3. THERMAL PROPERTIES UNDER HIGH PRESSURE 1 General survey
3.3 Heat capacity at high pressure
field measurements have been carried out by using strain gages and a conventional active-dummy method (Sakai et al., 1999).
3.3.2 CeRhIn5
Knebel et al. (2004)studied pressure–temperature phase diagrams of the HF antiferromagnet CeRhIn5under hydrostatic pressure by ac calorime- try using diamond-anvil cell with argon as the pressure medium (Knebel et al., 2004).Figure 32shows heat capacity of CeRhIn5at different pres- suresP. The data are normalized toT¼5 K. The inset shows specific heat previously measured at ambient pressure. The link between the collapse of the superconducting heat capacity anomaly and the broadening of the antiferromagnetic transition to an inhomogeneous appearance of SC below Pc 1.95 GPa. Homogeneous bulk SC is only observed above this critical pressure. Knebel et al. discussed the influence of pressure inhomogeneities on specific heat anomalies, which emphasizes that the broadening of the transition near Pc is connected with the first-order nature of the transition.
3.3.3 CeIrSi3
Tateiwa et al. (2006)studied the pressure-induced superconductor CeIrSi3
with the non-centrosymmetric tetragonal structure under high pressure by means of the electrical resistivity and ac heat capacityCacin the same run for the same sample as shown inFigure 33. The critical pressure was
CeRhln5 2.5
3
C/T (a.u.)
2
1.5
1
0.5
0
P= 0 2
2 1
0 4
0 T (K)
C/T (J/mol K2) P (GPa)
2.55 2.01 1.90 1.85
1.60 1.38 1.07 0.65
1 1.5 2 2.5 3 3.5 4 4.5
T (K)
FIGURE 32 Heat capacity of CeRhIn5at different pressuresP. The data are normalized toT¼5 K. The inset shows specific heat measured at ambient pressure (Knebel et al., 2004).
determined to be Pc¼2.25 GPa, where the antiferromagnetic state dis- appears. The Cac shows both antiferromagnetic and superconducting transitions at pressures close toPc. On the other hand, the superconduct- ing region is extended to high pressures of up to about 3.5 GPa, with the maximum transition temperature Tsc¼1.6 K observed around 2.5–
2.7 GPa. At 2.58 GPa, a large heat capacity anomaly was observed at Tsc¼1.59 K. The jump of the heat capacity in the form ofCac/Cac(Tsc) is 5.70.1. This value is the largest one among previously reported super- conductors, indicating the extreme strong-coupling SC. The electronic specific heat coefficient atTscis, however, approximately unchanged as a function of pressure, even atPc(Tateiwa et al., 2006).
3.3.4 CeRhSi3
Umehara et al., (2007) studied the pressure-induced superconductor CeRhSi3with the non-centrosymmetric tetragonal structure under high pressure by means of adiabatic specific heat and ac heat capacity.
Figure 34shows the temperature dependence of specific heat of CeRhSi3
Celrsi3 CelrSi3
1.31 GPa 2.30 GPa
1.99 GPa
r (mΩcm) Cac/T (a.u.) 10
5
10 0
5
10 0
5
10 0
5
50
0 0
0 0
1 1
2
2 2
2
3 4
4
4 0 2
4 TN
TN
TN
TN Tsc
Tsc
Tsc
Tsc
Tsc
2.14 GPa
T (K) T (K)
2.39 GPa
2.58 GPa
2.19 GPa
Cac/T (a.u.) r (mΩcm)
FIGURE 33 Temperature dependences ofCacof CeIrSi3(circles) and electrical resis- tivity (line) measured in the same experiment (Tateiwa et al., 2006).
