Ferromagnetic -spin glass transition induced by pressure in Gd$_2$Mo$_2$O$_7$

R$_2$Mo$_2$O$_7$ compounds show a ferromagnetic metal-insulator spin glass transition tuned by the radius of the rare earth ion R$^{3+}$. We have studied Gd$_2$Mo$_2$O$_7$ located on the verge of the transition, by neutron diffraction on a $^{160}$Gd isotopic sample, $\mu$SR and X ray diffraction using the synchrotron radiation. All measurements were done both at ambient and under applied pressure. At ambient pressure, a ferromagnetic state is observed below the Curie temperature (T$_{\rm C}$ = 70 K). The ordered magnetic moments at 1.7 K are parallel and equal to 5.7(5) $\mu_{\rm B}$ and 0.8(2) $\mu_{\rm B}$ for Gd and Mo, respectively. The relaxation rate measured by $\mu$SR evidences strong spin fluctuations below T$_{\rm C}$ and down to the lowest temperature (6.6 K). A spin reorientation occurs in the range 20 K$<$T$<$T$_{\rm C}$. The ferromagnetic state is strongly unstable under pressure. T$_{\rm C}$ sharply decreases (down to 38 K at 1.3 GPa) and Bragg peaks start to coexist with mesoscopic ferromagnetic correlations. The ordered moments decrease under pressure. At 2.7 GPa long range magnetic order completely breaks down. In this spin glass state, Gd-Gd spin correlations remain ferromagnetic with a correlation length limited to the fourth neighbor, and Gd-Mo spin correlations turn to antiferromagnetic. The unique combination of three microscopic probes under pressure provides a detailed description of the magnetic transition, crucial for further theories.