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LOW TEMPERATURE NUCLEAR SPIN
RELAXATION OF NORMAL LIQUID 3He IN
CONFINED GEOMETRIES
M. Béal-Monod, D. Mills
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6,
supplement au n"
8,
Tome
39,
aout
1978,
page
C6-290
LOW TEMPERATURE NUCLEAR SPIN RELAXATION OF NORMAL LIQUID
3H
eIN CONFINED GEOMETRIESX
M.T. Beal-Monod+ and D.L. Mills"
Physique des SoVides, Urdversite de Paris-Sud, 91400 Orsay, France
Résumé.- Des prédictions théoriques par les auteurs pour la variation en température du temps de re-laxation Tj de l'3He liquide normal en contact avec des substances magnétiques, ont souligné le rô-le des susceptibilités magnétiques locarô-les de part et d'autre de l'interface. Une comparaison entre ces prédictions et de récentes mesures à Grenoble pour Tj et la susceptibilité de l'3He liquide
con-finé dans différentes poudres, apparait très encourageante pour la compréhension du comportement de
Abstract.- Previous theoretical predictions by the authors for the temperature dependence of the longitudianl relaxation time Tj of normal liquid 3He in contact with magnetic substrates emphasized
the role of the local static spin susceptibilities on both sides of the interface. Comparison bet-ween these predictions and measurements recently performed at Grenoble for T] and the susceptibili-ty of liquid 3He confined in various powders, appears quite encouraging to understand the behaviour
of T,.
1. INTRODUCTION.- We recently studied the tempera-ture variation of the longitudinal nuclear spin re-laxation time T of liquid 3He in its normal phase,
at very low temperature, when the He spins are coupled to electronic moments in (or at the surfa-ce of)' a substrate. We investigated various cases : for the coupling, dipolar or exchange type ; for the substrate, disordered arrays of local moments, or ferromagnets near their critical temperature, or dilute metallic alloys of spin-glass type ; for the susceptibility of 3He, the practically constant (in the milliKelvin range) Stoner value of a nearly fer-romagnetic Fermi liquid or the anomalous Curie-Weiss type susceptibility recently observed, close to a surface, by various experimental groups /2,4/. This last feature was proposed to be attributed to a ferromagnetic instability inside the first few layers of liquid 3He near the walls /5,6/, which
does not exclude (see discussion in reference / 6 / ) , in addition, a possible ferromagnetic tendency of the two dimensional solid 3He sheet sticking on the surface. In reference /l/ we presented extensively the detailed calculations for T (T) in the various cases mentionned above, but we ended with a general discussion to show that the temperature dependence of T is directly linked to the ones of the
suscep-tibilities that the substrate and the 3He assume
locally near the interface (section 4 of reference /1,7/). We also showed that similar general con-siderations apply for the temperature variation of the magnetic Kapitza resistance R between the sub-strate and the 3He which we had previously studied /8/. We gave in reference /l/ simple aymptotic re-lations between T ,R^ and the static suscpetibili-ties of the substrate and the 3He near the
interfa-ce. In this paper we wish to compare our predic-tions with the recent data of Grenoble group /4/
who measured simultaneously T, and x (for pure u 3 He
3He and when a small amount of ^He coats the
sur-faces), for 3He confined into different powders.
^Since the substrates studied are so different and the data for T. behave so similarly, we propose that the measured relaxation rate has its source in the scattering of the 3He spins on disordered paramagnetic spins close to, or at the surface of, the substrate, via the magnetic coupling existing between them, as the scattering potential. Follo-wing such a picture, we show that one of the case that we studied in reference /l/ applies and can, at least qualitatively, allow to understand the observed behaviour for Tj(T) ; in particular, the crucial point of our comparison is that the very low temperature increase of T with increasing T is directly linked to the strong decrease of the inverse susceptibility of 3He, i.e. of the
anoma-lous Curie-Weiss behaviour, near the surface. ^ This work was partially supported by a Nato
con-tract .
+ Until October 1978 : I.L.L., ave des Martyrs,
38042 Grenoble, France
° Permanently : Physics, U.C.I., Irvine, California 92717 U.S.A.
2.COMPARISON BETWEEN THE THEORY OF REFERENCE /l/ AND THE GRENOBLE DATA.- We confine ourselves to a comparison with the Grenoble data since only those ones give simultaneously susceptibility and nuclear relaxation time results, in the same temperature range (a 3 to 100 mK) for liquid 3 ~ e confined in various powders : A1203, grafoil, (for Pt, only T
1 is given, but not X). The general behaviour for
~3~~ is the same %.that already exhibited in other experiments /2,3/ for 3 ~ e in confined geometries, when the surface to volum ratio of 3 ~ e is not ne- gligible :
x~~~
is strongly enhanced over its bulk Stoner value /g/, the anomalous part roughly follo- wing a Curie-Weiss law (with a Curie-Weiss tempera- ture < l mK). Correspondingly T 1 , at the lowest tem- peratures, first increases with T. For all substra- tes, when a small amount of 4 ~ e is introduced and coats the surfaces, the anomalous Curie-Weiss part of X is depressed, and, correspondingly, the magni- tude of TI is strongly increased, at a given tem- perature, compared to its value in absence of 4 ~ e . Moreover, while in absence of 4 ~ e , T continues to1
further increase at higher T, although less stron- gly than at very low T, in presence of '~e, it reaches a plateau around 20 mK, with a slight de- crease above, but only one point is available at 65 mK so that no definitive statement can be provi- ded there, except that T1 does not vary much above 20 mK in presence of 4 ~ e , whereas it goes on in- creasing, in absence of ' ~ e .
