5. NEW PHENOMENA UNDER HIGH PRESSURE
5.1 Pressure-induced magnetic order .1 CeNiSn
The Kondo semimetal CeNiSn, which has the orthorhombice-TiNiSi-type crystal structure (space group Pnma), has lattice constant a¼7.54 A˚ , b¼4.60 A˚ , c¼7.61 A˚ ) and it forms a pseudogap in the DOSs at the Fermi level (Takabatake et al., 1990). Hydrostatic pressure measurements have been done by many authors (Hiraoka et al., 1994; Kurisu et al., 1988;
Uwatoko et al., 1992a). The pseudogap in CeNiSn is strongly suppressed by the increase of the degree of hybridization. The carrier concentration increases together with the recovery of the DOSs at the Fermi level. Further, suppression of antiferromagnetic correlations upon applying pressure was deduced from a neutron inelastic-scattering experiment (Sato et al., 1996).
It is interesting to compare the effect of pressure with that of uniaxial pressure. Unlike under uniaxial pressure, CeNiSn exhibits a transition from a pseudogapped state to a magnetically ordered state forP//b-axis andP//c-axis, while no transition occurs underP//a-axis. The magnetic susceptibility w at various uniaxial pressures is shown in Figure 131.
At ambient pressure, the temperature dependence of the susceptibility
50 6 7 c (10–3 emu/mol)
8 P//H//a-axis B= 1 T CeNiSn 9
2 4 6 8 10 12 14 16 18 0.34 GPa 0.21 GPa 0.1 MPa
20 22 T (K)
P//H//c-axis B= 1 T
1 2 3 c (10–3 emu/mol)
4 B 5 A
0.42 GPa 0.25 GPa 0.14 GPa 0.07 GPa 0.1 MPa
0 5 10 15 20 25
T (K) CeNiSn
FIGURE 131 wplotted versus temperature at various pressures applied to a single crystal of CeNiSn along (A)a- and (B)c-axes. Solid line represents earlier data (Umeo et al., 1999).
is identical to previous results (Takabatake et al., 1996). ForP//H//a, the susceptibility decreases with increasing pressure P, whereas the maxi- mum temperature at 13 K hardly changes. But, forP//H//c,xis strongly increased with development of a pronounced maximum at 3.7 K above 0.25 GPa. This maximum ofwmay be associated with the occurrence of antiferromagnetic order.
To clarify the origin of maximum inw, the specific heat Chas been measured under pressure up to 0.37 GPa. The temperature dependencies ofC of CeNiSn at several pressures parallel to thea-,b-, andc-axes are shown inFigure 132. ForP//a-axis, the value ofCdecreases slightly with pressure in the temperature range of the measurements. By contrast, for P//b-axis andP//c-axis,Cincreases with pressure and shows a maximum around 3.7 K at 0.25 and 0.13 GPa, respectively. With further increase in pressure, another peak appears around 3 K.
TheCel/Tfor selected pressures is shown inFigure 133. ForP//c-axis
¼0.16 GPa, the coexistence of the maximum around 6 K with the peak at 3 K implies that the AF state evolves from the state where the pseudogap remains. As is shown by the solid curves, the temperature variations of Cel/T in the nonordered state could be reproduced by the use of the V-shaped DOS (see inset ofFigure 133) with a finite value at the Fermi level (Nishigori et al., 1996; Takabatake et al., 1998).
The peak of bothCandwclearly indicates that AFM order sets in. This is consistent with theT3dependence ofCbelow 2.5 K forP//c-axis, which can be regarded as characteristic of the excitation of AFM magnons.
The dependence of the AF transition temperatureTN on the applied pressure forP//cis shown inFigure 134. The most significant feature is that onceTNappears at 4 K above 0.1 GPa, it does not change with further increase inP. This fact indicates the pressure-induced transition to be a first-order transition.
CeNiSn undergoes a transition from a pseudogapped state to a mag- netically ordered state under uniaxial pressure for P//b-axis and P//c- axis, while no transition occurs underP//a-axis. Since the critical pressure for this transition is as small as 0.1 GPa, CeNiSn should be located in the vicinity of the QCP. As to the microscopic origin of the anisotropic response, the local symmetry of Ce ions in this compound is quasitrigonal when viewed along the a direction (Higashi et al., 1993). This trigonal symmetry is thought to be a prerequisite for the formation of the pseu- dogap in the renormalized band which is originated from the anisotropic c–f hybridization (Ikeda and Miyake, 1996; Kagan et al., 1997). Here, c means the conduction electrons. When a uniaxial pressure is applied along theb-andc-axes, the trigonal symmetry would be lowered, while it is maintained for P//a-axis. The loss of the quasitrigonal symmetry may be responsible for the pressure-induced magnetic transition.
