# Resistivities of CeAl3 and LaAl3 compounds under pressure

Denis Jerome, A. Percheron Gueguan, O. Gorochov, J. Achard, B. Cornut, Bernard Coqblin

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Denis Jerome, A. Percheron Gueguan, O. Gorochov, J. Achard, B. Cornut, et al.. Resistivities of CeAl3 and LaAl3 compounds under pressure. Solid State Communications, 1973. hal-04981087

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RESISTIVITIES OF CeAl₃ AND LaAl₃ COMPOUNDS UNDER PRESSURE

A. Percheron and J.C. Achard

Laboratoire des Terres rares du C.N.R.S., 1, place A. Briand, 92 - Bellevue, France

O. Gorochov

Laboratoire de Chimie Minérale, Faculté de Pharmacie, 4, avenue de l'Observatoire,
75 - Paris 6éme, France

B. Cornut

Centre de Recherches sur les Trés Basses Températures, B.P. 166 Centre de tri, 38042 - Grenoble-Cedex, France

and

D. Jérome and B. Coqblin

Laboratoire de Physique des Solides*, Université Paris-Sud, Centre d'Orsay, 91405 - Orsay, France

(Received 26 January 1973; in revised form 14 March 1973 by M. Balkanski)

The electrical resistivity of CeAl₃ and LaAl₃ compounds has been measured in the 1.3 - 300K temperature range and under pressure up to 17 kbar. The pressure dependence of the resistivity above 25K is theoretically explained by the influence of the crystalline field on the Kondo effect, while the variation of the resistivity at low temperatures or with pressure cycles is qualitatively discussed.

CERIUM in CeAl₂ or CeAl₃ compounds is magnetic and presents a Kondo effect due to the large resonant scattering which arises from the mixing between conduction and 4f electrons, because the cerium 4f level is close to the Fermi level. Such cerium compounds exhibit also a crystalline field (CF) effect which affects deeply the nature of the Kondo effect.¹ Previous resistivity measurements on CeAl₂ compound under pressure up to 16 kbar have been quite well accounted from 5 to 300K by a theoretical model which takes into account both the influence of the CF on the Kondo effect of cerium and the increase with pressure of the 4f level compared to the Fermi level.² So, the purpose of this letter is to study the resistivity under pressure of CeAl₃ compound which has a 4f level closer to the Fermi level than CeAl₂ compound

and is consequently nearer the magnetic-non magnetic transition.¹

The definite compounds CeAl₃ and LaAl₃ were prepared by melting together steochiometric amounts of the components (Al: 99.9999%; La: 99.9%; Ce: 99.9%) in tantalum crucibles sealed under argon. The thermal treatments must be made with an extreme care because, above the peritectoid temperature, i.e. 1135°C for CeAl₃, the compound is decomposed according to the chemical reaction: CeAl₃ → CeAl₂ + CeAl₄³ and traces of the resulting compounds have been observed in some preparations. Metallographic examination of etching samples by Keller solutions, X-ray diffraction and microhardness measurement have shown that the samples were single phases. These compounds crystallize in the h.c.p. system Ni₃Sn type structure. The lattice parameters, obtained by

<footnote>* Laboratoire associé au C.N.R.S.</footnote>
<figure><img src="image_2.png" /><figcaption>FIG. 1. Experimental plots of the total resistivity of CeAl₃ and LaAl₃ vs. temperature at normal (○), 10 kbar (Δ) and 15 kbar for LaAl₃ or 16.4 – 16.8 kbar for CeAl₃ (●).</figcaption></figure>

Nelson–Riley extrapolation method are: $a = 8.66 \pm 0.01$ Å, $c = 4.61 \pm 0.01$ Å for LaAl₃ and $a = 8.54 \pm 0.01$ Å, $c = 4.61 \pm 0.01$ Å for CeAl₃, in good agreement with the previously reported values.⁴

The variation of the magnetic susceptibility with temperature for CeAl₃ has been measured between 77 and 300K and is in agreement with previous results.⁵ Analysis of the Curie–Weiss law gives a Curie temperature of –40K and an effective magnetic moment of $2.4 \mu_B$, which shows the trivalent character of cerium in CeAl₃. The magnetic susceptibility of LaAl₃ measured between 10 and 300K, is equal to $0.644 \times 10^{-6}$ e.m.u./g at room temperature and is almost insensitive to the temperature.

