HAL Id: jpa-00217520
https://hal.archives-ouvertes.fr/jpa-00217520
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
KAPITZA RESISTANCE BETWEEN CMN AND 3He
AROUND THE mK
B. Hebral, G. Frossati, H. Godfrin, G. Schumacher, D. Thoulouze
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6,
supplement au n°
8,
Tome
39,
aout
1978,
page
C6-262
KAPITZA RESISTANCE BETWEEN CMN AND
3H
eAROUND THE mK
B. Hebral, G. Frossati, H. Godfrin, G. Schumacher and D. Thoulouze
Centre de Rechevches sur les Tres Basses TenrpSratures, C.N.R.S., B.P. 1SS X, 38042 Grenoble Cedex, France.
Résumé.- Nous présentons les résultats de mesures de résistance thermique à l'interface 3He-CMN. Avec 3He pur (< 100 ppm ''He) la résistance de contact présente un maximum vers 12 mK. Avec 3He
con-tenant environ 200 ppm ''He, la résistance de contact augmente jusqu'aux plus basses températures : ceci s'interprète par un affaiblissement du couplage magnétique dû à l'absorption préférentielle de "*He à la surface du CMN. Les résultats avec 3He pur sont également comparés pour deux tailles de
grains de CMN : en géométrie confinée des effets de taille semblent apparaître.
Abstract.- We present the results of thermal resistance measurements at the CMN-3He interface. With
pure 3He (< 100 ppm ''He), the thermal resistance shows a maximum around 12 mK. With 3He containing about 200 ppm ''He, the thermal resistance increases down to the lowest temperature : this is inter-preted in terms of a smaller magnetic coupling, due to the preferential ""He absorption at the CMN surface. The pure 3He results are also compared for two CMN grain sizes : in confined geometry size effects seem to play a role.
Some years ago it was discovered that the classical phonon heat transfer process was by-passed at very low temperatures by another mechanism in the CMN-3He system /]/. This was explained through
a magnetic coupling between the CMN electronic spins and the 3He nuclear spins /2,3/.
Later experiments using He samples contai-ning larger quantities of He impurities showed that the thermal contact was worse and below 6 or 8 mK the liquid sample was no longer in equilibrium with the CMN but remained at a higher temperature / 4 / .
We presented recently the results obtained for powdered CMN (grain size < 50 y) in contact with liquid He /5/ in an adiabatic demagnetization cell attached to a dilution refrigerator. We observed al-so an anomalously small thermal resistance with pure
3He, but not the T dependence expected from the
ma-gnetic coupling theory. We emphasized that this could be due to possible size effects originated in the small diameter of the pores and the small size of the grains tightly packed (81 %) .
We report here the results obtained in ano-ther demagnetization cell containing 20.7 g of CMN grains, with a well-defined size between 80 and
125 U. packed at 60 %, in contact with ^ 7 cm3 3He.
The estimated CMN area is about 1.5 m2. The
magne-tic temperature T is deduced from the CMN suscep-tibility measurement and a Curie law is extrapolated to the lowest temperatures (T ^ 1 . 8 mK).
Liquid 3He with two ''He impurity
concentra-tion was used. It is well-known that, due to the Van der Waals forces, the "*He atoms are
preferen-tially adsorbed at the CMN surface. With "pure"
3He (< 100 ppm "*He) the ''He amount is less than
ne-cessary to have a monolayer coverage of the CMN sur-face. With more "He (y 200 ppm "He) the CMN is co-vered by about two "He layers.
In the measurements after a heat pulse, the CMN temperature recovery is exponential. Assuming that both relaxation time in CMN and 3He are very short, we deduce from the measured relaxation time T the thermal boundary resistance R in a two bath
mo-T . — . del as R = n where the average specific heat C is
C given by :
- _ Sielium °CMN
r +c ' helium CMN
Above 10 mK the measured relaxation time is independent of the "He concentration. Below 10 mK, it ranges around 20 s with "pure" 3He but increases
to about 80 s at 3 mK with 3He containing 200 ppm "He. The respective thermal resistivities are shown on figure 1 where the present results are summarized together with previous ones obtained for grains of smaller size (< 50 u) : with pure He, the boundary resistance exhibits a maximum at about 12 mK, but with 3He containing 200 ppm "He the thermal
resis-tance varies as T-1'2. In this last case the thermal
contact between the liquid and the powder is good down to the lowest temperature : at 2 mK the resi-dual 1.5 erg/min. heat leak on the cell gives a AT 'V/ 20 uK. This is confirmed by the fact that the heat capacity measurements are not affected by the
3He purity to the lowest temperatures.
