Magnetic structures under pressure in cubic heavy-fermion compounds

Journal of Low Temperature Physics, Vol. 70, Nos. 3/4, 1988

Magnetic Structures under Pressure in Cubic Heavy-Fermion Compounds

P. Morin

Laboratoire Louis Ndel,** CNRS, Grenoble, France

C. Vettier

Institut Laue-Langevin, Grenoble, France

J. Flouquet, M. Konczykowski,t Y. Lassailly, and J.-M. Mignot

Centre de Recherches sur les Tr~s Basses Ternpdratures, CNRS, Grenoble, France

U. Welp

Max Planck Institut fiir Festk6rperforschung, Grenoble, France

(Received August 4, 1987)

Neutron diffraction experiments under pressure on the cubic heavy-fermion compounds Celn 3 and CePb3 are reported. Resistivity measurements were performed on Celn 3 in order to study the approach to the magnetic-nonmagnetic transition. Comparisons are made with previous results obtained on CeAl2. In CePb3 and CeAl2, the pressure-induced change in the magnetic structure from modulated to simple-antiferromagnetic may correspond to a reduction of the magnetic anisotropy. The strong pressure decrease of the Ndel temperature of Celn 3 for P> 15 kbar indicates the proximity of the transition from a magnetic to a nonmagnetic ground state. In cubic heavy-fermion compounds, the appear- ance of a nonmagnetic ground state seems to be directly connected to the recovery of the full multiplet degeneracy of the rare-earth ion.

1. INTRODUCTION

The purpose of the experiments described in this paper is to arrive at a general understanding of the magnetic properties under pressure P in some cubic heavy-fermion systems exhibiting long-range magnetic order,

** Laboratory associated with the Universit~ Scientifique, Technologique et M~dicale de Grenoble.

t Permanent address: SESI, CEN, Fontenay-aux Roses, France.

377

oo22-2291/88/020o-o377506.00/0 @)1988 Plenum Publishing Corporation

378 P. Morin et al .

namely CePb3, CeA12, and Celn 3. Neutron experiments on CePb 3 with supplement previous results reported for CeAI2 (ref. 1) and Celn3 (ref. 2), and high-P resistivity (p) measurements on Celn3 will yield a more precise estimate of the pressure dependence of its N~el temperature TN(P). These measurements will provide a basis for disentangling Kondo, crystal-field, and interaction effects.

In a recent work it was established that the compound CePb3 enters a modulated antiferromagnetic phase below TN = 1.16 K . 3 The propagation vector is close to the X point of the Brillouin zone and the magnetic moments point along the [001] axis. The modulation amplitude (mo=0.55~B at 30 mK) is smaller than the value expected for a pure F7 doublet ground state. Due to the Kondo coupling this modulated structure is stable at zero temperature. In this respect C e P b 3 behaves similarly to CeA12: in CeA12 a modulated magnetic structure is also observed at zero pressure; applying a pressure of P = 20 kbar favors an antiferromagnetic structure of type II; a second transition into a nonmagnetic mixed-valent state is induced at about 40 kbar. 4'5 This behaviour is fully reminiscent of the simple antifer- romagnet C eln3, which has a propagation vector (1/2, 1/2, 1/2).6 It is known that at P = 0, the Kondo-like coupling (characterized by its energy kBTK relative to the crystal-field splitting CcF) is larger in Celn3 than in CeA12 and in CePb3, which both appear to be archetypes of magnetically ordered Kondo lattices with a doublet ground s ta te /

2. E X P E R I M E N T S

2.1. C e P b 3

CePb3 crystallizes in the A u C u 3 structure with the O~ space group. A monocrystalline sample of about 0.15 cm 3 was grown in a Bridgman furnace as previously described. 3 The same dilution refrigerator as in ref. 3 was used, which allowed for fast sample loading after varying the pressure.

Up to 10 kbar, the high-pressure conditions were achieved by mounting the sample in a clamped Cu-Be pressure vessel using Fluorinert FC75 as the pressure medium. However, upon cooling, FC75 freezes, thereby producing a drop in pressure, which may result in some nonhydrostatic stress components. As a consequence the actual pressure in the cell was determined by monitoring the lattice constant of a pressure calibrant, NaC1 placed inside the cell together with the CePb3 sample.

