SURFACE MAGNETISM IN SUPERFLUID 3He

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SURFACE MAGNETISM IN SUPERFLUID 3He

P. Kumar

To cite this version:

JOURNAL DE PHYSIQUE Colloque C6, supplement au n" 8, Tome 39, aout 1978, page C6-279

SURFACE MAGNETISM IN SUPERFLUID

H e

P. Kumar

Department of Physios, University of Southern California, Los Angeles, California 90007, U.S.A.

Résumé.- On étudie l'effet de la transition superfluide 3He sur les propriétés magnétiques d'une

couche de 3He sur la surface des solides.

Abstract.- The effect of a superfluid transition in bulk 3He on the magnetic properties of a surface

layer of 3He are studied.

I. INTRODUCTION.- In recent experiments /1-3/ of 3He in confined geometry, the susceptibility of the li-quid has been found to contain a Curie-Weiss term with a ferromagnetic transition temperature.

Here B is the susceptibility of a uniform degenerate Fermi liquid (for temperatures above the superfluid transition temperature), the temperature T represents the ferromagnetic transition tempera-ture and the ratio A/B is proportional to surface to volume ratio with A amounting to a single monolayer. Expressions like eq. (1) have been seen for the li-quid 3He between mylar plates l \ l , in the interstices of fine carbon powder /2/ and between grafoil sheets /3/. Except for the fine carbon-powder, the system has a superfluid transition for the bulk liquid at a temperature higher than T .

In this paper, we analyse the following sys-tem. We consider a monolayer of adsorbed 3He repre-sented by a free energy F /A/,

where T is the transition temperature for the mono-layer, the surface magnetization m = u„ s , k_ .

' O . B 0 B is the Boltzman's constant and b is a measure of the saturation magnetization. This adsorbed film is coupled to a bulk liquid given by

FB = ~ f dr dr* s(r) K(r, r') s(r') - ug / dr s(r)

H(r) (3) where K is the inverse of the nonlocal susceptibi

-lity, s(r) is the dimensionless magnetization

(m(r)/\i„) and H(r) is the external field. The total

a

system is then written in terms of (X is a coupling constant)

which we. analyse for the effect of the bulk liquid on the surface magnetism. This is accomplished by writing an effective free energy F1 for the surface spins. We note that

F1 = F + f

s s

where the integral in the parenthesis is a functional integral. Eq. (5) represents changes in the tran-sition temperature as well as the effective-nuclear Bohr-magneton. We now look at them in detail.

2. NORMAL FLUID.- The simplest case is that of a normal fluid. The susceptibility is local and of short range ; the free energy is given by /5/,

|2

The coordinate z is perpendicular to the surface, N(0) is the density of states at the Fermi surface, a = (1 + z /4) where z.. is the Landau coefficient and C« is the characteristic exchange lengtti of the system. Eqs. (6) and (2) can be mini-mized simultaneously for equilibrium surface magne-tization. The differential equations that describe the magnetization are such that

Eq. (7) can be integrated subject to the boundary condition -~— 0, starting from a

distance far from the surface (S(-)

pN(O)H/a).

The integrated equation describing the surface mag-

netization so is found to be,

kB

[T

-

TJ so

-

qff

H +

bsi

with

and

3. SUPERFLUID BULK.- If the bulk fluid undergoes

superfluid transition then, at least in the B-phase,

the uniform susceptibility as a function of tempe-

ratures decreases with decreasing temperature. The

1

decrease is only for a small q however, for

q

>

5-

where

5-I

is the superfluid correlation length, the

system is normal and the susceptibility should be

that of a degenerate Fermi liquid. This implies a

rather complicated q-dependence and for thisreason,

we study the system in q-space. An added complica-

tion is the anisotropy of the susceptibility

we

overcome this by choosing the field to be parallel

to z the inhomogeneity direction. For eq.

(5) we now

have

and

(9)

The function f is evaluated in the usual

manner by expressing the delta function as an in-

tegral and changing the order of integration. We

have (with A

C

4 xq

i

ias

o

ia

f

- x

tn

~ d a e exp

xq ( H ~

- B ) ]

2AA

kT C Rn (21lkT

(10)

PO2

-

2s0

5

xq

HA

-

The relevant part of f is only the first factor.

Putting it along side eq. (5), we find the effective

free energy for the surface spins, (for H

H

6

(q))

4

and

The function A

CX can be replaced by

9 9

N(0) EO/

G

subject to an error of order c,/&

5

where

5

is the superfluid correlation length. Given

that X(q

0, T) decreases for T below Tc, the

implication on peff is clear. The reduction of

surface response as T goes below T should be ob-

servable in the ratio A/B.

ACKNOWLEDGEMENTS.- It is a pleasure to thank H.

Bozler, K. Maki and D. Vollhardt for many stimula-

ting discussions.

References

/l/ Ahonen, A. I.,

Kokko,

Lounasmaa,

Paalanen, M.A., Richardson, R.C., Schoepe, W.,

and Takano, Y., J.Phys. C

Solid State Physics

9 (1976) 1665.

-

/2/ Ahonen, A.I., Kodama, T., Krusius, M.,Paalanen,

M., Richardson

R.C., Schoepe, W., and Takano,

Y., in "Quantum Fluids and Solids" Ed. S.B.

Trickey, E.D. Adams and J.W. Dufty, (Plenum

Press, New York) 1977.

/3/ Bozler, H., Luey, K., Thomson, A., to be pu-

blished

978)

/ 4 /

Such a free energy could be derived in Guyer's

model, see Guyer, R.,Phys.Rev.Lett.g (1977)

1091. An interesting feature of this model is

the rather small value for b.