are strongly broadened. This is in agreement with expectations from nonadiabatic theoretical descriptions in which the broadening is ascribed to a strong damping of these high-wave-vectors spin waves by Stoner excitations. Similar to the observations in previously studied systems, we also observe a strong dependence of the measured spin wave intensities on the kinetic energy of the incident electrons $\left(E_{\mathrm{kin}}\right)$. Highest spin wave intensities were found for low kinetic energies $(E_{\mathrm{kin}}<10\mathrm{eV})$.

Figure 1

The left panel shows SPEEL spectra of $I_{\uparrow }$ (▵) and $I_{\downarrow }$ (▾) measured for a wave vector transfer of $0.88{\mathrm{\AA }}^{-1}$ on an 8 ML Co film. The spectra are corrected for the incomplete polarization of the incident electron beam. In the right panel, the difference $I_{\downarrow }\text{−}{I}_{\uparrow }$ (●) is plotted. The solid line shows a fit to the difference, consisting of a Gaussian peak for the spin wave and a background, both are also shown separately as dashed and dotted lines, respectively. The spectra were measured with primary energy $E_{\mathrm{kin}}=4\mathrm{eV}$, ${\theta }_0=80°$, and an energy resolution of $\Delta E=40\mathrm{meV}$.

Figure 2

SPEEL spectra and differences measured at $E_{\mathrm{kin}}=4\mathrm{eV}$, ${\theta }_0=80°$ (a,b), and $E_{\mathrm{kin}}=25\mathrm{eV}$, ${\theta }_0=90°$ (c,d) on 8 ML hcp Co. The spectra in the upper (lower) panel were measured with $\Delta K_{\Vert }=1.00{\mathrm{\AA }}^{-1}$ $(\Delta K_{\Vert }=1.12{\mathrm{\AA }}^{-1})$. The total counting time for each data point in (a) and (c) was 10 and $50\mathrm{s}$, respectively. The features in (a) and (c) around 130 and $240\mathrm{meV}$ are due to adsorbates, as discussed in the text. In the difference spectra, the fits and the separate contribution of spin wave and background are shown. The energy resolution in these scans was $\Delta E=40\mathrm{meV}$.

Figure 3

The spin wave intensity as a function of different kinetic energies of the incident electrons measured by SPEELS. All points were measured for $\Delta K_{\Vert }=0.88{\mathrm{\AA }}^{-1}$.

Figure 4

Spin wave dispersion for 8 ML hcp Co on W(110) (∎) and 8 ML fcc Co on Cu(001) (엯) measured by SPEELS. The dashed lines are the dispersion relations for an acoustic surface spin wave mode calculated using a nearest-neighbor Heisenberg model (see text for details). The dotted lines mark the surface Brillouin zone boundaries for the two crystals. In regions A, B, and C, the SPEEL spectra on hcp Co were obtained using $E_{\mathrm{kin}}=4\mathrm{eV}$, ${\theta }_0=80°$, and $\Delta E\approx 25\mathrm{meV}$ (for A); $E_{\mathrm{kin}}=4\mathrm{eV}$, ${\theta }_0=80°$, and $\Delta E\approx 40\mathrm{meV}$ (for B), and $E_{\mathrm{kin}}=25\mathrm{eV}$, ${\theta }_0=90°$, and $\Delta E\approx 40\mathrm{meV}$ (for C). In the lower panel, the full width at the half maximum of the spin wave peak is shown. The width is corrected for the finite energy resolution of the spectrometer. The width for the peak at $1.64{\mathrm{\AA }}^{-1}$ could not be determined accurately and is not included in the graph.