The neutron diffraction experiments were carried out on the D10 diffractometer at the high-flux reactor of the Institut Laue-Langevin. The instrument was used in a triple-axis mode set to zero energy transfer in order to improve the signal-to-noise ratio. Focusing pyrolitic graphite crys- tals were used as monochromator and analyzer at ki = 2.662 ~-1 with a PG

Magnetic Structures under Pressure in Cubic Heavy-Fermion Compounds 379

filter for reducing high-order contamination. The C e P b 3 sample was moun- ted with a twofold axis vertical to give a (hhl) scattering plane. Due to the actual propagation vector q = (/~ =0.135,/z2=0.058,1), tilt angles were adjusted to look for the eight magnetic intensities, which could be observed around the X point of the Brillouin zone. In comparison with the previous measurements at P = 0 kbar, 3 large experimental difficulties arise from the smaller sample size and the large background from the pressure cell.

2.2. Celn3

The sample preparation and the experimental setup for the neutron measurements were similar to those of C e P b 3. A clamped A1203 pressure cell (the same as in ref. 1) was used for the neutron experiments up to 20 kbar. 2 Resistivity measurements were performed in a commercial steel clamp (Unipress, Warsaw). A mixture of light hydrocarbons served as the pressure-transmitting medium. P values at ditterent temperatures were deduced from the resistivity of an InSb manometer. 8 Typical pressure changes between room temperature (RT) and 4.2 K were - 4 kbar at 7.5 kbar and only -2.5 kbar at the highest applied pressure Pmax(RT)= 27.3 kbar. Negligible P variations took place in the temperature interval (1 < T < 15 K), where the magnetic transition occurs. Resistivities were measured by the van der Pauw technique using either an ac or a dc method.

3. RESULTS

3.1. C e P b 3

Experiments were performed at three different applied pressures, 0.5, 3.0, and 7.0 kbar. The compressibility was found to be K = 2.1 x 10 -3 kbar -1 at T=0 . 1 K. These values are in good agreement with determinations (K = 1.8 × 10 -3 kbar -1) by elastic constants measurements. 9'~° They differ, however, from x-ray powder diffraction results, la

At low pressures, P -- 0.5 and 3.0 kbar, the magnetic structure remains unchanged, apart from slight modifications in the propagation-vector components /Xl and ~2 (Fig. 1) and a reduction in TN (TN = 1.10 and 0.98 K, respectively) with increasing pressure. The temperature dependence of the integrated intensities corrected from the A/2 contribution is reported in Fig. 2. In contrast to what is observed for P = 0 , applying pressure leads to strong differences in the intensities of the four pairs of satellites close to a given X point (0, 0, 1/2). This appears to be the result of a nonhydrostatic stress distribution at low temperature, which destroys the cubic symmetry.

At P -- 7 kbar, the magnetic satellites at (/x~,/z2,½) have disappeared. Instead, new magnetic reflections are found at various points (1, 5, 0.5, 0.5), (0.5, 0.5, 0.5), (0.5, 1.5, 1.5), indicating a different magnetic

380 P. Morin et al.

L 0.05~ 0.060

--!

- 2 :t~ 0.055

0.050

0.045 -

I

~ L . . . .

I

o []

[] []

0.140

/ /

/11"

/

I

P ( k b a r ) 5

I

• •

o •

o

0.135 CePb 3

0.5 T//T N

v

::L

0.135

Fig. 1. Temperature dependence of the components of the propagation vector (/zl,/z2, 2 t-) for the modulated structure of CePb3. O(11), O([]) : ~t I (/z2) at P = 0.5 and 3 kbar, respectively; ( - - ) the temperature variations at P = 0 from ref. 3; (- • -) the variation of/x~ at P = 3 kbar. Inset: pressure dependence of ( 0 ) tzt and (11)/z 2 at low temperature.

