Nature of the high-pressure tricritical point in MnSi

Abstract

It is argued that M. Otero-Leal et al. [PRB 79, 060401 (2009) 1 ] wrongly identified the second order term of the Arrott equation with the coefficient at the quartic term of the Landau expansion, therefore deriving absolutely unsupported conclusions on the phase diagram of MnSi. PACS numbers: 75.30.Kz, 75.40.Cx. Despite a long history of extensive studies of the magnetic phase transition in the helimagnet MnSi its phase diagram is not completely understood. Most important but still controversial issues concerning the phase diagram of MnSi are the existence, location and nature of a tricritical point on the phase transition line in MnSi, first suggested in Ref. 2 . Since then until recently, the existence of the tricritical point has been never in doubt though its location was disputed in Ref. 3 . Meanwhile a careful study of the magnetic phase transition in MnSi confirmed a first order nature of the transition at least at ambient pressure 4,5,6 , as was proposed long ago in Ref. 7 . This observation reversed the situation. It was believed before that a second order phase transition in MnSi became first order at high pressure. Then the only conclusion could be made that the phase transition in MnSi turned to second order at high pressure. The latter of course is valid if a tricritical point does exist at the transition line. However new experiments at high pressure using helium as a pressure medium showed that the early claims on the existence of a tricritical point at the phase transition line, based on an analysis of behavior of magnetic susceptibility, are most probably a result of misinterpretation of the experimental data 8 . As was said in Ref. 8 :"The new measurements unambiguously show that the striking change of the magnetic susceptibility curve is a result of non-hydrostatic stresses in pressure media and has nothing to do with a change of character of the phase transition in MnSi". So the general conclusion was that the magnetic phase transition in MnSi continued to be first order in the whole pressure range studied 8 . In the paper 1 an attempt was made to resolve the above mentioned issues based, as the authors said, on "a direct analysis of the magnetic phase transition under pressure". Under "a direct analysis" the authors implied applications of the equationwhere H-magnetic field, M -magnetization. Equation(1), suggested by Arrott 9 , is a typical mean field relation and can be readily derived from the Landau expansion 10 . Normally the relation (1) is used to plot H/M vs M 2 (Arrott plot), which would yield a straight line at the temperature of second order ferromagnetic phase transition when the critical fluctuations can be neglected. Eq. (1) needs to be modified to account for the contribution of critical fluctuations (see Ref. 11 ). It has to be emphasized that a causal relationship between the Landau expansion and Eq.1 limited to ferromagnetic materials, since only in this case the magnetization M can serve as an order parameter with the magnetic field H as a conjugate variable. Neglectin...

Skyrmions and spirals in MnSi under hydrostatic pressure

“…2(d)]. Therefore, the magnetic moment does not vanish, which is in agreement with previous studies 11,[26][27][28] . Finally, the temperature depen- dence of the total scattered intensity also indicates that the weak first-order phase transition, as seen at ambient pressure [19][20][21]29 , persists up to p C .…”

Quantum order-by-disorder driven phase reconstruction in the vicinity of ferromagnetic quantum critical points

“…The free energy of a d-wave spin-nematic state in the presence of the distortion is given by the sum of Eqs. ( 29) and (32). We can rewrite this in the form…”

Phase diagram of UGe2.:Whether there are quantum phase transitions ?

“…where we have substituted typical sound velocity c ≈ 10 5 cm/sec and used known [22] density value ρ = 10.26 g/cm 3 . Thus, we have for the combination Eq.…”

“…Thus at high pressures and low temperatures the ferromagnetic and paramagnetic states are divided by the first order type transition whereas at higher temperatures and lower pressures this transition is of the second order. Such type of behavior is typical for MnSi [1][2][3][4], itinerant ferromagnet-superconductor UGe 2 [5,6] (see Fig. 1), ZrZn 2 [7].…”