The resistivity measurements are made by an alternative current method. The solderings on the

samples are done by indium ultrasonics; the high pressure apparatus and the method for the determination of the temperature have been described elsewhere.⁶ The resistivity curves of several CeAl₃ and LaAl₃ samples, measured between 1.3 and 300K, at normal, 10 kbar and 16.8 kbar pressures, are shown on Fig. 1. The CeAl₃ resistivity is measured firstly on a newly prepared sample at 0 kbar (giving the curve labelled ‘0 kbar - 1’ on Fig. 1), then, when pressure is applied, at 10 kbar (curve ‘10 kbar - 1’) and at 16.8 kbar (curve ‘16.8 kbar - 1’); then, when pressure is released down to 0 kbar, the resistivity is again measured (curve ‘0 kbar - 2’): a large irreversibility is observed in this first pressure-cycle between the two curves 1 and 2 at 0 kbar. Figure 1 shows the variation of resistivity for four pressure-cycles between the extreme pressures 0 and roughly 17 kbar. The first normal pressure resistivity (curve ‘0 kbar - 1’) is in
<figure><img src="image_3.png" /><figcaption>FIG. 2. Experimental plots of the magnetic resistivity of CeAl₃, i.e. the difference between the resistivities of CeAl₃ and LaAl₃ vs. temperature in logarithmic scale, at normal (○), 10 kbar (△) and 16.4–16.8 kbar (●).</figcaption></figure>

good agreement with previous measurements.⁷,⁸ The resistivity of LaAl₃, which is equal to 0.4 µΩ × cm at 4.2K, does not depend on the pressure-cycle and varies only by 5 per cent between 0 and 15 kbar at 300K, which corresponds in fact to the order of magnitude of the experimental accuracy. So, the variation of the CeAl₃ resistivity under pressure is surely due to the behaviour of the cerium atoms alone. The magnetic resistivities, i.e. the differences between CeAl₃ and LaAl₃ resistivities, are plotted on Fig. 2 as a function of LnT, for different pressures and pressure-cycles.

The main results of Fig. 1 and 2 can be summarized as follows:

(i) At temperatures above roughly 50K, the resistivity is always increasing with pressure in any

given pressure-cycle. On the opposite, at very low temperatures, the resistivity is always decreasing with pressure in any given pressure-cycle and this decrease is huge, for example at 4.2K from 85 µΩ × cm at normal pressure to 11 µΩ × cm at 16.8 kbar. Moreover, at any temperature, the value of the resistivity increases with the number of cycles at a given pressure and remains constant after the third cycle.

(ii) The temperature of the maximum of the magnetic resistivity $ρ$ increases from 34 to 70K between 0 and 16.8 kbar and is completely independent of the pressure-cycle.

(iii) The slope $S_∞$ at high temperatures of the $ρ$ vs LnT curves given by the Fig. 2 increases in absolute value with pressure in any pressure-cycle as it is normally expected,¹,² but also with the number of cycles at a given pressure. If we call 1 the $|S_∞|$ value for the
<figure><img src="image_4.png" /></figure>

FIG. 3. Plot of the magnetic resistivity of CeAl₃ vs. temperature in logarithmic scale. The points give the experimental measurements for the '0 kbar-2' (○) and the '16.8 kbar-1' (●) curves and the lines give the corresponding theoretical curves with the parameters presented in Table 1 and in reference 1.

curve 0 kbar-1, the values of $|S_∞|$ become 1.05 for 0 kbar-2, 1.15 for 0 kbar-3, 1.22 for 0 kbar-4, then 1.085 for 10 kbar-1 and finally 1.275 for 16.8 kbar-1, 1.29 for 16.8 kbar-2 and 1.43 for 16.4 kbar-3 and 16.8 kbar-4.

