ELSEVIER Physica B 217 (1996) 97-101

High pressure effect on the magnetic transition in heavy fermion systems CePd2A13 and CePdA1

J. Tang*, A. Matsushita, H. Kitazawa, T. Matsumoto National Research Institute for Metals, 1-2-1 Sengen, Tsukuba-shi. Ibaraki 305. Japan

Received 18 April 1995; revised 1 August 1995

Abstract

We have investigated the pressure dependence of the antiferromagnetic transition temperatures TN for CePd2A13 and CePdA1. Although the T N of both compounds are almost equal at ambient pressure, the pressure dependences are different; T N of CePd2A13 initially increases at a rate of 0.3 K/GPa, then passes through a maximum near 0.75 GPa and falls rapidly at higher pressures while T N of CePdA1 is pressure insensitive in the low pressure region and decreases monotonically in the high pressure region. The results are discussed in terms of the competition between the Kondo effect and the RKKY interaction and it is shown that the results can be understood by the phase diagram proposed by Doniach.

1. Introduction

Recently, CePd2A13 [1] and CePdA1 [2] have been reported to be the heavy fermion compounds which show antiferromagnetic ordering of Ce spins below TN = 2.8 K and 2.7 K, and the electronic specific heat coefficients 7 of 380 and 270 m J/ mo l K 2, respectively. Both compounds crystallize in hexagonal symmetry; PrNi2A13-type structure (similar to the heavy fermion superconductors UM2A13, M = Ni, Pd) in CePd2A13 and ZrNiA1- type structure in CePdAI (high temperature phase) [3]. The magnetic ordered moments of CePd2AI3 are coupled ferromagnetically in basal planes with an antiferromagnetic stacking along the c-axis [4,5]. The cerium nearest neighbor distance dce-ce of 3.74 ~ (perpendicular to the c-axis) in CePdA1 is smaller than that of 4.213/~ (parallel to the c-axis) in CePd2AI3 [2]. The magnetic suscepti-

*Corresponding author.

bility of CePdA1 follows the Curie-Weiss law at high temperature with an effective magnetic mo- ment of 2.49#B which is close to the free ion value for Ce 3 + of 2.54/~B [6].

Doniach [7] established a magnetic phase dia- gram of the one-dimensional system theoretically, by comparing the binding energy of the Kondo singlet,

kBT K oc (1/N(EF)) exp ( - 1/l Joe IN(EF)),

with that of an RKKY-type antiferromagnetic state,

kBTgKKy oC Jc 2 N(EF),

where N(EF) is the density of conduction electron states at the Fermi energy EF, and Jcf is the ex- change coupling strength. Thus the Kondo effect and the RKKY interaction are competing with each other depending on the value of IJ~dN(EF). For a small value of I J~flN(EF), the RKKY interac- tion dominates and the magnetic order will occur. For a large value of IJcf lN(EF), the Kondo term

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98 J. Tang et al. /Physica B 217 (1996) 97-101

dominates and the magnetic order is suppressed due to the Kondo compensation. As a result, the maximum of TN is formed at a certain value of I Jcf[N(Ev). Recently, this Kondo lattice phase dia- gram has been applied successfully to account for the experimental results on a variety of Ce-based systems [8].

Application of pressure is known to increase the value of IJcflN(Ev) in Ce compounds [9]. In this paper we investigate the pressure effect on the mag- netic order transition temperature of CePd2Al3 and CePdAI to know how the competition changes under high pressure and clarify the behavior of CePdzA13 and CePdAI in the magnetic phase dia- gram.

2. Experimental

We have prepared polycrystalline samples by arc-melting the pure elements of Ce(3N), Pd(3N), Ni(3N), and AI(5N) in their stoichiometric ratio using an argon atmosphere under continuous tita- nium gettering. The CePd2AI3 sample was an- nealed at 900°C for 120 hours in sealed quartz ampules. The PrNizAl3-type structure and the ZrNiAl-type structure were confirmed at room temperature by X-ray diffraction patterns for an- nealed CePdzA13 and as-cast CePdA1, respectively.

