Magnetic order and crystalline electric field excitations of the quantum critical heavy-fermion ferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Ce</mml:mi><mml:msub><mml:mi>Rh</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mi>Ge</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

CeRh$_6$Ge$_4$ is an unusual example of a stoichiometric heavy fermion ferromagnet, which can be cleanly tuned by hydrostatic pressure to quantum critical point. In order understand the origin this anomalous behavior, we have characterized magnetic ordering and crystalline electric field (CEF) scheme system. While Bragg peaks are not resolved in neutron powder diffraction, coherent oscillations observed zero-field $\mu$SR below $T_{\rm C}$, consistent with in-plane ferromagnetic consisting reduced Ce moments. From analyzing susceptibility inelastic scattering, propose CEF-level accounts for easy-plane magnetocrystalline anisotropy, where low lying first excited CEF exhibits significantly stronger hybridization than ground state. These results suggest that orbital anisotropy state doublets important realizing anisotropic electronic coupling between $f$- conduction electrons, gives rise highly photoemission experiments.