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Submitted on 1 Jan 1978
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HEAT TRANSFER BETWEEN Ce SALTS AND
DILUTE 3He BELOW 50 mK
M. Chapellier
To cite this version:
JOURNAL DE PHYSIQUE
Collogue
C6,
supplement au n°
8,
Tome
39,
aout
1978,
page
C6-273
HEAT TRANSFER BETWEEN Ce SALTS AND DILUTE
3He BELOW 50 mK
M. Chapellier
DPh/G/SRM Orme des Merisiers BP n° 2 - 91190 Gif-sur-Yvette
Résumé.- Nous avons mesuré par la méthode de la constante de temps la résistance de transfert ther-mique entre du CMN pur, dilué au 1/10, du sel de HAPI et 3He (6,4%). Cette résistance est indépen-dante de la température pour les deux premiers sels et s'interprète par un goulot d'étranglement des phonons dépendant du champ magnétique. Il faudra connaître la capacité calorifique du dernier sel pour analyser son comportement.
Abstract.- We have measured by the time constant method the heat transfer resistance between CMN, dilute CMN, HAPI salt (Hexa-antipyrene iodide of Ce or CIP) and dilute 3H e ( 6 . 4 % ) . The resistance is temperature independent for the two first and is interpreted as a field dependent phonon b o t t -leneck. The behaviour of the third salt cannot be analysed for the moment due to the lack of know-ledge on heat capacity.
1. EXPERIMENT.- In the mixing chamber of a dilution
cryostat a cylinder of powdered salt with height equal to length is magnetized in a weak field (14 to
28 G ) and then demagnetized. The temperature of the
salt is recorded by low frequency susceptibility at
constant liquid temperature (measured by Pt nuclear
resonance at 250 k H z ) .
Experiments are done with grain size smaller than . 1 mm. The time constant T is extracted from a
decay which is a rather good exponential.
2. RESULTS.- They are shown on figure 1.
F o r CMN T < * T ~1 - 7 T*. = 1.7 ± 0 . 0 5 mK m m
F o r LMN.9 CMN.l T <* T 2 T*. = 0 . 8 ± 0 . 0 5 mK m m
For HAPI salt T <* T~ T*. = 1.9 i 0.1 mK m m
Fig. 1 : Equilibrium time constant T in seconds bet-ween CMN, dilute CMN HAPI salt and 3He at
6.4% versus T in mK. T h e r e s u l t s a r e e s s e n t i a l l y t h e s a m e if t h e t i m e c o n s t a n t a r e r e c o r d e d a f t e r a m a g n e t i z a t i o n ( o r a d e m a g n e t i z a t i o n ) t o a field o f 14 o r 2 8 g a u s s . T h e m i n i m u m m a g n e t i c t e m p e r a t u r e s a s c o m p a r e d w i t h t h e P t t e m p e r a t u r e s c a l e ( d e f i n e b y a K o r r i n g a l a w T i T = 3 0 m s K ) a r e q u o t e d a b o v e . 3. T H E O R Y . L e t u s d e a l w i t h t h e t w o f i r s t , f o r w h i -ch T i s p r o p o r t i o n a l t o t h e h e a t c a p a c i t y . F o l l o w i n g S t o n e h a m / l / t h e s y s t e m is r e p r e s e n t e d b y t h r e e b a t h s ( F i g . 2 ) w i t h t h r e e t e m p e r a t u r e s , t h e s p i n s a t T , t h e p h o n o n s w h i c h i n t e r a c t w i t h t h e m a t T . s y, p n _
(define by the occupation number p = £ e x p — ^ = Q k Tph
Cs =
Fig. 2 : The three baths model.
and the dilute 3H e the bath at T_, maintained
cons-13
tant by the dilution. W e can write for small
diffe-rence in temperature the linearized equation of heat transfer (U energy, C heat capacity)
where T is the usual spin phonon relaxation time
and T . is the time taken by a phonon to be
dU
Because
r
<<
T I
--$
decrease very quickly and
ph
then
A
normal T 1 ,
independent of the size of the sample
will be observed if
T
is much longer than the se-
1
cond term. It is not the case for these experiments
121.
"
b
We have then
T= T2
,
which for
T=
CS
'h
Cph
suggest
=constant
.
ph
This could be explained if
R
-
T =-
28 being the average dimension of the
Ph
v
grain. Each phonon emitted by a spin disappears in
the bath as soon as it reaches the crystal surface.
-
The spin interact only with phonons on speaking
terms with them, that is from w
= 0to w
=%
(Fig.
3)
being of the order of the local internal
field produced on one Ce by the others. Indeed we
have
w~
0
P(U)
is the density of mode of phonons of frequency
W.
In a Debye model and for
$
<
I
one can show
/2/ that
N number of atom in the volume
V
considered, UL Debye
frequency. We have C
=constant.
ph
Fig.
3
:Number of available phonons at frequency
wand temperature T and the part of the spectrum in-
teracting with spin. a)
H
=0
,
b) small H #
0.If we calculate
%
for CMN and dilute C m
from experiment and existing data on v and C (refe-
rence in 121) we find respectively
WL =124
MHz
and
=
32 MHz which compare favourably with the
electronic linewidth of these salts. The model is
certainly consistent with these experiments, consi-
dering the over simplified model (ignoring the g
anisotropy).
w
0
When a small field H
.
=-
is applied,the
Y
band of phonons is enlarged from
0
to
(U:+ o$)
l / '(see figure 3.b) C
and CS increase.
ph
The ratio
2
is
surprisingly a constant in
weak field.
ph
Concluding remarks
-
There is no magnetic coupling observed in these
experiments.
If the film of Keyston-Laheurte /3/ is
of
0
