Fig. 1

Temperature–pressure phase diagrams of MnSi and (Mn,Fe)Si. a Temperature versus hydrostatic pressure phase diagram in pure MnSi and (Mn,Fe)Si in zero magnetic field. Open triangles represent the magnetic transition temperature determined by resistivity and susceptibility,¹¹ gray-colored triangles from MuSR,¹³ and closed triangles represent the onset temperature of diffuse scattering “partial order” in quasi-elastic neutron scattering (QNS).¹² The yellow-colored region (S) represents the helically ordered phase, the green colored region (P) indicates phase separation between ordered and paramagnetic phases, and the blue colored region (D) indicates slow, dynamic, diffusive helical spin fluctuations.^{12, 13} The small pink region (HF) above T _C has helical spin fluctuations leading to a weakly first-order thermal transition. Red circles indicate the transition temperature for (Mn_0.85Fe_0.15)Si, determined by the present MuSR measurements. b–d Expected phase diagrams of itinerant-electron magnets according to theories by Belitz, Kirkpatrick and co-workers^{8, 9, 34,35,36,37} with the effect of disorder. TCP denotes the tri-critical point and QCP denotes the quantum critical point. The blue line indicates a second-order phase transition, while the red line shows a first-order phase transition. The first-order line in b intersects the p axis vertically at T = 0. The MuSR results for pure MnSi¹³ can be viewed as a manifestation of case c, and the present results for (Mn,Fe)Si as case d. The recent MuSR results on V₂O₃ ⁴⁰ may correspond to c, while the second-order phase transition in a highly random percolation network may be related to d