KONDO-LIKE RESISTIVITY IN SINGLE CRYSTALS OF dhcp Pr AT MILLIKELVIN TEMPERATURES

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KONDO-LIKE RESISTIVITY IN SINGLE CRYSTALS

OF dhcp Pr AT MILLIKELVIN TEMPERATURES

M. Hauschultz, N. Andersen, M. Olsen, F. Rasmussen, K. Mcewen

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-860

KONDO-LIKE RESISTIVITY IN SINGLE CRYSTALS OF dhcp Pr AT MILLIKELVIN TEMPERATURESt

M.Hauschultz,N.H.Andersen, M.Olsen, F.B.Rasmussen and K.A.McEwen*

Physics Laboratory I, H.C. 0rsted Institute, Vniversitetsparken 5, DK-2100, Copenhagen, Denmark,

* Physisas Dept., University of Salfovd, Salford M6 4 WT, England.

Résumé._ La résistance électrique de Pr dhcp a été mesurée entre 15 mK et 5 K dans la direction C. En-dessous de 0,4 K nous avons observé une contribution de type Kondo. L'ordre nucléaire, comme l'indique le temps de relaxation thermique, est observé vers 25 mK dans un cristal, mais paraît ab-sent dans un autre.

Abstract- Electrical resistance of dhcp Pr has been measured between 15 mK and 5 K in the c-direc-tion. Below 0.4 K a Kondo-like behaviour is observed. Cooperative ordering indicated by the thermal time constant, which has been observed near 25 mK in one crystal, seemed to be absent in the present sample.

INTRODUCTION.- In dhcp Pr the crystal field ground states of the ions are singlets, i.e., non-magnetic. The ratio between effective exchange interactions and crystal field level splitting, however, appears to be close to the critical value for spontaneous magnetic order, since polycrystalline material exhi-bits an ordered state with transition temperature above

20 K /l/, while no such transition has been found in magnetic studies of single crystals down to 0.4K

111. Murao /3/ and Triplett and White / 4 / predicted that at low enough temperatures a subcritical system would order as a consequency of an effective nuclear exchange interaction mediated by hyperfine induced ionic moments and conduction electrons. In specific heat measurements, Lindelof et al./5/ have approa-ched this nuclear cooperative ordering and estima-ted a transistion temperature T„ between 25 and 30 mK. Since the transition involves a polarization of ions by nuclei it would be interesting to detect possible effects in the resistivity.

RESISTANCE MEASUREMENTS.- Our sample was a single crystal of dhcp Pr, approximate lenght 7 mm and cross section 1mm , cut along the c-direction. Cur-rent and potential leads were tinned, thin copper wires attached by ultrasonic soldering. The crystal was mounted directly in the mixing chamber of the dilution refrigerator and supported only by the leads so as to minimize strain. Temperature was mea-sured with Speer carbon resistors also immersed in the liquid.

Work supported by the Danish Natural Science Re-search Council. 1 9[ I 1 I | I I ! l [ 1 r I [ u I I I 1 1 I I j I H|19 Praeseodymium I single crystals / I ^ c - a x i s I '8- I -18 E *, I

!

f \

2 " ~ \ V -17

£ I \ J

4 \ \« /

~—

pr

' x \

7 5 - ~~--—r^+__+-+-+ ' L 1 1—I I i i 111 I I i I i i i 11 i i i I i i 11 0.05 0.1 0.5 I S Temperature / K

Fig.l : Resistivity of dhcp Pr in the c-direction Pr2 - this work. Pr 1 - data from /6/ Resistivity-was calculated from relative measurements by adop-ting the value 680 nftn at room temperature.

Results are shown in figure 1 ("Pr 2 " ) . From 0.7 K down to 20 mK resistance is seen to increa-se smoothly by about 15%. For comparison our pre-vious measurements lb I on the same crystal as used in /5/ ("Pr 1") have also been plotted, but displa-ced to make the resistance minima coincide. Pr 1 is a 7 mm long cylinder of 5 mm diameter, making the current direction less well defined than in Pr 2, and its axis is about 15° from the c-direc-tion.

THERMAL TIME CONSTANTS.- Using the resistance curve as a temperature indicator for the crystal, we can study thermal relaxation times if they are several minutes or more. The method is to change the mi-xing chamber temperature stepwise and monitor

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tal resistance as it approaches equilibrium. In Pr I /6/ it was observed that the thermal time constant increased steeply as the ordering temperature was approached. This phenomenon obvious- ly is connected with the increase in heat capacity of the crystal 151. In the present crystal, Pr 2,

similar time constants were observed only at tempe: ratures a factor of four lower than with Pr 1. At these low temperatures our resolution did not allow precise measurements

,

but to illustrate the stri- king difference between the two crystals we have indicated in figure 2 the observed range of relaxation times. Due to the difference in temperature regimes, the thermal bottle-neck may well be of different origin in the tx7o cases. The relaxation times observed in Pr 2 around 20 mK are up to an order of magnitude shorter than estimated under the assumption of a hyperfine specific heat of 1 J/mole K and a Kaptiza boundary resistance as between Cu

4 and He.

Fig.2 : Thermal relaxation time of two crystals of dhcp Pr.Pr 2

-

This work. Pr 1

-

data from 161, same crystal as studied in 151, showing cooperative ordering near 25 mK.

DISCUSSION

.-

In a quite narrow temperature range the resistivity varies linearly with ln(~-l), being indicative of a Kondo effect. The resistance contribution from possible magnetic impurities alone does no immediately seem 1arge;enough to explain the observed variation so one is led to involve the Pr- ions also. The elastic spin-flip processes associa-

ted with the Kondo theory are not allowed of the Pr-ions, being all in the singlet ground state at these temperatures. If, however, the Pr-ions may be polarized via a coupling either to the nuclei or to impurities of the Kramers type a channel for these scattering processes is opened. The former sug- gestion is ruled out by the size of our experimen- tal findings which are 5 orders of magnitude larger than estimated by a rough third order perturbation calculation. The second possibility seems more pro- mising for two reasons. First of all because the size of the anomal&es in the two samples scales with the residual resistivity, secondly because one Kramers ion (e.g.Nd) may produce a coupling with several Pr-ions 2nd thereby increase the effective number of scatterers 171.

Another possibility is formation of spontaneous- ly polarized clusters around the Kramers ions /7/ providing increasing incoherent scattering towards lower temperatures. Due to the extended temperature range of the anomaly in our experiments we conslider influence of critical fluctuations from a possible antiferromagnetic cooperative ion-nucleus ordering for unrealistic.

It should be mentioned in conclusion that a qualitatively similar anomaly has been found in low temperature resistivity measurements on a c-axis Tb-sample. 181.

References

/I/ Andres,K., Bucher,E., Maita.J.P..Longinotti,L.D.

and Flukiger,R., Phys. Rev. (1972) 313 121 Houmann, J.G., Lebech,B., Mackintosh,A.R.,

Buyers,W.J.L., McMasters,O.D. and Gschneidner, K.A., Physica 86-88B (1977) 1156

131 Murao,T., 3.Phys.Soc.Japan

2

(1971) 683 and 33 (1972) 33

-

14.1 Triplett,B.B.and White; R.M., Phys.Rev. (1973) 4938

/5/ Lindelof, P.E., Miller,I.E.and Pickett,G.R., Phys. Rev. Lett.

35

(1975) 1297

/6/Hauschultz,M., Andersen,N.H.,Pickett,G.R. and Rasmussen,F.B., to be published

171 Jensen,J., private communication.