Spin-Polarized Electron Energy Loss Spectroscopy of High Energy, Large Wave Vector Spin Waves in Ultrathin fcc Co Films on Cu(001)

The realm of high energy, large wave vector spin waves in ultrathin films and at surfaces is unexplored because a suitable method was not available up to now. We present experimental data for an 8 ML thick Co film deposited on Cu(001) which show that spin-polarized electron energy loss spectroscopy can be used to measure spin-wave dispersion curves of ultrathin ferromagnetic films up to the surface Brillouin zone boundary.

Figure 1

SPEELS intensity spectra $I_{\uparrow }$ (○) and $I_{\downarrow }$ (●), normalized to the average intensity $(I_{\uparrow }+I_{\downarrow })/2$ at 0 meV energy loss, for $E_0=6.7\mathrm{e}\mathrm{V}$ and $\Delta K=-0.87{\AA }^{-1}$. The dashed line indicates qualitatively the contribution of Stoner excitations to $I_{\downarrow }$. The inset describes the scattering geometry: $S_z^{\downarrow (\uparrow )}$ is the spin polarization of the incident beam, M is the magnetization direction, $k_i,k_f$ are the wave vectors of the incident and scattered electron, $\theta$ is the incident angle, and ${\theta }_0=90°$ is the angle between the monochromator and the detector.

Figure 2

Series of normalized SPEELS intensity spectra (a) $I_{\uparrow }$ and (b) $I_{\downarrow }$. (c) Asymmetry spectra for different angles of incidence, corresponding to the $\Delta K$ values plotted in panel (a). $E_0=6.7\mathrm{e}\mathrm{V}$. The intensity curves are offset by 0.025 and the asymmetry curves by 0.15 with respect to each other.

Figure 3

Spin wave energy versus parallel wave vector transverse $\Delta K$ derived from the spin-wave peak position in the $I_{\downarrow }$ EEL spectra. $E_0=6.7\mathrm{e}\mathrm{V}$, ${\theta }_0=90°$ (●), ${\theta }_0=80°$ (■). All lines and the gray area result from the NN Heisenberg model with $JS=15\mathrm{m}\mathrm{e}\mathrm{V}$: The solid thick line is the surface mode of a semi-infinite solid and the gray area the surface projected bulk modes. The thin solid lines are the eight dispersion curves for an 8 ML thick slab, from which the lowest mode nearly coincides with the surface mode. For comparison the available neutron data on fcc Co (8% Fe) along the $[110]$ direction in the bulk are plotted as well (○, Ref. 14). The dashed line is the bulk spin-wave dispersion curve along the $[110]$ direction using the same value for $JS$ as for the SPEELS data.