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We present an extensive study of the ferromagnetic heavy fermion compoundU$_4$Ru$_7$Ge$_6$. Measurements of electrical resistivity, specific heat andmagnetic properties show that U$_4$Ru$_7$Ge$_6$ orders ferromagnetically atambient pressure with a Curie temperature $T_{C} = 6.8 \pm 0.3$ K. The lowtemperature magnetic behavior of this soft ferromagnet is dominated by theexcitation of gapless spin-wave modes. Our results on the transport propertiesof U$_4$Ru$_7$Ge$_6$ under pressures up to $2.49$ GPa suggest thatU$_4$Ru$_7$Ge$_6$ has a putative ferromagnetic quantum critical point (QCP) at$P_c \approx 1.7 \pm 0.02$ GPa. In the ordered phase, ferromagnetic magnonsscatter the conduction electrons and give rise to a well defined power lawtemperature dependence in the resistivity. The coefficient of this term isrelated to the spin-wave stiffness and measurements of the very low temperatureresistivity allow to accompany the behavior of this quantity as the theferromagnetic QCP is approached. We find that the spin-wave stiffness decreaseswith increasing pressure implying that the transition to the non-magnetic Fermiliquid state is driven by the softening of the magnons. The observed quantumcritical behavior of the magnetic stiffness is consistent with the influence ofdisorder in our system. At quantum criticality ($P = P_c \approx 1.7 \pm 0.02$GPa), the resistivity shows the behavior expected for an itinerant metallicsystem near a ferromagnetic QCP.

Magnon excitations and quantum critical behavior of the ferromagnet U$_4$Ru$_7$Ge$_6$