Superconductivity of CeRhIn5 under High Pressure

Journal of the Physical Society of Japan Vol. 70, No. 11, November, 2001, pp. 3362{3367

Superconductivity of CeRhIn5 under High Pressure Takaki M URAMATSU, Naoyuki T ATEIWA1 , Tatsuo C. K OBAYASHI, Katsuya SHIMIZU1 , Kiichi A MAYA1 , ¯ NUKI2;3 Dai AOKI2 , Hiroaki S HISHIDO2 , Yoshinori HAGA3 and Yoshichika O Research Center for Materials Science under Extreme Conditions, Osaka University, Toyonaka, Osaka 560-8531 1 Graduate School of Engineering Science, Osaka university, Toyonaka, Osaka 560-8531 2 Graduate School of Science, Osaka University, Toyonaka, Osaka 560-8531 3 Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195 (Received May 23, 2001)

The pressure dependence of transport properties in CeRhIn5 was studied up to 8.5 GPa by using a diamond-anvil cell. The electrical resistivity does not follow the T 2 -dependecne of a Fermi liquid nature under any pressure. In this non-Fermi liquid state, superconductivity was observed in a wide pressure range of 1:5 GPa < P < 7:6 GPa. The superconducting temperature TC has a double-maximum structure with a minimum at 5.2 GPa. A maximum of TC ¼ 2:2 K was observed at P ¼ 2:5 GPa, where the corresponding electrical resistivity just above TC has the maximum. The upper critical ;eld HC2 and the magnetoresistances were also investigated under pressure. KEYWORDS: electrical resistivity, magnetoresistance, superconductivity, high pressure, CeRhIn5

x1.

Introduction

Research for the pressure-induced superconductivity has been carried out in order to understand a relation between magnetism and superconductivity in heavy fermion systems. Recently there has been discovered superconductivity in several Ce-based compounds. In these compounds, the application of pressure suppresses the magnetic ordering, and ;nally the ordering temperature becomes zero at a critical pressure PC . Superconductivity was induced around PC in some compounds. Pressure-induced superconductivity is classi;ed into two categories. For example, superconductivity appears in the vicinity of PC in CeIn3 and CePd2 Si2 .1,2) On the other hand, superconductivity in CeCu2 Si2 and CeCu2 Ge2 is observed in a relatively wide pressure range with characteristic enhancement of TC .3{5) A di>erence between them might be attributed to competition between the Ruderman{Kittel{Kasuya{ Yoshida (RKKY) interaction and the Kondo e>ect. The Kondo temperature TK is approximately related to Tmax where the electrical resistivity has the maximum. We note that Tmax in CeIn3 and CePd2 Si2 is larger than that in CeCu2 Si2 and CeCu2 Ge2 : Tmax ¼ 50 K in CeIn3 and 60 K in CePd2 Si2 , while Tmax ¼ 10 K in CeCu2 Si2 and 20 K in CeCu2 Ge2 . The heavy fermion superconductivity with a low Tmax was recently discovered in CeRhIn5 by Hegger et al.6{10) The Tmax value at PC ¼ 1:5 GPa was about 18 K, which is close to those of CeCu2 Si2 and CeCu2 Ge2 . The crystal structure of CeRhIn5 is a unique tetragonal structure with a quasi-two dimensional character, which can be viewed as alternating layers of CeIn3 and RhIn2 , stacked sequentially along the tetragonal c-axis. CeRhIn5 is an antiferromagnetic compound with a Ne´el temperature TN ¼ 3:8 K. Application of pressure induced a ;rstorder-like transition from an antiferromagnetic state to