(iv) No minimum in the $ρ$ vs $T$ curves has been observed at low temperatures down to 1.3K.

The variation of the magnetic resistivity $ρ$ with pressure in a given pressure-cycle can be accounted by the previous model of the Kondo effect with crystal-line field.¹ We have chosen to fit on Fig. 3 the two curves ‘0 kbar-2’ and ‘16.8 kbar-1’ which correspond to the same pressure-cycle, because, since there is an irreversibility in the resistivity, it is clear that there are less modifications in the material and thus in the resistivity, during a decrease than during an increase of pressure. Let us recall here the main points of the theoretical model which was extensively described in reference 1 and in reference 2 where it has been applied

to CeAl₂. The hexagonal CF of CeAl₃ splits the cerium level in three doublets of negative energies $E₁$, $E₂$ and $E₃$ compared to the Fermi level, separated by $Δ₃₁ = E₃ - E₁$ and $Δ₂₁ = E₂ - E₁$. The overall CF splitting $Δ₃₁$ is determined by the temperature of the maximum for the $ρ$ curve, while $Δ₂₁$ is estimated with a smaller precision and has to be a sizeable fraction of $Δ₃₁$. The $E_M$ values are then given by the LnT behaviour of $ρ$ for $kT > Δ₃₁$, through the determination of the exchange integrals $J_{MM'}$. Finally the ratio between the resistivities for $kT \ll Δ₃₁$ and for $kT > Δ₃₁$, leads theoretically to the evaluation of the direct scattering potential $U$ and also of the theoretical cut-off $D$.

So, we have obtained very good fits of the experimental results by the theoretical model of reference 1, from roughly 20K to room temperature. Taking the same fixed parameters as in references 1 and 2, we have determined with a good precision the values of $E₁$, $E₂$, $E₃$, $Δ₂₁$ and $Δ₃₁$, in order to obtain the best
<table><caption>Table 1. Values of the parameters used for deducing the theoretical plots of Fig. 3</caption><thead><tr><th>Pressure (kbar)</th><th>0</th><th>16.8</th></tr></thead><tbody><tr><td>E<sub>1</sub> (K)</td><td>-425</td><td>-430</td></tr><tr><td>E<sub>2</sub> = E<sub>1</sub> + Δ<sub>21</sub> (K)</td><td>-400</td><td>-335</td></tr><tr><td>E<sub>3</sub> = E<sub>1</sub> + Δ<sub>31</sub> (K)</td><td>-375</td><td>-325</td></tr><tr><td>U (eV)</td><td>0.29</td><td>0.34</td></tr><tr><td>D (in K)</td><td>700</td><td>700</td></tr></tbody></table>

fit to the experimental $\rho$ curves above 20K and especially the broad maximum and the high temperature LnT behaviour of $\rho$. On the opposite, the resistivity cannot be fitted at low temperatures by the theoretical model of reference 1 which always predicts a minimum of $\rho$ around 5K and a less rapid decrease of the resistivity with decreasing temperature at high pressures. Thus, the $D$ and $U$ parameters cannot be really estimated for CeAl$_3$ and we have chosen here a constant value $D = 700$K. The theoretical curves are plotted on Fig. 3 and the corresponding values of the parameters are given in Table 1.

Thus, the two physically important deductions coming from Table 1 and Fig. 3 concern the variations under pressure of the values of $|E_M|$ and $\Delta_{31}$. The overall CF splitting $\Delta_{31}$ increases by a factor 2 under a 16 kbar pressure, in contrast to the decrease of the CF splitting in CeAl$_2$.$^2$ The mean value of the $4f$ level becomes closer to the Fermi level under pressure, as it was already observed in CeAl$_2$,$^2$ cerium metal and alloys. The CF splitting does not vary at all with the pressure cycles, while the $|E_3|$ value would be a little smaller after the 4th pressure cycle than after the first one.

