LOW TEMPERATURE ELECTRICAL RESISTIVITY
OF a-CERIUM UNDER PRESSURE

M. Nicolas-Francillon, Denis Jerome

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M. Nicolas-Francillon, Denis Jerome. LOW TEMPERATURE ELECTRICAL RESISTIVITY OF a-CERIUM UNDER PRESSURE. Solid State Communications, 1973. hal-04990799

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LOW TEMPERATURE ELECTRICAL RESISTIVITY OF α-CERIUM UNDER PRESSURE

M. Nicolas-Francillon

Laboratoire des Terres-Rares, CNRS, Bellevue

and

D. Jerome

Laboratoire de Physique des Solides,* Université Paris-Sud, Centre d'Orsay, 91 405 Orsay, France

(Received 1 December 1972 by P.G. de Gennes)

We report a new method which is used to study the α-phase of cerium without inclusions of β-phase. A pressure independent low temperature resistivity has been observed. None of the exchange enhancement effects previously observed in high pressure susceptibility experiments have been detected on transport properties.

THE α ↔ γ allotropic phase transformation in cerium has been rather well understood on the basis of a virtual bound state theory within the Hartree–Fock approximation.¹ At room temperature and atmospheric pressure the γ-phase exhibits a Curie–Weiss paramagnetism with a localized moment of 2.5 µB, whereas at low temperature and under high pressure the α allotrope behaves like a Pauli paramagnet.²

In the limit of low pressure the γ → α phase transformation which occurs around 106 K is masked by the formation of an hexagonal paramagnetic modification of cerium which is formed on cooling at ~260 K.³,⁴ The α-phase thus obtained by cooling the γ phase down to helium temperature presents a mixture of β and α phase. The zero pressure γ → α (β) phase transformation has been extensively studied by many investigations cited in reference 3 using different types of experiments.

The β, α mixture makes the examination of the electronic properties of the α-phase very difficult unless some 'artefact' is used to prepare the α phase pure without any traces of β-phase.²,⁵

As noticed by Gschneidner et al.³ the β-phase does not form upon cooling at pressure above ~4 kbar.

In this communication we report a new method to prepare cerium in its α-phase based on the use of hydrostatic pressure. We also report transport properties measurements performed on α and γ phase in the pressure domain 0–8.5 kbar and down to the temperature of 1.3 K.

We wanted to check whether the exchange enhancement in the α-phase is visible on the transport properties and in this eventuality would it change under pressure.

The sample with a purity better than 99.9% comes from 'Rare Earth Products Ltd'. The major impurities are: Al, 10 ppm; Ca, 100 ppm; Mg, 10 ppm; Si, 10 ppm and La, 100 ppm. It has been annealed under high vacuum (10⁻⁸ torr) at 500°C.

We have used the pressure equipment existing at Orsay.⁶ The sample is first pressurized in the helium gas equipment at room temperature up to a pressure above the γ → α transformation. Then the pressure vessel is slowly cooled down to 77 K. At this temperature the pressure in readjusted to the desired

<footnote>* Laboratoire associé au CNRS.</footnote>
<figure><img src="image_2.png" /><figcaption>FIG. 1. Phase diagram of cerium after reference 3, showing the method used in this work.</figcaption></figure>

pressure of the equipment. During the cooling down to helium temperature the freezing of fluid helium is performed with a temperature gradient applied to the pressure vessel, Fig. 1. The procedure allows a constant pressure solidification of helium.⁷ The pressure during the experiment is read by the resistance of a calibrated manganine gauge kept at room temperature in the high pressure equipment. A countercheck can be performed by watching at the fusion temperature of solid helium under pressure during the slow warm up of the vessel.⁸

The resistance of α-cerium is measured with an a.c. technique at 30 Hz and the voltage is recorded against the temperature given by a calibrated GaAs diode located on the outside wall of the vessel. For an accurate reading of the temperature the warming rate is kept below 0.1 K per minute.

Resistivity of cerium vs. temperature has been studied at pressure 0, 3.8, 6.8 and 8.5 kbar. The different $ρ(T)$ curves are similar within the accuracy of the long term stability of the electronics ≈ (1%), Fig. 2. An initial $T^{3.4}$ temperature dependence has been noticed between 4.2 and 10 K, Fig. 3 for the three pressure points and between 1.3 and 10 K for

<figure><img src="image_3.png" /><figcaption>FIG. 2. Resistivity of α-cerium for different pressures. No change has been observed within experimental accuracy (10%).</figcaption></figure>

the zero pressure experiment. No signs of superconductivity have been observed down to 1.3 K at zero pressure.

The atmospheric pressure run being performed after the high pressure runs, the sample has been taken up to room temperature and down again to helium temperature, Fig. 4. The $α → γ$ transformation begins at the temperature of 162 K and manifests itself by a cusp-like singularity on the $ρ(T)$ curve. The transition temperature is lower than the one reported by Gschneidner et al.³ The effect of $β-α$ mixture is clearly observable by the increase of the residual resistivity in the second run.⁹

In the second run of Fig. 4 the $α → γ$ transition occurs at the temperature of 168 K. We are led to believe that a small fraction of $β$-phase would act as a pressure on the remaining $α$-phase and then increase the $α → γ$ transition temperature.

