Specific Heat Study of Magnetic and Superconducting Transitions in CePtSi\abst
Measurements of specific heat between 80 mK to 4 K and electrical resistivity between 80 mK to 10 K were carried out for polycrystalline CePtSi samples cut into small pieces (typically 10 mg). In the specific heat measurements, we observed an antiferromagnetic transition jump at = 2.2 K for all the samples, while the heights have large variations. As regards superconductivity, we observed two distinct transition jumps at 0.45 K and 0.75 K, which were the same for all the samples. From the measurements of specific heat and resistivity, systematic relations were found between antiferromagnetic and superconducting transitions. We conclude that antiferromagnetism, whose transition temperature is 2.2 K, coexists with superconductivity, whose transition temperature is . In this sample, residual electronic specific heat coefficient in the superconducting state was quite small, and specific heat divided by temperature below decreased almost linearly with decreasing temperature. In order to reveal the characteristic properties of the magnetism and superconductivity of the CePtSi system, it is important to study the two superconducting phases with and , respectively. \kwordCePtSi, non-centrosymmetry, antiferromagnetism, heavy fermion superconductor, specific heat measurement
Bauer et al. reported that CePtSi exhibits an antiferromagnetic (AFM) order at = 2.2 K and superconducting (SC) transition at = 0.75 K, and that normal state electronic specific heat coefficient is approx 0.39 J/(Kmol). This compound is a heavy fermion superconductor having a characteristic crystal structure that lacks inversion symmetry (space group ). Therefore, the superconductivity of CePtSi exists in a particular environment compared with that of a conventional superconductor. Previous theoretical studies have shown that a non-centrosymmetric heavy fermion has several possible states for realizing unconventional superconductivity[2, 3, 4, 5, 6].
Many experimental studies of superconductivity have been carried out. Previous studies of specific heat by Bauer et al. and Takeuchi et al. have shown marked contrasts between polycrystalline and single crystal samples[1, 7]. The former showed a small AFM transition jump at = 2.2 K and an SC transition jump at = 0.75 K for a polycrystalline sample. The latter showed a large AFM transition jump at the same and an SC transition jump at different of 0.46 K for a single crystal sample. In the single crystal sample, the SC jump was sharp and large, and the residual electronic specific heat coefficient in the SC state, , was small, however, its was low compared with that of the polycrystalline sample. In addition, a double anomaly of the SC state in the specific heat measurement was observed by Scheidt et al. They suggest that it was a signalling two consecutive phase transitions. On the other hand, Nakatsuji et al. showed that the Meissner effect of SC started increasing from 0.8 K and the rate of increase changed below 0.5 K. They suggest that the SC domain has a volume fraction. The pressure dependence of the Meissner effect and seemed to indicate that the volume fraction was due to some inhomogeneous property that leads to a spatial variation of local pressure in the sample.
The temperature dependence of specific heat divided by temperature () in the SC region preferred a linear dependence over a exp dependence. In addition, the dependence of thermal conductivity in the range of 40 mK to 0.2 K was well fitted by a linear function of . These results indicate the presence of line nodes in the SC energy gap. On the other hand, the dependence of nuclear spin-lattice relaxation rate () did not simply follow an exponential law or a -power law. The plot of () showed a coherence Hebel-Slichter peak at , indicating a full-gap state without nodes. Another NMR measurement indicated that the plot of () showed no obvious Hebel-Slichter peak and a drastically decreasing ()[13, 14]. Therefore, CePtSi is expected to be an unconventional superconductor. In addition, the pressure phase diagram of and for this system was unusual compared with that of the previous magnetic superconductor[15, 16, 17]. Although and decreased with increasing , SC still existed even after AFM disappeared. The decreasing rate of slowed down only at around , at which AFM disappeared. The pressure corresponding to the maximum in this system was not . Some heavy fermion magnetic superconductors show a dome structure for the pressure dependence of at the critical point .
