ELECTRONIC STRUCTURE, MAGNETISM AND DYNAMICS

120 ESRF

Fig. 104: Low-energy excitation RIXS spectra on titanates.

a) XAS spectrum around Ti L3-edge of conducting STO.

b-c) RIXS data as function of incoming photon energy along

the XAS Ti L3 absorption edge for bulk insulating (b) and

conducting (c) STO. Different colours correspond to different

incoming photon energies, namely A3 (blue), B0 (red) and

B1 (dark blue) (from top to bottom). d) FFT smoothed data

at A3 (blue line) and B1 (green line) for STO insulating sample and red dashed lines indicating

the three main phonon peaks compared to (e) tabulated phonon dispersions along

G-M and G-X for STO.

(90-100 meV w3) features, matching with LO1 (TO1) LO2 (TO3) and LO3 optical phonons. (Figure 104e). The additional higher energy features at about 200 and 300 meV are two and three LO3 phonon replicas, while the particularly strong peak around 130 meV is a new kind of composite excitation comprising an intra-t2g d-d transition (25-40 meV) and the high-energy (90-100 meV) LO3 optical phonon.

A simultaneous fitting of A3, B0 and B1 RIXS spectra, using a model including the phonon and the mixed d-d + LO3-phonon contributions, is able to reproduce all the data and allows the determination of the LO3-EPC constant (g) for both t2g and eg electrons, as shown in Figure 105. It is found that the LO3 EPC decreases as a function of the carrier density from values of the order of 2.0 (1.0) for eg (t2g) electrons in insulating STO, to values of the

Fig. 105: LO3 EPC as function of the volume carrier density estimated from the analysis of the RIXS

data. Red spheres are g(t2g), blue spheres are g(eg), orange sphere is the LO3 coupling estimated in the

LAO/STO ML from spectra at A3 spectra (close to g(t2g)). In the graph, a doping of 1015 cm-3 has been

assigned to insulating STO.