structure with a propagat ion vector q, = (½, ½, ½). This corresponds to a simple antiferromagnetic order of alternating ferromagnetic [111] planes with a cubic magnetic cell. The N6el temperature TN (7 kbar) is 675 mK. There are no q-domains, but S-domains corresponding to different magnetic moment directions. It is not possible to determine the moment direction in the absence of symmetry-breaking fields, a2 The type of magnetic order is the same as previously observed in CeA12 at 20 kbar 1 and in Celn3 at normal pressure. 6

Whereas the N6el temperature decreases rather gradually with increasing pressure, there is no continuous variation of the propagat ion vector, but a sudden change, which seems to occur just below 7 kbar. The corresponding phase diagram, including the N6el temperatures determined at P = 10 and 14 kbar by transport measurements, ]3 is presented in Fig. 3 together with the diagram obtained for CeAI2)


t~

I-- tt~ Z lad I.--- Z

t.)

tl.l Z

~r

I05 ' '~3~~ P(kbar)=7\ 3 / \ \0

~05 ~,, I I I I I i ~ I I I II 0"5~ I i 0 05 I T(K)

Fig. 2. Tempe ra tu r e d e p e n d e n c e of the m a g n e t i c in tens i t ies in CePb 3 normalized at low temperature for different pressures. The curve at P = 0 is from ref. 3.

3.2. CeIna

3.2.1. Neutron Diffraction

The experiments were performed at three applied pressures P(4.2 K) = 0, 11, and 21 kbar . The compressibility estimated at 300K was r = 1.7x 10 -3 kbar -1, in reasonable agreement with the x-ray determination (1.5 X 10 -3 kbar -1) of ref. 14. The same magnetic structure (propagation vector ½, i ~, ~) persists throughout the pressure range investigated. The temperature dependence of the integrated magnetic intensity is displayed in Fig. 4. Due to beam contamination problems, the intensity of the magnetic line 1 1 (~, ~, ½) was obtained by subtracting spectra below and above TN.

The resulting pressure dependence of TN is plotted in Fig. 5. The data for the higher pressures are affected by substantial uncertainties because of the reduced value of the ordered moment.

3.2.2. Electrical Resistivity

The electrical resistivity of CeIn3 was measured at seven different pressures ( 0~ < P~<25 kbar) between 1.5 and 300 K. A selected set of p(T) curves is presented in Fig. 6 after subtraction of the lattice contribution, which was assumed to be pressure independent and identical to that in Laln3.~5'~6 The data at ambient pressure are in good agreement with published results. 15,16 The overall amplitude of the 4 f resistivity agreement with published results. 15"16 The overall amplitude of the 4 f resistivity increases under pressure, while the maximum at TMax is shifted to higher temperatures by approximately +0.6 K/kbar , which corresponds to a Griineisen parameter l)rMax - - a In Traax/a In V ~ 7.

382 P. Morin et al.

I---

0.5

I I

_ ~ CePb3 P

"%m Q

( P,1 ,I J-2,1/2)

® 0 I =

0 S 10 k b a r 15

I I

CeAt 2

4 -

2 -

® 0 10 20 k b a r 30

Fig. 3. Temperature-pressure magnetic phase diagrams. P corresponds to the paramagnetic phase. Incommensurate and com- mensurate magnetic phases are indicated by their propagation vectors. (a) CePb3; (b) CeAI z from Ref. 1; note the coexistence region of the low-pressure modulated phase (@) and the high- pressure, type II phase (©).

The effect o f the A F orde r ing on p is shown in Fig. 7. The p(T) curves exhib i t a d is t inct k ink, which can be t r acked f rom ambien t pressure up to 25 kbar . Theore t ica l ly , 17 the e lect r ica l resist ivi ty o f an an t i f e r romagne t near the N r e l po in t is d o m i n a t e d by shor t - range f luctuat ions, l ead ing to a s ingular i ty in dp/dT at TN. In the presen t case, however , the s t rong asym- met ry o f p ( T ) a r o u n d TN, w o u l d make such an analys is ra ther inaccura te ,


k Ce In 3

0.