Our purpose here is to show that within the simple model of paramagnetic impurities (or possi- bly dangling bonds) on the surface of the substra- tes and the help of our calculations of reference /l/, taking into account the Curie-Weiss behaviour of X 3He(T) near the surfaces, we may reasonably un- derstand, on physical grounds, the low temperature behaviour of the observed Tl(T). In such a picture, from table I1 of reference /l/ the temperature de- pendence of l/T1 is qualitatively given by :
up to some minor temperature corrections. With :
A
x2(T) = ~3~~ = X
xBulk
+ AX = xB +-
T - 8 (2)where X is the small percentage of atoms with a
bulk susceptibility value, in the "surface" region B and A are constants.
It follows imediately that T1 increases li- ke l / ~ ~ ~ ~ , i . e . T increases with T, as is experi-
1
mentally observed, up to 10to 20 mK ; above X
Bulk itself starts to become temperature dependent /g/ and slightly decreases for increasing T, so that although AX becomes smaller and smaller, T con-
l
tinues to increase with increasing T. When 4 ~ e is added and coats the surfaces, two consequences fol- low : first, AX is strongly depressed since 4 ~ e has replaced most of the 3 ~ e surface layers responsible for the Curie-Weiss behaviour, secondly, the magni- tude of the scattering potential between the 3 ~ e spins and the surface spins is strongly diminished since the dipolar coupling is decreased by the third power of the 4 ~ e thickness ; these two featu- res amount to strongly reduce l/T1 and thus to strongly enhance T 1 over its value in absence of %e. This is indeed what happens experimentally. (Note that, in presence of 4 ~ e and if the coupling between the 3 ~ e and the substrate spins would be of purely contact type instead of dipolar, the 4 ~ e would completely inhibit the wall relaxation mecha- nism considered here). From the smooth curves that the experimentalists of reference /4/ drew among their experimental points, we deduce for the ratio of the product with and without 4 ~ e and for the grafoil substrate, a value which seems in- sensitive to temperature and would measure how much stronger is the 3~e/substrate coupling in the latter case compared to the former one :
p l ~ a
( 3 ~ e + 4 ~ e ) = 0.59 0.62 0.60 0.58 F 1 A ) ; I (3~e) (3) T(mK)= 4 6 8 10We wish that the experimentalists provide measure- ments of the kpitza resistance RK between 3 ~ e and the same substrates, in order to further check our predictions which suggest that one could expect (see table I1 of reference /l/) :
R~ = TIT (4)
It would also be interesting to have more experi- mental points within the decade above 20 mK, for the 3 ~ e against grafoil and A1203, in presence of 'He, in order to check whether TI (T) exhibit a ma-
ximum or just a plateau. (Data for x(~H~) against Pt powder would also be welcomed).
or dangling bonds on the surface of the substrate, the observed low T decrease of T1 for decreasing T is intimately linked to the increase (Curie-Weiss type) in r;ne susceptibility of 3 ~ e below 'l. 10mK,
while if x(~H~) would restrict to its Stoner type constant bulk value in that temperature range, then (l) would yield a temperature independent T
1' Such a direct qualitative agreement between our theoretical predictions and the observed behaviour for T1 and X of 3 ~ e near a wall allows to hope for a better understanding of the magnetic properties of 3 ~ e in contact with a substrate and consequently for low temperature cooling possibilities.
References
/l/ B6al-Monod,M.T. and Mills,D.L., J. Low Temp. Phys.
30
(1978) 289/ 2 / Ahonen,A.I., Alvesalo,T.A., Haavasoja,T. and Veuro,M.C., this conference
/3/ Bozler,H.M., Bartolac,T. Luey,K. and Thomson, A.L., this conference
141 Frossati,G.,Godfrin,H.J-P, Thoulouze,D., Chapellier,M. and Clark,W.G., this conference 151 B6al-Monod,M.T. and Doniach,S., J. Low Temp.
Phys.
8
(1977) 175/6/ Spanjaard,D., Mills,D.L. and BLal-Monod,M.T., this conference
/7/ Some misprints appeared in the published ver- sion of reference / l / : a) in formulas (54) and (SS), aF(zl)/azl and aF(z2)/az2 should be read instead of F(zl) and F(z2) ; b) the right hand side of formula (55) should be read as being multiplied by a factor of T.
/8/ Mills,D.L. and BLal-Monod,M.T., Phys. Rev. A10
(1 974) 343, 2473 ; Maki,K., ~6al-~onod,~.~: and Mills,D.L., Phys. Rev.,