an unconventional superconducting state with a transition temperature TC ’ 2:1 K. Strange is that TN does not decrease but slightly increases with increasing pressure up to 1.5 GPa, although another transition at just below 3 K appears above 1 GPa. Superconductivity was observed in a pressure range from 1.7 to the measured highest pressure of 2.1 GPa. More recently it was reported that a series of compounds, CeIrIn5 and CeCoIn5 , are heavy fermion superconductors.11{20) The transition temperature TC and the electronic speci;c heat coeCcient are 0.4 K and 680 mJ/K2 mol in CeIrIn5 , and 2.3 K and 300{ 1000 mJ/K2 mol in CeCoIn5 . Here, the value in CeCoIn5 is about 300 mJ/K2 mol at TC but increases with decreasing the temperature, reaching about 1000 mJ/K2 mol at 0.1 K, which was obtained by the speci;c heat measurement in magnetic ;elds. This means that the speci;c heat coeCcient C=T in magnetic ;elds does not saturate at low temperatures, increasing with decreasing temperature. Moreover, the electrical resistivity shows a linear temperature dependence below about 10 K instead of a Fermi liquid T 2 -dependence, the magnetic susceptibility increases steeply below 10 k, and the magnetoresistance is negative in the temperature range from 10 to TC ¼ 2:25 K. These experimental results indicate that CeCoIn5 is most likely sited in the quantum critical point.19,20) To clarify the superconducting property furthermore, we measured the electrical resistivity in a wide pressure range from ambient pressure to 8.5 GPa by using a diamond-anvil cell (DAC) and established a superconducting TC {P phase diagram. The transport properties in magnetic ;elds were also investigated. We show in this paper that pressure-induced superconductivity of CeRhIn5 is classi;ed as the latter case as in CeCu2 Si2 and CeCu2 Ge2 , being observed in a wide pressure range from 1.5 to 7.6 GPa. Moreover, the characteristic

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2001)

Superconductivity of CeRhIn5 under High Pressure

property in both the normal and superconducting states under P ¼ 2:5 GPa is almost the same as that of a heavy fermion superconductor CeCoIn5 .19,20) x2.

Experimental

A single crystal of CeRhIn5 was grown by the In-Iux method. Purity of the starting materials was 4N(99.99% pure)-Ce, 4N-Rh and 5N-In. The electrical resistivity measurement was carried out by a four-probe ac resistance bridge (Linear Research, LR-700) under high pressures up to 8.5 GPa by using a diamond-anvil cell (DAC). The current was directed parallel to the c-plane. Superconductivity of In was not observed in the pressure experiment, indicating that In is not included in the present sample. Four gold-wires with 10 m in diameter were bonded to the sample using a micro-manipulating electric-discharge technique.21,22) The sample and some small ruby chips were clamped with Daphne 7373 oil as a pressure medium.23) The determination of the pressure value was carried out by the ruby Iuorescence method at room temperature and 4.2 K. An experimental error for pressure was within 10%. The spectrum of the ruby Iuorescence at 8.5 GPa was as sharp as that at the

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ambient pressure. DAC was then assembled in the 3 He/ 4 He dilution refrigerator, and the sample was cooled down to 0.1 K. Other details of the DAC experiment are given in ref. 24. x3.

Experimental Results and Analyses

Figure 1(a) and 1(b) show the temperature dependences of the electrical resistivity and the magnetic resistivity under pressure, respectively, where the magnetic resistivity was obtained by subtracting the resistivity of a non-4f reference compound LaRhIn5 from that of CeRhIn5 under pressure: mag ¼ ðCeRhIn5 Þ ðLaRhIn5 Þ. At ambient pressure an antiferromagnetic ordering and the temperature where the magnetic resistivity shows the maximum were observed at TN ¼ 3:8 K and Tmax ’ 60 K, respectively. The residual resistivity 0 and the residual resistivity ratio RRR (¼ RT = 0 ) is 0.18 cm and 106, respectively. When pressure is induced, Tmax decreases from 60 K at 0 GPa to 20 K at 1.5 GPa. In addition, the resistivity value at Tmax is enhanced and a peak of the resistivity becomes sharp with increasing pressure up to 1.8 GPa. These features are consistent with the recent results

Fig. 1. (a) Temperature dependence of the electrical resistivity in CeRhIn5 under pressure, (b) and the corresponding magnetic resistivity and the (c) low-temperature resistivity under pressure in CeRhIn5 .

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Takaki M URAMATSU et al.

