Phase separation and suppression of critical dynamics at quantum phase transitions of MnSi and (Sr1−xCax)RuO3

Quantum phase transitions (QPTs) at zero temperature are generally studied by means of pressure or composition tuning. Volume-integrated probes such as neutron and magnetization measurements, as well as pressure uncertainties in NMR studies using powder specimens, however, have limited the characterization of magnetism and detection of discontinuous changes at QPTs. Overcoming these limitations, we carried out muon spin relaxation measurements that have a unique sensitivity to volume fractions of magnetically ordered and paramagnetic regions, and studied QPTs from itinerant helimagnet or ferromagnet to paramagnet transitions in MnSi (single crystal; varying pressure) and (Sr1−xCax)RuO3 (ceramic specimens; varying x). Our results provide the first clear evidence that both cases are associated with phase separation and suppression of dynamic critical behaviour, reveal slow dynamics of the ‘partial order’ diffuse spin correlations in MnSi above the critical pressure and suggest the possibility that a majority of QPTs in correlated electron systems involve first-order transitions and/or phase separation.