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Submitted on 1 Jan 1978
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REINFORCEMENT OF THE LOW TEMPERATURE
SURFACE FERROMAGNETIC INSTABILITY OF
LIQUID 3He DUE TO THE ATTRACTION
BETWEEN 3He AND THE WALL. SUGGESTED
NEUTRON EXPERIMENT
D. Spanjaard, D. Mills, M. Béal-Monod
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6,
supplement au n°
8,
Tome
39,
aout
1978,
page
C6-293
REINFORCEMENT OF THE LOW TEMPERATURE SURFACE FERROMAGNETIC INSTABILITY OF LIQUID
3H
eDUE TO THE ATTRACTION BETWEEN 3He AND THE WALL. SUGGESTED NEUTRON EXPERIMENT*
D, Spanjaard, D.L. Mills and M . T . Beal-Monod***
Physique des Solidee, Universite de Paris-Sud, 91400 Ovsay, France
Résumé.- Nous présentons un modèle simple destiné à simuler l'attraction de van der Waals entre un substrat et un liquide de Fermi, plus spécifiquement l'3He liquide dans la région du milll-degré. L'état lié ainsi formé contre la paroi renforce l'instabilité ferromagnétique en surface du liquide dont le bulk reste paramagnétique ; on en déduit une susceptibilité du type Curie-Weiss en surface qui est observée expérimentalement. De nouvelles expériences sont suggérées.
Abstract.- We present a simple model to mimic the Van der Waals attraction between a Fermi liquid and a substrate, with special attention paid to liquid 3He in the milliKelvin range. The subsequent bound state formed against the wall acts to reinforce the ferromagnetic surface instability of the
otherwise paramagnetic bulk liquid, yielding a surface Curie-Weiss type susceptibility as is experi-mentally observed. Further experiments are suggested.
1. INTRODUCTION.- A number of experiments have re-cently appeared /l/ measuring the spin susceptibility of liquid 3He in confined geometries in the milli-Kelvin range. In contrast with the very weak tempe-rature dependence of the paramagnetic, Pauli type, bulk susceptibility (in the normal phase), the above measurements exhibit an overall Curie-Weiss behavior with an extrapolated ferromagnetic Curie-Weiss tem-perature 0 of the order of .5 mK ; moreover, this anomalous temperature dependence is suppressed by coating the surfaces with ^He. This particular
feature indicates that the Curie-Weiss susceptibility originates in a surface region of 3He close to the walls, and becomes measurable when the surface to volum ratio of He is sufficient. Due to the strong van der Waals forces between the substrate and He, the first (at least) layer of 3He against the sub-strate is a highly pressurized, close packed, two or quasi two dimensional solid 111 fit ; it is follo-wed by a high density fluid part /3/, one or possibly
two layers thick, before reaching the bulk liquid at normal density ; the number of layers involved both in the solid part and the high density fluid one essentially depends on the substrate. Below 1 mK a rounding of the experimental curves x versus T possibly extrapolating to 0 K, may be linked to the two or quasi two dimensional character of the 3He part responsible for the anomalous
Curie-Weiss contribution at higher temperatures. The solid part is so pressurized (y 400 atm.) that
the nearest neighbor direct spin exchange inter-action is of the order of the yK /4/ which would be difficult to reconcile with the observed 8 of .5 mK. On the other hand in the past few years it has been proved 151 that at the surface between vacuum and a nearly magnetic, strongly interacting, Fermi liquid a ferromagnetic instability can take place for values of the spin-spin interaction for which the bulk remains paramagnetic. When the above expe-riments appeared it was then proposed 161 that these new data could be the first experimental evidence of a ferromagnetic instability in the surface region of 3H e , more specifically in the high density fluid part. However, the question whether the Curie-Weiss law is only due to that high density fluid part, or could possibly be attributed, partly, or in totality, to the quasi bidimensional localized solid part, is not
comple-tely settled. In particular, a possibly non negli-gible indirect spin interaction / 7 / among the atoms of the solid layer might arise via the liquid, analogous to the R.K.K.Y. /8/ indirect interaction among paramagnetic impurities in di-lute metallic alloys, yielding, possibly, the finite ferromagnetic Curie-Weiss temperature. Or a vacancy induced ferromagnetic 19/ could arise in part of the solid 3He region, not too dense in or-der that vacancies could exist (which excludes the first layer), but dense enough to speak of a solid with vacancies (which excludes the high density fluid) ; although this appears tempting to describe * This work was partially supported by a Nato
contract
** Permanently, Physics, U.C.I., Irvine, Cal.92717 *** Until oct.78, I.L.L., av. des Martyrs,
38042 Grenoble, France
a submonolayer adsorbed on a substrate, its applica- by a matrix diagonalization procedure analogous to tion to the present case is less clear. At present, the one described in ref. / 1 1 / . We find in the well we feel that better candidates to explain the anoma- region a considerable enhancement of the magnetiza- lous Curie-Weiss observed susceptibility are rather tion in a uniform field (versus z on a fig, 1) :
the first solid layer with the indirect R.K.K.Y.
interaction via the liquid, and the ferromagnetic M(Z)lM(m) =
I
~ ( ~ l ~ ' ) ~ ~ ' / j ~ t ~ * ~ ' ) ~ ~ ' (3) instability of the high density fluid, Obviously ifit can be proved in the future that both contribute, they will certainly react on each other through mutual induced polarization ; however, as a first
step, one may consider them independently. In the present paper we confine our attention on the ferro- magnetic instability at the surface of the liquid ;
we show that accounting for the attractive forces between 3 ~ e and the walls all the more favorizes that instability. We end by suggesting experiments (neutrons in ~articular) which would be helpful to clarify the structure of the first couple of layers of 3 ~ e on a substrate.