obtained by Hegger et al.,6) although its characteristic features are di>erent from the conventional Ce-based heavy fermion systems.3{5) On the other hand, at higher pressures than P ¼ 1:8 GPa, Tmax increases and ;nally reaches 165 K at 8.5 GPa. The corresponding resistivity peak at Tmax becomes broad as in the usual Kondo lattice system. At 1.5 GPa, both antiferromagnetic ordering at TN ¼ 3:8 K and the broad superconducting transition at TC ¼ 1:3 K were observed, where TC was determined as the zero resistivity. With increasing pressure, antiferromagnetic ordering disappears most likely in a pressure range of P > 1:8 GPa, and then the superconducting transition temperature increases with increasing pressure. The maximum of TC was observed at 2.5 GPa with a narrow transition, as shown in Fig. 1(c). In 1:8 GPa < P < 3:8 GPa, TC does not change drastically, but the magnitude of the resistivity just above TC is extremely enhanced around 2.5 GPa, as shown in Fig. 2(a). Namely, the residual resistivity less than 1 cm at ambient pressure increases up to 10.7 cm just above TC at 2.5 GPa. An enhanced value of the resistivity is, however, reduced with further increasing pressure. The present characteristic feature is discussed later. As noted above, a temperature width at the superconducting transition, TC [¼ TC ðonsetÞ TC ðzero resistivityÞ] becomes minimum at 2.5 GPa, as shown in Fig. 2(b), where TC (onset) and TC (zero resistivity) correspond to a temperature showing onsetsuperconductivity and a temperature showing a zero resistivity, respectively. Here we note that the electrical resistivity in both the normal and superconducting states at P ¼ 2:5 GPa is almost the same as that of a heavy fermion superconductor CeCoIn5 with TC ’ 2:25 K and the electronic

(Vol. 70,

speci;c heat coeCcient ’ 1 J/K2 mol at ambient pressure. Figure 3 shows the temperature dependence of the electrical resistivity of CeCoIn5 , together with that at 2.5 GPa in CeRhIn5 . The resistivity in CeCoIn5 indicates the maximum at Tmax ¼ 40 K and becomes zero at TC ¼ 2:25 K. As in CeRhIn5 , the resistivity does not follow a T 2 -dependence of the Fermi liquid nature but a T -linear dependence below 10 K. The present result of CeRhIn5 under pressure, shown in Fig. 2(a), explains a reason why the value of the electrical resistivity at TC in CeCoIn5 , about 5 cm, is large. A superconducting TC {P phase diagram in CeRhIn5 was obtained, as shown in Fig. 4, indicating a doublemaximum structure. Superconductivity was observed in a wide pressure range from 1.5 to 7.6 GPa. In CeRhIn5 , Tmax ¼ 20 K at 1.5 GPa is almost the same as that in CeCu2 Ge2 .3,4) This low Tmax value might account for the wide pressure range of a superconducting phase. At 5.2 GPa TC shows the minimum of TC ¼ 0:74 K with a broad transition. At 6.3 GPa TC becomes slightly larger than that at 5.2 GPa, indicating TC ¼ 0:99 K. With

Fig. 3. Temperature dependence of the electrical resistivity in CeRhIn5 , LaRhIn5 and CeCoIn5 at ambient pressure, and that in CeRhIn5 under pressure P ¼ 2:5 GPa.

Fig. 2. (a) Pressure dependence of the electrical resistivity just above TC and (b) of the transition width in CeRhIn5 .

Fig. 4. Pressure dependence of TC and TN in CeRhIn5 .

2001)


increasing pressure furthermore, TC decreases and ;nally disappears at 8.5 GPa. The minimum at 5.2 GPa in the TC {P phase diagram might corresponds to that around 17 GPa in CeCu2 Ge2 or to the 1/8 anomaly reported in doped lanthanum cuprates.25,26) It is noted that an electronic state of CeRhIn5 is quasi-two dimensional.6) Next we measured the transverse magnetoresistance at 2.5 GPa, as shown in Fig. 5. The magnetic ;eld was applied parallel to the c-axis, which is perpendicular to the current direction. From these data, the upper critical ;eld HC2 was determined as a function of the corresponding temperature. The superconducting H{T phase diagram at 2.5 GPa was obtained, as shown in Fig. 6, together with HC2 at 5.2 and 6.3 GPa as well as HC2 in CeCoIn5 .20) Solid lines are a guide to eyes, calculated on the basis of the well-known WHH theory in the dirty limit.27) HC2 at 2.5 GPa is estimated as 10.2 T at zero temperature. This HC2 value is larger than 4.95 T in CeCoIn5 , indicating that the value at 2.5 GPa in CeRhIn5 is at least close to about 1 J/K2 mol as in CeCoIn5 . A slope of the upper critical ;eld just below TC , dHC2 =dT , is 15 T/K. The coherence length was estimated as ¼ 57 & A by using a relation of HC2 (¼ (0 =22 ), where (0 is a quantum Iuxoid. Similarly, HC2 (0) and -dHC2 =dT for 5.2 and 6.3 GPa are 5 T (9.3 T/K) and 2.0 T (3.0 T/K), respectively. We summarize these superconducting properties in Table I, together with those in CeCoIn5 .

Fig. 5. Temperature dependence of the electrical resistivity under several magnetic ;elds in CeRhIn5 .

