We report ${}^{73}\mathrm{Ge}$ nuclear quadrupole resonance (NQR) and magnetic resonance (NMR) spectroscopy in the heavy-fermion quantum-critical ferromagnet ${\mathrm{CeRh}}_6{\mathrm{Ge}}_4$. NQR and NMR spectral measurements at the two nonequivalent Ge sites reveal electric field gradient tensors and the directions of their principal axes relative to the hexagonal basal plane. The spin-lattice relaxation rate $1/T_1$ experiments reveal a clear critical slowing down approaching the ferromagnetic transition. $1/T_1$ in the paramagnetic state is found to be predominantly caused by fluctuating $4f$-local moments. The Knight shift shows Curie-Weiss behavior at high temperature and a deviation from this below $T^{*}\approx 25\mathrm{K}$ possibly due to a mixture of crystalline electric field effects and Kondo screening. Order-parameter-like behavior of hyperfine fields at the Ge sites and ferromagnetic signal enhancement are observed in Zeeman-perturbed NQR, with uniform ferromagnetic order and a small ordered moment of $\approx 0.26{\mu }_{\mathrm{B}}/\mathrm{Ce}$ confined within the $ab$ plane. The ordered moment shows a notable in-plane magnetic stiffness against out-of-plane radio-frequency fields and has an (XY-type) in-plane isotropic nature. Our results reveal a strong easy-plane anisotropy of $4f$-electron moment and suggest an involved interplay of hybridization and local moment physics in this quantum critical heavy-fermion ferromagnet.

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• Critical phenomena
• Electronic phase separation
• Ferromagnetism
• Frustrated magnetism
• Magnetic phase transitions
• Magnetic susceptibility
• Magnetism
• Order parameters
• Phase transitions
• Quantum criticality
• RKKY interaction
• Spin dynamics