INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 16 (2004) 2395–2406

PII: S0953-8984(04)75193-0

Alloying and pressure effect on the mixed-valence
state of Yb in YbInCu4
N V Mushnikov1,2,5 , T Goto2,3 , A V Kolomiets2 , K Yoshimura4 ,W Zhang4 and H Kageyama2,4
1 Institute of Metal Physics, Kovalevskaya Street 18, 620219 Ekaterinburg, Russia
2 Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa,
Chiba 277-8581, Japan
3 Department of Electronic Structures, Charles University, Ke Karlovu 5, 121 16 Prague,
Czech Republic
4 Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502,
Japan

E-mail: mushnikov@imp.uran.ru

Received 21 January 2004
Published 19 March 2004
Online at stacks.iop.org/JPhysCM/16/2395 (DOI: 10.1088/0953-8984/16/13/018)
Abstract
The susceptibility and thermal expansion of Yb1−x Rx InCu4 (x  0.25; R = Y,
La and Ce) have been measured at ambient and high pressures. These
compounds undergo a first-order valence transition from an intermediatevalence state to a nearly trivalent state with increasing temperature. The
valence change at the transition is δv ∼ 0.1 for YbInCu4. It decreases onboth alloying and applying pressure for all the compositions studied. From thepressure effect on the susceptibility of YbInCu4, the Grüneisen parameter for the
Kondo energy K is determined to be −34.5 and −20 for the low-temperatureand the high-temperature state, respectively. The  coefficient characterizing
the hybridization strength between the 4f and conduction electrons for theintermediate-valence state is nearly five times larger than that for the hightemperature local-moment state. The obtained results suggest that the changeof the 4f–conduction band electron hybridization rather than the volume
dependence of the Kondo interaction is responsible for a large modificationof the physical properties of the YbInCu4 -based compounds at the valencetransition.

1. Introduction
The YbInCu4 compound undergoes a first-order temperature-induced isostructural valence
phase transition at ambient pressure [1, 2]. Above the critical temperature Tv ∼ 40 K the
5 Author to whom any correspondence should be addressed.