under various pressures up to P¼1.22 GPa in the temperature range from 0.7 to 2.5 K. At ambient pressure, a pronounced anomaly in the specific heat is observed, indicating the transition to an antiferromagne- tically ordered state atTN ¼1.61 K.TNwas defined as the temperature at which a peak appears in theCversusTplot. At 0.55, 0.78, 1.02, and 1.22 GPa,TNare 1.81, 1.8, 1.58, and 1.44 K, respectively. Initially,TNincreases with increasing pressure and then decreases with increasing pressure up to 1.22 GPa. The specific heat jump at TN is broadened with increasing pressure. And, a shoulder around 1.4 K can be seen forP ¼0.55 GPa, and at the same temperature, a corresponding anomaly was found in the electrical resistivity data (Kimura et al., 2005). This anomaly may be a new magnetic transition. The magnetic contribution to the specific heat in CeRhSi3 can be obtained by subtracting specific heat of nonmagnetic LaRhSi3from that of CeRhSi3. LaRhSi3exhibits superconducting transi- tion atTc¼2.4 K at ambient pressure. Thus, the magnetic fieldB¼0.5 T was applied to LaRhSi3in order to bring it to the normal state. The specific heat of LaRhSi3in the magnetic fieldB¼0.5 T shows the classical behav- iorC¼gTþbT3withg¼5.84 mJ/mol K2andb¼0.144 mJ/mol K4.
InFigure 35, it can be seen thatTNlowers down to 1.2 K, and a minor discontinuity corresponding to SC appears around 0.8 K under pressure of 1.58 GPa (Tomioka et al., 2008). The magnetic entropy atTN reaches 4.5% ofRln 2. It is remarkable that the discontinuity for the supercon- ducting transition is very small in magnitude compared to what is observed in CeRhIn5(Section 3.3.2) and CeIrSi3(Section 3.3.3).
CeRhSi3 4
3
2
1
00.5
C (J/Kmol)
1.5
1.0 2.0
T (K)
2.5 1.22 GPa
1.02 GPa 0.78 GPa 0.55 GPa 0 GPa
FIGURE 34 Temperature dependence of the specific heat of CeRhSi3at various pressures up toP¼1.22 GPa (Tomioka et al., 2008).
Figure 36shows the ac heat capacity of CeRhSi3at pressures ranging from 2.2 to 2.71 GPa. At 2.2 GPa, the heat capacity shows both antiferro- magnetic and superconducting transitions. The superconducting transi- tion is extremely weak at pressures close to Pc. However, the superconducting transition discontinuity becomes larger at 2.4–2.7 GPa, and the superconducting transition itself is observed at Tsc¼1.2 K. At 2.71 GPa, the magnitude of the discontinuity in the heat capacity repre- sented in the form of DCac/Cac(Tsc) is about 4. This suggests that the strong-coupling SC appears in CeRhSi3 as also observed in CeRhIn5
(Section 3.3.2) and CeIrSi3(Section 3.3.3).
3.3.5 UGe2
Figure 37A showsC/Tof UGe2as a function of temperature at pressure of 1.13 GPa inside the pressure region where ferromagnetic phase is stable below ca. 1.8 GPa (see alsoSection 4). The anomaly associated with bulk superconducting transition is clearly observed at 0.7 K. The g value rapidly increases around 1 GPa, which corresponds to the divergence of Avalue in the expression forAT2in the measurement of electrical resis- tivity as shown in Figure 37B. This strong enhancement of Aand gby applying pressure is in a reasonably good agreement with that calculated by a simple Stoner model and with ND measurements described in Section 2.2.2. This result strongly supports claims that decreasing ofTx
is an important key in the mechanism of exotic SC of UGe2. The details of physical properties in UGe2under high pressure will be further discussed inSection 4.
0 GPa CeRhSi3
C (J/K mol)
3
2
1
00 1 2 3
T (K)
4 1.58 LaRhSi3 (0 GPa)
FIGURE 35 Specific heat of CeRhSi3at ambient pressure and at 1.58 GPa (Umehara et al., 2007).
