Magnetism induced by external pressure ($p$) was studied in a FeSe crystal sample by means of muon-spin rotation. The magnetic transition changes from second-order to first-order for pressures exceeding the critical value $p_{{\rm c}}\simeq2.4-2.5$ GPa. The magnetic ordering temperature ($T_{{\rm N}}$) and the value of the magnetic moment per Fe site ($m_{{\rm Fe}}$) increase continuously with increasing pressure, reaching $T_{{\rm N}}\simeq50$~K and $m_{{\rm Fe}}\simeq0.25$ $\mu_{{\rm B}}$ at $p\simeq2.6$ GPa, respectively. No pronounced features at both $T_{{\rm N}}(p)$ and $m_{{\rm Fe}}(p)$ are detected at $p\simeq p_{{\rm c}}$, thus suggesting that the stripe-type magnetic order in FeSe remains unchanged above and below the critical pressure $p_{{\rm c}}$. A phenomenological model for the $(p,T)$ phase diagram of FeSe reveals that these observations are consistent with a scenario where the nematic transitions of FeSe at low and high pressures are driven by different mechanisms.
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