We have measured the specific heat for both compounds with a quasi-adiabatic method under pressures up to 1.2 GPa between 1.5 and 10 K. The sample was filled into a Teflon cell with Fluorinert as the pressure transmitting medium. A Be-Cu piston and cylinder clamp were used to generate and retain hydrostatic pressure which was applied at room temperature.

In order to know the compressibilities of the two compounds, we also carried out the in situ X-ray experiment under high pressures at room temper- ature. A cubic-anvil type of high pressure apparatus was used in connection with an X-ray diffraction system with a rotary target type X-ray source. The sample was placed into the center hole of the cubic pressure medium made of amorphous boron and epoxy resin in the ratio of 1:4. The cemented tung- sten carbide anvils with square faces of 4 and 6 mm and the cube-shaped pressure transmitting media

of 6 and 8 mm were used. The powder X-ray dif- fraction experiment was carried out by the energy dispersive method with a solid state detector moved vertically. The pressure was calibrated by the diffraction lines of NaCI according to Decker's scale at 25°C based on the equation of state of NaCI [10]. With the obtained relative changes of the lattice constants under high pressure, we esti- mated the pressure dependence of the exchange coupling strength Jcf.

3. Results

Fig. 1 shows the result of the specific heat measure- ment under pressure for CePd2A13. The specific heat exhibits a peak at about 2.9 K, which we define as the antiferromagnetic transition temperature TN. The specific heat at ambient pressure is obtained from a usual specific heat measurement. It can be observed that there is an initial increase of TN with the rate of dTN/dP ~ 0.3 K/GPa, a little larger than the rate obtained by Nolting et al., 0.2 K/GPa [11], as above 0.75 GPa, TN starts to decrease. The pres- sure dependence of TN is plotted in the inset of Fig. 1.

-,-~_ c"-

o

C e P d 2 A I 3 . ' . o o ° • 0.1Mb=ar ~ " - * 3,kF:._oO o o o o • o 03GPa =" ~ ~ '17 o 0 s a ~ " o °'~ ~ h o 075GPa • o o 251-

, 12GPa : " ~

. " o o ° , ~ P(GPa)

..'o o o~ ~.. • e e e e e e • • e e

• , ¢ , , ~ , ~, e = o o o " A o

• ' , [ , , S o o e e e O O ~ & " gt D O O O O o

o o ~ A v W A , 3 , 0 0 0 0 0 0 o ~' ~' v W , , ,, ,,

o @ ~, v A A & a

~> ,= v v v v v v v v v A v

2 3 4 T(K)

Fig. 1. The result of the specific heat measuremen t of CePd2Al 3. The inset shows the pressure dependence of the magne t i c t rans i t ion t empera tu re T N. The curves were shifted vert ical ly for easier visual izat ion.

J. Tang et al. / Physica B 217 (I 996) 97-101 99

CePdAI i I • 0 .1Mbar O O O 0 .15GPa g 0 .3GPa • ~2 . o o0°GP. ~ 2 ~ ° A 0 .7GPa • o¢1~O O v 0 .9GPa • I I I I I I I I I I I

• o • f ~ , ~ , . o c ~ 0 0 .5 1

, , P(GPa)

to.j.: io: o • o o o o • o

0 0 0 [] 13 0

[ ~ W v w w A A A 0 o

, i , h , , I , , , J

2 3 4 T(K)

Fig. 2. The result of the specific heat measurement of CePdAI. The inset shows the pressure dependence of the magnetic transition temperature T N. The curves were shifted vertically for easier visualization.

Fig. 2 shows the result for CePdAI. TN for CePdAI seems to be pressure independent in the low pressure region but decreases rapidly in the high pressure region. Although the transition tem- peratures of CePd2A13 and CePdAI are almost equal at the ambient pressure, the behaviors of TN are different.