0953-8984/04/132395+12$30.00© 2004 IOP Publishing Ltd

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N V Mushnikov et alcompound exhibits a Curie–Weiss susceptibility with an effective paramagnetic moment close
to the free Yb3+ ion value of 4.54 µB . The valence of the Yb ion decreases suddenly by ∼0.1
at Tv [3, 4]. In spite of the small change in the valence, both the susceptibility and the electricalresistivity greatly decrease and a Pauli paramagnetic state is realized below Tv .
Because of such unusual behaviour, the valence transition in YbInCu4 has extensively beenstudied with different experimental techniques. Neutron and x-ray diffraction studies showthat YbInCu4 has a cubic AuBe5 -type structure, in which the Yb ions are completely orderedat the 4c site [5, 6]. On cooling the compound a sharp lattice expansion (a/a = 0.15%)
takes place at Tv without change in the crystal symmetry [3–5]. A study of the Cu nuclear
quadrupole resonance shows that a stable localized 4f-electron state for T > Tv changes
to a Fermi-liquid state with strong hybridization between the 4f and conduction electrons
for T < Tv [7]. Electrical resistivity and Hall effect measurements reveal that the carrier
concentration increases by a factor of ten on decreasing the temperature below Tv [2, 4].
The valence transition of YbInCu4 is easily affected by either applying high pressure or
alloying. The pressure effect on the critical temperature Tv was studied by means of resistivity,
magnetic susceptibility and thermal expansion measurements [2, 8–10]. The value of Tv isfound to decrease by applying pressure; dTv /d P ∼ −20 K GPa−1 . This result is consistent
with the stabilization of the high-temperature trivalent state of Yb having smaller size. The
size effect is usually also observed by chemical alloying. The substitution of ion with larger
radius (La or Eu2+ for Yb, and Sn or Ag for In) increases the valence transition temperature,
while the alloying of ions with smaller radius decreases Tv [3]. In Yb1−x Rx InCu4 with R = Y,
Lu, however, the observed transition temperature decreases rapidly with increasing x, whichcannot be explained by the volume effect [11]. It should be noted that the change of the electron
count has a large impact on Yb valence in the YbXCu4 materials with different X metals [2].
The valence of Yb in some of YbXCu4 compounds including X = In was determinedby measurements of x-ray absorption at the Yb LIII edge [3, 4]. On the other hand,thermal expansion measurements also give direct information on the change in the 4f electron
occupancy at the valence transition since the volume change at Tv is proportional to the valencechange [3, 4]. An important advantage of this technique is that the valence change at Tv can be
determined accurately as a function of pressure [10]. In the present study we have measured
the thermal expansion of Yb1−x Rx InCu4 with R = Y, La or Ce for x  0.25 at ambient andhigh pressures to examine the effects of alloying and pressure on the valence state of Yb in
YbInCu4 -type compounds.
2. Experimental details
Polycrystalline samples of Yb1−x Rx InCu4 with R = La or Ce were prepared by induction
melting of the high-purity constituents in alumina crucibles. Due to the volatile nature ofYb, a small excess of this constituent was used in the initial melt. The ingots were crushed
and remelted using a semi-levitation technique to achieve better mixing of the components
and smaller grain size. They were wrapped with Ta foils, sealed in quartz tubes filled withpurified argon gas and annealed for one month at 870 ◦ C. After annealing the samples, thevalence phase transition for most of the compositions occurs within a temperature range ofless than 2 K, which is indicative of a good homogeneity and is comparable to the best samples
reported [2]. However, the Y-substituted samples, prepared and annealed by such a methodfor x > 0.08, display a broadened double-step valence transition [11]. Therefore, we used inthis study single crystals of Yb1−x Yx InCu4 with x = 0, 0.1 and 0.2 grown in an In–Cu flux,
having a sharper transition. Details of the single-crystal growth are reported in [12]. Powder
x-ray-diffraction study indicates that all the samples are single phase with the cubic C15b

