Magnetic and electronic properties of heavy fermion compound CeCu4In and valence fluctuating compound CeNi4In

Journal of Alloys and Compounds 481 (2009) 40–43

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Magnetic and electronic properties of heavy fermion compound CeCu4 In and valence fluctuating compound CeNi4 In a ´ A. Kowalczyk a , T. Tolinski , M. Falkowski a,∗ , B. Andrzejewski a , A. Szewczyk b , M. Reiffers c a b c

Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Pozna´ n, Poland Institute of Physics, Polish Academy of Sciences, Al. Lotników32/46, 02-668 Warszawa, Poland Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 043 53 Koˇsice, Slovakia

a r t i c l e

i n f o

Article history: Received 3 February 2009 Received in revised form 10 March 2009 Accepted 12 March 2009 Available online 21 March 2009 Keywords: Intermetallics Electronic transport Heavy fermions Kondo effects Magnetic measurements

a b s t r a c t The CeCu4 In and CeNi4 In compounds were investigated by means of magnetization, specific heat and electrical resistivity measurements. These compounds are paramagnetic down to 2 K. CeCu4 In follows the Curie–Weiss law with eff = 2.40 ␮B /f.u. and  P = −27 K. The experimental value of eff is close to the calculated one for a free Ce3+ ion, thus indicating the presence of well-localized magnetic moments carried by the stable Ce3+ ions. The determined electronic heat capacity coefficient  = 235 mJ mol−1 K−2 confirms heavy fermion character of this compound. The temperature dependence of electrical resistivity is characteristic of heavy fermion systems. Similar analysis for CeNi4 In provided eff = 0.89 ␮B /f.u. and  P = 0.5 K. This effective paramagnetic moment is lower than the free Ce3+ value. The temperature dependence of resistivity is typical of the Kondo impurity system, i.e. it shows a minimum at low temperatures. The reduced effective paramagnetic moment and a small electronic specific heat coefficient  = 16 mJ mol−1 K−2 indicate on a valence fluctuation in this compound. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The hybridization between the 4f electron and the itinerant conduction electron states in cerium-based compounds depends sensitively on the electronic band structure. When the hybridization is weak the localized 4f-derived cerium magnetic moments order magnetically, due to the indirect RKKY exchange interaction mediated by the conduction electrons. The increase of the hybridization by various substitutions or by applying a pressure leads to the correlation effects developing a mixed valence state or Kondo interactions. The Kondo screening modifies the magnetic properties and a paramagnetic ground state can be obtained [1]. The parent CeCu5 compound was identified as a Kondo lattice compound exhibiting antiferromagnetism below 4 K [2]. The substitution of M (M = Ga, Al) into CeCu5 , which increases the average electron density is sufficient to screen all the localized 4f moments in CeCu4 M, which leads to a transition from the magnetic ground state in CeCu5 to a nonmagnetic ground state in CeCu4 M [2–5]. Experimental studies have shown that CeCu4 Al is paramagnetic and follows the Curie–Weiss law with eff = 2.53 ␮B /f.u. and  P = −10 K [3]. The experimental value of eff is close to the calculated one

∗ Corresponding author. E-mail address: [email protected] (M. Falkowski). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.03.049

for a free Ce3+ ion (2.54 ␮B ), thus indicating the presence of welllocalized magnetic moments carried by the stable Ce3+ ions. Below the Fermi energy the total density of states contained mainly dstates of Cu atoms which hybridized with the Ce 4f electronic states. The analyses of the Ce 3d and 4d XPS spectra confirmed the localized character of the Ce f-states and the electronic specific heat coefficient  = 210 mJ mol−1 K−2 was a signature of heavy fermion behavior of CeCu4 Al. For the CeCu4 Ga compound it was found that the ground state is nonmagnetic down to 30 mK [5]. The estimated value of the electronic specific heat coefficient  was equal to about 280 mJ mol−1 K−2 . Below 2 K Cp /T showed a strong increase with a value of about 3.15 J mol−1 K−2 at 0.9 K [5]. The temperature dependence of the electrical resistivity was characteristic of the heavy fermion systems. The parent compound for CeNi4 M system is CeNi5 , which is a paramagnet with magnetic susceptibility, which is almost isotropic and shows a broad maximum around 100 K [6]. The maximum of the bulk susceptibility in CeNi5 corresponds to the Ni atoms. This maximum arises from the thermal smearing of the 3d Ni electron density of states at the Fermi level enhanced by spin fluctuations. The presence of the spin fluctuations in CeNi5 was also inferred from the T2 behavior of the resistivity and the magnetic susceptibility at low temperature [7]. The behavior of CeNi5 indicates that in this compound the cerium atom is in the nonmagnetic Ce4+ (4f0 , J = 0) state and that Ni d band is filled. Specific heat

