~ Solid State Communications, Vol. 76, No. I0, pp. I173-i176, 1990.

Printed in Great Britain. 0038-1098/9053.00+.00

Pergamon Press plc

AN(J~%LIES OF RESISTIVITY AND ITS T3-D~mNDENCE AT

LOW TEMPERATETRES IN Eu-BASED VALENCE FLUCTUATING SYST~R~

Sujata Patil , R. Nagarajan, L.C. Gupta, B.D. Padalia

and R. Vijayaraghavan

Tata Institute of Fundamental Research, Bombay 400 005, India

Indian Institute of Technology, Bombay 400 076, India.

(Received September 3, 1990 by C.N.R. Rao)

Ce-based valence fluctuating systems, in general, are known to exhibit anomalous temperature dependence of resistivity, p(T). In contrast, resistivity measurements have been reported thus far on only two Eu-based valence fluctuating (VF) systems and therefore further investigations are required on such materials. Here we report the results of our measurements of the temperature dependence of the resistance R(T) of three Eu-based VF - systems, viz., EuIr2Si2, Eu2Ni3Si5 and EuNiSi2. The measurements of R(T) have also been carried out in Eu2AusSi5 and EuNi2Si2, where Eu is divalent and trivalent

respectively. These studies reveal an anomalous behaviour of R(T) in

the above-mentioned Eu-based VF-systems.

INTRODUCTION

Considerable amount of work has been done in the last decade on the transport properties of valence fluctuating (VF) rare-earth systems[i,2,3]. In contrast to the well known resistivity behaviour of metallic systems (wherein p(T) ~ T at high temperatures and p(T) ~ T at T << ~D ; @D = Debye temperature), piT)

of VF-systems exhibits a variety of temperature dependencies[3]. For instance, p(T) of Ce-based VF systems often exhibits a minimum[4] which bears a similarity to that observed in Kondo systems. The resistivity minimum, however, is not observed in all the cases e.g. CeRh2[3]. p(T) of most of the Yb-based VF-systems, though anomalous, does not show a minimum. Occassionally, however, one does come across Yb-based materials, such as YbCuAI[5], in which p(T) exhibits a minimum. Wohlleben and Wittershagen[3] have analysed the resistivity of many Ce, Yb and dilute Eu VF systems and emphasized that (i) the magnitude of p(T) of VF systems, as compared to that of the corresponding and analogous normal metallic

systems, is large and (ii) The deviation of p(T) from the normal metallic behaviour can be correlated to the spin fluctuation temperature Tar in a given VF material.

Only two measurements of the temperature dependence of resistance, R(T), have been reported so far on Eu based VF systems, viz., EuCu2Si2[6] and EuPd2Si2[7]. Therefore in order to obtain a deeper understanding of resistivity in Eu-based materials, we considered

1173

it essential that such measurements be carried out on as many Eu-based VF-samples as possible. We had earlier identified three Eu-based VF-systems, EuNiSi2[8], EuIr2Si2[9] and Eu2NisSiS[10]. In the present communication, we describe our studies of RIT) of these three materials and discuss the results in the light of current understanding of R(T) in VF compounds. For the sake of comparison, we have also studied R(T) of the stable and integral valent systems such as EuNi2Si2 (where Eu is trivalent) and Eu2TsSi5 iT - Ag, Au, Pd; where Eu is divalent).

EXPERIMENTAL

The samples EuNiSi2, Eu2NisSi5 and EuIr2Si2 were prepared by melting stoichiometric amounts of the high purity constituent elements in an

arc and/or induction furnace under an inert atmosphere of argon. Loss of Eu was compensated during melting. The ingots were sealed under vacuum in quartz tubes and heated at ~ 1000K for several days. Formation of the single phase

samples was confirmed by measuring their powder X-ray diffraction pattern. Eu intermetallics investigated here are highly brittle. It was, therefore, not possible to make regular shaped samples for absolute resistivity measurements. Consequently, only the relative resistance R(T)/R(300) of the materials could be measured. dc electrical resistance measurements were made using standard four-probe technique. In order to avoid possible complications arising due to thermo-emfs, each observation was repeated with

1174 LOW TEMPERATURES IN Eu-BASED VALENCE FLUCTUATING SYSTEMS VOl. 76, NO. i0

current in forward and reverse directions and the average of the two values taken. The measurements were performed over the temperature range 4.2 K s T ~ 300 K using a home made liquid helium cryostat.