Alloying and pressure effect on the mixed-valence state of Yb in YbInCu4

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structure. For the three systems studied, partial replacement of Yb with R = Y, La or Ce leads
to an increase in the lattice parameter, as reported previously [11, 12].
The dc magnetic susceptibility of YbInCu4 under pressure was measured using a Quantum
Design SQUID magnetometer in the temperature range 5–200 K in a magnetic field 0.5 T.
Hydrostatic pressure up to 1.4 GPa was applied to the sample using a specially designed
high-pressure clamp cell of 8.8 mm in diameter made of a CuTi alloy with a very small
susceptibility [13].
Thermal expansion measurements under pressure were carried out with WK-09-031CF350 strain gauges (Micro-Measurements, USA). A gauge glued on the sample and a reference
gauge glued on a quartz plate were placed inside the pressure cell and connected to a dc
Wheatstone bridge. A clamp-type pressure cell of 25 mm in outer diameter was used toapply high hydrostatic pressure up to 1.6 GPa. For both magnetization and thermal expansion
measurements, the samples inside the cell were placed in a Teflon capsule filled with a liquidpressure medium, Fomblin. Since the pour point of Fomblin is ∼220 K, the pressure variation
inside the pressure cell is expected to be small within the temperature range 5–140 K.
The temperature dependences of both the susceptibility and the sample length measured
on cooling and heating the sample show a small hysteresis around Tv . All the dependences
presented in this study were measured on heating the sample.
3. Experimental results and discussion
3.1. Effect of alloying with Y, La or Ce on the valence state of Yb
Both single-crystalline and polycrystalline YbInCu4 samples studied show a very sharp valence
phase transition. The transition temperature Tv , defined as the temperature at which dχ/dT
becomes a maximum, is slightly different: Tv = 39 K for the polycrystal of YbInCu4
and 42 K for the single crystal. However, the values correspond well to those reported
previously [2, 10]. The susceptibility measurements for the Yb1−x Yx InCu4 single crystals
show that Tv decreases with increasing x [2, 11, 12]. At high temperatures the molar
susceptibilities of the crystals for different x coincide, indicating that both the effective
magnetic moment µeff and the paramagnetic Curie temperature θp are unchanged (according
to our measurements, µeff = 4.13 µB /Yb and θp = −1.3 K for YbInCu4 single crystal). For
La- and Ce-substituted materials, the valence phase transition shifts to the high-temperature
region with increasing concentration [11]. The transition remains very sharp for all the Lasubstituted samples and at least up to x = 0.12 for the Ce-substituted ones. At higher Ceconcentration the temperature dependence of the susceptibility shows a broad anomaly. Thisbehaviour seems to be similar to that of the dense Kondo lattice compound YbAgCu4 [14].
However, we found that the Yb1−x Ce x InCu4 samples for x = 0.16 and 0.20 exhibit a first-orderfield-induced valence transition at low temperatures [15], which changes to a second-order one
with increasing temperature. At high temperatures the molar susceptibility slightly decreases
with increasing both the La and Ce concentrations. For Yb1−x La x InCu4 the estimated value ofµeff does not change, while θp gradually decreases with increasing x with dθp /dx = −26 K.
Alloying with Ce also causes the decrease of θp at small x, while for x  0.08 the susceptibility
in the temperature range 80–150 K does not follow the Curie–Weiss law [11].
For most of the samples, a small upturn of the susceptibility appears at low temperatures
below 10 K, which is usually attributed to a small amount of impurities [12] or a partial Yb
disorder. However, it was shown recently that for Yb1−x Yx InCu4 single crystals the Curie-likeupturn can be eliminated completely using proper sample preparation conditions [16]. For
Yb1−x Ce x InCu4 the upturn will be caused mainly by magnetic Ce ions. By subtracting the2398

N V Mushnikov et al

Figure 1.
Linear thermal expansion curves of Yb1−x Yx InCu4 , Yb1−x La x InCu4 andYb1−x Ce x InCu4 , for different x at ambient pressure.

temperature-independent Pauli-paramagnetic term and fitting the susceptibility upturn to theCurie law we estimated the value of µeff for the substituted Ce ions, which does not exceed
half of the value of the free Ce3+ ion µeff = 2.54 µB [11]. This suggests that the Ce ion is in
the mixed valence state.
Figure 1 shows the linear thermal expansion L/L of the Yb1−x Rx InCu4 (R = Y, La
and Ce) samples as a function of temperature. The valence transition is very sharp at Tv ,indicating that these samples are of high quality. For parent YbInCu4 an abrupt change ofL/L at Tv , δL/L = (L/L)low − (L/L)high = 0.15%, is consistent with the data reported
previously [3, 5, 6, 10]. For all the compositions, the transition temperature corresponds well tothat determined from the susceptibility measurements [11, 12]. The change of L/L decreases
monotonically with increasing x. Since the crystal structure of YbInCu4 is unchanged by thetransition [3], the volume change at Tv is equal to three times as large as the change of L/L.
The concentration dependence of the volume change δV /V (Tv ) is shown in figure 2(a).
The valence change of Yb at Tv can be estimated from the thermal expansion data as follows [3].

Alloying and pressure effect on the mixed-valence state of Yb in YbInCu4

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Figure 2. Concentration dependence of the volume change at the valence transition in
Yb1−x Rx InCu4 for R = Y, La, Ce (a), low-temperature valence for R = Y, La (b) and valencechange at the transition for R = Ce (inset).