I / I . i I . . . . I kbar o "0 5 10 T(K}

0 . 0 . 8 ~ i 1 kbar

5 10 15 T(K)

Fig. 4. Temperature dependence of magnetic intensities of CeIn 3 normalized at low temperature for different pressures. The large background above T N is due to a k/2 contamination of the magnetic satellites.

especially for the higher pressures. We thus chose to determine TN somewhat arbitrarily as the intersection of the curves extrapolated from both sides of the transition. The resulting values are summarized in Fig. 5, together with the foregoing neutron data and previous specific heat results. 18 Except for a small systematic difference of ~0.2 K, which we ascribe to our way of

\%%\ o l L t a "', 0 10 20 30 Pc

P (kbar) Fig. 5. Temperature-pressure magnetic phase dia-

gram of CeIn3 deduced from (O) neutron, (©) specific heat, and ( , ) resistivity measurements.

384 P. Morin et el.

40 E 1,,,I

=t 30 v ( - , 3

t-

O --.I

o. 20 &

10

I I i I I I

0 I I I I I I 0 100 200 300

T(K)

Fig. 6. Selected set of 4 f resistivity curves of Celn3 under pressure (0, 13.5, and 24.8 kbar).

C~ 10

a-, 8

2 o .... +,,~+++ . . . . . . . g.5 o° I I i i 9

g. 5 10 10.5 11 T IK) 0 I I I I

3 5 7 9 11 13 T(K)

Fig. 7. Low-temperature variation of the resistivity of Cain 3 at different pressures. The inset shows the determination of TN for P = 3.5 kbar either from the kink in p (T) or from the j ump in Op/OT.


d e t e r m i n i n g TN, a very good agreement is found between the various sets of data.

4. DISCUSSION

4.1. Phase Diagrams

At low pressure, CePb3 exhibits a modulated structure. The observed inequivalent intensities of the satellites around a given (0, 0, ½) point seem to indicate that there exist magnetic q-domains but that a multi-q structure is unlikely. However, couplings betweendifferent [001] directions are still possible, which would lead to a rhombohedral symmetry. The strong initial P dependence of TN implies a rather large magnetic Griineisen parameter:

01n TN [~M(P'->O) . . . . 36

Oln V

Above 7 kbar in the simple-antiferromagnetic phase, TN increases slightly and reaches a faint maximum for P = 14kbar (Fig. 3); the main observation is that the pressure dependence of TN is far weaker than that found in the low-pressure modulated phase. It is also clear that in CePb3 the critical pressure Pc of the transition from the magnetic to the nonmagnetic (M-NM) ground state [ TN(Pc) = 0] is larger than 20 kbar. The results for CePb3 are reminiscent of the situation previously encountered in CeAI2 (Fig. 3), 1 where the low-pressure phase is characterized by a large value of ~M = --12, in contrast to the type II phase (P = 20 kbar), in which f/~a ~ -3. In both compounds the large initial value of rIM is a precursor effect of the subsequent structure change at P1-,2, while the rather low value above P1~2 reflects the stability of this new ground state over a significant P range.

In Celn3, the same magnetic phase is retained under pressure even when TN has substantially decreased. The rather weak P dependence of TN observed at high pressure in C e P b 3 (P>7kbar ) and in CeAI: ( P > 15 kbar) corresponds to the low-pressure regime of Celn3. It therefore appears promising to interpret the magnetic properties of all three compounds on the same basis. Table I summarizes their N6el temperatures and the corresponding Griineisen coefficients at P = 0.

At ambient pressure, C e P b 3 and CeAI2 correspond to the situation of a 4f electron exhibiting both localized (e.g. crystal field) and delocalized (Kondo coupling to the conduction band) character. Indeed, the crystal-field splitting CCF (equal to 65 and 100 K for C e P b 3 and CeAI:, respectively) is clearly observed, for instance, by inelastic neutron scattering experiments 3"7 and is responsible for the occurrence of two maxima in the temperature variation of /9.19-21 The Kondo-like coupling deeply affects the resistivity

386 P. Morin et al.

TABLE l N6el Temperature T N and Griineisen Coefficients f~M = -01n TN/Oln V of CePb3,CeA12, and CeIn 3 at Ambient