In order to study precisely the competition be- tween the RKKY interaction and the Kondo effect, it is necessary to know the volume change under high pressure. Figs. 3(a) and (b) show the pressure variations of the lattice parameters a/ao, C/Co and volume V/Vo obtained by the cubic-anvil appar- atus for CePd2AI3 and CePdA1, respectively. Con- cerning the pressure-volume relationship, we can fit the data to the Birch equation [12]:

p = 3 Ko[(Vo/V)7/3 _ (Vo/V)5/3].

The obtained bulk moduli at ambient pressure K0 are 68.0+2.4 and 47.8 + 1.7 GPa for CePd2A13 and CePdA1, respectively.

4. Discussion

According to the Anderson model, the parameter Jcf c a n be expressed as follows [13]:

dcfoc IVcfl2/(Ev - Ef) , (1)

0.98

096

::~ 0.94

0 .92

0 .90

to 0.88

0 . ~

0 8 4

0 82

• , . J • i . i i

1 0 o ~ ' o u 8 (a) o o CePd2AI3 0 .98

Q

>o ~ 0 .96

0 .94

a

0 .92

0.90 I I I I I I

1.02 , , , , e

too ~,, 8 CePdA1 (b)

" ~ B o o a [] Do o . %--47 a 7~

i i i __

P (GPa)

Fig. 3. The relative changes in volume V/V o (A) and the lattice parameters a/a o (IS]) and c/c o (©) of(a) CePd2Al 3 and (b) CePdAl as a function of pressure at room temperature. The solid lines are fits to Birch's equation of state.

where V c f is the matrix element for the conduction- f-electron hybridization, Ef is the location of the f level and EF is the Fermi energy.

Although there was a suggestion that f-d hybridi- zation plays a dominant role in CePd2AI3 [14], recent experiments have shown that the hybridiza- tion between the f electron of cerium and the s, p electron cloud of the aluminium atoms is also important [15]. In the structure of CePd2AI3, the A1 atoms exist between the Ce layers which are coupled with each other with antiferromagnetic order. According to the band calculation of CePdzA13 [16], the conduction band states around EF are mainly made of the AI-3p states. Therefore, f-p hybridization is believed to have a major con- tribution to Vcf.

Harrison [17] has shown theoretically that if the hybridization occurs between f and p states, Vcf has

I00 J. Tang et al. /Physica B 217 (1996) 97 101

the dependence given by

Vcf ~ (rSf/2/d 9/2) (2)

where rf is the ionic radius of the fatom, and d is the interatomic distance between the f and p atoms. From this relation, the value Vcf strongly depends on the interatomic distance d and, therefore, a strong pressure dependence of Va is expected.

We assume that the variation of Ev - Ef is con- stant compared with that of V~f in our pressure range. This assumption is confirmed by the photo- electron-spectroscopy measurement in the case of the Ce(Rhl xRux)3 B 2 series [18]. Thus, the value of Jcf should depend only on the ionic radius of Ce and the separation of the f and p atoms as shown in the expression

Jcf z~ [Vcf[ 2 oc (rfS/d9). (3)

We now estimate the change in Jcf for CePd2AI3 with the result of the X-ray diffraction experiment under high pressures and at ambient pressure. The interatomic distance between Ce and A1 is given by d = ( a 2 +c2)X/2/2 for CePdzA13 . Although the magnetic structure of CePdAI has not been clarifi- ed, both the result of the band calculation and TN of CePdA1 are similar to those of CePd2AI3 [2, 16]. Therefore, we analyze the experimental re- sults of CePdAI with the same method as that of CePd2A13. The interatomic distance between Ce and A1 is d = (u2a2 + C2)1/2/2 for CePdAI [19], where a is the lattice parameter and u is an internal parameter. In CePdA1 we assume that the variation of the internal parameter u can be neglected. In the present pressure range, the ionic radius of Ce is also assumed to remain unchanged. Then the ratio of Jcf to Jo at the ambient pressure becomes

Jcf/Jo ---- ((ag + c2)/(a 2 + C2)) 9/2 (4)

for CePdEAl3 and

Jc f /Jo = ((u2a 2 -k- CZo)/(u2a 2 + c2)) 9/2 (5)

for CePdA1. Here a0, Co and a, c are the lattice parameters at the ambient pressure and those un- der high pressures, respectively.