The cubic Laves phase compound YbAl2 has a lattice parameter larger by 1.5% than that
expected for Yb3+ Al2 because Yb is in a mixed valence state with a valence v = 2.5.
Considering the Vegard rule and taking into account that the Yb content in YbInCu4 is only
half of that in YbAl2 , the valence change at Tv is estimated to be v = 0.1. In order toobtain the absolute value of the valence in YbInCu4 , the valence state in the high temperaturephase was assumed to be +3 [10] since the effective paramagnetic moment µeff is close tothat expected from the free Yb3+ ion. However, careful measurements of the susceptibility
always show that the value of µeff is slightly lower than the free ion value 4.54 µB [17–19].
The crystal-field effect cannot give an appreciable decrease of µeff since the splitting of theJ = 7/2 multiplet of the Yb3+ ion in the cubic crystal electric field does not exceed 44 K in
YbInCu4 [20]. According to the Anderson single-impurity model, the deviation of the valencefrom 3+ is expected in the high-temperature phase by the Kondo effect (TK = 25 K), which
reduces the effective 4f hole occupation [4]. Measurements of x-ray absorption at the Yb LIII
edge show that the valence of Yb in the high-temperature phase of YbInCu4 is slightly lower
than 3:v = 2.9 [3] or 2.93–2.96 [4, 21, 22]. In the present study we adopt the value v = 2.94
for the valence of Yb in the high-temperature phase of YbInCu4 . The valence is decreased to
2.83 in the intermediate-valence state [4]. Our susceptibility data for the Y- and La-substituted
compounds indicate that the value of µeff remains almost unchanged [11, 12]. Therefore
the valence of Yb at high temperatures is considered to be nearly constant. Considering theamount of Yb in Yb1−x Rx InCu4 (R = Y and La), we calculated the low-temperature valenceof Yb in the alloys from the volume change at Tv . As seen from figure 2(b), the valence

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N V Mushnikov et al

for Yb1−x La x InCu4 remains unchanged at least up to x = 0.2, while Y alloying leads to anincrease of the valence. Probably the interaction of the 4f electrons of Yb with the 4d-band
electrons of Y is weaker than that with the 5d-band electrons of La, which reduces the Kondo
effect and increases the valence in the mixed-valence state.
On the other hand, Ce ions are usually unstable and have an intermediate valence between
Ce3+ and Ce4+ . Therefore one can expect that the Ce substitution for Yb in YbInCu4 will
increase the concentration of the valence electrons and reduce the valence of Yb. We observedthat the volume change of Yb1−x Ce x InCu4 at Tv is smaller than those of the Y- and Lasubstituted compounds with the same concentration. In order to explain these results weconsider that the Yb valence in the high-temperature phase of Yb1−x Ce x InCu4 is not constantand decreases with increasing x. This consideration is supported indirectly by the measurementof the concentration dependence of the lattice parameters. The ionic radius of Ce3+ is smaller
than that of La3+ , while the lattice expansion due to the Ce alloying is considerably larger [11].
Taking into account the ionic radii of the corresponding elements and intermediate valenceof Ce, we can expect that the lattice expansion of Yb1−x Ce x InCu4 for a fixed Yb valence
should be somewhat intermediate between those of the systems with La (da/dx = 9.4 pm)
and Y (da/dx = 4.6 pm) [11]. The observed large lattice expansion da/dx = 15.2 pm forYb1−x Ce x InCu4 [11] can be explained by the decrease of the Yb valence dv/dx = −0.75±0.23
at room temperature. Since the estimation is very rough, LIII -edge absorption measurements
are strongly needed to clarify the Yb valence state in Yb1−x Ce x InCu4 . We cannot determine
the absolute value of the Yb valence in the mixed valence state, so we show the valence change
at the transition in the inset of figure 2, which decreases with increasing x.
3.2. Pressure effect on the susceptibility and thermal expansion
Although the effect of hydrostatic pressure on the valence phase transition in YbInCu4
was studied in several papers, these data are mainly restricted to the pressure variation of
Tv [2, 8, 23]. We carefully measured the magnetization of single-crystal YbInCu4 underpressure using a SQUID magnetometer to establish the pressure effect on the susceptibility
in both the low-temperature and high-temperature phases. Figure 3 shows the magnetic
susceptibility of YbInCu4 as a function of temperature for several fixed pressures up to 1.4 GPa.
The valence phase transition remains very sharp under pressure and Tv gradually decreases.
As seen from the inset in figure 3, the pressure dependence of Tv is slightly non-linear. The
value of dTv /d P amounts to −20 K GPa−1 up to pressure ∼0.7 GPa and decreases with further
increasing pressure. The non-linearity of dTv /d P was evidenced previously by measuring theresistivity under high pressure up to 3.3 GPa [24].
The temperature-independent susceptibility in the low-temperature state increases withincreasing pressure. According to the exact Bethe ansatz solution of the Coqblin–
Schrieffer impurity model [25], the thermodynamic properties in the Fermi-liquid state at low
temperatures, in which the f and conduction-band states are strongly hybridized,are determinedby the Kondo energy scale T0 . The zero-temperature susceptibility χ(0) is proportional to
1/T0 [25]:NA ν(ν 2 − 1)g 2J µ2B,(1)
χ(0) =
24πkB T0
where NA is the Avogadro number, ν = 2 J + 1 is the degeneracy of the ground state andg J is the Lande factor. The Kondo scale T0 determined using equation (1) is shown as
a function of pressure in the inset in figure 3. The value of T0 decreases nearly linearly;
dT0 /d P = −184 K GPa−1 . Sarrao et al [26] measured the susceptibility under high pressure.
Their data give a slightly lower value dT0 /d P = −158 K GPa−1 . The decrease of T0

