Anomalies of resistivity and its T3 -dependence at low temperatures in Eu-based valence fluctuating systems

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Solid State Communications, Vol. 76, No. I0, pp. I173-i176, 1990. Printed in Great Britain.

AN(J~%LIES O F R E S I S T I V I T Y A N D ITS T 3 - D ~ m N D E N C E

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L O W TEMPERATETRES IN E u - B A S E D V A L E N C E F L U C T U A T I N G S Y S T ~ 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 ( V F ) 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.

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).

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.

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

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

1174

current in forward and reverse d i r e c t i o n s and the average of the two values taken. The m e a s u r e m e n t s were p e r f o r m e d over the t e m p e r a t u r e range 4.2 K s T ~ 300 K u s i n g a home m a d e l i q u i d h e l i u m cryostat.

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At high t e m p e r a t u r e end, we n o t i c e that drop in R(T) with d e c r e a s e in t e m p e r a t u r e is less than that in the stable valent systems. In fact, in the case of EuIr2Si2, i n s t e a d of the drop e x p e c t e d of a simple m e t a l l i c system, there is an increase in R(T) with decrease in t e m p e r a t u r e (in the t e m p e r a t u r e range 300 K to 150 K). We expect a s i m i l a r b e h a v i o u r of R(T) to emerge in EuNi2P2 (in the t e m p e r a t u r e range 300 K to 100 K) a n d EuPd2Si2 (in the t e m p e r a t u r e range 300 K to 150 K) if one c o u l d subtract the p h o n o n - i n d u c e d c o n t r i b u t i o n to the resistance. This s u b t r a c t i o n p r o c e d u r e c o u l d not be c a r r i e d out due to the n o n - a v a i l a b i l i t y of regular s h a p e d samples. The i n c r e a s e of r e s i s t i v i t y with d e c r e a s e in t e m p e r a t u r e (negative slope) implies that, apart from electron phonon scattering, there must be an additional m e c h a n i s m of c o n d u c t i o n e l e c t r o n s scattering. The strength of this s c a t t e r i n g m e c h a n i s m seems to d o m i n a t e over the e l e c t r o n p h o n o n s c a t t e r i n g in a c e r t a i n t e m p e r a t u r e range.

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Fig. i also displays the t e m p e r a t u r e d e p e n d e n c e of the a v e r a g e v a l e n c e V of Eu in these VF m a t e r i a l s that has b e e n determined from M6ssbauer and dc magnetic susceptibility results(9,10]. We have also reproduced in Fig. 1 the results of the m e a s u r e m e n t s of R(T) in two other well k n o w n VF systems, EuPd2Si2[7,12] and EuNi2P2[13,14].

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In contrast, R(T)/R(300) of V F - s y s t e m s Eu3Ni3Si5, EuIr2Si2 a n d EuNiSi2 is a n o m a l o u s c o m p a r e d to the results d e s c r i b e d above. Though all these curves appear to be different, a rather general feature is d i s c e r n i b l e if we divide and examine the data into three t e m p e r a t u r e regions: (i) h i g h t e m p e r a t u r e region where r e s i s t i v i t y R(T) a p p e a r s to s a t u r a t e or have a t e n d e n c y to saturate, (ii) i n t e r m e d i a t e temperature region w h e r e R(T) has a linear t e m p e r a t u r e d e p e n d e n c e a n d (iii) low temperature

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The t e m p e r a t u r e d e p e n d e n c e of R(T)/R(300) of various samples is shown in Figs. I a n d 2 R(T) of the stable valent Eu systems (Fig. 2) Eu2Au3Si5 (Eu2+) and EuNi2Si2 (Eu3+), follows the e x p e c t e d linear t e m p e r a t u r e d e p e n d e n c e above -40 K. The drop in R(T) of Eu2Au3Sis. b e l o w 40 K is due to the m a g n e t i c t r a n s i t i o n of the s y s t e m at ~ 35K[11]. A very similar behaviour is o b s e r v e d 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.

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RESULTS AND D I S C U S S I O N

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VOl. 76, NO. i0

L O W T E M P E R A T U R E S IN E u - B A S E D V A L E N C E F L U C T U A T I N G SYSTEMS

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Fig.l. R ( T ) / R ( 3 0 0 K) and V(T) of EuNiSi2, Eu2Ni3Si5, EuIr2Si2, EuNi2P2 and EuNi2P2 and EuPd2Si2. The data of EuPd2Si2 and EuNi2P2 have b e e n taken from Ref.7 and Ref.14 respectively.

EuNiSi2 b e l o w 200 K. This indicates that as the sample i8 c o o l e d b e l o w a c e r t a i n temperature, the a d d i t i o n a l s c a t t e r i n g m e c h a n i s m gets weaker.

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TEMPERATURE(K) Fig.2. R ( T ) / R ( 3 0 0 K) of EuNi2Si2. Eu2Au3Si5. Eu is trivalent in the former and d i v a l e n t in the latter system.