CeRhSi3
2.20 GPa
2.40 GPa
2.56 GPa
DC/C= 4.01
T (K) Cac (a.u.)
2.71 GPa
0 0.5 1 1.5 2
TSC TN
FIGURE 36 Temperature dependencies of the ac heat capacity of CeRhSi3at pressures between 2.4 and 2.7 GPa (Umehara et al., 2007).
1.13 Gpa
1.13
T (K)
C/T (mJ/mol k2) cac(a.u.) g (mJ/K2.mol)A (mΩcm/K2)
0
00 50 100
0.1
0.05
0 100
50
0
0 0.5
P (GPa)
1.0 1.5 2.0
1 2 –15
0 15
cac UGe2 A
UGe2 B
FIGURE 37 (A) Temperature dependence of specific heat in the form ofC/Tat 0 and 1.13 GPa, and the ac susceptibility at 1.13 GPa in UGe2. (B) Pressure dependence ofAandg values in UGe2(Tateiwa et al., 2001).
3.3.6 SmS
Black SmS is regarded as a nonmagnetic narrow-gap semiconductor crystal- lizing in the NaCl-type structure. It exhibits successive phase transitions with increasing pressure (Jayaraman et al., 1970). An isostructural first- order phase transition at low critical pressure Pc1 (0.7 GPa) at room temperature involves a valence change from divalent to mixed-valence state, accompanied by a spectacular color change from black to golden yellow. In the golden phase, it is assumed that the 4f6 level lies in the conduction bands, resulting in a mixed-valence state between 4f6and 4f5 configurations (Varma, 1976). The magnetic susceptibility shows a weak temperature dependence similar to that of the prototypical mixed-valence compound SmB6. Upon further increasing pressure above a high critical pressurePc21.9 GPa, the electrical resistivity switches to metallic behav- ior below a specific temperatureTM(Lapierre et al., 1981). Although broad studies during the past three decades revealed some aspects of SmS, it remains controversial whether there exists an energy gap atEFin the golden phase (forPc2< P < Pc2). Recent experimental development of specific heat
1.01 GPa
1.59 GPa
1.59 GPa 1.01
1.01 1 10
0.01 0.1
C (J/K mole)
10 1 8 6 4 2 0 8 6 4 2 0
0 5 10 15
T (K)
20 0.62
0.62 0.38
0.38 0 GPa
C (J/K mol)Ce (J/K mol)
T (K) T
SmS#10-1
FIGURE 38 (A) Temperature dependence of specific heat under pressure for SmS. Inset shows lnCversus lnTplot. (B) Electronic specific heatCeat selected pressures. Lines are fits using the Schottky model (Matsubayashi et al., 2007).
and thermal expansion measurements under pressure shed light on this problem and revealed that the pseudo gap state is formed below the critical pressurePc2, above which a magnetically ordered state appears.
Figure 38showsCof SmS under pressure. As the temperature is raised, C initially increases linearly with T (see the inset), indicating nonzero electronic specific heat g. Then, a broad peak of heat capacity forms, which can be described by a conventional Schottky model with an energy gap D. The Schottky peak shifts to lower temperatures with increasing pressure, that is,D decreases with P. The presence of the energy gap is also observed in thermal expansion measurements under pressure.
Figure 39shows theTdependence of the linear thermal expansion coeffi- cienta at pressures up to 2.16 GPa. In the ‘‘black phase’’ belowPc1,a is small and shows weakTdependence. When the system transforms into the golden phase, aLsuddenly changes and becomes strongly T dependent with a large negative peak. When pressure exceeds Pc21.9 GPa, the Schottky anomaly disappears, and instead a sharp anomaly with a positive sign appears atTM11 K. As seen inFigure 40, the same anomaly was also detected by the ac specific heat measurements. Together with the observation of the internal field by nuclear forward scattering experiments (Barla et al., 2004), we ascribe the sharp anomaly to the phase transition between the paramagnetic and magnetically ordered states.