Avoided ferromagnetic quantum critical point in pressurized La$_5$Co$_2$Ge$_3$

We present the pressure-temperature phase diagram La$_5$Co$_2$Ge$_3$ up to $\sim$ 5\,GPa, which was constructed from magnetization, resistivity and specific heat measurements. At ambient pressure, La$_5$Co$_2$Ge$_3$ is an itinerant ferromagnet with a Curie temperature $T_\textrm C\sim$ 4\,K. Upon increasing pressure up to $\sim$ 1.7\,GPa, $T_\textrm C$ is suppressed down to $\sim$ 3\,K. Upon further increasing pressure, our results suggest that La$_5$Co$_2$Ge$_3$ enters a different low-temperature ground state. The corresponding transition temperature, $T^*$, has a nonmonotonic pressure dependence up to $\sim$ 5\,GPa. Our results demonstrate that the ferromagnetic quantum critical point in La$_5$Co$_2$Ge$_3$ is avoided by the appearance of a different, likely magnetically ordered state that has an antiferromagnetic component.