  The temperature-pressure phase diagram of the ferromagnet LaCrGe$_3$ is
determined for the first time from a combination of magnetization,
muon-spin-rotation and electrical resistivity measurements. The ferromagnetic
phase is suppressed near $2.1$~GPa, but quantum criticality is avoided by the
appearance of a magnetic phase, likely modulated, AFM$_Q$. Our density
functional theory total energy calculations suggest a near degeneracy of
antiferromagnetic states with small magnetic wave vectors $Q$ allowing for the
potential of an ordering wave vector evolving from $Q=0$ to finite $Q$, as
expected from the most recent theories on ferromagnetic quantum criticality.
Our findings show that LaCrGe$_3$ is a very simple example to study this
scenario of avoided ferromagnetic quantum criticality and will inspire further
study on this material and other itinerant ferromagnets.
