High Pressure studies of the magnetic phase transition in MnSi: revisited
New measurements of AC magnetic susceptibility and DC resistivity of a high quality single crystal MnSi were carried out at high pressure making use of helium as a pressure medium. The form of the AC magnetic susceptibility curves at the magnetic phase transition suddenly changes upon helium solidification. This implies strong sensitivity of magnetic properties of MnSi to non hydrostatic stresses and suggests that the early claims on the existence of a tricritical point at the phase transition line are probably a result of misinterpretation of the experimental data. At the same time resistivity behavior at the phase transition does not show such a significant influence of helium solidification. The sharp peak at the temperature derivative of resistivity, signifying the first order nature of the phase transition in MnSi successfully survived helium crystallization and continued the same way to the highest pressure.
pacs:62.50.+ p, 75.30.Kz, 75.40.Cx.
As it was found long ago, the intermetallic compound MnSi acquired a long period helical magnetic structure at T 29 K (1); (2). Itinerant nature of magnetism in MnSi was established in (3). First experiments on the influence of high pressure on the phase transition in MnSi showed that the transition temperature decreased with pressure and tended to zero at about 1.4 GPa (4). This feature of MnSi promised the opportunity of observation of quantum critical behavior.
Since then, quite a number of papers has been devoting to high pressure studies of the phase transition in MnSi (see for instance (5); (6); (7); (8); (9); (10); (11); (12); (13); (14); (15)). Among them one should point at a paper (5)(see also (9)) where authors claimed the discovery of a tricritical point at the phase transition line of MnSi, based on the evolution of the AC magnetic susceptibility of MnSi () with pressure. Later on a theory was developed that declared generic nature of first order character of phase transitions in ferromagnets at low temperatures (6).
Non-Fermi liquid behavior has been observed in an extended region of pressure above the quantum critical point (11). The specific magnetic structure (partial order) of the non-Fermi-liquid phase of MnSi was described in Ref. (12). Phase inhomogeneity in the region surrounding the transition line from about 10 K to the lowest temperatures was reported in Ref. (13); (14). Incidentally, studies of the AC magnetic susceptibility of MnSi at high pressure (15) using fluid and solid helium as a pressure medium showed somewhat different results from the data (5). In particular authors (15) concluded that the radical change of the AC magnetic susceptibility of MnSi with pressure, observed in Ref. (5), could be influenced by non-hydrostatic stresses, developing in a frozen pressure medium. Precise lattice constant measurements at high pressure seemingly indicate that the phase transition in MnSi is first order (16).
Meanwhile new studies of thermodynamic and transport properties of a high quality single crystal of MnSi at ambient pressure suggested also a first order nature of the corresponding magnetic phase transition (17); (18); (19) that again questioned the early proposed phase diagram (5); (6); (7); (8); (9).
Having a high quality single crystal of MnSi, which reveals sharp features of the phase transition, never so clearly observed before, it was appealing to conduct new studies of the phase diagram of MnSi with helium as a pressure medium.
In this paper we report results of new measurements of resistivity and AC magnetic susceptibility of MnSi at high pressure, created by compressed helium.
The samples for the current measurements as well as for a earlier study (17) were cut from a single crystal of MnSi, grown from melt by the Bridgman method. The resistivity was measured by a four-terminal DC method. Measurements of the AC magnetic susceptibility were carried out with a standard modulation technique at a modulation frequency of 19 Hz. Temperature was measured by a calibrated Cernox sensor imbedded in the cell body. Accuracy of the Cernox sensor in the temperature range under study is about 0.02 K. Pressure was measured by a calibrated manganin gauge while helium was still in the fluid phase. Pressure in solid helium was calculated using its known EOS. Details of the experimental techniques are described in Ref. (15); (20); (21); (22).