Alloying and pressure effect on the mixed-valence state of Yb in YbInCu4

2401

Figure 3. Temperature dependence of the molar susceptibility of single-crystal YbInCu4 fordifferent pressures. Inset: pressure dependence of the valence transition temperature Tv (circles)
and the low-temperature Kondo scale T0 (squares) for YbInCu4 .

implies that the low-temperature coherent Kondo state is destabilized by the external pressure.
According to our data, a good linear relation holds between T0 and Tv , similar to that reported
for the Yb1−x Yx InCu4 and Yb1−x Lux InCu4 systems [11, 12].
In materials where the physical properties are dominated by the Kondo effect, themagnitude of the volume dependence of the Kondo interaction is characterized by the Grüneisenparameter for the Kondo temperature TK ,
B dTK
B dT0
d ln TKK = −==,(2)d ln VTK d P
T0 d P
where B is the bulk modulus. The Kondo temperature is defined as TK = C/χ(0) (where
C = NA µ2B J (J + 1)/3kB is the J = 7/2 Curie constant for Yb) and it is proportional to the
low-temperature scale T0 : TK = [2π/(2 J + 1)]T0 [17]. Using the value of B = 83 GPa(at T = 20 K) [10] we obtain LT
K = −34.5 for the low-temperature mixed-valence
state of YbInCu4 . This value practically coincides with that determined from specific heatmeasurements [26] and is consistent with LT
K = −40 estimated from the magnetostriction
data [27].
Since the effect of pressure on the susceptibility is very small for T > Tv as shownin figure 3, we could not determine the pressure dependences of the values of µeff and θpobtained by direct fitting of the susceptibility to the Curie–Weiss law. In order to obtain thesedependences we carefully measured the temperature dependences of the susceptibility underpressure up to 0.7 GPa along the three main crystallographic directions of the single crystal andthen averaged the data at fixed pressures. The observed anisotropy of the magnetic properties of
YbInCu4 is small, which was discussed thoroughly in a previous paper [19]. As representative
data, we show in figure 4(a) the pressure variation of the susceptibility χ(P)/χ(0) at 150 K.
The susceptibility increases linearly with pressure with a rate d ln χ/d P = 0.043 GPa−1 .
Svechkarev et al [27] obtained a similar value from susceptibility measurements at fixed
temperatures under pressure up to 0.15 GPa (closed circles in figure 4(a)). However, theauthors of [27] reported a large negative value of θp = −13 K, positive pressure derivativedθp /d P = 6.4 K GPa−1 and pressure-independent effective moment. According to our data