Polycrystalline CePtSi and CePtSi samples were synthesized by arc-melting Ce of 99.9 % (3N) purity, Pt of 3N5 purity, and Si of 6N purity, using a laboratory-made furnace. The synthesized melt became solidified by quenching on Cu-hearth in Ar atmosphere of 6N purity. The chemical compositions of our samples were determined from those of the starting materials. The weight loss of the constituent materials was negligible during the preparation. An ingot sample (12 g) was cut into two lumps, and one lump was heat-treated. Heat treatment for annealing was carried out under well-controlled conditions: the temperature was maintained at 950C for one week and lowered to room temperature over three days. We labeled heat-treated and non-heat-treated samples as ”annealed” and ”as-cast”, respectively. Then, each lump was cut into small pieces ( 10 mg) for measurement. We prepared three CePtSi as-cast (#1, 2 and 3), two CePtSi as-cast (#4 and 5), and their annealed samples (#1-a, #2-a and so on) to investigate sample dependence[18, 19]. Moreover, we conducted measurements using different pieces from the same batch (#2-a-1, #2-a-2, and so on).
Temperature dependence of specific heat was measured using the adiabatic heat pulse method between 80 mK to 4 K. Electrical resistivity was measured using the conventional dc four-terminal method down to 80 mK using the same piece as that used in specific heat measurement. Measurements were carried out using a laboratory-made dilution refrigerator.
3 Results and Discussion
Figure 1(a) shows the dependence of specific heat divided by () of the CePtSi as-cast (#1) and CePtSi annealed (#4-a-2) samples. They showed quite different characteristics despite having the same polycrystalline CePtSi system. The of the CePtSi annealed showed a distinct AFM transition with a large jump at (= 2.2 K) and SC transition with a sharp jump at low (= 0.45 K). The residual extrapolated to 0 K was almost zero. These results were similar to those reported by Takeuchi et al. for their single crystal, as shown by the solid line. On the other hand, the of CePtSi as-cast exhibited a very small jump of AFM transition and a jump of SC transition appearing at high (=0.75 K) compared with that of CePtSi annealed. The AFM transition of this sample had not only a small jump but also a broad tail above , from 2.2 K to 4.0 K. clearly increased at the onset of with decreasing , but the peak broadened. These behaviors were similar to that observed by Bauer et al. for their polycrystalline sample, as shown by the broken line. Figure 1(b) shows the temperature dependence of the electrical resistivity () of the CePtSi as-cast and CePtSi annealed samples. Measurements were carried out using very small pieces. Because the absolute value might include some ambiguity, values are presented. The residual resistivity ratio () of CePtSi as-cast was 20 and that of CePtSi annealed was 120. We confirmed reproducibility by some measurements. All of the measured CePtSi annealed including different batches had exceeding 100. These were remarkably large, but other measured samples indicated 20. A kink of was observed at =2.2 K for both samples. The of the CePtSi annealed showed a clear kink at and decreased rapidly below with decreasing temperature. The decrease plateaued immediately just above . On the other hand, the kink of the of the CePtSi as-cast broadened, and the decrease of continued to . These results of and indicate that CePtSi annealed has a more regular AFM ordering (which is a long-range ordering with a narrow at 2.2 K) and a more regular lattice (which is an ideal CePtSi lattice, that is a non-centrosymmetric lattice) than CePtSi as-cast. Figure 1(c) shows the X-ray diffraction patterns. No extra-phase was observed in the X-ray diffraction patterns of both samples. There was no difference in the accuracy of measurement between the lattice constants of the two samples. The results in Fig. 1 indicate that 1% variations in Ce-concentration and heat treatment yield small structural changes that strongly affect SC and AFM but not powder diffraction patterns. In our speculation, these structural changes concern the non-centrosymmetric structure, which is an ordering of Pt and Si atoms occupying the two 1(a)-sites of the structure. Because, it is considered that non-centrosymmetricity is important for both SC of this system and AFM whose magnetic structure consists of ferromagnetic c-planes stacked antiferromagnetically along the c-axis. Therefore, although CePtSi annealed has 1% opening Pt and Si sites, it might have two well-ordered 1(a)-sites of occupied by Pt and Si atoms. Then, the opening sites might be available for removing and ordering Pt and Si atoms when a sample is heat-treated. Conversely, although CePtSi as-cast has a stoichiometric composition, it might have some disorders of Pt and Si at the two 1(a)-sites, because there is a quenching process in the preparation of polycrystalline samples.