McPherson et al.² have measured the magnetic susceptibility of α-cerium between 10 and 18 kbar. These authors found a low and only weakly temperature dependent susceptibility. The results of susceptibility and of electronic specific heat¹⁰ under pressure have led Coqblin¹¹ to consider the α-Ce as an exchange-enhanced paramagnet,² with a 4f level lying just above the Fermi level and moving upwards under pressure. With this picture the exchange enhancement effects decrease under pressure. In the case of strong Pauli paramagnet, virtual spin waves give rise to a large contribution in the low temperature resistivity. Schindler, Rice¹² and Mills, Lederer¹³ have shown that the scattering of s electrons against the spin fluctuations in the *d* or *f*
<figure><img src="image_4.png" /><figcaption>FIG. 3. A log-log plot of the low temperature resistivity of α-cerium.</figcaption></figure>

electron spin density of a uniformly enhanced paramagnet leads to a $T^2$ resistivity contribution at vanishingly small temperature. The effect of nearly magnetic ions such as Ni dissolved in an exchange enhanced paramagnet such as Pd has been discussed by Lederer and Mills¹⁴ and in reference 12. The effect of the spin fluctuations on the resistivity is enhanced in the vicinity of the impurity cell. The $T^2$ term of the alloy contains a contribution proportional to the impurity concentration.

It appears clearly from our experimental results on α-cerium, Fig. 3 that no $T^2$ law is observed at helium temperature and that the $T^{3·4}$ law is presumably related to the electron-phonon mechanism.

Thus, from the transport properties data only, no exchange enhancement is observed in α-cerium. This is in disagreement with a recent study performed on α-Ce by Katzman and Mydosh¹⁵ where the strongly pressure dependent resistivity between 0 and 10 kbar in α-cerium is attributed to the effects of spin fluctuations.

The large increase of the coefficient of a $T^2$ law found at low temperature for decreasing pressures was attributed to the proximity of a magnetic transition in α-Ce. The $T^2$ to T gradual conversion at high temperature was interpreted in terms of the temperature change of the exchange enhancement factor. The data fit reasonably well with the Kaiser, Doniach¹⁶ theory

<figure><img src="image_5.png" /><figcaption>FIG. 4. The α → γ transformation observed at mesospheric pressure and a subsequent temperature cycle showing the presence of a small fraction of β-phase.</figcaption></figure>

and with the assumption of uniform spin fluctuations.

Although it was rather satisfying from the theoretical point of view to observe a quadratic contribution in the low temperature resistivity,¹⁵ one is led to believe from our data that the $T^2$ behaviour is not an intrinsic effect of the α-phase. It results more likely from the existence in the α-phase of almost magnetic centers; presumably inclusions of cerium with a valency different from the α-phase valency. As discussed above these nearly magnetic ions lead to spin-fluctuation contribution in the resistivity for s electrons of α-cerium proportional to their concentration.¹⁴

The results reported in this communication are in agreement with those of Katzman and Mydosh¹⁵ at 20 kbar. Consequently, our data clearly show that one must be extremely careful in the interpretation of the different physical measurements obtained in the α-phase. It does not seem possible to obtain a pure α-phase free from trivalent ions at low temperature unless a truly hydrostatic pressure method is used.

However, even in the case of enhancement effects seen on the susceptibility, for example in Pd¹⁷ the enhancement effects on the low temperature resistivity on a uniform paramagnet are much smaller.¹² We can thus draw a parallel between the case of pure Pd and that of α-cerium from which Coqblin¹¹ deduced an enhancement factor of 13 at 11 kbar. In this case the coefficient A of the $T^2$ law should be much smaller than $10^{-3} \mu\Omega \text{ cm K}^{-2}$ otherwise it would have been observed in our data. For comparison, Schindler and Rice data¹² give $A = 3 \times 10^{-5} \mu\Omega \text{ cm K}^{-2}$ in pure Pd.
In conclusion, the question whether α-cerium can be considered as an exchange enhanced metal with a pressure dependent enhancement factor or not remains open. These preliminary results should trigger more

experimental work in α-cerium.

*Acknowledgements* – We would like to thank B. Coqblin with whom the authors had pleasure talking.

REFERENCES

1. COQBLIN B. and BLANDIN A., *Adv. Phys.* **17**, 281 (1968).

2. MACPHERSON M.R., EVERETT G.E., WOHLLEBEN D. and MAPLE M.B., *Phys. Rev. Lett.* **26**, 20 (1971).

3. GSCHNEIDNER K.A., ELLIOTT R.O. and MCDONALD R.R., *J. Phys. Chem. Solids* **23**, 555 (1962).

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5. PANOUSIS N.T. and GSCHNEIDNER K.A., *Solid State Commun.* **8**, 1779 (1970).

6. MALFAIT G. et JEROME D., *Rev. Phys. appl.* **4**, 467 (1969).

7. SCHIRBER J.E., *Physics of Solids at High Pressures*, (Edited by TOMIZUKA C.T. and EMRICK R.M.), Academic Press, New York (1965).

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12. SCHINDLER A.I. and RICE M.J., *Phys. Rev.* **164**, 759 (1967).

13. MILLS D.L. and LEDERER P., *J. Phys. Chem. Solids* **27**, 1805 (1966).

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Nous présentons une nouvelle méthode utilisant un cycle pression hydrostatique temperature qui a permis de préparer le Cerium dans la phase α sans présence de phase β. La résistivité observée à basse température est indépendante de la pression. Nous n'avons observé sur les propriétés de transport aucun des effets d'augmentation d'échange précédemment mis en évidence dans les mesures de susceptibilité magnétique sous haute pression.