Knight shift measurements probing Fermi surface changes under pressure in CeRhIn$_5$

We report nuclear magnetic resonance (NMR) Knight shift measurements of the In(1) and In(2) sites in CeRhIn$_5$ as a function of pressure. In contrast to the $c$ axis, the in-plane components of the In(1) Knight shift tensor exhibit little to no pressure dependence. These results indicate that the dipolar component of the tensor is strongly suppressed at the In(1) site, while it remains constant with pressure at the In(2) site. We analyze the hyperfine coupling in terms of a tight binding model for the electronic structure, and determine that the pressure dependence of the In(1) shift cannot be explained in terms of changes to the crystal field parameters, but rather can be understood in terms of an increase in the 4f electron content at the Fermi surface. Our results indicate that the hyperfine coupling reflects changes in the electronic structure near a Kondo breakdown quantum critical point.

💡 Research Summary

In this work the authors investigate how the electronic structure of the heavy‑fermion compound CeRhIn₅ evolves under hydrostatic pressure by measuring the ¹¹⁵In nuclear magnetic resonance (NMR) Knight shift at the two inequivalent indium sites, In(1) (located in the Ce‑In plane) and In(2) (situated between the Ce‑Rh layers). While previous NMR studies on this material were limited to magnetic fields applied along the crystallographic c‑axis, the present study applies the field within the ab‑plane, thereby allowing a full tensorial analysis of the hyper‑fine coupling.

The experiments were performed on high‑quality single crystals placed in a piston‑cylinder pressure cell with Daphne oil as the pressure medium. Pressures up to ≈2.5 GPa were calibrated by ruby fluorescence. Field‑sweep and frequency‑sweep Hahn‑echo spectra were recorded at fixed frequencies (≈62 MHz) and temperatures ranging from 2 K to 10 K. By carefully analyzing the quadrupolar splitting and the angular dependence of the resonances, the authors extracted the Knight shift components Kₐₐ, K_{bb}, and K_{cc} as well as the electric‑field‑gradient (EFG) parameters for each site.

The key experimental observations are:

1. In(1) site: The in‑plane Knight shift Kₐₐ shows virtually no pressure dependence over the entire pressure range, remaining flat as a function of temperature. In contrast, the c‑axis component K_{cc} decreases by roughly a factor of two when pressure is increased from 0 to 2 GPa. Decomposition of the shift tensor reveals that the dipolar term K_{dip} (which gives the characteristic anisotropy) is strongly suppressed with pressure, while the isotropic term K_{iso} remains essentially constant. By ≈2 GPa the In(1) shift becomes almost purely isotropic.

2. In(2) site: All three components (Kₐₐ, K_{bb}, K_{cc}) are essentially pressure‑independent. The dipolar contribution dominates the shift tensor for In(2) and does not change with pressure, indicating that the transferred hyper‑fine coupling to the Ce 4f moments at this site is robust against pressure.

3. EFG evolution: Both sites display a smooth, nearly linear increase of the principal EFG components with pressure, consistent with earlier reports. No discontinuity near 1.5 GPa (previously suggested as a signature of a Fermi‑surface reconstruction) is observed in the present data.

To interpret these findings, the authors consider two possible mechanisms that could modify the hyper‑fine coupling under pressure: (i) changes in the crystal‑field (CEF) scheme of the Ce 4f ion, and (ii) variations in the hybridization between Ce 4f and In 5p orbitals. They employ a minimal tight‑binding model (based on the work of Maehira et al.) that includes Ce‑Ce, In‑In, and Ce‑In hopping terms (V_{ff}, V_{pp}, V_{pf}) together with a CEF Hamiltonian expressed in Stevens operators. By adjusting only the CEF parameters they cannot reproduce the observed pressure‑independent in‑plane shift of In(1). However, when they introduce a pressure‑dependent fraction f of 4f character at the Fermi surface—i.e., an increase of the itinerant 4f contribution with pressure—the model simultaneously accounts for (a) the strong suppression of K_{dip} at In(1), (b) the near‑constancy of K_{iso}, and (c) the unchanged hyper‑fine tensor at In(2).

This phenomenology points to a scenario in which pressure enhances the Kondo screening of the Ce moments, thereby pulling more 4f weight onto the Fermi surface. Such a redistribution of spectral weight is precisely what is expected at a Kondo‑breakdown quantum critical point (QCP). The results are consistent with de Haas‑van Alphen and Hall‑effect studies that report a sudden enlargement of the Fermi surface and a divergence of the effective mass near 2.3 GPa in CeRhIn₅. Moreover, the work demonstrates that NMR Knight shift measurements, especially when the full hyper‑fine tensor is resolved, provide a highly sensitive probe of f‑electron delocalization in heavy‑fermion systems.

In summary, the paper establishes that (i) the dipolar hyper‑fine coupling at the In(1) site is dramatically reduced by pressure, (ii) the In(2) site remains largely unaffected, and (iii) these contrasting behaviors are best explained by an increase of 4f electron participation at the Fermi surface rather than by simple crystal‑field effects. The findings reinforce the view that CeRhIn₅ undergoes a pressure‑driven Kondo‑breakdown QCP, and they highlight the utility of site‑specific NMR as a microscopic tool for tracking electronic reconstruction in correlated electron materials.