Charge Excitations in Nd$_{2-x}$Ce$_x$CuO$_4$ Observed with Resonant Inelastic X-ray Scattering: Comparison of Cu K-edge with Cu L$_3$-edge

TL;DR

This study uses resonant inelastic X-ray scattering to compare charge excitations in Nd$_{2-x}$Ce$_x$CuO$_4$ at Cu K-edge and L$_3$-edge, revealing consistent excitations across both edges.

Contribution

It demonstrates that charge excitations observed at Cu K-edge and L$_3$-edge are identical in Nd$_{2-x}$Ce$_x$CuO$_4$, confirming the equivalence of these RIXS measurements.

Findings

Charge excitations are consistent at both edges.

Peak position and width match across edges.

Same charge excitations observed in Nd$_{2-x}$Ce$_x$CuO$_4$.

Abstract

We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of momentum-dependent charge excitations in Nd$_{2-x}$Ce$_x$CuO$_4$ ($x$ = 0.075 and 0.18). The peak position and width of the excitations coincide excellently with those observed in Cu L$_3$-edge RIXS. It demonstrates that the same charge excitations are observed at the two edges.

Full text

Low-energy electron dynamics in high-$T_{\mathrm{c}}$ cuprates is characterized by the motion of charge and spin. Among the various experimental technique for studying the electron dynamics, resonant inelastic x-ray scattering (RIXS) has gained a great deal of attention because one can measure electronic excitation spectra with momentum resolution and element selectivity.[1, 2] Cu $K$- and $L_{3}$-edges are mostly used for the RIXS study of the cuprates. Energy resolution has been improved significantly in the last two decades and it reaches a few tens of meV at best at the edges.[3, 4] While spin excitation (single spin-flip process) is allowed only at the $L_{3}$-edge, charge excitation can be observed at both edges.

In the electron-doped cuptate Nd2-xCexCuO4 (NCCO), momentum-dependent charge excitations, which are located at higher energy than the spin excitations, are indeed observed in the K-[5, 6, 7] and $L_{3}$-edge RIXS spectra,[7, 8, 9] even though different interpretations, intraband particle-hole excitations[5, 7] and a certain mode associated with a symmetry-breaking state,[8] were proposed. Recently, the charge excitations in the $L_{3}$-edge RIXS were found to depend not only on the the in-plane momentum but also on the out-of-plane one and ascribed to a plasmon mode[9] which was proposed theoretically.[10, 11] In order to further investigate the character of the charge excitations, for example, contrasting behavior at high temperature within a slight difference of carrier concentration ($\sim$0.02 electron per Cu atom),[8] it is important to verify whether the same excitation is observed at the two edges because each edge has a suited energy-momentum range for observing the excitations. In Ref. \citenIshii2014, the charge excitations at the $K$-edge are compared with the one at the $L_{3}$-edge. However the comparison is made only at a few momentum points and the out-of-plane momentum is not considered. In this short note, we report a Cu $K$-edge RIXS study of NCCO in comparison with the $L_{3}$-edge and conclude that the momentum-dependent charge excitations in the Cu $K$-edge RIXS spectra are the same as in the $L_{3}$-edge.

RIXS experiments were performed at BL11XU of SPring-8. Incident x rays were monochromatized by a Si(111) double-crystal monochromator and a Si(444) channel-cut monochromator, and horizontally scattered x rays were analyzed in energy by a Ge(733) analyzer. Experimental geometry was the same as the previous works;[5, 7] $\pi$-polarized incident photons with 8991 eV were irradiated on the $ac$-plane of NCCO, but the energy resolution of 100 meV was improved better than the works.[5, 6, 7] All the spectra were taken at 10 K. We use Miller index ($H$, $K$, and $L$) of the body-centered-tetragonal crystallographic unit cell for momentum transfer (${\mathbf{Q}}$).