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N V Mushnikov et al

Figure 4. Pressure dependence of the reduced magnetic susceptibility χ (P)/χ (0) and the reduced
effective magnetic moment M = χ T /C at 150 K (a) and the parameters θP and µeff obtained
from the Curie–Weiss fit (b) for single-crystal YbInCu4 . The lines represent the linear fits to theexperimental data.

presented in figure 4(b), θp is of the order of −1 K and decreases with increasing pressure
with a rate dθp /d P = −1.4 K GPa−1 . The value of µeff increases slightly with pressure,dµeff /d P = 0.11 µB GPa−1 . Similar changes of the Curie–Weiss parameters under pressure
were reported by Matsumoto et al [9].
In the Kondo regime, the deviation of the effective moment from its free-ion value isconsidered to be a monotonic function of TK . For YbInCu4 the deviation is small, and thevalue of TK ≈ 25 K is determined from inelastic neutron scattering [28] and from fitting the
reduced effective moment χ T /C to the prediction of the J = 7/2 Kondo model [2, 4]. In
figure 4(a) we show representative data of the values M ≡ χ T /C for T = 150 K as a functionof pressure. (Actually, χ T /C means the ratio of the square of the effective moment of Yb andthat of the free Yb3+ ion.) The value of M is found to be practically temperature independentand increases linearly with pressure. This is indicative of the decrease of the Kondo effectby applying pressure. The average value of dM/d P determined at different temperatures isdM/d P = 0.035 GPa−1 . The increase of M with pressure is caused by the increase of the
4f hole occupation n f , which is related to the valence v of the Yb ion by n f = v − 2. On theother hand, in the Kondo impurity limit the Kondo temperature is connected with the value ofn f as follows [4, 29]:

1 − nf2J + 1
TK =

.
(3)
π
nf
Here the coefficient  = Vkf2 ρ(εf ) is the hybridization strength between the 4f and the
conduction electrons. Vkf is the hybridization matrix of the 4f and conduction electrons andAlloying and pressure effect on the mixed-valence state of Yb in YbInCu4

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Figure 5. Linear thermal expansion curves of YbInCu4 , Yb0.9 La0.1 InCu4 and Yb0.92 Ce0.08 InCu4
for different pressures.

ρ(εf ) is the conduction electron density of states at the Fermi level. Therefore, for smallchange of n f produced by applying pressure, an approximate linear relation can be expected
between M and TK . Then we obtain dTK /d P = −5 K GPa−1 and the Gruneisen parameterHTfor the high-temperature Kondo state HT
K = −20. The absolute value of K is lower thanHTthe previous estimate K = −32 [27]. Yb-based compounds have negative values of K ,but Ce-based compounds have positive values [27], which reflects the general tendency of
f-state depopulation in Ce- and Yb-based compounds on applying pressure. The observed
small difference in the values of the Gruneisen parameters for the low- and high-temperaturephases implies that the Kondo volume collapse model [30] cannot explain the valence phasetransition in YbInCu4 because this model considers a strong volume dependence of the Kondo
temperature.
From the comparison of the Gruneisen parameters for the low- and high-temperaturestates of YbInCu4 one can see that the change of the Kondo temperature at the transition will
decrease with increasing pressure. Therefore, the change of the 4f hole occupancy will also

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N V Mushnikov et al

Figure 6. Pressure dependence of the volume (a) and valence (b) change at the valence phasetransition in YbInCu4 , Yb0.9 La0.1 InCu4 and Yb0.92 Ce0.08 InCu4 . Inset: T0 as a function of Yb
valence v for YbInCu4 .