Pressure

TN, K f~

CePb3 1 .16 -36(modulated structure) CeA12 3.8 -12(modulated structure) CeIn 3 10 -2(type II AF)

(In T term) and the specific heat. The simultaneous occurrence of crystal- field phenomena and Kondo-like couplings realizes the condition for a modulated structure to be stable at 0 K, i.e., existence of a magnetic anisotropy (CcF> kBTK) and singlet mechanism producing an induced magnetic moment (Kondo effect), a3

In Celn3, on the contrary, the crystal field is hardly detected at P = 0 in experiments involving dynamical processes (resistivity, ~5'~6 inelastic neutron scattering 2, but appears clearly in static experiments. 2,7 For example, as shown in Fig. 5, only one broad maximum is observed in the temperature dependence of the resistivity.

Applying a hydrostatic pressure is known to increase the exchange interaction F between 4 f and conduction electrons, and the Kondo coupling is therefore drastically enhanced. 23'24 This in turn leads to a drop in the magnetic anisotropy that initially stabilized the modulated structure. Thus, the loss of the modulation at PI-~Z indicates that we are no longer in the case CcF/ka TK >> 1, but rather in a crossover regime where CCF/kBTK ~ 1; the associated crystal-field effects are strongly damped.

From the foregoing discussion. Celn3 seems to be the most favorable case where moderate pressures can produce a complete collapse of the crystal-field splitting with respect to the Kondo energy: CcF/kBTK<< 1.

4.2 . T r a n s i t i o n to a N o n m a g n e t i c G r o u n d S t a t e

Although in the present experiments on CeIn3, the system could not be pressurized all the way to the nonmagnetic state, a linear extrapolation of TN leads to Pc ~ 35 kbar with a Griineisen coefficient r im = - 4 8 . This conclusion is confirmed by resistivity measurements at higher pressures, which failed to indicate any magnetic transition at 60 kbar. 26 Table I I shows similar Griineisen coefficients, which can be derived from studies in which the M - N M transition is achieved by alloying: the huge anomalous rIM found in CeInxSn3_x ~7 may reflect the importance of environmental effects in those particular alloys. On the contrary the "chemical pressure" effects in Cel-xYxIn3,27 Ce1_xYxA12,28 and CeNixPtl_x 29 lead to values for I~a4 (Pc)

Magnetic Structures under Pressure in Cubic Heavy-Fermion Compounds

TABLE II

Griineisen Parameters f~M of Some Quasibinary Com- pounds and Critical Composition xc for the Magnetic-

Nonmagnetic Transition

~ M X c Ref.

Celn3Sn3_ ~ -700 0.5 16 Cel_xYxln 3 -42 0.4 27 Cel_:,YxAl2 -75 0.1 28 CeNixPtl_x -36 0.95 29

387

comparable to that found here for Celn3. It is noteworthy that the P variation of TN does not display any dramatic acceleration on approaching Pc. More detailed measurements in the critical region are needed in order to character- ize the (linear ?) functional dependence of TN(P). The present data suggest that the M - N M transition at T = 0 might be second order and thus compat- ible with a mean-field description. We recall that in Celn3 at P = 0 the neutron magnetic intensity (square of the sublattice magnetization) almost follows a linear T dependence for (TN- T)/TN<< 1, which was interpreted as an indication of strong quantum fluctuations. 6

At high pressures, it can be expected that some crossover value Pw exists above which the 4 f angular momentum J is so strongly quenched by the Kondo mechanism that the electrostatic coupling with the surrounding can be neglected. 23'24 The 4 f electron recovers its full 2J + 1 = 6 degeneracy and TK is strongly enhanced. 3°'3~ In various Kondo-lattice models 32-35 it was found that the nonmagnetic ground state cannot be understood without considering the major role played by the orbital degeneracy. Actually, this high-TK regime cannot be distinguished from an intermediate-valence (IV) state in low-energy experiments. The intersite coupling E~ between two cerium ions drops drastically in comparison with the Kondo energy kBTK (i.e., the single-site energy characterizing the formation of a nonmagnetic ground state3°'31).