Another scenario is that the elongation along thea-axis underP//b-axis
and P//c-axis may weaken the c–f hybridization and thus brings the system to the magnetically ordered state, as is expected from Doniach’s phase diagram (Doniach, 1977; Iglesias et al., 1997).
CeNiSn
P II a
P II b
P II c 0 GPa
0.37 GPa
0.37 GPa 0.25 0.13 0
0.28 GPa 0.19 0.16 0.13 0.06 0 1.0
0.5
0
1.0
0.5
C (J/mol K)
0
1.0 1.5
0.5
00 2 4
T (K)
6
FIGURE 132 Specific heatCof CeNiSn as a function ofTunder uniaxial pressure (Umeo et al., 1999).
5.1.2 YbInCu4
Yb compounds, which are a counterpart of Ce compounds, are known to show numerous anomalies of physical properties under high pressure (Mignot and Wittig, 1981; Nowik et al., 1988; Umeo et al., 2007;
Winkelmann et al., 1998). The response of the physical properties of Yb
0.4
0.2
00 5
0.37 GPa 0.06 GPa 0.16 GPa
EF N0
D
2W
N(E)
D
P II a P II c CeNiSn
Cel/T (J/mol K2)
T (K) 0 GPa
10
FIGURE 133 Temperature dependence of the electronic specific heatCeldivided by temperature. Solid lines are the fits with a V-shaped density of states depicted in the inset. (Umeo et al., 1999).
CeNiSn
00 2 4 6
0.1 0.2
P (GPa) TN (K)
0.3 P II c
FIGURE 134 Pressure dependence ofTNof CeNiSn (Umeo et al., 1999).
compounds to applied pressure is in sharp contrast to that of Ce com- pounds. For example, the temperature of the resistance maximumTmax, which roughly corresponds to the Kondo temperatureTK, increases with pressure for almost all Ce compounds (Kagayama and Oomi, 1993b), but it decreases for Yb compounds. In some Yb compounds, the CK state is induced by applying pressure as in YbAgCu4 (Graf et al., 1995) and YbCo2Zn20(Matsubayashi et al., 2010b; Saiga et al., 2008). The intermetal- lic compound YbInCu4, which crystallizes in the AuBe5 type (C15b) structure with the lattice constant, a¼7.156 A˚ (Felner et al., 1987;
Kojima et al., 1990), is one of the interesting Yb compounds. The most interesting feature of YbInCu4is that it shows a valence transition from a high-temperature stable trivalent Yb3þ to a low-temperature mixed- valence Yb around 50 K (¼Tv).Tvis found to be strongly dependent on pressure with dTv/dP 20 K/GPa (Kojima et al., 1988).Nowik et al.
(1988)reported an anomaly near 0.6 GPa in the pressure dependence of Tv. However, no anomaly in theTv–Pcurve was observed byKojima et al.
(1988) and Matsumoto et al.(1992). In this section, we discuss the effect of pressure on the valence transition of YbInCu4by measuring bulk modu- lus, magnetization, and electrical resistivity up to 13 GPa.
Figure 135shows the relative change in the lattice constanta/a0as a function of pressure at room temperature, whereaanda0are the lattice constants at high and ambient pressure, respectively. Since there are no new Bragg peaks up to 13 GPa, the AuBe5 structure is stable at room temperature at least to 13 GPa. A discontinuous change in the value of a/a0, to be caused by theg–atransition in Ce metal (Franceschi and Olcese, 1969), is not observed in the present pressure range within experimental error. This result indicates that a discontinuous valence transition as observed at Tv is not induced by pressure up to 13 GPa at room
YbInCu4
at room temperature
1
0.99
0.98
0.97
0 5
P (GPa) 10 a/a0
15
FIGURE 135 Pressure dependence of the relative change of lattice parametera/a0of YbInCu4at room temperature (Oomi et al., 1994b).
temperature. In order to estimate the bulk modulus, we attempted a least- squares fit of the data inFigure 135to the Murnaghan’s equation(1)(see the solid curve inFigure 135). The values ofB0andB00were found to be B0¼(112 2) GPa and B00 ¼4.00.2, respectively. B0 of YbInCu4 is slightly larger than that of the YbAgCu4, 108 GPa (Bauer et al., 1993).
The results obtained until now are summarized inTable 5together with those of the related CK or HF compounds: YbAl2(Penney et al., 1982), YbAgCu4(Bauer et al., 1993), and CeInCu2(Kagayama et al., 1990) for comparison. The small value ofB00indicates a relatively slow stiffening of the lattice with increasing pressure, which is similar to Ce compounds.
