On the phase diagram of the itinerant helimagnet MnSi: does MnSi become   quantum critical ?
  We performed a series of resistivity measurements of a MnSi single crystal at high pressures, created by a piston-cylinder device with a liquid pressure medium. The form of the resistivity curve at ambient pressure clearly indicates a first order nature of the magnetic phase transition in MnSi. Application of high pressure shows fast degradation of the first order features of the phase transition. The temperature derivative of resistivity demonstrates two notable features of the phase transition that disappear on pressure increasing. They are a sharp peak marking the first order phase transition and a shallow maximum, situated slightly above the critical temperature and pointing to the domain of prominent helical fluctuations. The current experimental data rule out any strong first order phase transition in MnSi at high pressures and low temperatures, which would prevent development of a quantum critical region. On the contrary, there should exist true quantum critical phenomena in MnSi at high pressures because a tiny first order transition, if it survives at high pressures to the lowest temperature, hardly could suppress the entire quantum critical region. 
Alla E. Petrova and Sergei M. Stishov
cond-mat.str-el