Relaxation Time of Terahertz Magnons Excited at Ferromagnetic Surfaces

The temporal and spatial properties of terahertz magnons excited at ferromagnetic fcc Co(100) and bcc Fe(110) surfaces are investigated experimentally. The magnon lifetime is found to be a few tens of femtoseconds at low wave vectors, which reduces significantly as the wave vector approaches the Brillouin zone boundary. Surprisingly, the lifetime is very similar in both systems, in spite of the fact that the excitation energy in the Co(100) film is by a factor of two larger than in the Fe(110) film. The magnon wave packets propagate only a few nanometers within their lifetime. In addition to the fact that our results describe the damping mechanism in ultrafast time scales, they may provide a way to predict the ultimate time scale of magnetic switching in nanostructures.

Figure 1

Typical spectra recorded at an incident electron energy of 4 eV and a wave vector transfer of $0.6{\AA }^{-1}$. The red spectrum indicates the intensity of the scattered electrons for incidence of minority electrons $I_{\downarrow }$, and the blue one is for the incidence of majority electrons $I_{\uparrow }$. The green curve is the difference between the red and blue spectra ($I_{\downarrow }-I_{\uparrow }$). The beam polarization was about 65%. The peak at about 65 meV in the red spectrum is attributed to the magnon excitations. The scattering geometry is schematically sketched in the inset.

Figure 2

(a) The difference spectra are plotted as a contour map for the wave vectors from 0 to $1{\AA }^{-1}$. The section profiles for a wave vector at $0.7{\AA }^{-1}$ and energy at about 82 meV are shown in (b) and (c), respectively. The magnon peak in (b) is fitted by the convolution of a Gaussian and a Lorentzian function. The intrinsic linewidth of the peak is 55 meV. The intensity profile along the horizontal line at $E=82\mathrm{meV}$ in (c) is fitted by a Gaussian profile shown as a solid curve.

Figure 3

(a) Magnon dispersion relation in 8 ML $\mathrm{Co}/\mathrm{Cu}(001)$ (open circles) and 2 ML $\mathrm{Fe}/\mathrm{W}(110)$ (open squares). Solid symbols mark the center of three states for Fe and Co surfaces, which are named as $S_{\mathrm{Fe}}$, $S_{\mathrm{Co}}^1$, and $S_{\mathrm{Co}}^2$ respectively. $S_{\mathrm{Fe}}$ and $S_{\mathrm{Co}}^1$ are at nearly the same wave vectors $0.8{\AA }^{-1}$, $S_{\mathrm{Fe}}$, and $S_{\mathrm{Co}}^2$ are at almost the same energy 100 meV. The dotted lines at about 1.21 and 1.49 mark the surface Brillouin zone boundaries of Co(001) and Fe(110) surfaces. (b) The plot of the evolution of wave packets for the states $S_{\mathrm{Fe}}$ ($0.80{\AA }^{-1}$, 95 meV) at Fe surface, $S_{\mathrm{Co}}^1$ ($0.81{\AA }^{-1}$, 174 meV) and $S_{\mathrm{Co}}^2$ ($0.55{\AA }^{-1}$, 101 meV) at Co surface. The amplitude may be regarded as the transverse component of a precessing spin projected to the wave propagation directions or the modulus of the magnon wave function.

Figure 4

The magnon lifetime as a function of the in-plane wave vector measured for 2 ML $\mathrm{Fe}/\mathrm{W}(110)$ (solid symbols) and 8 ML $\mathrm{Co}/\mathrm{Cu}(001)$ (open symbols). Inset shows the intrinsic linewidth of the magnon peaks.