An experimental proof that Celn3 is close to the IV regime at P = 0 is given by the weak value of the Grfineisen coefficient ~'~Tmax ~ 7. Referring to the common assumption 36'37 that TMax is a scaling parameter that charac- terizes the regime above TN, we can remark that f~rmax = 7 is a typical value for cubic IV phases. In archetypal IV compounds such as CeSn3, CeBe13, and CePd3, specific heat, thermal expansion, and acoustic measurements lead to 4 f electronic Griineisen coefficients of the order of + 10 at T ~ 0 K. 38

In nonmagnetic heavy-fermion systems, on the other hand (CeAI3,CeCu2Si2, and CeCu6), ~TMax amounts to 22,20, and -100, respectively, 36-39 whereas the Griineisen coefficients derived for T - 0 are

388 P. Morin et al .

E

E Pc° P

b) "

__~/Ei j ;/--~,

Pl.-,.2 Pc P

CcF E ~~,.,..,. (c}

_ ~'K ~" E - E K ~

~ WO, I I-,2 Pc P~ Fig. 8. Schematic P variation of (- -) the intersite coupling E u and of ( - - ) the Kondo-like energy E K in (a) crude Kondo model or (b) by taking into account that E~j and E K must be renormalized in the crossover regime P1~2 < P<Pc. (c) The expected P dependence of Ccz/E with E = E K o r E K.


respectively -200, 50, and 100. 39 Another interesting point is that in CeIn3 the P dependence of TMax is quasilinear, while a strong downward curvature is observed in TN(P). No single scaling parameter can thus describe this kind of compound in the heavy-fermion regime (P < Pc). It must be emphasized that x-ray measurements o n CeA12 5'14 and CeIn314 have shown that no discontinuity exists in their pressure-volume dependence. Since the crossover from heavy-fermion (CcF/kBTK> 1) to IV (CcF/kBTK<< 1) is apparently gradual, the definition of Pw is ambiguous, but Pc is well defined. It is even conceivable that both parameters might coincide. The importance of the 4f-level degeneracy and the valence instability in the magnetic properties of anomalous rare-earth systems has been already emphasized in the case of the Tm chalcogenides TmSe and TmS, 4° where pressure dependences of TN and changes in magnetic structure similar to those reported here have been observed. For example, the proximity of the valence instability leads to ~M ~ 40, close to the values observed in cerium compounds for P-> Pc.

An important outcome of the neutron experiments on CeIn3 is the strong wavevector dependence of the static susceptibility in the paramagnetic phase. 2 This observation suggests that the intersite coupling E~ is comparable to the two preceding energies EK and CcF, thus making the situation even more intricate. Considering the cerium ion as essentially isolated and hence weakly coupled via RKKY interactions is not realistic. When E~ -- C c F - - EK, the 4f electrons have a strong itinerant character and the single-site approximation breaks down. In the paramagnetic phase, the cerium ions interact via near-neighbor couplings in such a way as to lower their mutual Kondo energy EK .7'25 The coupling among pairs, triplets, quartets, or clusters of cerium ions reduces the TK of such entities and prevents the quenching of the angular momentum. Both energies (EK, Ev) are strongly renormalized, leading to new variables EK and E~. The decrease of EK also enhances the ratio CCF/EK, which implies a stronger electrostatic coupling of the 4f shell to the environment and a reappearance of crystal- field effects. The depression of the Kondo coupling due to multisite interactions is well known for 3d impurities such as Co in Au, Cu, or Pt. 4~

A schematic pressure variation of Eij and EK as suggested by our data is shown in Fig. 8. At low pressure, these variations correspond to the model of a Kondo lattice with a competition between a singlet tunneling mechanism [EK = exp-(1/NoF), where No is the density of states at the Fermi level] and an RKKY-like coupling (Eo ~ NoI "2) (Fig. 8a). However, above P~-~2, when EK ~ E 0 ~ CcF, this naive Kondo-lattice scheme breaks down: it would predict a transition to a nonmagnetic ground state at pO far lower than Pc. The relative variation of EK/E U will depend more weakly on P for P~2 < P << Pc because of the subtle competition processes outlined above (Fig. 8b).