This fact indicates that the electronic state of the compounds having unstable 4f electrons has a strong effect not only on the value ofB0but also onB00. The small value ofB00of YbAgCu4suggests a large change in the electronic state due to increasing hybridization by pressure (see Table 1in Section 1). There seems to be a relationship between B0, the electronic specific heat coefficientg, and the lattice constanta0.
The electronic state of YbInCu4changes from IV state to the CK state by substituting In for Ag (Yoshimura et al., 1990; Kojima et al., 1992). This is considered to be due to a decrease in the hybridization between the localized 4f electrons and the conduction band caused by the substitution of Ag. Since the application of pressure essentially results in an increase in the hybridization, the effect of Ag addition is opposite to that of pressure.
Taking into account these facts and the pressure dependence of Tv, YbInCu4 may correspond to a hpp or a kind of compressed state of YbAgCu4to have a larger bulk modulus than YbAgCu4. This consider- ation explains qualitatively the above-mentioned values for the bulk modulus. Further, from the theoretical calculations (Lavagna et al., 1983), it was revealed that the bulk modulus in the Kondo state is always lower than that in the non-Kondo or normal state. If we consider that YbAgCu4is in the Kondo state and YbInCu4in the normal trivalent state, the bulk modulus of YblnCu4would be larger than that of YbAgCu4. This is also consistent with the present results. On the other hand, for YbInCu4,
TABLE 5 Summary of the present results and data of some CK compounds
a0(A˚ ) g(mJ/
mol K2) B0
(GPa) B00 Tmax
(K)
@Tmax/@P (K/GPa)
YbInCu4 7.16 22 112 4.0 – –
YbAgCu4 7.07 245 108 3.3 100 14
YbInAu2 6.84 40 54.7 19.7 275 4.2
YbAl2 7.88 10 43.1 5.0 – –
CeInCu2 6.78 1200 90 3.9 27 0.4
the effect of the electronic state on the lattice stiffening may be relatively small, which indicates that the Yb3þ state is stable up to 13 GPa. This result is consistent with that of the electrical resistivity in which theP–T curve of YbInCu4shows normal properties aboveTv(Felner et al., 1987).
Electrical resistivity measurements of YbInCu4were performed under high pressure up to 7.0 GPa and temperature down to 0.3 K (Kurita et al., 2006). Figure 136A and B shows the temperature dependence of the electrical resistivity of YbInCu4at low temperature. The electrical resis- tivity of YbInCu4 decreases with temperature almost linearly above valence transition temperature Tv and then drops abruptly at Tv, as shown inFigure 136A.Tvdecreases linearly with increasing pressure up to 1 GPa as shown in Figure 142. At ambient pressure, the resistivity
0
1000 150 200 250 B 300 A
2 4 6
YblnCu4 8 0
100 200
3.76
3.39 2.22
2.94
1.48 1.11 0.74 GPa
3.3 GPa 4.0 4.6 7.0 6.0 5.5 300
10 20
T (K)
T (K)
30 40 50
r(mΩ·cm)r(mΩ·cm)
FIGURE 136 (A) Temperature dependence of the electrical resistivity of YbInCu4at low-temperature measured using piston cylinder cell (A) (Hedo et al., 2003) and diamond-anvil cell (B) (Kurita et al., 2006). Arrows indicate the temperature where there is a ‘‘knee’’ inr(T) in (B).
above Tv increases rapidly due to a large internal strain of the sample, induced by thermal cycling through the transition. At high pressure, the resistivity does not change much after the transition has taken place.
YbInCu4exhibits large hysteresis below 3 GPa aroundTvas shown in Figure 137. The resistivity at 2.9 GPa exhibits hysteresis near the valence transition temperatureTv¼6.2 K. For P¼3.39 GPa; the valence transi- tion disappears, with no detectable hysteresis at low temperature. There is no observed hysteresis at the transition, and then the transition dis- appears above 3 GPa.
We tentatively fit the data obtained in previous and this work at low temperature to r¼r0þAT2. Both the residual resistivity r0 and the resistivity coefficient A as a function of pressure show broad peaks around 3.5 GPa. And then, r0 at low temperature is suppressed by increasing pressure from 3.3 to 5.5 GPa. This suggests that YbInCu4
around 3.5 GPa may be in the vicinity of a QCPPc, given the report of similar variations of A and is reported for pressure-induced supercon- ductor CeCu2Ge2 (Jaccard et al., 1999), although pressure-induced changes in carrier density and ground-state degeneracy could provide an alternative interpretation (Figures 138 and 139).