Here we can obtain the Jcf dependence of TN for both compounds. Fig. 4 shows the relationships of T N / T y . . . . v e r s u s Jcf /JT ..... for C e P d 2 A 1 3 and CeP- dA1, where TN . . . . and J r ..... denote the

E Z 1 0.9

I -

0.8

O

O

O O

I . . . .

O

O

i i = i I = i i i / i

0.95 1.00 1.05

O CePO2AI3

CePdAI

J/JTN,max

Fig. 4. The magnetic transition temperature T N versus the coupling strength Jcf for CePd2AI 3 (©) and CePdAI (~). Both quantities are normalized to their values where T N exhibits the maximum value.

maximum transition temperature and the value of coupling constant which gives TN . . . . respectively. It can be seen that the value of Jcr increases with pressure for CePd2AI3 and CePdAI and all data points can be mapped to a universal curve which was predicted by Doniach [7] for the one-dimen- sional Kondo necklace, like that of some other Ce compounds [20]. This Jcf dependence of TN sug- gests that CePdA1 is located on the right side of CePd2Ala and is close to the maximum of TN in the Doniach phase diagram. In fact, the y value of CePdAI is smaller than that of CePdzAla at ambi- ent pressure [1,2], indicating that the value of TK in CePdA1 is higher than that of CePd2A13.

On the other hand, if the hybridization occurs between f and d states, Vcf is given by

Vcf oc ((r~ r3)'/Zld6 ) (6)

where rf and ra are the ionic radii of the f and d atoms, respectively, and d is the interatomic dis- tance between them. Therefore, the pressure de- pendence of J a can be expressed as

Jcf/Jo = (ao/a) 12 (7)

for CePd2A13. The relationship of TN versus J a was similar to that for the case of f-p hybridization described above. A similar relationship has also

J. Tang et al. / Physica B 217 (1996) 97-101 101

1.08

1.06

1.04

1.02 [0.151

1.oo! [P=0 GPa]

0.98 •

"~ 0.96 o(o.5) o (0.3)

0.94 i o (o.2)

0.92 °(P=° GPa) I L I ~ I ~ I

1.96 0.98 1.00 1.02 1,04

Jcf(f-p)/J (TN,max)

I I I I

[ " CePdAI ] (1.2) [0.7] o CePd2AI3[ o

(1.0) [o.5] O

• [0.31 []

(0.75)

Fig. 5. The relationship between ~p and f-d hybridization un- der various pressures for CePd2AI 3 (O) and CePdAI (11). Both quantities have been normalized to their values where T~ is maximum. The values of pressure are denoted in parentheses.

been obtained for CePdA1 by using the shorter Ce-Pd distance between two Pd sites. Thus, we have got the correlations between the f-p and f-d hybridizations at various pressures for both com- pounds as shown in Fig. 5. Since the slopes of two curves are close, either model off-p and f~l hybrid- izations gives a Doniach-like universal curve.

In this work, we successfully analyzed the rela- tionship between Jef and TN in terms of Doniach's diagram. However, it is likely that the hybridization between the f and conduction electrons occurs not via only the simple f-p or f-d model but through the mixture of both. By establishing the magnetic struc- ture of CePdA1 and the quantitative estimation of the specific heat under pressure, we might discuss in detail the hybridization in these systems.

5. Conclusion

Summarizing the results of the specific heat experiments for CePd2A13 and CePdA1, it has been shown that the magnetic ordering TN is suppressed with increasing pressure in the competition between the RKKY interaction and the Kondo effect. For CePd2A13, TN initially increases with increasing pressure, followed by a maximum and

a subsequent rapid drop. On the other hand, the pressure dependence of TN in CePdAI is small in the low pressure region and then decreases rapidly with increasing pressure. Therefore, we can con- clude that CePd2A13 resides on the left side of the maximum of TN while CePdAI is close to the max- imum of TN in Doniach's magnetic phase diagram.

Acknowledgements

The authors would like to thank Professor J.S. Schilling for helpful discussions.

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