Yb valence change in Ce${}_{1-x}$Yb${}_x$CoIn${}_5$ from spectroscopy and bulk properties

The electronic structure of Ce${}_{1-x}$Yb${}_x$CoIn${}_5$ has been studied by a combination of photoemission, x-ray absorption, and bulk property measurements. Previous findings of a Ce valence near 3$+$ for all $x$ and of an Yb valence near 2.3$+$ for $x⩾0.3$ were confirmed. One new result of this study is that the Yb valence for $x⩽0.2$ increases rapidly with decreasing $x$ from 2.3 toward 3+, which correlates well with de Haas van Alphen results showing a change of Fermi surface around $x=0.2$. Another new result is the direct observation by angle resolved photoemission Fermi surface maps of $\approx$50$\%$ cross-sectional area reductions of the $\alpha$ and $\beta$ sheets for $x=1$ compared to $x=0$, and a smaller, essentially proportionate, size change of the $\alpha$ sheet for $x=0.2$. These changes are found to be in good general agreement with expectations from simple electron counting. The implications of these results for the unusual robustness of superconductivity and Kondo coherence with increasing $x$ in this alloy system are discussed.

Figure 1

(a) Photoelectron intensity in a window of 200 meV around the Fermi energy in dependence of the $x$- and $y$-sample position perpendicular to the sample-analyzer axis. Brighter color means higher intensity of the photoelectrons. The cross marks the position where the photoelectron spectroscopy was performed. (b) Image of the same sample in the scanning electron microscope. The cross marks the position where the XEDS analysis was performed. (c) Nominal Yb concentration vs the actual Yb concentration as obtained by the XEDS analysis (please compare with Table ). The results are compared with the results of Capan et al.[14]

Figure 2

(a) X-ray absorption measurements at $T=20$ K near the Ce $M_4$ and $M_5$ edges show that Ce is essentially trivalent. The topmost curves, labeled on the right side with $f^0$ or $f^1$, are multiplet calculations.[36] Below are measured spectra for the series Ce${}_{1-x}$Yb${}_x$CoIn${}_5$. The curve for $x=0$ is from Ref. 40. The box in (a) indicates the region displayed in (b), which is the magnification of the low intensity region where the $f^0$ component shows up.

Figure 3

XPS spectra of the Ce${}_{1-x}$Yb${}_x$CoIn${}_5$ samples at $T=20$ K. The spectra are sorted by their nominal Yb content. Except for the reversed order in (d), the topmost spectrum is for $x=1$ and the bottom one is for $x=0.1$. (a) Spectra of the valence band region near the Fermi energy taken at $h\nu =865$ eV. The doublet labeled ${}^2{F}_{5/2}{-}^2{F}_{7/2}$ is due to bulk Yb${}^{2+}$. The two peaks due to surface Yb${}^{2+}$ are labeled “S”. The inset of (a) shows a wide scan over a large binding energy region. This spectrum is dominated by the In $3d$ doublet, which was used to normalize the spectra. Near the Fermi energy, a peak originating from In $4d$ and Ce $5p$ is visible. (b) Spectra of the same valence band region as in (a) but on the Ce resonance at photon energies of $h\nu =833$ eV. This increases the visibility of the Ce component in the spectra. (c) A magnification of the region in the spectra of (a) where the Yb${}^{3+}$ component can be detected. The topmost curve is a theoretical calculation for the Yb${}^{3+}$ $5f^{13}\to 5f^{12}$ spectrum from Ref. 41. (d) The same spectrum as (c) but normalized to the maximum of the ${}^2{F}_{7/2}$ peak as shown in the inset. The peak maximum originating from Co $d$ weight and the low-energy edge “E” of the Yb${}^{3+}$ $5f^{13}\to 5f^{12}$ multiplet are marked.

Figure 4

Example of the line fits performed in order to determine the Yb valence. The spectra shown are the same as in Fig. 3a, at $h\nu =865$ eV. For the fit, we divided the spectrum into components from Yb${}^{2+}$, surface Yb${}^{2+}$, and Yb${}^{3+}$. Furthermore, we use a Shirley background and a linear background and some subsequently added Lorentzians, just enough to optimally fit the spectrum (denoted as “rest”). The inset of $x=1$ shows seven Lorentzians we used to model twelve Yb${}^{3+}$ 5$f^{13}\to 5f^{12}$ lines.

Figure 5

$x$ dependence of Yb valence from the XPS spectra at photon energies of $h\nu =550$ and 865 eV. The line is a guide to the eye. Open circles are the calculated Yb valences from the susceptibility analysis of the next section using Eq. (4).

Figure 6

(a) Inverse magnetic susceptibility ${\chi }_{ab}^{-1}\left(T\right)=H/M_{ab}\left(T\right)$ vs temperature $T$ along the crystallographic $ab$ plane for Ce${}_{1-x}$Yb${}_x$CoIn${}_5$ with Yb concentrations $0.0⩽x⩽0.775$. Curie-Weiss temperature ${\theta }_{\mathrm{CW}}$ and effective magnetic moment ${\mu }_{\mathrm{eff}}$ as determined from fits to a Curie-Weiss law ${\chi }_{ab}=N_A{\mu }_{\mathrm{eff}}^2/3k_B(T-{\theta }_{\mathrm{CW}})$ (please see text) as a function of Yb concentration $x$ are shown in (b) and (c), respectively. Solid line in (c) is a linear fit of ${\mu }_{\mathrm{eff}}\left(x\right)$.

Figure 7

Unit cell volume $V$ as a function of Yb concentration $x$ in Ce${}_{1-x}$Yb${}_x$CoIn${}_5$. Filled circles: measured values of $V$. Open circles: calculated $V$ using Eq. (5). Open circles: calculated $V$ using Eq. (5).

Figure 8

Second, third, and and fourth rows show Fermi-surface maps for the $\Gamma$ and $Z$ planes for $x=0$, 0.2, and 1 at 26, 26, and 20 K, respectively. Top row figures on the right and left show respectively mesh models[49] of the columnar $\alpha$ and $\beta$ sheets as calculated in LDA, and middle figure shows the Brillouin zone and measurement planes. The change of size of the $\alpha$ and $\beta$ sheets is easily seen.