Hedo et al. (2003)observed a ‘‘filamentary’’ SC (with a nonzero resis- tivity) above 0.74 GPa and below1.4 K, though it could not be detected
FIGURE 137 Electrical resistivity of YbInCu4versus temperature below 8 K atP¼2.94 and 3.39 GPa (Hedo et al., 2003).
at ambient pressure, as shown in Figure 140. The drop of resistivity vanishes in magnetic field above 0.036 T. This SC survives up to 4 GPa and the superconducting temperature Tc is almost independent of the pressure. AbovePc, the resistivity follows the linear behavior versusTin the range 0.9 to 2.5 K.
Figure 140 shows magnetization plotted versus temperature for a single crystal of YbInCu4 at various pressures (Sarrao et al., 1998).
At 1 bar, the temperature dependence of the susceptibility is identical to previous results (Sarrao et al., 1996), within experimental error. The sharp FIGURE 138 Pressure dependence of the residual resistivityr0and coefficientAof YbInCu4in the relationr¼r0þAT2(Kurita et al., 2006).
0.0 215 220 225
H= 0.05 T
YbluCu4 P= 3.76 GPa H= 0 T
Tc
Resistivty (mΩcm)
230 235
0.5 1.0 1.5 2.0
Temperature (K)
2.5 3.0
FIGURE 139 Low-temperature resistivity of YbInCu4inH¼0 and 0.05 T under P¼3.76 GPa. Solid line isT-linear line as guide to the eye (Hedo et al., 2003).
rise atT¼40 K (P¼l bar) due to the Yb valence change with increasing temperature decreases with increasing pressure at the rate of dTv/ dP¼ 22.3 K /GPa, which is slightly larger than previously reported (Immer et al., 1997). This difference may be caused mainly by variation of pressure inside the microcell with temperature. At high temperatures, the susceptibility follows the Curie–Weiss law, with values of the paramag- netic temperature and paramagnetic moments,yP¼ 7 K andmYb¼4.50 (mB/Yb) at 1 bar. This Curie–Weiss behavior does not change under pressure within experimental error.
Mito et al. (2003)measured the temperature dependence of the magne- tization at several pressures blow 3.5 K and up to 27 GPa as shown in Figure 141, where all the data were taken following zero-field-cooled heating protocol underH¼3 Oe. At 0.98 GPa, there is no sign of magnetic ordering in the range of measuring temperature.Tvdrastically decreases with increasing pressure like in the previous report (Koyama et al., 2005;
Mito et al., 2003). On the other hand, once TM abruptly appears at Pc
(around 3 GPa),TMshows a very weak pressure dependence up to 27 GPa.
The resulting pressure dependence of the onset temperaturesTM,Tv
(Mito et al., 2003; Koyama et al., 2005; Kurita et al., 2006), andTc(Hedo et al., 2003) are summarized in the pressure–temperature (P–T) phase diagram in Figure 142. The valence phase transition temperature Tv
decreases linearly at the rate of19.5 K /GPa with increasing pressure up to 1.5 GPa. Many other groups have reported similar values for the pressure dependence of Tv. At above 1.0 GPa, however, Tv decreases more gradually and is suppressed below 1.5 K at 2.5 GPa (Hedo et al., 2003; Kurita et al., 2006; Sarrao et al., 1998; Uchida et al., 2002).
0.08
0.06
0.04
0.02
c(emu/mol)
0.00
0 25 50
YbInCu4
0.28 0.37 0.51 0.67 0.82
T (K)
0 GPa
75
FIGURE 140 Magnetic susceptibility of YbInCu4as a function of temperature at various fixed pressures (Sarrao et al., 1998).
The transition between the two low-temperature phases, the mixed- valence and the magnetically ordered phases, is of first order with respect to pressure. This implies that there is no QCP in theP–Tphase diagram
0.4
0.3
0.2
0.1
0.00
3.45 GPa 3.22 GPa
6.25 GPa
>27 GPa
0.98 GPa 13.9 GPa 18.9 GPa 23.5 GPa
1 2
Temperature (K)
M (a.u.)
3
FIGURE 141 Temperature dependence of magnetization of YbInCu4at various pressures (Mito et al., 2007).
FIGURE 142 Pressure dependence ofTM,Tv, andTcof YbInCu4.
for YbInCu4, as suggested from previous high-pressure nuclear quadru- pole resonance (NQR) studies (Koyama et al., 2005; Young et al., 2005).
The NQR measurements indicate that the whole phase boundary between the low-temperature mixed-valence state and the adjacent phases is of first order, and the magnetic ordering forP >Pcis of second order. From these experimental results, it is concluded that YbInCu4abovePcVis in the vicinity of the QCP (Miyake and Narikiyo, 2002). Contrary to Ce-based systems, the HF state becomes robust with pressure increase in this Yb- based system. Therefore, the enhancement of the coefficientA and the residual resistivityr0in YbInCu4under pressure corresponds to a rapid decrease of those quantities observed in CeCu2Ge2with the increasing pressure (Jaccard et al., 1999).