As is seen in Figs. 1 and 2, the sharp maximum of AC magnetic susceptibility does not change much up to pressure of about 0.3 GPa, then starts to decrease rapidly at higher pressures, as observed before (15). But one could notice subtle differences between present data and the data (15) (see Fig. 2). As it is evident from Fig. 2, a drastic change of the form of the magnetic susceptibility curve in the current data closely coincides with the helium melting point that clearly indicates the effect of non hydrostatic stresses arising on helium solidification. Slightly different behavior of observed in (15), most probably is connected with a smaller size of the sample used in the old measurements compare with the new one. So the non-hydrostatic stress amplitude could reach a critical value only at some distance from the melting point inside the solid helium domain. This situation led to ignoring possible non-hydrostatic effects in the experiments (15) with subsequent misinterpretation of the experimental data. 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 (5); (15); (23).
Now we turn to Fig. 3 where temperature derivatives of resistivity d/dT in the vicinity of the phase transition are depicted as a function of pressure. As one can see, d/dT does not experience so dramatic a change across the helium melting line as the AC magnetic susceptibility does. However, two obvious trends are seen. Both of them are better illustrated in Fig.4. The first trend is broadening the sharp peaks of d/dT that become obvious at a pressure of 0.66 GPa. As was discussed earlier (17), sharp peaks of d/dT originate from the first order nature of the phase transition in MnSi. Hence, broadening of the peaks in d/dT at high pressure implies smearing the phase transition by non-hydrostatic stresses. The second one is narrowing of the global anomaly in d/dT, which accompanies the phase transition and reveals itself as a satellite rounded peak on the high temperature side of the phase transition. Note that the d/dT anomaly scales perfectly with the corresponding anomalies in heat capacity and thermal expansion coefficient data of MnSi (17); (19). Fig. 5 shows an evolution of the width of maxima in d/dT on pressure increasing. Surprisingly, in contrast with the case of magnetic susceptibility, no trace of the helium crystallization is seen on the corresponding curve. As it follows from Fig. 3 and 4 narrowing of the anomaly signifies its general reduction despite the fact that its amplitude slightly increases (24). More specifically this implies decreasing the general abundance of spin fluctuations along the transition line since electron scattering on spin fluctuations provides a major contribution to the resistivity of MnSi around the phase transition. Simple extrapolation of the curve in Fig. 5 to the zero width leads to the pressure value about 1.5 GPa, which almost exactly corresponds to the phase transition pressure at T=0, as should be expected.
Another effect observed in the current study of resistivity of MnSi is defect generation upon pressure releasing, as is illustrated in Fig. 6. It is seen that, after decreasing pressure from to zero in a time span of less then one hour, the peak of d/dT appears to be highly distorted. Remarkably, after holding the sample for a week at ambient pressure and room temperature, the form of the peak completely recovered its initial shape. All that did not happen when the sample was loaded by 0.7 GPa of helium pressure. This observation tells us that at some pressure, obviously more then 0.7 GPa, MnSi experiences some sort of irreversible change on a short time scale that facilitates generation of defects on pressure releasing.
Despite all these complications and even ignoring the data obtained above 0.7 GPa, we are still able to derive certain conclusions in regard to the phase transition in MnSi at high pressure.
First of all, nonhydrostatic stresses arising in solid helium strongly influence the form of AC magnetic susceptibility of MnSi and the latter can not serve as an indicator of the type of phase transition. So, claims of the existence of a tricritical point on the phase transition line in MnSi seem to be a result of misinterpretation of the experimental data (5); (10); (15). Second, the electrical resistivity of MnSi appears to be almost insensitive to the non-hydrostatic stresses and the persistent sharp peak of d/dT experiences only slight broadening with pressure. Third, the existence of d/dT peaks at the highest pressures provides evidence that the magnetic phase transition in MnSi continues to be first order in the whole pressure range studied and most probably will stay the same way with further increase of pressure.
Finally, the different sensitivity of AC magnetic susceptibility and electrical resistivity to non-hydrostatic environment probably indicates the dual role of the spin fluctuations involved in the corresponding physics. But detailed analysis of the situation should wait until there is a proper understanding of the nature of the satellite rounded maxima in d/dT as well as the heat capacity and the thermal expansion coefficient at the phase transition in MnSi.