RESULTS AND DISCUSSION

The temperature dependence of R(T)/R(300) of various samples is shown in Figs. I and 2 R(T) of the stable valent Eu systems (Fig. 2) Eu2Au3Si5 (Eu2+) and EuNi2Si2 (Eu3+), follows the expected linear temperature dependence above -40 K. The drop in R(T) of Eu2Au3Sis. below 40 K

is due to the magnetic transition of the system at ~ 35K[11]. A very similar behaviour is observed for Eu2Ag3Si5 (TN ~35K) and Eu2Pd3Si5 (TN -20 K) (not shown in the figure). R(T) of EuNi2Si2, exhibits a saturation at low temperatures due to nonmagnetic impurities and/or vacancies etc. Thus R(T) of the integral valent Eu systems does not show any anomalous behaviour.

In contrast, R(T)/R(300) of VF-systems Eu3Ni3Si5, EuIr2Si2 and EuNiSi2 is anomalous compared to the results described above. Though all these curves appear to be different, a rather general feature is discernible if we divide and examine the data into three temperature regions: (i) high temperature region where resistivity R(T) appears to saturate or have a tendency to saturate, (ii) intermediate temperature region where R(T) has a linear temperature dependence and (iii) low temperature r~gion where R(T) fit8 best to a T--dependence. Fig. i also displays the temperature dependence of the average valence V

of Eu in these VF materials that has been determined from M6ssbauer and dc magnetic susceptibility results(9,10]. We have also reproduced in Fig. 1 the results of the measurements of R(T) in two other well known VF systems, EuPd2Si2[7,12] and EuNi2P2[13,14].

At high temperature end, we notice that drop in R(T) with decrease in temperature is less than that in the stable valent systems. In fact, in the case of EuIr2Si2, instead of the drop expected of a simple metallic system, there is an increase in R(T) with decrease in temperature (in the temperature range 300 K to 150 K). We expect a similar behaviour of R(T) to emerge in EuNi2P2 (in the temperature range 300 K to 100 K) and EuPd2Si2 (in the temperature range 300 K to 150 K) if one could subtract the phonon-induced contribution to the resistance. This subtraction procedure could not be carried out due to the non-availability of regular shaped samples. The increase of resistivity with decrease in temperature (negative slope)

implies that, apart from electron phonon scattering, there must be an additional mechanism of conduction electrons scattering. The strength of this scattering mechanism seems to dominate over the electron phonon scattering in a certain temperature range.

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Fig.l. R(T)/R(300 K) and V(T) of EuNiSi2, Eu2Ni3Si5, EuIr2Si2, EuNi2P2 and EuNi2P2 and EuPd2Si2. The data of EuPd2Si2 and EuNi2P2 have been taken from Ref.7 and Ref.14 respectively.

In the case of EuIr2Si2, R(T) decreases rapidly below 150 K. Similar behaviour is observed in EuNi2P2 below 80 K; in EuPd2Si2 below 150 K; in Eu2Ni3Si5 below 200 K; and in

EuNiSi2 below 200 K. This indicates that as the sample i8 cooled below a certain temperature, the additional scattering mechanism gets weaker.

Vol. 76, NO. i0

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~-C-- < - I

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LOW TEMPERATURES IN Eu-BASED VALENCE FLUCTUATING SYSTEMS

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TEMPERATURE (K)

Fig.2. R(T)/R(300 K) of EuNi2Si2. Eu2Au3Si5. Eu is trivalent in the former and divalent in the latter system.