A. Kowalczyk et al. / Journal of Alloys and Compounds 481 (2009) 40–43

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measurement confirmed a temperature independent Sommerfeld coefficient  = 40 mJ mol−1 K2 [8]. We have previously studied the CeNi4 M (M = Al, Cu, Ga) compounds crystallizing in the hexagonal CaCu5 -type structure, space group P6/mmm [9–12]. These compounds are of special interest due to the nearly filled Ni (3d) band, implying a negligible contribution of Ni atoms to the resultant magnetic moment. In the temperature dependence of electrical resistivity we have observed a shallow minimum for CeNi4 M below 20 K [9–12]. It has been ascribed to a Kondo-like behavior. Both the susceptibility and the X-ray photoemission (XPS) spectra have shown that the Ce ions are in the intermediate valence state in CeNi4 M. In this paper we describe our new studies of the magnetic (dc magnetic susceptibility), transport (electrical resistivity) and thermodynamic (heat capacity) properties of the CeCu4 In and CeNi4 In compounds. 2. Experimental details The CeCu4 In and CeNi4 In compounds were prepared by induction melting of stoichiometric amounts of the constituent elements in a water-cooled boat, under an argon atmosphere. The samples were inverted and re-melted several times to ensure homogeneity. The crystal structure was checked by a powder X-ray diffraction (XRD) technique, using Co K␣ radiation. Our XRD measurements have shown that CeNi4 In crystallizes in the cubic MgSnCu4 type structure (space group F-43m) with a = 7.062 Å in agreement with Ref. [13]. This structure evolves from CaCu5 -type structure of CeNi5 as a result of partial substitution of Ni by In. From the XRD study for CeCu4 In we have found that the structure is orthorhombic of the CeCu4.38 In1.62 type (space group Pnnm) [14] with lattice constants: a = 16.675 Å, b = 10.589 Å and c = 5.046 Å. This structure is obtained from CeCu6 by doubling the a parameter and the exchange of the b and c parameters. Heat capacity measurements were performed by PPMS commercial device (Quantum Design) in the temperature range 2–300 K by relaxation method using the two-␶ model. The magnetic susceptibility and the magnetization curves were measured also on the PPMS system. The electrical resistivity was measured on a bar-shaped sample using a standard four-probe technique.

3. Results and discussion We start the discussion of the experimental results with the magnetometric studies carried out for CeCu4 In. The temperature dependence of H/M for CeCu4 In is presented in Fig. 1(a). We assume here that the magnetic susceptibility is described by M/H ratio but, in principle, it is only true if the M vs. H dependence is linear at low temperatures and for magnetic fields used for the magnetic moment measurements. The data were fitted with the Curie–Weiss law (T) = C/(T −  P ). We have obtained  P = −27.3 K and C = 0.72 K emu/mol. The experimental value of eff = 2.40 ␮B /f.u. is in agreement with theoretical value for a free Ce3+ ion, which indicates on the localized character of the Ce3+ magnetic moments. This large negative paramagnetic Curie temperature serves as an additional signature of the strong negative exchange interaction between spins of the 4f electrons and the conduction electrons. The parameter  P enables a rough estimation of the Kondo temperature as TK = | P /2| = 13.5 K. The magnetic field dependencies of magnetization at different temperatures for CeCu4 In are presented in Fig. 1(b). The temperature evolution confirms the previous observation of the absence of any magnetic ordering down to 2 K. The Ce magnetic moment measured at 2 K in a field of 9 T amounts to 0.3 ␮B /f.u. The substitution of In into CeCu5 , which increases the average electron density, seems to be sufficient to screen all the localized 4f moments in CeCu4 In, which leads to a crossover from a magnetic ground state in CeCu5 to a nonmagnetic ground state in CeCu4 In. The temperature dependence of M/H for CeNi4 In is presented in Fig. 2(a). The experimental data were fitted with the modified Curie–Weiss law (T) = 0 + C/(T −  P ). We have obtained 0 = 1.9 × 10−4 emu/mol,  P = 0.5 K and C = 9.9 × 10−2 emu K/mol. The effective magnetic moment eff = 0.89 ␮B /f.u. derived from the

Fig. 1. The temperature dependence of H/M (a) and the M vs. H dependence at different temperatures (b) for CeCu4 In.

