Determining the Crystal-Field Ground State in Rare Earth Heavy Fermion Materials Using Soft-X-Ray Absorption Spectroscopy

We infer that soft-x-ray absorption spectroscopy is a versatile method for the determination of the crystal-field ground state symmetry of rare earth heavy fermion systems, complementing neutron scattering. Using realistic and universal parameters, we provide a theoretical mapping between the polarization dependence of Ce $M_{4,5}$ spectra and the charge distribution of the Ce $4f$ states. The experimental resolution can be orders of magnitude larger than the $4f$ crystal-field splitting itself. To demonstrate the experimental feasibility of the method, we investigated ${\mathrm{CePd}}_2{\mathrm{Si}}_2$, thereby settling an existing disagreement about its crystal-field ground state.

Figure 1

Calculated $M_{4,5}$ soft-x-ray absorption spectra for pure $|J_z⟩$ states of ${\mathrm{Ce}}^{3+}$ for the incoming light polarized $\parallel$ and $\perp$ $\mathbf{c}$ ($\mathbf{z}\parallel \mathbf{c}$ in tetragonal symmetry), together with the corresponding $4f$ spatial distributions.

Figure 2

Top: Calculated $M_{4,5}$ soft-x-ray absorption spectra for the mixed states $a|\pm 5/2⟩-b|\mp 3/2⟩$ for mixing factors $a^2$ from 0 to 1 for light polarized $\parallel$ and $\perp$ $\mathbf{c}$.

Figure 3

Bottom: experimental $M_{4,5}$ soft-x-ray absorption spectra of ${\mathrm{CePd}}_2{\mathrm{Si}}_2$ at $T=50\mathrm{K}$ for light polarized $\parallel$ and $\perp$ $\mathbf{c}$. Top: simulated $M_{4,5}$ spectra with $a^2=0.29$ and corresponding $4f$ spatial distribution.

Figure 4

Temperature dependence of the experimental (left) and calculated (right) $M_5$ soft-x-ray absorption edge of ${\mathrm{CePd}}_2{\mathrm{Si}}_2$. Inset: crystal-field energies as in 21.