Figures 2(a) and 2(b) show the of various samples in order to consider sample dependence in detail. Fig. 2(a) shows the results for the as-cast samples and Fig. 2(b) shows those for the annealed samples. In Figs. 2(a) and 2(b), the data were arranged according to the decrease in the height of the specific heat jump in AFM transition from bottom to top. First, we note both AFM and SC transitions, respectively. The height of the jump in AFM transition, , decreased gradually without changing , and the broad tail above enlarged gradually from the bottom to top data. This relation is plotted in Fig. 3(b). We observed two peaks for SC transition in both Figs. 2(a) and 2(b). We define ( 0.45 K) as the temperature of the specific heat peak at lower and ( 0.75 K) as the onset temperature of the specific heat peak at higher. and were almost constant for all the samples. However, the heights of the specific heat jump at and , and , differed for each sample. As increased, decreased. These results indicate that does not move to and that the SC at and compete against each other. CePtSi as-cast (#1) has only one large peak at . However, this peak might include some components of , because it is broadened from to . Unfortunately, we were unable to prepare a sample that shows only a sharp jump at and a small residual . Next, the relations between the two SC transition jumps, and , and the AFM transition jump, , should be noted. In Figs. 2(a) and 2(b), increased from the top to bottom data, that is, as increased, increased as well. The most typical example of this case is CePtSi annealed (#4-a-2). increased from the bottom to top data. It should be noted that and almost vanished in the sample with the largest . These data of correlation between , and are plotted in Fig. 3(a). These relations are described later. Next, we compare the annealed samples in Fig. 2(b) with the as-cast samples in Fig. 2(a). The and of the annealed samples were almost larger than those of the as-cast samples, while the of the annealed samples were smaller than those of the as-cast samples. These results are shown in Figs. 3(a) - 3(c) as open and closed symbols for as-cast and annealed, respectively.
The relations of , , (2.4 K) and versus are plotted in Figs. 3(a) - 3(c), respectively. In Fig. 3(a), when increases, decreases and increases. It is clear that SC at and compete against each other, and that SC at is on competitive relation with AFM at but SC at is not. In Fig. 3(b), (2.4 K), which reflects the broad tail above , increased with decreasing . This enhancement might have some relation with an increase in . In Fig. 3(c), the relation between and is not clear, but at least the of as-cast was large and the of annealed with a large was small. , and were decided in accordance with Fig. 3(d). These absolute values have some ambiguities because of their broadness. However, it has no significant effects on their relations.
As mentioned above, the present experiment leads us to conclude that the CePtSi system is spatially separated into two superconducting regions, SC and SC, whose transition temperatures are ( 0.45 K) and ( 0.75 K), respectively. SC develops in a more regular AFM ordering and a more regular lattice. CePtSi annealed (#4-a-2) is considered to have an almost single phase in which SC and AFM with coexist. Because, the volume fraction of this sample exhibited SC with a particularly small residual and AFM with the most distinct and largest peak for this sample are probably bulk properties. On the other hand, SC does not seem to coexist with AFM having =2.2 K at least. In what kind of phase is this SC included? To answer this question, the broad tail gradually enlarging above might give us some hints. We suggest that the region of SC is included in some magnetic phase which causes enhancement of the broad tail above (for example, a heavy fermion non magnetic phase and an AFM phase with broad from 2.2 to 4.0 K.) We suggested in our earlier discussion of Fig. 1 and in refs. 18 and 19 that as-cast samples contain some defects, which are reduced in number by heat treatment and annealing. The annealed samples exhibit large , a marked transition at a narrow and a less ferromagnetically anomaly at 3.0 K. A sample having a perfectly regular structure would have perfect non-centrosymmetry. The presence of some defects will affect non-centrosymmetry and produce some partial disorders. In particular, we consider Pt and Si atoms occupying the two 1(a)-sites of the structure as important parts. From this viewpoint, there is a relation between the inhomogeneity of this system and the two volume fractions of SC and SC. The as-cast sample that has some disorders in the non-centrosymmetric structure exhibits a large volume fraction of SC, and the annealed sample with well-ordered non-centrosymmetricity exhibits a large volume fraction of SC. It might be implied that SC develops in the centrosymmetric part and SC develops in the non-centrosymmetric part.