2. THEORETICAL MODEL OF MAGNETISM IN AN EXCHANGE ENHANCED FERMI FLUID IN CONTACT WITH A WALL.- Ref.
/ S / studied, at 0 K, the static spin susceptibility of a nearly magnetic Fermi liquid with strong repul- sion I among the fermions, in presence of a surface described as an infinite barrier limiting a semi- infinite jellium. Translational invariance was supposed to be preserved parallel to the surface allowing to only account for breakdown of transla- tional invariance perpendicular to the surface and to reduce the problem to a one dimension, in the z direction perpendicular to the wall. Here, we consider in extra the actual van der Waals attrac- tion of the He by a real substrate ; we mimic that attraction by introducing a square (for simplicity) attractive well of width a (in the z direction) and depth-V.
,
between the infinite barrier and the jellium. We thus solve a one-dimensional Schri;dinger equation for the 3 ~ e particles in the potential V(z) = m for z = 0,-V for O f o r z z a (1)We obtain the single particle wave functions and the Green's functions. We conf ine our attention to that combination of V. and a, such that one has one bound state
h
the well. We then compute the free particle static spin susceptibility /10/ XO(z,z') and solve, also on a computer, the Bethe-Salpeter equation giving the non uniform susceptibility x(z,zt) in presence of the spin-spin interaction 1 :y(z,z1) = XO(z,z')
*
~XO(~,~'f) I x(z~',z')~z" (2)1.0.66 ( s c a l e x 1 0 )
I 2 3 z / a
Fig. 1 : Magnetization in a uniform field for two values of I = I/E < I
F c
We obtain the critical value I above which, while the bulk remains paramagnetic, the susceptibility near the surface diverges, yielding a ferromagnetic instability near the surface. With the parameters :
the Fermi energy of the liquid EF = 5 K, V. = 7.5 K, e
a = 3.6 A, we find :
-
being the first solid 3 ~ e layer to which the high density fluid is bound with the binding energy
(vol
= 7.5 K.3. DISCUSSION AND SUGGESTED EXPERIMENTS.- We have shown tha the 3 ~ e atoms of the high density fluid tightly bound to the solid 3 ~ e layer but free to move parallel to it, considerably enhance the spin susceptibility yielding the surface instability in that region to occur at a value of the bulk spin- spin interaction which is lower than in absence of a bound state and which assume a realistic value. Therefore the high density fluid part indeed parti- cipates to the observed anomalous Curie-Weiss susceptibility. The next step would be to compute the effect of three dimensional bound states to describe the localized array of 3 ~ e atoms of the first solid layer itself and the subsequent R.K.K.Y. interaction via the liquid in order to check if that layer also participates to the Curie-Weiss law or remains of pure Curie type down to 0 K, or exhibits a spin glass behaviour 1131. But this involves also the knowledge of the structure of these first few layers of 3 ~ e near the surface. So in order to proceed more quantitatively, we believe that neutrons data would be most helpful, (even at higher tempera- tures than .5 K below which the spatial structure will not change much, and even for 'He whose
structure should be analogous), to study the second layer of He on a variety of substrates (in particular
ZYX graphite).
References
/l/ See in this conf. : Ahonen, A.I. et al., Bozler, H.M. et al., Frossati, G. et al.
/2/ Nielsen, M. et al., J. Physique
38
(1977) C4-10; Carneiro, K. et al. Phys.Rev. Letters,21 ,
(1976) 1695131 See for instance Brewer, D.F. and Rolt, J.S., Phys.Rev.Letters
9
(1972) 1485/4/ Cowan, B.P. et al., Phys.Rev.Letters
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(1977) 165/ 5 / Muscat, J.P. et al., Phys.Rev., B11 (1975) 1437
/6/ BQal-Monod, M.T. et al., J.Low.Temp.Phys.
8
(1977) 175/7/ Maki, K. private com. and Sokoloff, J.B. et al. Proc.Fort.Col1ins Conf. (1977)
/8/ See for instance Yosida K., Phys.Rev.
106
(1957) 893/g/ Guyer, R.A., Phys.Rev.Letters
39
(1977) 1091 /10/ The complete details will be publishedelsewhere
/ll/ Kumar, P. et al., Solid State Commun.
11
(1972) 8551121 See in ref. 5 and Zaremba, E. et al., Solid State Comnun.
