Quantum bicriticality in Mn$_{1-x}$Fe$_{x}$Si solid solutions: exchange and percolation effects

The $T{-}x$ magnetic phase diagram of Mn$_{1-x}$Fe$_x$Si solid solutions is probed by magnetic susceptibility, magnetization and resistivity measurements. The boundary limiting phase with short-range magnetic order (analogue of the chiral liquid) is defined experimentally and described analytically within simple model accounting both classical and quantum magnetic fluctuations together with effects of disorder. It is shown that Mn$_{1- x}$Fe$_x$Si system undergoes a sequence of two quantum phase transitions. The first "underlying" quantum critical (QC) point $x^*\sim 0.11$ corresponds to disappearance of the long-range magnetic order. This quantum phase transition is masked by short-range order phase, however, it manifests itself at finite temperatures by crossover between classical and quantum fluctuations, which is predicted and observed in the paramagnetic phase. The second QC point $x_c\sim 0.24$ may have topological nature and corresponds to percolation threshold in the magnetic subsystem of Mn$_{1- x}$Fe$_x$Si. Above $x_c$ the short-range ordered phase is suppressed and magnetic subsystem becomes separated into spin clusters resulting in observation of the disorder-driven QC Griffiths-type phase characterized by an anomalously divergent magnetic susceptibility $\chi\sim 1/T^\xi$ with the exponents $\xi\sim 0.5{-} 0.6$.