As a first step to get an insight into this

additional scattering mechanism, we tried tO correlate R(T) and V(T) (of Eu ions) in these

systems. From Fig. 1 it appears that the temperature dependencies of V(T) and R(T) are similar in all the cases except in EuIr2Si2. In order to obtain a proper correlation, however, it would have been very helpful if we could subtract the phonon contribution from R(T). An important feature to be noticed in the case of EuPd2Si2 is that the sharp drop in R(T) Occurs at a temperatures ~100 K less than that of V(T) which seems to support the existence of

additional scattering mechanism.

Wager and Mott[15] considered the problem of anomalous resistivity in certain intermetallic compounds, such as VF-systems, and suggested the breakdown of hybridization at elevated temperatures in some intermetallic compounds. The 'dynamic alloy' model of Wohlleben and Wittershagen[3] - which, later on, has been further discussed by Zipper et. ai.[16] also - provides a possible mechanism for an additional scattering of conduction electrons in VF systems. This model treats the observed R(T) in two regions of temperature, one below and the other above a characteristic temperature Tc, termed as charge fluctuation temperature. Tc is to be inferred as the temperature at which the deviation of R(T) from the normal metallic behaviour is maximum. Physically speaking, a conduction electron undergoes at T > Tc elastic Coulomb scattering, besides the usual phonon scattering, due to the fact that it ~sees' the rare earth ions fluctuating between two charge states. The two charge states are ~visible' in the LIIz-edge or XPS measurements. This charge disorder is dynamic, however. The elastic Coloumb scattering is responsible for the high and anomalous resistivity and does not depend on temperature explicitly. It depends on average valence V(T) which, by itself, is a function of temperature. This model suggests that the charge fluctuation temperature Tc, as obtained from the analysis of resistivity, should be nearly the same as the spin fluctuation temperature Tsf. We compare the values of Tsf obtained from our M6ssbauer and dc magnetic susceptibility

1175

data[8-10] and the values of Tc obtained from resistivity d~ta (temperature at which the slope dR/dT decreases from a maximum value to a minimum with positive sign). The values of Tsf

and Tc for EuIr2Si2, EuNi2P2 and EuPd2Si2 are -148 K (Tsf at 4.2 K) & ~160 K, ~80 K & 90 K and -I00 K (Tsf at 4.2 K) and 130 K respectively. Thus, in these materials Tsf and Tc are nearly

the same which is consistent with the spirit of the ~dynamic alloy' model. In the cases of EuIr2Si2[gl and EuPd2Si2[17], where Tsf is reportedly temperature dependent, we have taken the 10w temperature value of Tsf. In the cases of EuNiSi2 and Eu2Ni3Si5, saturation of R(T) is observed around 300 K, and therefore data at higher temperatures are needed to determine the value of Tc.

At temperatures T < To, the conduction electron ~sees' the rare earth ions as having a ~time-independent' and average valence V. This

usually leads to a T2-dependence of R(T) at 10w tempeartures consistent with the observed behaviour in almost all Ce-based VF s~stems[18-22]. It is well known that a T--dependence of p(T) is a natural consequence of the fact that the system is a Fermi liquid[18-20-23] or the scattering is mediated via spin fluctuations[21]. Kaiser and Doniach[24] proposed a spin-fluctuation theory to explain the low temperature behaviour of resistivity, p(T) ~ T 2, in dilute alloys, such as PdNi, IrFe and RhFe. It has also been applied with reasonable success intermetallics

2 such as CeIr2Si2 where a T -dependence has been observed at low temperatures[21]. In constrast to th~se, in systems reported here, as T 0 K, a T -dependence of R(T) represents the data best. Fig. 3 shows the result of such a fit in the case of EuIr2Si2. The results for EuNiSi2 a~d Eu2Ni3Si5 are similar. We note that a T -dependence of R(T) has been observed in the EuCu2Si2[6] also.

The data presented here sugges~ that, the temperature Tt in whose vicinity T -dependence of R(T) transforms to T-dependence, is nearly the same for all the three samples and is -50 K.

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1176

At present, we do not know if it is a mere coincidence or has any physical significance.

CONCLUSION

LOW TEMPERATURES IN Eu-BASED VALENCE FLUCTUATING SYSTEMS VOI. 76, NO. I0

Wohlleben and Wittershagen[3]. The values of Tsf and Tc are in qualitative agreement as required by their model.