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We found an anomalous feature in magnetic ;elds. Figure 5 shows the temperature dependence of the electrical resistivity at 2.5 GPa under several magnetic ;elds. The temperature dependence of the electrical resistivity under H ¼ 10 T is highly di>erent from those under smaller magnetic ;elds. A shoulder appears around 1 K and a kink also appears at 0.45 K. We assumed that the kink corresponds to the onset of a superconducting transition. Therefore we considered that the shoulder at 1 K might be caused by the reduction of magnetic Iuctuations based on the Kondo e>ect. The reduced residual resistivity becomes the order of 1 cm at 10 T. The similar shoulder-like structure in the resistivity is observed around 3 K at 1.8 GPa, as seen in Figs. 1(b) and 1(c). The origin of these characteristic features is not clear at present. Application of the external ;eld at 2.5 GPa increases the resistivity. Figure 7(a) shows the ;eld dependence of the resistivity at 2.2 K under 2.5 GPa, where the current is directed parallel to the c-plane and the ;eld is applied perpendicularity to the c-plane, namely along the c-axis. The magnetoresistance has the maximum at 8 T. This behavior is obviously di>erent from the H 2 -dependence which is based on the cyclotron motion of the carriers, and most likely indicates the increment of magnetic Iuctuations in the magnetic ;elds. The similar magnetoresistance is observed in CeCoIn5 , as shown in Fig.

Fig. 6. Temperature dependence of HC2 in CeRhIn5 under pressure, together with that in CeCoIn5 at ambient pressure, shown by broken lines.

Table I. Superconducting properties at 2.5 GPa in CeRhIn5 , together with those of CeCoIn5 , cited from ref. 19 and 20. CeRhIn5 at 2.5 GPa H k c-axis

CeCoIn5 H k c-plane

c-axis

(K)

2.25

HC2 (0)

(T)

10.2

4.95

11.6

-dHC2 =dT (at TC )

(T/K) &) (A

15

11.0

24.0

57

35

82

50

110

TC

2.25

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Takaki M URAMATSU et al.

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suppression of the magnetic Iuctuations. Moreover, at 2.5 GPa, the breaking of superconductivity by applying the magnetic ;elds of 10 T reveals the similar shoulderlike temperature dependence of the resistivity, and the residual resistivity indicates a small value. We might say that pressure corresponds to the magnetic ;eld in this system. In addition, the magnetoresistance at just above TC was measured at 2.5 GPa. It increases with increasing the magnetic ;eld and reaches a broad maximum around 8 T. Such a magnetoresistacnce as well as the temperature dependence of the electrical resistivity in the whole temperature range and HC2 under 2.5 GPa in CeRhIn5 are almost the same as those in CeCoIn5 . We conclude that these features reIect the electronic state at the quantum critical point. Acknowledgements This work has been supported by CREST (Core Research for Evolutional Science and Technology) of Japan Science and Technology Corporation (JST), Grant-in-Aid for the COE Research (10CE2004) and for Scienti;c Research (A) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

Fig. 7. Magnetoresistance (a) at 2.2 K in CeRhIn5 under 2.5 GPa and (b) at 4.2 K in CeCoIn5 at ambient pressure.

7(b). The electronic state is similar between two compounds. The temperature dependence of the resistivity does not obey the Fermi liquid nature of a T 2 -dependence in the whole pressure range. Below 2.5 GPa the resistivity is complicated indicating the shoulder-like structure, as described above. At 3.2 and 3.8 GPa the resistivity obeys a T -linear dependence in a wide temperature range from about 2 K to 10 K, as shown in Fig. 1(c). The T linear dependence is observed in the quantum critical region of the pressure-induced superconductor as in CeCu2 Ge2 .3) Even at 8.5 GPa, the temperature dependence of resistivty does not obey the T 2 -dependence in spite of disappearance of superconductivity. In the case of the other heavy fermion superconductors, the T 2 dependence is clearly observed when TC is suppressed by pressure. The reason is not clear at present. x4.

Summary

Superconductivity of CeRhIn5 was observed in a wide pressure range from 1.5 to 7.6 GPa. The superconducting transition temperature has a maximum value at 2.5 GPa and correspondingly the resistivity just above TC becomes maximum at this pressure. The P {TC diagram indicates a double-maximum structure with the minimum at 5.2 GPa. At 1.8 GPa, the resistivity has a shoulder-like structure around 3 K, which means the

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