Curie constant C is much lower than the magnetic moment of a free Ce3+ ion (≈2.54 ␮B ). The relatively large values and the steep increase of M/H at the lowest temperatures may be a result of the tendency of CeNi4 In to a heavy fermion state, which is fully developed already for CeCu4 In. This tendency is also visible in heat capacity measurements (see Fig. 6, inset). However, a contribution of the magnetic susceptibility of a small amount of impurities cannot be also definitely excluded. In Fig. 2(b) the field dependence of the magnetic moment at 2 and 20 K is plotted. The Ce magnetic moment measured at 2 K and in a magnetic field of 9 T is 0.15 ␮B /f.u. Both the saturated and the effective magnetic moment are strongly reduced compared to the free ion value. Since the magnetic moment of Ce4+ is zero, the reduction of the moment in CeNi4 In may be due to the Ce intermediate valence. The experimental susceptibility data are similar to those obtained in Ref. [3] for CeCu4 Al. The temperature variation of electrical resistivity of CeCu4 In is shown in Fig. 3. It amounts to about 75 ␮ cm at room temperature, rises with decreasing temperature up to 100 ␮ cm near 25 K, where (T) forms a broad maximum, and then rapidly drops down. A negative temperature coefficient of the resistivity, accompanied by an enhanced negative value of paramagnetic Curie temperature and a reduced value of the low-temperature magnetic moment, is the characteristic feature of Kondo systems, frequently found amidst the Ce-based intermetallics. The variation of resistivity with temperature in CeCu4 In can be explained by the interplay of the crystal electric field (CEF) splitting

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A. Kowalczyk et al. / Journal of Alloys and Compounds 481 (2009) 40–43

Fig. 4. Temperature dependence of the electrical resistivity for CeNi4 In.

connected with a magnetic phase transition below this temperature [2]. The resistivity of CeCu4 In above the maximum can be described by the formula: (T ) = (0 + 0∞ ) − cK ln T

(1)

and the Kondo effect. The incoherent Kondo scattering is known to give rise to the ln T variation of resistivity with temperature. The sharp drop in the resistivity below 25 K can be attributed to the coherence effect in a Kondo lattice associated with the fully degenerate 4f level or with the CEF split ground state alone [15]. For comparison (T) of CeCu5 is characterized by a kink at 4 K which is

where the first term accounts for the scattering of the conduction electrons on the lattice defects and disordered magnetic moments and the second term represents the spin-flip scattering of the conduction electrons on the magnetic centers (the Kondo effect). Applying Eq. (1) yields a good approximation of the (T) curve above 50 K (note the solid line in the inset of Fig. 3) with the fit parameters 0 + 0∞ = 159 ␮ cm and cK = 15.9 ␮ cm. At low temperatures, below the characteristic maximum at around 25 K, a linear decrease of resistivity is visible. It may be a signature of a non-Fermi liquid scaling. Fig. 4 shows the temperature dependence of electrical resistivity for CeNi4 In. A metallic behavior has been revealed. At about 10 K a shallow minimum in (T) (inset of Fig. 4), typical of a Kondo impurity systems, is observed. The increased 0 (≈300 ␮ cm) can be connected with the atomic disorder as has been also observed for CeNi4 Al [3] and CeNi4 Cu [9] compounds. Fig. 5 shows the temperature dependence of the heat capacity C(T) of CeCu4 In in the temperature range 2–300 K and in zero mag-

Fig. 3. Temperature dependence of the electrical resistivity for CeCu4 In.

Fig. 5. The heat capacity C(T) of the CeCu4 In compound up to 300 K. Inset: A low temperature part of the C/T vs. T2 dependence used to determine the  value.

Fig. 2. The temperature dependence of M/H (a) and the M vs. H dependence at different temperatures (b) for CeNi4 In.

A. Kowalczyk et al. / Journal of Alloys and Compounds 481 (2009) 40–43

Fig. 6. The heat capacity C(T) of the CeNi4 In compound up to 300 K. Inset: A low temperature part of the C/T vs. T2 dependence used to determine the  value.

netic field. We have not observed any sign of the magnetic order down to 2 K. In Fig. 5 (inset) the low temperature part of C(T)/T as a function of T2 is presented. An extrapolation to T = 0 K of the temperature range above 8 K yields the electronic specific heat coefficient  of about 235 mJ mol−1 K−2 . Extrapolation of the lowest temperatures range of C/T(T2 ) provides a large value of 0.6 J mol−1 K−2 . Even the lower value confirms the presence of a heavy fermion state in this compound. The steep increase of C/T at the lowest temperatures can be a confirmation of the tendency to a non-Fermi liquid behavior, which has been also suspected in the electrical resistivity results discussed for Fig. 3. The C/T behavior in CeCu4 In can be analyzed in terms of the single impurity Kondo model [16]. For the impurity Kondo system with a spin s = 1/2 the Kondo temperature is related to the maximum value  (T → 0) by  max TK = 0.68R, where R denotes the gas constant. Using this expression we deduce for CeCu4 In a Kondo temperature of about 9 K. For comparison CeNi4 In is characterized by  = 16 mJ mol−1 K−2 (Fig. 6). Extrapolation of the lowest temperatures range of C/T(T2 ) to T = 0 provides for CeNi4 In a larger value of  = 0.2 J mol−1 K−2 characteristic of heavy fermion systems. The behavior of CeNi4 In at lowest temperatures confirms the tendency to the enhancement of the effective electron mass, mentioned also in the discussion (Fig. 2) of the magnetic susceptibility. 4. Conclusions Magnetic, thermodynamic and electrical transport properties of CeCu4 In and CeNi4 In compounds have been reported. CeCu4 In is paramagnetic with the effective magnetic moment eff = 2.40 ␮B /f.u. close to that expected for trivalent Ce ions. The