Authors are thankful to J.D. Thompson for reading the manuscript and valuable remarks. TAL wish to acknowledge the support of the U.S. Department of Energy, Basic Energy Sciences. AEP, SMS and VNK appreciate support of the Russian Foundation for Basic Research , Program of the Physics Department of RAS on Strongly Correlated Systems and Program of the Presidium of RAS on Physics of Strongly Compressed Matter.
- H.J. Williams, J.H. Wernick, R.C. Sherwood, and G.K. Wertheim, J.Appl.Phys. 37, 1256 (1966).
- Y. Ishikawa, K. Tajima, D. Bloch and M. Roth, Solid State Commun. 19, 525 (1976).
- J. H. Wernick, G. K. Wertheim and R. C. Sherwood, Mat. Res. Bull. 7, 1431(1972)
- J.D. Thompson, Z. Fisk, and G.G. Lonzarich, Physica B 161, 317 (1989)
- C. Pfleiderer, G.J. McMullan, G.G. Lonzarich, Physica B 206-207, 847 (1995)
- D. Belitz T.R. Kirkpatrick, and T. Vojta, Phys.Rev.Lett. 82, 4707 (1999)
- C. Thessieu, J. Flouquet, G. Lapertot, A.N. Stepanov, D. Jaccard, Solid State Comm. 95, 707 (1995)
- C. Thessieu, C. Pfleiderer, J. Flouquet, Physica B 239, 67, (1997)
- K. Koyama, T. Goto, T. Kanamata, R. Note, Phys.Rev. B 62, 986 (2000)
- C. Pfleiderer, G.J. McMullan, S.R. Julian, G.G. Lonzarich, Phys.Rev.B 55, 8330 (1997)
- N. Doiron – Leyraud, I.R. Walker, L. Taillefer, M.J. Steiner, S.R. Julian and G.G. Lonzarich, Nature 425, 595 (2003)
- C. Pfleiderer, D. Reznik, L. Pintschovius, H.V. Löhneysen, M. Garst and A. Rosch, Nature 427, 227 (2004)
- W.Yu, F.Zamborszky, J.D. Thompson, J.L. Sarrao, M.E. Torelli, Z. Fisk, and S.E. Brown, Phys.Rev.Lett. 92, 086403 (2004)
- Y.J. Uemura, T. Goko, I.M. Gat-Malureanu, et al., Nature Physics, 3, 29 (2007)
- A.E. Petrova, V.Krasnorussky, John Sarrao and S.M. Stishov, Phys.Rev.B, 73, 0524091 (2006)
- C. Pfleiderer, P. Böni, T. Keller, U.K. Rößler, A. Rosch, Science 316, 1871 (2007)
- S.M. Stishov, A.E. Petrova, S. Khasanov, G.Kh. Panova, A.A. Shikov, J.C. Lashley, D. Wu, and T. A. Lograsso, Phys.Rev. B 76, 052405, 2007.
- S.M. Stishov, A.E. Petrova, S. Khasanov, G.Kh. Panova, A.A. Shikov, J.C. Lashley, D. Wu, and T. A. Lograsso, Physica B 403, 1347 (2008)
- S.M. Stishov, A.E. Petrova, S. Khasanov, G.Kh. Panova, A.A. Shikov, J.C. Lashley, D. Wu, T. A. Lograsso, J. Phys.Condens. Matter 20, 235222 (2008)
- A.E. Petrova, V.A. Sidorov, S.M. Stishov, Physica B 359-361, 1463 (2005)
- A.E. Petrova, E.D. Bauer, V. Krasnorussky, and S.M. Stishov, Phys. Rev. B 74, 092401 (2006).
- S.M. Stishov and Alla E. Petrova, J. Phys. Soc. Jpn. 76, Suppl. A, 212-215, (2007).
- Holding the cell at 35 K and at 0.5 GPa pressure of solid helium for more than 12 hours in attempt to reduce non hydrostatic stresses did not effect the magnetic susceptibility of the sample.
- Eventually, the maximum in the d/dT and the d/dT itself disappear in the low temperature limit by the general law.