Here, we need to explain why the regular lattice has a low superconducting transition temperature, . From the above sample characterization, we found that SC was affected by the AFM state and the disorder of the non-centrosymmetric structure. We suggest three scenarios to explain . (i) One scenario is that SC exists in the non magnetic heavy fermion state in contrast to the coexistence of SC and AFM at of 2.2 K. might be reduced by an internal magnetic field of AFM. In this case, the broad tail of above is due to a non magnetic heavy fermion state. (ii) The second scenario is that SC exists in another inhomogeneous AFM phase with a broad transition temperature from 2.2 K to 4.0 K, . This inhomogeneous AFM phase transition is the cause of the broad tail. This scenario is consistent with the - phase diagram. In the - phase diagram, and decrease with increasing pressure. If effective pressure caused by the inhomogeneity of a lattice were reduced in the region of SC, the enhancement to and the broad tail of could be explained. A degree of the inhomogeneity causes a broad and a broad tail of . (iii) The third scenario is that SC exists in a well-ordered non-centrosymmetric region and SC exists in a disordered region. Some previous theoretical works have shown that is suppressed by enhancing antisymmetric spin-orbit coupling[5, 6]. In general, antisymmetric spin-orbit coupling is weakened by the disorder of a non-centrosymmetric structure. Therefore, was suppressed by enhancing antisymmetric spin-orbit coupling, and was hardly suppressed. These are simple illustrations. In fact, it might be described by combining the above scenarios and others.
Figure 4 shows the magnified of the CePtSi annealed (#4-a-2) and CePtSi as-cast (#1) samples below 1 K. The former exhibited the largest jump at , while the latter exhibited the largest jump at . As shown in the figure, the of sample #4-a-2 decreased linearly to temperatures below and the extrapolated residual to 0 K was very small. In contrast, the of sample #1 seemed to have a different temperature dependence, and the extrapolated residual to 0 K was finite. In order to reveal the dependence of below , we need to prepare a sample with only a sharp jump at and a small residual .
In conclusion, we observed an AFM transition jump in specific heat measurements of the polycrystalline CePtSi system. We observed = 2.2 K for all the measured pieces, but tended to vary among pieces. As decreased, a broad tail above enlarged gradually. We observed two SC transition jumps at and , which showed no sample dependence. SC and SC volume fractions are considered to be spatially separated to each other in a piece. A larger appeared in a piece that showed a larger . In contrast, a larger appeared in a piece that showed a smaller . Moreover, the piece with the largest jump at had a small and the largest , and these properties appeared in both heat-treated and annealed pieces. Thus, SC was concluded to coexist with the AFM having = 2.2 K in a regular lattice as non-centrosymmetricity. The volume fractions of SC and SC change with the state of AFM ordering and the defects in crystal structures.
We thank A. Sumiyama, T. Kohara, K. Ueda, and Y. Hasegawa for helpful discussions. This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
-  E. Bauer, G. Hilscher, H. Michor, Ch. Paul, E. W. Scheidt, A. Gribanov, Yu. Seropegin, H. Noël, M. Sigrist, and P. Rogl: Phys. Rev. Lett. 92 (2004) 027003.