Figure 1 shows the Cu $K$-edge RIXS spectra of NCCO. A peak at 2 eV and a momentum-dependent feature below the peak are consistent with the previous work, [5] but the improved energy resolution enables us to observe the latter more clearly, especially at low in-plane momenta ($H$, $K$). The 2-eV peak is an interband excitation across the charge-transfer gap and it is also observed in parent Nd2CuO4.[6] On the other hand, the momentum-dependent feature appears when electrons are doped. We fit the spectra by the sum of elastic scattering, the momentum-dependent charge excitation, the interband excitation, and a tail of high energy charge excitation peaked around 6 eV.[12] The experimental resolution is considered for the momentum-dependent charge excitation and the interband excitation. Filled circles in Fig. 2(a) and (b) are the peak position and width (full-width at half maximum) of the momentum-dependent feature obtained from the fitting analysis, respectively. Because intensity of the feature is roughly proportional to the carrier density, the feature of $x$ = 0.075 forms continuum-like spectral shape in contrast to the salient peak in $x$ = 0.18. It makes the fitting analysis of $x$ = 0.075 difficult and this is the reason why the error is larger than $x$ = 0.18.

Open circles in Fig. 2(a) are the peak positions in our Cu $L_{3}$-edge study,[7] where the crystals from the same batch as this work were used. Momentum transfer along the ${\mathbf{c}}^{\ast}$-direction ($L$) varies between 1.55 and 1.65 and it is almost equivalent to that in the present data in Fig. 1, considering that the dispersion is folded at even numbers of $L$.[9] The peak positions are consistent between the Cu $K$- and $L_{3}$-edges. In addition, we plot the peak positions of La2-xCexCuO4 (LCCO) of $x$ = 0.175 and $L$ = 1.65 (open squares) taken from a recent high-energy-resolution work at the Cu $L_{3}$-edge.[9] The positions of LCCO $x$ = 0.175 agree very well with those of NCCO $x$ = 0.18.

In Fig. 2(b), the width of the peak is compared between the $K$-edge and the $L_{3}$-edge. The momentum dependence of the width of LCCO $x$ = 0.175 at the $L_{3}$-edge is connected smoothly to that of NCCO $x$ = 0.18 at the $K$-edge. It means that the broadening of the peak comes from intrinsic electronic properties of the cuprates rather than some effects in the RIXS process. While momentum-independent lifetime of electron is phenomenologically taken into account in a theoretical work,[11] RIXS can provide experimental data to discuss microscopic origin of the broadening quantitatively.

The excellent agreement of the peak position and width between NCCO $x$ = 0.18 and LCCO $x$ = 0.175 proves that the momentum-dependent charge excitation in the Cu $K$-edge RIXS spectra has the same origin as the dispersive mode observed at the Cu $L_{3}$-edge. Our result approves the complementary use of the two edges for exploring the charge excitations throughout the energy-momentum space. In general, the $L_{3}$-edge is advantageous for the excitations at low energy due to weak elastic scattering while it has limitation of the accessible Brillouin zone. In the case of cuprates, huge $dd$ excitations above 1.5 eV hampers the observation of the charge excitations at the energy. On the other hand, the $K$-edge does not have the shortcomings of the $L_{3}$-edge, but it is difficult to measure the inelastic signal at very low energy. Even though the lower limit in the energy resolution of this study is 0.4-0.5 eV, we will have change to access lower energy if the best resolution (25 meV) is achieved.[3]

Another finding is that the peak position of the charge excitations shifts to higher energy with increasing electron doping. Although the data of $x$ = 0.075 scatter, Fig. 2(a) shows that the peak position of $x$ = 0.18 is higher in energy than that of $x$ = 0.075. Such doping dependence has been reported in the $L_{3}$-edge RIXS work[9] as a character of plasmon excitation and we confirm it here at the $K$-edge. It is noted that doping dependence was measured at higher in-plane momentum in the previous $K$-edge work [5, 6] and it just shows increase of intensity with increasing doping. It may indicate that the high-energy shift is limited at low in-plane momentum and doping effect of the charge excitations changes at a certain momentum.

In summary, we performed a Cu $K$-edge RIXS study of NCCO and analyzed the momentum-dependent charge excitations below the charge transfer gap. The peak position and width agree very well with those at the Cu $L_{3}$-edge and we conclude that the same charge excitations are observed at the two edges.

{acknowledgment}

The authors would like to thank T. Tohyama and H. Yamase for fruitful discussion. The synchrotron radiation experiments were performed at the BL11XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposals No. 2013B3502 and 2014A3502). This work was financially supported by JSPS KAKENHI Grants No. 25400333. and No. 16H04004.