At last, we would like to discuss qualitatively the two preceedingly unexplained points: the variation of $\rho$ with the number of pressure cycles and the low temperatures behaviour of $\rho$. To answer the first point, we have made X-ray diffraction diagrams at room temperature on CeAl$_3$ samples which have undergone all the pressure cycles. These diagrams show new diffraction lines of weak intensity, in addition to the normal lines of the initial h.c.p. structure of CeAl$_3$ before the application of pressure. These new lines could be indexed on the DyAl$_3$ structure$^{4,9}$ and with a very neighbouring lattice parameter. The lines of the DyAl$_3$ structure can be indexed either on the

double hexagonal structure of type Ni$_3$Ti or on the rhombohedral structure with fifteen layers in their hexagonal unit cells as in HoAl$_3$. The sequence of transformations h.c.p. → $\delta$-$Sm$-type → d.h.c.p. → f.c.c., which is observed in pure rare-earths from Lu to La,$^{9,10}$ has been also looked at in the RAl$_3$ structures along the rare-earth series from La to Lu$^{4,9}$ and also under applying pressure on rare-earth metals and alloys.$^{11}$ This sequence of transformations has been accounted by a decrease of the difference $r_0 - r_{4f}$ between the atomic radius $r_0$ and the radius $r_{4f}$ of the $4f$ shell.$^{10,12}$

So, in the case of CeAl$_3$, applying pressure reduces drastically the atomic radius and gives probably rise to a small amount of the new allotropic DyAl$_3$-type form. The difference due to the new form of CeAl$_3$ inside the original h.c.p. structure enhances the resistivity and, since probably the amount of the new form increases with the number of pressure cycles, the resistivity increases after each cycle.

The second point concerning the behaviour of $\rho$ at very low temperatures is more difficult to explain. At normal pressure, the experimental decrease of $\rho$ with decreasing temperature is relatively smooth and could be roughly accounted by the model of reference 1 as shown on Fig. 3, although no resistivity minimum has presently been observed down to 1.3K. But, the very rapid fall of the 16.8 kbar resistivity at low temperatures cannot be explained by the model of reference 1 and could be perhaps attributed to a change from the magnetic and trivalent state to a less magnetic or even non magnetic state when temperature is decreased. This assumption has arisen from a comparison with the case of pure cerium where a discontinuous change from a magnetic to a non magnetic phase occurs with increasing pressure and decreasing temperature. In this approach, CeAl$_3$ would exhibit a continuous and sluggish change from the magnetic and trivalent state to a less magnetic state with a valency larger than 3 and then to a non magnetic phase, with increasing pressure and at sufficiently high pressure with decreasing temperature. The validity of such an assumption could be checked on the CeSn$_3$ compound which is already known to have a slight change of valency with decreasing temperature at normal pressure.$^{13}$

So, the variation of $\rho$ at high temperatures can be accounted by the model of reference 1, while the
variation of $\rho$ at very low temperatures or with the cycles is not presently unambiguously explained. To check the qualitative explanations preceedingly developed, work is in progress in the following

directions: study of the new allotropic form of CeAl₃, extension of resistivity measurements below 1.3 K in CeAl₃ and study of the resistivity under pressure of CeSn₃ compound.

REFERENCES

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La résistivité électrique des composés de CeAl₃ et de LaAl₃ a été mesurée de 1.3 à 300K sous pression jusqu'à 17 kbar. La dépendence en pression de la résistivité au dessus de 25 K a été expliquée théoriquement par l'influence du champ cristallin sur l'effect Kondo, tandis que la variation de la résistivité à basses températures ou avec les cycles en pression est qualitativement discutée.