-  P. A. Frigeri, D. F. Agterberg, A. Koga, and M. Sigrist: Phys. Rev. Lett. 92 (2004) 097001.
-  S. Fujimoto: J. Phys. Soc. Jpn. 75 (2006) 083704.
-  N. Hayashi, K. Wakabayashi, P. A. Frigeri, and M. Sigrist: Phys. Rev. B. 73 (2006) 024504.
-  H. Tanaka, H. Kaneyasu, and Y. Hasegawa: J. Phys. Soc. Jpn. 76 (2007) 024715.
-  Y. Yanase and M. Sigrist: J. Phys. Soc. Jpn. 76 (2007) 043712.
-  T. Takeuchi, T. Yasuda, M. Tsujino, H. Shishido, R. Settai H. Harima, and Y. Ōnuki: J. Phys. Soc. Jpn. 76 (2007) 014702.
-  E-W. Scheidt, F. Mayr, G. Eickerling, P. Rogl and E. Bauer: J. Phys.: Condens. Matter 17 (2005) L121.
-  K. Nakatsuji, A. Sumiyama, Y. Oda, T. Yasuda, R. Settai and Y. Ōnuki: J. Phys. Soc. Jpn. 75 (2006) 084717.
-  Y. Aoki, A. Sumiyama, G. Motoyama, Y. Oda, T. Yasuda, R. Settai and Y. Ōnuki: J. Phys. Soc. Jpn. 76 (2007) 114708.
-  K. Izawa, Y. Kasahara, Y. Matsuda, K. Behnia, T. Yasuda, R. Settai, and Y. Ōnuki: Phys. Rev. Lett. 94 (2005) 197002.
-  M. Yogi, Y. Kitaoka, S. Hashimoto, T. Yasuda, R. Settai, T. D. Matsuda, Y. Haga, Y. Ōnuki, P. Rogl, and E. Bauer: Phys. Rev. Lett. 93 (2004) 027003.
-  K. Ueda, K. Hamamoto, T. Kohara, G. Motoyama and Y. Oda: Physica B. 359-361 (2005) 374.
-  K. Ueda, T. Kohara, G. Motoyama and Y. Oda: J. Mag. Mag. Mat. 310 (2007) 608.
-  T. Yasuda, H. Shishido, T. Ueda, S. Hashimoto, R. Settai, T. Takeuchi, T. D. Matsuda, Y. Haga and Y. Ōnuki: J. Phys. Soc. Jpn. 73 (2004) 1657.
-  N. Tateiwa, Y. Haga, T. D. Matsuda, S. Ikeda, T. Yasuda, T. Takeuchi, R. Settai and Y. Ōnuki: J. Phys. Soc. Jpn. 74 (2005) 1903.
-  E. Bauer, H. Kaldarar, A. Prokofiev, E. Royanian, A. Amato, J. Sereni, W. Brämer-Escamilla, and I. Bonalde: J. Phys. Soc. Jpn. 76 (2007) 051009.
-  G. Motoyama, S. Yamamoto, H. Takezoe, Y. Oda, K. Ueda and T. Kohara: J. Phys. Soc. Jpn. 75 (2006) 013706.
-  G. Motoyama, M. Watanabe, K. Maeda, Y. Oda, K. Ueda and T. Kohara: J. Mag. Mag. Mat. 310 (2007) e126.
-  N. Metoki, K. Kaneko, T. D. Matsuda, A. Galatanu, T. Takeuchi, S. Hashimoto, T. Ueda, R. Settai, Y. Ōnuki and N. Bernhoeft: J. Phys.: Condens. Matter 16 (2004) L207.
-  W. Higemoto, Y. Haga, T. D. Matsuda, Y. Ōnuki, K. Ohishi, T. U. Ito, A. Koda, S. R. Saha and R. Kadono: J. Phys. Soc. Jpn. 75 (2006) 124713.