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Register a new userAnisotropic c-f hybridization in the ferromagnetic quantum critical metal CeRh$_6$Ge$_4$
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Heavy fermion compounds exhibiting a ferromagnetic quantum critical point have attracted considerable interest. Common to two known cases, i.e., CeRh$_6$Ge$_4$ and YbNi$_4$P$_2$, is that the 4f moments reside along chains with a large inter-chain distance, exhibiting strong magnetic anisotropy that was proposed to be vital for the ferromagnetic quantum criticality. Here we report an angle-resolved photoemission study on CeRh6Ge4, where we observe sharp momentum-dependent 4f bands and clear bending of the conduction bands near the Fermi level, indicating considerable hybridization between conduction and 4f electrons. The extracted hybridization strength is anisotropic in momentum space and is obviously stronger along the Ce chain direction. The hybridized 4f bands persist up to high temperatures, and the evolution of their intensity shows clear band dependence. Our results provide spectroscopic evidence for anisotropic hybridization between conduction and 4f electrons in CeRh$_6$Ge$_4$, which could be important for understanding the electronic origin of the ferromagnetic quantum criticality.
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We report resistivity measurements under pressure for Kondo-lattice ferromagnet CeRh$_6$Ge$_4$, and present that a quantum ferromagnetic (FM) phase transition is easily achieved. In most clean metallic ferromagnets, a quantum critical point (QCP) at zero field is avoided by changing the FM transition to a discontinuous transition or to an antiferromagnetic transition. In CeRh$_6$Ge$_4$, to the contrary, the Curie temperature of 2.5 K decreases continuously as increasing pressure without any clear signature that the transition changes to first order. The obvious non Fermi liquid behavior is observed in the vicinity of the quantum FM phase transition. The experimental data do not contradict a picture in which CeRh$_6$Ge$_4$ shows the FM QCP at zero field. Band structure calculation suggests the unusual electronic state of CeRh$_6$Ge$_4$ among Ce-based Kondo lattices. CeRh$_6$Ge$_4$ deserves further investigations and will be a key material to understand the matter of the FM QCP.
The heavy fermion ferromagnet CeRh$_6$Ge$_4$ is the first example of a clean stoichiometric system where the ferromagnetic transition can be continuously suppressed by hydrostatic pressure to a quantum critical point. In order to reveal the outcome when the magnetic lattice of CeRh$_6$Ge$_4$ is diluted with non-magnetic atoms, this study reports comprehensive measurements of the physical properties of both single crystal and polycrystalline samples of La$_x$Ce$_{1-x}$Rh$_6$Ge$_4$. With increasing $x$, the Curie temperature decreases, and no transition is observed for $x$ $>$ 0.25, while the system evolves from exhibiting coherent Kondo lattice behaviors at low $x$, to the Kondo impurity scenario at large $x$. Moreover, non-Fermi liquid behavior (NFL) is observed over a wide doping range, which agrees well with the disordered Kondo model for 0.52 $leq$ $x$ $leq$ 0.66, while strange metal behavior is revealed in the vicinity of $x_c$ = 0.26.
Ferromagnetic quantum critical points were predicted to be prohibited in clean itinerant ferromagnetic systems, yet such a phenomenon was recently revealed in CeRh$_6$Ge$_4$, where the Curie temperature can be continuously suppressed to zero under a moderate hydrostatic pressure. Here we report the observation of quantum oscillations in CeRh$_6$Ge$_4$ from measurements using the cantilever and tunnel-diode oscillator methods in fields up to 45 T, clearly demonstrating that the ferromagnetic quantum criticality occurs in a clean system. In order to map the Fermi surface of CeRh$_6$Ge$_4$, we performed angle-dependent measurements of quantum oscillations at ambient pressure, and compared the results to density functional theory calculations. The results are consistent with the Ce 4f electrons remaining localized, and not contributing to the Fermi surface, suggesting that localized ferromagnetism is a key factor for the occurrence of a ferromagnetic quantum critical point in CeRh$_6$Ge$_4$.
Using the state-of-art dynamical mean-field theory combined with density functional theory method, we have performed systematic study on the temperature and pressure dependent electronic structure of ferromagnetic quantum critical material candidate CeRh$_6$Ge$_4$. At -3.9 GPa and -8.3 GPa, the Ce-4$f$ occupation variation, the local magnetic susceptibility, and the low-frequency electronic self-energy behaviors suggest the Ce-4$f$ electrons are in the localized state; whereas at 6.5 GPa and 13.1 GPa, these quantities indicate the Ce-4$f$ electrons are in the itinerant state. The characteristic temperatures associated with the coherent Kondo screening is gradually suppressed to 0 around 0.8 GPa upon releasing external pressure, indicative of a local quantum critical point. Interestingly, the momentum-resolved spectrum function shows that even at the localized state side, highly anisotropic $mathbf{k}$-dependent hybridization between Ce-4$f$ and conduction electrons is still present along $Gamma$-A, causing hybridization gap in between. The calculations predict 8 Fermi surface sheets at the local-moment side and 6 sheets at the Kondo coherent state. Finally, the self-energy at 0.8 GPa can be well fitted by marginal Fermi-liquid form, giving rise to a linearly temperature dependent resistivity.
CeRh$_6$Ge$_4$ is an unusual example of a stoichiometric heavy fermion ferromagnet, which can be cleanly tuned by hydrostatic pressure to a quantum critical point. In order to understand the origin of this anomalous behavior, we have characterized the magnetic ordering and crystalline electric field (CEF) scheme of this system. While magnetic Bragg peaks are not resolved in neutron powder diffraction, coherent oscillations are observed in zero-field $mu$SR below $T_{rm C}$, which are consistent with in-plane ferromagnetic ordering consisting of reduced Ce moments. From analyzing the magnetic susceptibility and inelastic neutron scattering, we propose a CEF-level scheme which accounts for the easy-plane magnetocrystalline anisotropy, and suggests that the orbital anisotropy of the ground state and low lying excited state doublets is an important factor giving rise to the observed anisotropic hybridization.
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