In conclusion, R(T) of Eu-based VF systems exhibits anomalous behaviour as compared to that of normal Eu-based systems. Our data are consistent with the existence of two competing mechanisms of resistivity. One of them is the usual electron phonon scattering. The other

mechanism is the Coulomb scattering due to the dynamically fluctuating valence as suggested by

Below a ~haracteristic temperature Tt, R(T) exhibits a T -dependence unlike a T -dependence observed in Ce- and Yb-based VF-systems. We do not understand, at present, the reason for this

difference in the low-T behaviour of Eu-based systems. However, this may have to be kept in mind in the further development of the theory

and understanding of VF-phenomenon in general.

I.

2.

3.

4.

5.

REFERENCES

'Valence Instabilities' edited by P.Wachter and H.Boppart, (Amsterdam, North-Nollond,

1982).

'Valence Fluctuations' edited by E. Muller- hartman, B.Roden, D. Wohlleben, (Amsterdam, North-Hollond, 1984).

D. Wohlleben and B. Wittershagen, Advances in Phys.,34, 403 (1984).

D. Muller, S. Hussain, E. Cattaneo, H. Schneider, W. Schlabitz and D. Wohlleben, in ref. i, p. 463.

J.M. Mignot and J. Wittig, 'Physics of Solids Under Pressure', edited by J.S. Schilling and R.N. Shelton, (Amsterdam,

North-Hollond, 1981).

6. B.C. Sales and R. Vishwanathan, J. Low Temp. Phys., 23, 449 (1976).

7. Vijay Murgai, Ph.D. Thesis, University of

Rochester, 1982.

8. R. Nagarajan, Sujata Patil, L.C. Gupta and R. Vijayaraghavan, J. Magn. Magn. Mater.,

54-57, 349 (1986).

9. Sujata Patil, R. Nagarajan, L.C. Gupta, R. Vijayaraghavan and B.D. Padalia, Solid State Commun., 63, 445 (1987).

10. Sujata Patil, R. Nagarajan, L.C. Gupta, C. Godart, R. Vijayaraghavan and B.D. Padalia, Phys. Rev. B37, 7708 (1988).

ii. R. Nagarajan, Sujata Patil, L.C. Gupta, R. Vijayaraghavan and B.D. Padalia, to be

published.

12. G. Schmeister, B. Perscheid, G. Kaindl and J. Zukrovsky, in ref. 1 p. 219.

13. R. Nagarjan, G.K.Shenoy, L.C. Gupta and J. Zukrovsky, in ref. 1 p. 219.

14. L.C. Gupta and J.D. Thompson, unpublished.

15. M. Weger and N.F. Mott, J. Phys. C, 18, L201 (1985).

16. E. Zipper, M. Drzazga and A. Freimuth, J. Mag. Mag. Mat., 71, 119 (1987).

17. E. Zirngiebl, S. Blumenr~der, G. G~ntherodt, A. Jayaraman, B. Batlogg and M. Croft, Phys. Rev. Lett. 54, 213 (1985).

18. D. Gignoux, F. Givord, R. Lemaire and F. Tasset, J. Less Common Metals, 94, 165 (1983).

19. B. Bellarbi, A. Benoit, D. Jaccard, J.M. Mignod and H.F. Braun, Phys. Rev. B30, 1182 (1984).

20. J.D. Thompson, J.O. Willis, C. Godart, D.E. Mac Laughlin and L.C. Gupta, J. Magn. Magn.

Mater. 47-48, 281 (1985).

21. B. Buffat, B. Chevalier, M.H. Juiler, B. Lloret and J. Etourneau, Solid State Commun. 59, 17 (1986).

22. T. Ohyama, J. Sakarai, Y. Komura, J. Magn. Magn. Mater. 63-64, 581 (1987).

23. P.S. Riseborough, in 'Valence Fluctuations in Solids' edited by L.M. Falicov, W. Hanke and M.B. Maple, (North-Holland, Amsterdam,

1981) p. 225.

24. A.B. Kaiser and S. Donaich, Int. J. Magn. I, Ii (1970).