390 P. Morin et ai.

5. CONCLUSION

The nature of the magnetic phase diagrams has been discussed in terms of the P dependence of various electronic couplings. At ambient pressure, CePb3 and CeAI2 have a modulated antiferromagnetic structure reflecting the predominance of crystal-field effects, but also the existence of a Kondo coupling.

Above a critical pressure P1-~2, which is equal to 7 kbar in C e P b 3 , - 20 kbar in CeAI2, and less than 0 kbar in Celn3, a crossover regime is reached where the crystal-field splittings, the intersite interactions, and the single-site Kondo energy are comparable. The damping of the crystal field effects leads to a drop in the magnetic anisotropy and thus to a change in the magnetic structure with a (1/2, 1/2, 1/2) propagation vector.

The study of CeIn3 under pressure shows that the magnetic-nonmagnetic transition [ TN(Pc) = 0] is achieved for Pc >> P1~2. The recovery of the full degeneracy of the 4 f level appears to be the driving mechanism for reaching a nonmagnetic ground state. This conclusion is reinforced by the weak pressure variation of the temperature TMax of the resistivity maximum. In contrast to the continuous crossover into the intermediate-valence regime, the transition at Pc seems to be a second-order one with a mean-field behavior.

The lack of scaling behavior in the properties of these magnetic heavy- fermion compounds over a significant range of T above or below TN leads to the conclusion that it will probably be difficult as well to scale those of nonmagnetic heavy-fermion systems in which magnetic correlations also play a major role. It has been remarked that well-known heavy-fermion cerium compounds such as CeA13, CeCu6, and CeRu2Si2 are nonmagnetic at T = 0 even though their crystal-field ground state is a doublet. 24'3 The fact that all these materials are not cubic emphasizes the influence of the lattice symmetry on the development of electronic correlations.

ACKNOWLEDGMENTS

It is a great pleasure to thank C. Lacroix, P. Haen, and G. Bruls for fruitful discussions and R. Aleonard, A. Benoit, and S. Pujol for their help during the experiments.

REFERENCES

1. B. Barbara, M. F. Rossignol, J. X. Boucherle, and C. Vettier, Phys. Rev. Lett. 45, 938 (1980). 2. Y. Lassailly, Thesis, University of Grenoble (1985), unpublished. 3. C. Vettier, P. Morin, and J. Flouquet, Phys. Rev. Lett. 56, 1980 (1986). 4. C. Probst and J. Wittig, J. MaSh. Magn. Mater. 9, 62 (1978). 5. B. Barbara, J. Beille, B. Cheiato, J. M. Laurant, M. F. Rossignol, A. Waintal, and S.

Zemirli, J. Phys. (Paris) 48, 635 (1987).


6. A. Benoit, J. X. Boucherle, P. Convert, J. Flouquet, J. Palleau, and J. Schweitzer, Solid State Commun. 34, 293 (1980); J. L. Lawrence and S. M. Shapiro, Phys. Rev. B 22, 4379 (1980).

7. Y. Lassailly, S. K. Burke, and J. Flouquet, J. Phys. C 18, 5737 (1985). 8. J.-M. Mignot and M. Konczykowski, to be published. 9. P. Morin, J. Rouchy, and G. Creuzet, J. Magn. Magn. Mater. 69, 99 (1987).

10. D. Nikl, I. Kouroudis, W. Assmus, B. Liithi, G. Bruls, and U. Welp, Phys. B. Rev. 35, 6865 (1987).

11. F. Canepa, G.A. Corta, and G. L. Olcese, Solid State Commun. 454, 725 (1983). 12. G. Shirane, Acta Cryst. 12, 282 (1959). 13. U. Welp, P. Haen, G. Bruls, G. Remenyi, J. Flouquet, P. Morin, A. Briggs, G. Cors, and

M. Karkut, J. Magn. Magn. Mater. 63--64, 28 (1987); U. Welp and G. Bruls, Private communication.

14. I. Vedel, A. M. Redon, J.-M. Mignot, and J. M. Leger, J. Phys. F 17, 849 (1987). 15. H. J. Van Daal and K. H. J. Buschow, Phys. Stat. Sol. (a) 3, 853 (1970). 16. R. A. Elenbaas, C. J. Schinkel, and C. J. M. Van Deudekan, J. Magn. Magn. Mater. 15-18,