decrease. Figure 5 shows thermal expansion curves under pressure for three representative
samples: single-crystal YbInCu4 and polycrystalline Yb0.9 La0.1 InCu4 and Yb0.92 Ce0.08 InCu4 .
For all the samples, the abrupt change of δL/L at T = Tv decreases with increasing pressure.
This is consistent with the above consideration based on the susceptibility data under pressure.
The volume change at the transition δV /V (Tv ) is a nonlinear function of pressure (figure 6(a)).
These dependences are very similar for the three studied samples. The values of the valencechange at Tv (figure 6(b)) for pure YbInCu4 and the La-substituted sample almost coincide.
In the pressure range 0–0.8 GPa the valence increases with the rate dv/d P = 0.055 GPa−1 ,which is consistent with a value of dv/d P = 0.045 GPa−1 reported previously [10]. Above
0.8 GPa, the valence increases more gradually. The origin of this behaviour is not clear.
However, it correlates with the nonlinear dependence of Tv (P) [24] and may be associated withan additional interaction in YbInCu4 under high pressure. It was found recently that single
crystals of Yb1−x Yx InCu4 exhibit a weak ferromagnetic ordering under pressure [19, 31].
Taking into account a negative value of dθP /d P found in the present study, the appearanceof ferromagnetic interaction is difficult to explain. Weak ferromagnetism found in [31] may
originate from a canted antiferromagnetic structure. Additional low-temperature high-pressure
experiments are necessary to understand this behaviour in further detail.
From the comparison of the susceptibility and thermal expansion data it became clearthat the low-temperature susceptibility for both pure and doped YbInCu4 is determined by thevalence of Yb in the mixed valence state. In the inset of figure 6 we plotted the values of the lowtemperature scale T0 as a function of the Yb valence v for YbInCu4 . It is seen that the coherent

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Figure 7. Kondo temperature TK as a function of the 4f hole occupation n f for YbInCu4 . Closed
and open circles show the data for the low- and high-temperature states, respectively. The lines
represent the fits to equation (3).

Kondo interaction gradually decreases with increasing valence of Yb. On the other hand, inthe case of Yb1−x Ce x InCu4 , we observed that both Tv and χ(0) increase simultaneously withincreasing x [11]. This suggests that the valence does not directly affect the stability (i.e. thetemperature range of existence) of this state. In figure 7 we plotted the Kondo temperature TK
determined from susceptibility measurements of YbInCu4 under pressure versus the 4f hole
occupation n f obtained from thermal expansion measurements. The experimental data areshown for the low- and high-temperature states by solid and open circles, respectively. Fitting
the data to equation (3) gives  = 850 K for the low-temperature state. Cornelius et al [4]reported a similar value of  = 900 K for YbIn1−x Agx Cu4 compounds with different x. For
the high-temperature state with a weak Kondo interaction we obtain  = 185 K. Perhaps, alarge change of nearly fivefold in the hybridization strength  of the 4f and conduction band
electrons is the driving force for the drastic change of the physical properties observed at thevalence phase transition in YbInCu4 .
4. Conclusions
In summary, we have measured under pressure the magnetic susceptibility of YbInCu4 andthermal expansion of Yb1−x Rx InCu4 compounds with R = Y, La and Ce exhibiting theisostructural valence transition. We determined the alloying and pressure effect on the effective
magnetic moment, the paramagnetic Curie temperature and the valence of Yb ion. The
Grüneisen parameter for the Kondo temperature and the hybridization strength between the 4f
and the conduction electrons were estimated for both low-temperature and high-temperaturephases. The observed results can be interpreted in terms of the Kondo single-impurity
model. However, the volume dependence of the Kondo interaction (i.e., the Kondo volume
collapse model) cannot explain the observed strong variation of the Kondo temperature at thetransition. The large change of the 4f–conduction band electron hybridization is considered
to be responsible for the strong modification of the physical properties of YbInCu4 -based
compounds at the valence transition.

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N V Mushnikov et al

Acknowledgments
This work was supported by a Grant-in Aid for Scientific Research on Priority Areas (B) from
the Ministry of Education, Culture, Sports, Science and Technology of Japan. The stay of
NVM at ISSP was supported also by this ministry.
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