In the study of critical behavior and phase transition, muon spin relaxation (MuSR) can detect volume fraction of the ordered region independently from the local ordered moment size, unlike uniform magnetization or neutron scattering Bragg intensities that reflect products of these parameters in volume-integrated information. We recently performed MuSR experiments in prototypical Mott transition systems, RENiO3 (RE=Rare Earth) and V2O3, in quantum tuning with RE ionic substitutions in the former and hydrostatic pressure in the latter system. In these band-width tuning near the disappearance of antiferromagnetic (AF) order, we found that the AF phase is destroyed via reduction of volume, accompanied by phase separation, but without any change of the local ordered moment size in the ordered region . Behavior similar to this was observed by MuSR  and NMR  in the itinerant electron magnet (IEM) MnSi with pressure tuning. There results indicate first-order quantum phase transitions. In (Mn,Fe)Si with 15% of Fe doping, our MuSR results  in quantum tuning via pressure demonstrate a surprising recovery of second order criticality associated with magnetic order in the full volume fraction and continuous change of the local ordered moment size near the quantum critical point (QCP). The QCP of (Mn,Fe)Si seems to reveal the QCP in pure MnSi hidden by the first order quantum transition. This observation is consistent with a recent theory of Sang. Belitz, and Kirkpatrick  who predicted recovery of second order critical behavior in itinerant-electron ferromagnets due to disorder. We discuss these results in Mott and IEM systems and compare with other cases including FeAs and cuprate systems.
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