979 (1980). 17. M. E. Fisher and J. S. Langer, Phys. Rev. Lett. 20, 25 (1968). 18. J. Peyrard, Thesis, University of Grenoble (1980), unpublished. 19. C. L. Lin, J. Teter, J. E. Crow, T. Mihalisin, J. Brooks, A. I. Abou Aly, and G. R. Stewart,

Phys. Rev. Lett. 54, 2541 (1985). 20. C. L. Lin, J. E. Crow, P. Schlottmann, T. Mihalisin, S. Bloom, R. P. Guertin, and J. S.

Brooks, J. Magn. Magn. Mater. 63-64, 25 (1987). 21. B. Cornut and B. Coqblin, Phys. Rev. B 5, 4541, (1972). 22. A. Benoit, J. Flouquet, and M. Ribault, J. Phys. (Paris) 40, C5-330 (1979); J. Phys. (Paris)

39, 94 (1978). 23. B. Coqblin, A. K. Bhattacharjee, R. Jullien, and J. Flouquet, J. Phys. (Paris) 41, C5-297

(1980). 24. J. Flouquet, in A Travers la Physique (Editions de Physique, Paris, 1984), p. 293. 25. E. Abrahams, J. Magn. Mater. 63-64, 234 (1987); B. A. Jones and C. M. Varma, Phys.

Rev. Lett. 58, 843 (1987). 26. J.-M. Mignot and J. Wittig, in Valence Instabilities, P. Wachter and H. Boppart, eds.,

(North-Holland, Amsterdam, 1982), p. 203. 27. J. Teter, J. E. Crow, and T. Mihalisin, J. Appl. Phys. 55, 1978 (1984). 28. J. Aarts, F. de Boer, S. Horn, F. Steglich, and D. Meschede, in Valence Fluctuations in

Solids, L. M. Falicov, W. Hanke, and M. B. Maple, eds. (North-Holland, Amsterdam, 1981), p. 301.

29. D. Gignoux and J. C. Gomez-Sal, Phys. Rev. B 30, 3967 (1984). 30. T. V. Ramakrishnan and K. Sur, Phys. Rev. B 26, 1798 (1982). 31. T. V. Ramakrishnan, in Valence Fluctuations in Solids, L. M. Falicov, W. Hanke, and M.

B. Maple eds. (North-Holland, Amsterdam, 1981), p. 451. 32. C. Lacroix and M. Cyrot, J. Magn. Magn. Mater. 15-18, 65 (1980). 33. C. Lacroix, J. Magn. Magn. Mater. 63-64, 239 (1987). 34. P. Coleman, Phys. Rev. B 28, 5255 (1983). 35. N. Read, D. M. Newns, and S. Doniach, Phys. Rev. B 30, 3841 (1984). 36. B. Bellarbi, A. Benoit, D. Jaccard, J.-M. Mignot, and H. F. Braun, Phys. Rev. B 30, 1132

(1984). 37. J. D. Thompson, J. Magn. Magn. Mater. 63-64, 358 (1987). 38. R. Takke, M. Niksch, W. Assmus, B. Lfithi, R. Pott, R. Schefzyk, and D. K. Wohlleben,

Z. Phys. B 44, 33 (1981). 39. C. Fierz, D. Jaccard, J. Sierro, and J. Flouquet, Magnetism and Magnetic Materials

Conference, Chicago (1987). 40. F. Holtzberg, J. Flouquet, P. Haen, F. Lapierre, Y. Lassailly, and C. Vettier, J. Appl. Phys.

57, 3152 (1985). 41. R. Tournier, in Proceedings of the 13th International Conference on Low Temperature Physics,

K. D. Timmerhaus, W. J. O Sullivan, and E. F. Hammel, eds. (Plenum Press, New York, 1974), p. 257.

Documents

Magnetic structures under pressure in cubic heavy-fermion compounds