Dipolar Excitations at the $L_{\mathrm{III}}$ X-Ray Absorption Edges of the Heavy Rare-Earth Metals

We report measured dipolar asymmetry ratios at the $L_{\mathrm{III}}$ edges of the heavy rare-earth metals. The results are compared with a first-principles calculation and excellent agreement is found. A simple model of the scattering is developed, enabling us to reinterpret the resonant x-ray scattering in these materials and to identify the peaks in the asymmetry ratios with features in the spin and orbital moment densities.

Figure 1

Top curves, field-dependent energy scan for Gd. At each energy point the field was reversed many times and averaged to reduce systematic errors. Below, charge-magnetic XRIS asymmetry ratios [see Eq. (3)]. Experimental data (cyan), first-principles x-ray scattering theory (red) and model (blue). Statistical errors are smaller than the plotted points. In Tm (with scattering angle $<90°$), the asymmetry ratio reverses sign. Therefore we have simply inverted the curves for Tm in the figure. The curves consist of a dominant high energy peak and a lower energy shoulder that becomes more pronounced with increasing atomic number. The higher energy peak results from scattering off the spin moment and the lower energy peak arises from scattering from both the spin and orbital moments. The changing relative size and position of these peaks reflects the change in relative magnitude of these quantities. The zero of energy here is the $L_{\mathrm{III}}$ edge which we equate to the Fermi energy.

Figure 2

(a) Spin-polarized convoluted $5d$ DOS: Beyond Gd, the data are offset by $-0.1{\mu }_B/\mathrm{eV}$ with respect to the preceding element. The DOS have been convoluted with 3 eV wide Lorentzians to represent core hole broadening. The center of the occupied $5d$ spin moments is also shown below $E_F$, indicated by the arrows. The arrows above $E_f$ show the energy of the center of the $5d$ spin moment closure peaks. The near vertical dashed lines mark the position of features A and B in Fig. 1. (b) Orbital polarized convoluted $5d$ DOS: Data are scaled and offset as in (a). The dashed line represents the Hund’s rule state and the full line is for the non-Hund’s rule state.