As a first step to get an insight into this a d d i t i o n a l s c a t t e r i n g mechanism, we t r i e d tO c o r r e l a t e R(T) and V(T) (of Eu ions) in t h e s e systems. From Fig. 1 it appears that the t e m p e r a t u r e d e p e n d e n c i e s of V(T) and R(T) are similar in all the cases except in EuIr2Si2. In order to obtain a p r o p e r correlation, however, it w o u l d have been very h e l p f u l if we c o u l d subtract the p h o n o n c o n t r i b u t i o n f r o m R(T). An important feature to be n o t i c e d in the case of EuPd2Si2 is that the sharp d r o p in R(T) Occurs at a t e m p e r a t u r e s ~100 K less than that of V(T) which seems to support the existence of additional s c a t t e r i n g mechanism.

data[8-10] and the values of Tc o b t a i n e d from r e s i s t i v i t y d~ta (temperature at w h i c h the slope dR/dT decreases from a maximum value to a m i n i m u m with p o s i t i v e 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 m a t e r i a l s Tsf and Tc are n e a r l y the same which is c o n s i s t e n t with the spirit of the ~dynamic alloy' model. In the cases of EuIr2Si2[gl and EuPd2Si2[17], where Tsf is r e p o r t e d l y t e m p e r a t u r e dependent, we have taken the 10w t e m p e r a t u r e value of Tsf. In the cases of EuNiSi2 and Eu2Ni3Si5, s a t u r a t i o n of R(T) is o b s e r v e d a r o u n d 300 K, and t h e r e f o r e data at higher t e m p e r a t u r e s are n e e d e d to d e t e r m i n e the value of Tc.

At t e m p e r a t u r e s T < To, the c o n d u c t i o n e l e c t r o n ~sees' the rare e a r t h ions as h a v i n g a ~time-independent' and a v e r a g e v a l e n c e V. This u s u a l l y 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 n a t u r a l c o n s e q u e n c e of the fact that the system is a Fermi liquid[18-20-23] or the s c a t t e r i n g is m e d i a t e d via spin fluctuations[21]. Kaiser and Doniach[24] p r o p o s e d a s p i n - f l u c t u a t i o n t h e o r y to e x p l a i n the low t e m p e r a t u r e b e h a v i o u r of resistivity, p(T) ~ T 2, in d i l u t e alloys, such as PdNi, IrFe and RhFe. It has also b e e n a p p l i e d with reasonable success i n t e r m e t a l l i c s 2 such as CeIr2Si2 where a T - d e p e n d e n c e has b e e n o b s e r v e d at low temperatures[21]. In constrast

to K,

W a g e r and Mott[15] c o n s i d e r e d the p r o b l e m of anomalous resistivity in certain i n t e r m e t a l l i c compounds, such as VF-systems, and suggested the b r e a k d o w n of h y b r i d i z a t i o n at elevated temperatures in some intermetallic compounds. The 'dynamic alloy' model of W o h l l e b e n and Wittershagen[3] - which, later on, has been further d i s c u s s e d by Zipper et. ai.[16] also - provides a possible mechanism for an additional s c a t t e r i n g of c o n d u c t i o n e l e c t r o n s in VF systems. This m o d e l t r e a t s the o b s e r v e d R(T) in two regions of temperature, one b e l o w and the other above a c h a r a c t e r i s t i c t e m p e r a t u r e Tc, t e r m e d as charge f l u c t u a t i o n temperature. Tc is to be i n f e r r e d as the t e m p e r a t u r e at which the deviation of R(T) from the normal m e t a l l i c b e h a v i o u r is maximum. P h y s i c a l l y speaking, a c o n d u c t i o n e l e c t r o n u n d e r g o e s at T > Tc e l a s t i c Coulomb scattering, b e s i d e s the usual p h o n o n scattering, due to the fact that it ~sees' the rare earth ions f l u c t u a t i n g b e t w e e n two charge states. The two charge states are ~visible' in the LIIz-edge or XPS m e a s u r e m e n t s . This charge disorder is dynamic, however. The e l a s t i c C o l o u m b s c a t t e r i n g i s r e s p o n s i b l e for the high and anomalous r e s i s t i v i t y and does not d e p e n d on t e m p e r a t u r e explicitly. It d e p e n d s on a v e r a g e v a l e n c e V(T) which, b y itself, is a f u n c t i o n of temperature. This m o d e l s u g g e s t s that the charge f l u c t u a t i o n t e m p e r a t u r e Tc, as o b t a i n e d f r o m the analysis of resistivity, s h o u l d be n e a r l y the same as the spin f l u c t u a t i o n t e m p e r a t u r e Tsf. We c o m p a r e the values of Tsf o b t a i n e d f r o m our M6ssbauer and dc magnetic susceptibility

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Fig. 3 shows the result of such a the case of EuIr2Si2. The results for a~d Eu2Ni3Si5 are similar. We note T - d e p e n d e n c e of R(T) has b e e n o b s e r v e d EuCu2Si2[6] also.

fit in EuNiSi2 that a in the

The data p r e s e n t e d here sugges~ that, the t e m p e r a t u r e Tt in whose v i c i n i t y T - d e p e n d e n c e of R(T) transforms to T-dependence, is n e a r l y the same for all the t h r e e samples and is -50 K.

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LOW TEMPERATURES IN Eu-BASED VALENCE FLUCTUATING SYSTEMS

1176

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

VOI. 76, NO. I0

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

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CONCLUSION 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 ~ h a r a c t e r i s t i c 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.

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2.

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and J.

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ii.

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

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Kaindl

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