Distinguishing Quasiparticle-Phonon Interactions by Ultrahigh-Resolution Lifetime Measurements

We present a determination of quasiparticle-phonon interaction strengths at surfaces through measurements of phonon spectra with ultrahigh energy resolution. The lifetimes of low energy surface phonons on a pristine Ru(0001) surface were determined over a wide range of temperatures and an analysis of the temperature dependence enables us to attribute separate contributions from electron-phonon interactions, phonon-phonon interactions, and defect-phonon interactions. Strong electron-phonon interactions are evident at all temperatures and we show they dominate over phonon-phonon interactions below 400 K.

Figure 1

A top down schematic representation of the Cambridge HeSE spectrometer. A spin-polarized supersonic ${}^3\mathrm{He}$ beam is scattered from the Ru(0001) sample surface to probe surface phonons. The total scattering angle is ${\theta }_{\mathrm{tot}}=44.4°$. The angle of incidence ${\theta }_i$ can be varied to probe phonons with different momenta and energies.

Figure 2

(a) and (b) Raw data for the ${}^3\mathrm{He}$ nuclear spin polarizations along the $x$ and $y$ directions as a function of current magnitude $(I_1^2+I_2^2{)}^{1/2}$ are shown as blue points. The solid line is the result of a model describing the results after back transforming from the energy domain (see below). Note that the range of currents includes the complete polarization decay, which leads to the corresponding phonon spectrum. (c) The scattered intensity as a function of energy change, $\mathrm{\Delta }E$, of ${}^3\mathrm{He}$ atoms, which is the domain where the analysis is performed. The data, blue crosses, are transformed using the method described in [27]. The RW phonon is modeled with a Lorentzian profile and the broad background is represented by a quartic polynomial. In (a) and (b), the red curves are reconverted from the elastic peak and the RW phonon peak in (c) using the reverse method. The location of the RW mode phonon peak indicates that the energy of the phonon $\hslash \omega$ is 7.4 meV. The red bar, which is the FWHM of the peak, represents the phonon linewidth, denoted $\gamma$ in the text. The elastic peak around $\mathrm{\Delta }E=0$ is represented as a Gaussian function. The data shown correspond to a surface temperature of 625 K, an incident angle of ${\theta }_i=28.575°$, and the $[1\overline{1}00]$ azimuth. The mean kinetic energy of the incoming ${}^3\mathrm{He}$ atoms is 8.07 meV.

Figure 3

(a) and (b) Temperature dependence of RW phonon linewidths along the $[1\overline{1}00]$ azimuth: (a) ${\theta }_i=25.825°$ and the phonon energy is $\hslash \omega =3.8\mathrm{meV}$. (b) ${\theta }_i=28.575°$ and $\hslash \omega =7.4\mathrm{meV}$. Blue points represent experimental data with the error bars being 95% confidence bounds in peak fitting processes illustrated in Fig. 2. The red solid lines represent the calculated phonon linewidth $\gamma$ in Eq. (3), which can be expressed as the sum of contributions from electron-phonon interaction (yellow lines), phonon-phonon interaction (purple lines), and defect-phonon interaction (green lines). (c) and (d) $f(E)-f(E+\hslash \omega )$ as a function of temperature for various $E$. The values of $\hslash \omega$ correspond to the energies of phonons studied in (a) and (b), respectively.