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obtained magnetic data seem to indicate that the Ce magnetic moments are fairly well localized in CeCu4 In. However, the Ce moments do not order magnetically down to 2 K. The electrical resistivity shows a region of the negative logarithmic (−ln T) behavior indicating on the Kondo type interaction in this compound. The Kondo temperature estimated from the magnetic susceptibility and specific heat measurements is about 9–13.5 K. A typical heavy fermion behavior with the  value of about 235 mJ mol−1 K−2 or even 0.6 J mol K−2 for the lowest temperature range extrapolation has been observed. We have found that CeNi4 In shows features typical of mixed valence systems. The effective paramagnetic moment (eff = 0.89 ␮B /f.u) is lower than the free Ce3+ value. Since the magnetic moment of the tetravalent cerium is zero, the observed reduction of magnetic moment can be explained in a natural way by fractional occupation of 4f0 (Ce4+ ) and 4f1 (Ce3+ ) configurations. The temperature dependence of resistivity of CeNi4 In is typical of a Kondo impurity systems, i.e. it shows a minimum at low temperatures. The electronic specific heat coefficient of CeNi4 In is  = 16 mJ mol−1 K−2 . Acknowledgements This work was supported by the funds for science in years 2007–2009 as a research project no. N N202 1213 33 (A. Kowalczyk, ´ T. Tolinski, and M. Falkowski) and partly by Science and Technology Assistance Agency-APVT-51-031704, by VEGA 6165, by the contract CE of SAS. References [1] G.R. Stewart, Rev. Mod. Phys. 56 (1984) 755. [2] E. Bauer, D. Gignoux, D. Schmitt, K. Winzer, J. Magn. Magn. Mater. 69 (1987) 158. ´ [3] A. Kowalczyk, T. Tolinski, M. Reiffers, M. Pugaczowa-Michalska, G. Chełkowska, J. Phys.: Condens. Matter 20 (2008) 255252. [4] E. Bauer, E. Gratz, N. Pillmayr, Solid State Commun. 62 (1987) 271. [5] E. Bauer, N. Pillmayr, E. Gratz, D. Gignoux, D. Schmitt, K. Winzer, J. Kohlmann, J. Magn. Magn. Mater. 71 (1988) 311. [6] M. Coldea, D. Andreica, M. Bitu, V. Crisan, J. Magn. Magn. Mater. 157 (158) (1996) 627. [7] N. Naidyuk, M. Reiffers, A.G.M. Jansen, I.K. Yanson, P. Wyder, D. Gignoux, D. Schmitt, Int. J. Mod. Phys. B 7 (1993) 222. ´ Czech. J. Phys. 54 (2004) D311. [8] O. Musil, P. Svoboda, M. Diviˇs, V. Sechovsky, ´ [9] T. Tolinski, A. Kowalczyk, G. Chełkowska, M. Pugaczowa-Michalska, B. Andrzejewski, V. Ivanov, A. Szewczyk, M. Gutowska, Phys. Rev. B 70 (2004) 06441. ´ [10] A. Kowalczyk, M. Pugaczowa-Michalska, T. Tolinski, Phys. Status Solidi B 242 (2005) 433. [11] T. Tolinski, A. Kowalczyk, M. Pugaczowa-Michalska, G. Chełkowska, J. Phys.: Condens. Matter 15 (2003) 1397. [12] A. Kowalczyk, M. Falkowski, V.H. Tran, M. Pugaczowa-Michalska, J. Alloys Compd. 440 (2007) 13. [13] M. Koterlin, B. Morokhivskii, R. Kutyanskii, I. Shcherba, Ya.M. Kalychak, Phys. Solid State 40 (1998) 5. [14] Ya.M. Kalychak, V.M. Baraniak, V.K. Belskii, O.D. Dmytrah, Dopovidi AN URSR (Kiev) B 9 (1988) 39 (in Ukrainian). [15] M. Lavagna, M. Lacroix, M. Cyrot, J. Phys. F 13 (1983) 1007. [16] N. Andrei, K. Furuya, H. Lowenstein, Rev. Mod. Phys. 55 (1983) 331.