Evolution of ground-state wave function in ${\mathbf{CeCoIn}}_5$ upon Cd or Sn doping

We present linear polarization-dependent soft-x-ray absorption spectroscopy data at the Ce $M_{4,5}$ edges of Cd- and Sn-doped ${\mathrm{CeCoIn}}_5$. The $4f$ ground-state wave functions have been determined for their superconducting, antiferromagnetic, and paramagnetic ground states. The absence of changes in the wave functions in $\mathrm{CeCo}{\left({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x\right)}_5$ suggests that the $4f$-conduction-electron ($cf$) hybridization is not affected by global Cd doping, thus supporting the interpretation of magnetic droplets nucleating long-range magnetic order. This is contrasted by changes in the wave function due to Sn substitution. Increasing Sn in $\mathrm{CeCo}{\left({\mathrm{In}}_{1-y}{\mathrm{Sn}}_y\right)}_5$ compresses the $4f$ orbitals into the tetragonal plane of these materials, suggesting enhanced $cf$ hybridization with the in-plane In(1) atoms and a homogeneous altering of the electronic structure. As these experiments show, the $4f$ wave functions are a very sensitive probe of small changes in the hybridization of $4f$ and conduction electrons, even conveying information about direction dependencies.

Figure 1

Temperature-doping phase diagram of $\mathrm{CeCo}{\left({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x\right)}_5$ and $\mathrm{CeCo}{\left({\mathrm{In}}_{1-y}{\mathrm{Sn}}_y\right)}_5$, adapted from Refs. [24, 25]. Here, concentrations are given in %. The inset shows the crystallographic structure of ${\mathrm{CeCoIn}}_5$ with Ce (red orbital) in the middle, Co (gray), In(1) (yellow), and In(2) (dark yellow).

Figure 2

(a) and (c) Linear polarized $M_{4,5}$ x-ray absorption data of ${\mathrm{CeCoIn}}_5$ and all concentrations of $\mathrm{CeCo}{\left({\mathrm{In}}_{1-y}{\mathrm{Sn}}_y\right)}_5$ and $\mathrm{CeCo}{\left({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x\right)}_5$. For clarity, the spectra are shown with a vertical offset. (b) and (d) Linear dichroism $\mathrm{LD}=I(E\parallel c)\text{−}I\left(E\perp c\right)$ for all Sn and Cd concentrations, respectively. The LD have been been smoothed.

Figure 3

Evolution of LD size and ${\alpha }^2$ as a function of material composition. (a) Size of LD at the $M_5$ edge—definition in the inset on the left—vs Cd and Sn concentration. The sign of the LD is defined as in Ref. [15]. The broken lines are guides to the eye. The inset on the right shows the simulated LD size that follows the orange line. The color code for the concentrations is as in Fig. 2. (b) ${\alpha }^2$ values of ${\mathrm{CeCoIn}}_5$, $\mathrm{CeCo}{\left({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x\right)}_5$ (green), and $\mathrm{CeCo}{\left({\mathrm{In}}_{1-y}{\mathrm{Sn}}_y\right)}_5$ (orange), plus the values of ${\mathrm{CeRhIn}}_5$ (blue), ${\mathrm{CeIrIn}}_5$ (red), and ${\mathrm{CeRh}}_{1-\delta }{\mathrm{Ir}}_{\delta }{\mathrm{In}}_5$ from our previous study [15] (purple). The thick arrows indicate the increase of $cf$ hybridization within the respective substitution series. For ${\alpha }^2=0$ and 1, the corresponding orbitals are shown. The orange and red frames indicate that the two substitution studies should be seen independently due to the different direction dependence of hybridization.

Figure 4

(a) $M_{4,5}$ x-ray absorption of $\mathrm{CeCo}{\left({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x\right)}_5$ for $x=0.3$ and the simulation for ${\alpha }^2=0.137$. (b) Experimental and simulated linear dichroism.