Exploring small energy scales with x-ray absorption and dichroism

Soft x-ray linear and circular dichroism (XLD, XMCD) experiments at the Ce ${\mathrm{M}}_{4,5}$ edges are being used to determine the energy scales characterizing the Ce $4f$ degrees of freedom in the ultrathin ordered surface intermetallic ${\mathrm{CeAg}}_x$/Ag(111). We find that all relevant interactions, i.e., Kondo scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study demonstrates the usefulness of combining x-ray absorption experiments probing the temperature dependence of both linear and circular dichroism owing to their strong sensitivity for anisotropies in both charge distribution and paramagnetic response, respectively.

Figure 1

LEED patterns recorded at an electron kinetic energy of 70 eV from Ag(111) (left) and ${\mathrm{CeAg}}_x$ (right). The satellite reflections in the latter indicate the formation of a $(3\sqrt{3}\times 3\sqrt{3})R{30}^{\circ }$ superstructure as in ${\mathrm{CePt}}_5$/Pt(111) at comparable Ce dose [22, 29]. Ag(111) reflections merge with one of the satellite reflections around ${\langle 2\overline{1}\rangle }_{{\text{CeAg}}_x}$ (indicated by arrows), yielding a $(\frac{10}{9}\sqrt{3}\times \frac{10}{9}\sqrt{3})R{30}^{\circ }$ relation between ${\mathrm{CeAg}}_x$ and substrate unit cells, respectively.

Figure 2

Selection of experimental and simulated Ce ${\mathrm{M}}_{4,5}$ XA spectra for ${\mathrm{CeAg}}_x$/Ag(111). (a) Experimental low temperature ($T=15$ K) isotropic and high temperature ($T=250$ K) normal incidence spectrum. (b) Simulated isotropic spectrum and normal incidence spectra for pure $|m_j\rangle$ initial states. (c) Experimental normal incidence spectra at various temperatures. (d) Zoom-in on the main spectral features of both experimental and simulated normal incidence spectra for three temperatures (see text for details). In each panel, individual spectra were displaced along the ordinate for clarity.

Figure 3

Selection of experimental and simulated XMCD spectra. (a) low temperature XMCD obtained at ${\theta }_X={60}^{\circ }$ (“isotropic” configuration) alongside with the calculated XMCD spectrum, scaled such as to match the magnitude of the experimental data. (b) temperature dependent Ce ${\mathrm{M}}_4$ XMCD in NI geometry. (c) same as in (b) but for ${\theta }_X={60}^{\circ }$.

Figure 4

Inverse magnetic Ce $4f$ susceptibilities of ${\mathrm{CeAg}}_x$, determined from XMCD measurements, along with simulations according to Eq. (4). CF parameters are the same as in Fig. 2.