We investigate the effect of external pressure on magnetic order in undoped LnFeAsO (Ln = La, Ce, Pr, La) by using muon-spin relaxation measurements and ab-initio calculations. Both magnetic transition temperature $T_m$ and Fe magnetic moment decrease with external pressure. The effect is observed to be lanthanide dependent with the strongest response for Ln = La and the weakest for Ln = Sm. The trend is qualitatively in agreement with our DFT calculations. The same calculations allow us to assign a value of 0.68(2) $mu_B$ to the Fe moment, obtained from an accurate determination of the muon sites. Our data further show that the magnetic lanthanide order transitions do not follow the simple trend of Fe, possibly as a consequence of the different $f$-electron overlap.
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