Abstract
In second-order quantum phase transitions from magnetically ordered to paramagnetic states at T = 0, tuned by pressure or chemical substitution, a quantum critical point is expected to appear with critical behavior manifesting in the slowing down of spin fluctuations in the paramagnetic state and a continuous development of the order parameter in the ordered state. Quantum criticality is discussed widely as a possible driving force for unconventional superconductivity and other exotic phenomena in correlated electron systems. In the real world, however, quantum critical points and quantum criticality are often masked by a preceding first-order transition and/or the development of competing states. Pressure tuning of the itinerant-electron helical magnet MnSi is a well-known example of the suppression of a quantum critical point due to a first-order phase transition and resulting destruction of the ordered state. Utilizing muon spin relaxation experiments, here we report that 15% Fe-substituted (Mn,Fe)Si exhibits completely different behavior with pressure tuning, including the restoration of second-order quantum critical behavior and a quantum critical point at pQPC ~ 21–23 kbar, which coincides with the T = 0 crossing point of the extrapolated phase boundary line of pure MnSi. This result is quantitatively consistent with the recent theory of itinerant-electron ferromagnets by Sang, Belitz, and Kirkpatrick, who argued that disorder would restore a quantum critical point which is otherwise hidden by a first-order transition.
Highlights
A first-order phase transition is associated with a discontinuous change of the order parameter, while a second-order transition involves the slowing down of critical fluctuations at the phase boundary and a continuous development of the order parameter from zero in the disordered phase to non-zero values in the ordered phase
Zero-field nuclear magnetic resonance (NMR)[27] and MuSR13, 28 measurements in MnSi found that the magnitude of the static internal magnetic field at T → 0, which is proportional to the ordered moment size, exhibits only a slight reduction with increasing p at p* < p < pc, followed by an abrupt reduction to zero above pc
The results for pure MnSi and the more disordered (Mn0.85Fe0.15)Si are consistent with the theories of Belitz, Kirkpatrick and coworkers.[8, 9, 34,35,36,37]
Summary
A first-order phase transition is associated with a discontinuous change of the order parameter (such as staggered magnetization), while a second-order transition involves the slowing down of critical fluctuations at the phase boundary and a continuous development of the order parameter from zero in the disordered phase to non-zero values in the ordered phase. Zero-field nuclear magnetic resonance (NMR)[27] and MuSR13, 28 measurements in MnSi found that the magnitude of the static internal magnetic field at T → 0, which is proportional to the ordered moment size, exhibits only a slight reduction with increasing p at p* < p < pc, followed by an abrupt reduction to zero above pc This discontinuous change of the order parameter at pc clearly demonstrates the first-order character of the quantum phase transition in MnSi tuned with pressure p. The static magnetic order in (Mn0.85Fe0.15)Si survives up to pc = 21–23 kbar with clear signatures of dynamic critical behavior, a continuous evolution of the ordered moment size, and a full magnetically ordered volume fraction These behaviors demonstrate the restoration of second-order thermal and quantum phase transitions due presumably to substantial disorder caused by the (Mn,Fe) substitution.
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