Our results with pure 3He are in good
\ \O
Kho\atnlkov theory
\
\,Fig. 1 : Contact thermal resistivity versus tempe- rature at the liquid He-CMN interface :
0 mixture 1 .l % 3 ~ e ,
A
3~e(200 ppm 'He) in contact with Cm(< 50 1-1) ; 13 3~e(< 100 ppm 'He),(200 ppm 'He) in contact with CMN(% 100 1-1)
ment with those obtained earlier /I/ corresponding on figure 1 to the solid straight line defined by :
7.5 X 10' T* cm2 K/W but the temperature of the ma- ximum is lower. They confirm the enhanced thermal contact between 3 ~ e and CMN at low temperature. At high temperature we observe larger values than ex- pected from the classical acoustic mismatch model
/ 6 / : as it may be seen we measure the same value, which seems quite general with powders 171, with a mixture 3~e-'~e containing 1 . l % 3 ~ e /S/.
The results reported here, are analyzed in terms of magnetic coupling in parallel with the classical phonon process. At low temperature in pure 3 ~ e the dipolar interaction between the local elec- tronic moments in the CMN and the nuclear . 3 ~ e spins by-pass the phonon process and is characterized by a T dependence /2,3/. This dipolar coupling behaves like a contact interaction on a distance in theran- ge of
A
the Fermi wavelength of the 3 ~ e spinsF0
(AF
8 A at 0 bar).With 3 ~ e containing 200 ppm 'He impurities the nearest 3 ~ e atoms from the surface are at about
6 or 7 from the CMN spins, due to the presence of
the two 'He layers. This decreases deeply the magne- tic interaction as obserbed from the experimental results and possibly modify the temperature depen-
dence (nevertheless the present theories do not ac- count quantitatively for the few existing data). This is also in agreement with our results with a
3~e-'~e mixture (l. 1 % 3 ~ e ) where the magnetic re- sistance, using a contact model, is expected to be at least 300 times larger than in pure 3 ~ e due to the smaller number of 3 ~ e quasi particles /2/. We observed in that case a T-2 variation, to about 4 m K ,
which may attributed to the phonon process in the powder and no maximum or curvature which would show the appearance of magnetic coupling. On the other hand the thermal contact above 10 mK is independent of the 3 ~ e purity because the "He covering of the surface may not affect strongly the phonon process.
I
With pure 3 ~ e and both grain size we did not observe the same results : a lower resistivity with the small grains (diameter of the pores 1-5 and a larger value varying as T with the largegrains
(diameter of the pores % 30 1.1). This could be inter-
preted as possible size effects in series with a smaller thermal contact resistance (such a variation of the magnetic term has not been yet explained in the small grain cell where the mean free paths both in CMN and in 3 ~ e become comparable to the size of the grains and of the pores in the millikelvin range. At high temperature the poor 3 ~ e thermal conducti- vity hides the contact thermal conductivity in the small grain cell.
These results have to be considered together with recent experiments on the longitudinal spin relaxation time T1 and the susceptibility of liquid 3 ~ e in contact with mylar or confined powders /8,9/:
the presence of adsorbed 3 ~ e layers gives a Curie- Weiss contribution to the 3 ~ e susceptibility disap- pearing when 'He impurities are added. Recent theo- ries relate these magnetic properties and the magne- tic Kapitza resistance 110,
111 leading to a new
approach of the heat transfer problem at very low temperature.X
References
/I/ Abel, W.R., Anderson, A.C., Black, V.C., Wheatley, J.C., Phys. Rev. Lett.
16
(1966) 273/ 2 / Leggett, A.J., Vuorio, X., J. tow Temp. Phys.
2
(1970)359
/ 3 / Mills, D.L., Beal-Honod, PI.T., Phys. Rev. (1974) 343
/ 4 / Black, W.C., Mota, A.C., Wheatley, J.C., Bishop, J.H., Brewster, P.H., J. Low Temp. Phys. (1971) 391
/ 5 / Frossati, G., Godfrin, H., Hebral, B., Schumacher, G., Thoulouze, D., Proc. ULT HakonL Symposium (1977) 306 / 6 / Khalatnikov, I . P I . , 21. Eksp. Teor. Fiz.
2
(1952) 687 / 7 / Bishop, J . H . , Cutter, D.W., Mota, A.C., Wheatley, J.C.,J. Low Temp. Phys.
10
( 1 9 7 3 ) 379/ 8 / Ahonen, A . I . , Kodama, T., Krusius, M., Paalanen, K.A., Richardson, R.C., Schoepe, W., Takano, Y., J. Phys. C
2
(1976) 1665
/9/ Godfrin, H.J.P., Frossati, G., Thoulouze, D., Chapellier, M., Clark, W.G., this Conference
/10/ Beal-Monod, N.T., Mills, D.L., J. Low Temp. Phys.
30
(1978) 289
