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CeRh$_6$Ge$_4$ is an unusual example of a stoichiometric heavy fermionferromagnet, which can be cleanly tuned by hydrostatic pressure to a quantumcritical 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 inneutron powder diffraction, coherent oscillations are observed in zero-field$\mu$SR below $T_{\rm C}$, which are consistent with in-plane ferromagneticordering consisting of reduced Ce moments. From analyzing the magneticsusceptibility and inelastic neutron scattering, we propose a CEF-level schemewhich accounts for the easy-plane magnetocrystalline anisotropy, where the lowlying first excited CEF exhibits significantly stronger hybridization than theground state. These results suggest that the orbital anisotropy of the groundstate and low lying excited state doublets are important for realizinganisotropic electronic coupling between the $f$- and conduction electrons,which gives rise to the highly anisotropic hybridization observed inphotoemission experiments.

Magnetic order and crystalline electric field excitations of the quantum critical heavy fermion ferromagnet CeRh$_6$Ge$_4$