Growth of third ferromagnetic solid 3He layer on graphite

with and without 4He pre-plating

Akira Yamaguchi*, Takamichi Watanuki, Ryuichi Masutomi1, Hidehiko Ishimoto

The Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan

Abstract

We have measured the nuclear susceptibility of 3He in Grafoil filled with pure liquid 3He over the pressure region between 0.6 and

31.38 bar and at temperatures down to 0.5 mK with a cw NMR method. The nuclear magnetization corresponding to the adsorbed 3He layers

on the Grafoil surface shows a strong ferromagnetic tendency with a periodic behavior as a function of liquid pressure. This observation is

attributable to the growth of third and fourth solid 3He layer with the liquid pressure increase. The pressure dependence of the Weiss

temperature indicates that the third layer is completed at 19 bar and the fourth probably at 28 bar. The results for Grafoil pre-plated by 2.5 and

3.5 layers of 4He are consistent with this scenario.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: A. Surfaces; B. Epitaxial growth; D. Magnetic properties

1. Introduction

3He atoms bounded on the surface of various materials

form a unique system to study two-dimensional magnetism.

In particular, 3He films adsorbed on graphite have been

extensively studied owing to the atomically flat surface and

large surface area of graphite [1]. The previous investi-

gations on the film have revealed that the first and the

second atomic layer solidify on the graphite surface, while

the upper layers above the second one exist as liquid [1].

The second solid layer displays a spectacular evolution from

antiferromagnetism to ferromagnetism as a function of the

areal density. The behavior is understood as a consequence

of competing multiple spin exchange (MSE) interactions in

the solid layer. In addition to the intra layer interactions,

there is a long-standing controversy on a possible indirect

interaction mediated by 3He quasi-particles in the

over-layer liquid. Theoretically various models are

proposed and most of the models predict the existence of

RKKY (Ruderman–Kittel–Kasuya–Yoshida) type indirect

0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jpcs.2005.05.038

* Corresponding author.

E-mail address: yamagu@issp.u-tokyo.ac.jp (A. Yamaguchi).1 Present address: Department of Physics, Tokyo Institute of Technology,

2-12-1 Ookayama, Meguro-Ku, Tokyo 152-8550, Japan.

exchange interaction [1]. In this paper, we present the

systematic study with a cw NMR technique for the solid 3He

layer on graphite covered with bulk liquid 3He as a function

of liquid pressure.

2. Experimental

The experimental setup is described in our previous work

[2]. The substrate used is an exfoliated graphite (Grafoil

GTY grade dZ76 mm) [3], which consists of partially

aligned microcrystals of graphite. Six Grafoil sheets

(8 mm!8 mm) are stacked in a sample chamber made of

epoxy (Stycast 1266). They are dipped into pure liquid 3He,

which is cooled through a sintered powder heat exchanger,

the mixture of Ag and Pt powder with the surface area of

24 m2. It has a good thermal contact with the copper nuclear

stage. The pre-plated samples with 4He were prepared with

the procedure described previously [4]. 4He gas was

introduced at 4.2 K while monitoring isothermal adsorption

pressure. NMR measurements were made with a continuous

wave method at 698 kHz. A static field of 21.5 mT was

applied in parallel to the Grafoil sheets and swept to cover

the whole NMR line. A saddle type rf coil wound around the

sample chamber (145 mH) produces an rf field paralleled to

the Grafoil sheets. Magnetization (M) was obtained from

numerical integration of the whole absorption line. The

temperature was measured with a 3He melting curve

Journal of Physics and Chemistry of Solids 66 (2005) 1482–1485

www.elsevier.com/locate/jpcs

A. Yamaguchi et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1482–1485 1483

thermometer (MCT) and a Pt NMR thermometer both of

which are mounted on the nuclear stage.

3. Results

Total 3He magnetization consists of liquid magnetiza-

tion, which is due to the bulk liquid in the cell and solid

contribution from the layered spin (not shown). The liquid

contribution increases with increasing liquid pressure.

Based on the expression for a three-dimensional Fermi gas

[5] with the known Fermi temperature ðT��F Þ [6], the

calculated pressure dependence well reproduces the

observed behavior above 70 mK.

Subtracting the estimated liquid contribution, the

magnetization for the localized spins is obtained for various

pressures as shown in Fig. 1. Here, the change of the liquid

magnetization due to a superfluid transition is negligible

because of much smaller liquid magnetization itself below

the superfluid temperatures than the solid magnetization.

The solid magnetization shows a ferromagnetic tendency

over the whole pressures range. The magnetization at

0.62 bar shows the weakest temperature dependence. Below

7.7 bar, the data exhibit a rapidly rising magnetization

around 3 mK and the temperature corresponding to the rapid

rise shifts to lower temperature with increasing pressure.

This shift continues to exist up to 19.35 bar, where the

temperature dependence is week and close to that of

0.62 bar again. The evolution above 19.35–27.62 bar

resembles that in the lower pressure region. The pressure

dependence above 27.62 bar is much weaker than in the

low-pressure regions.

What causes such a periodic behavior of the magnetiza-

tion? It is difficult to explain by RKKY interaction through3He quasi-particles, because the Fermi momentum is a

monotonically and weakly increasing function of the

pressure. The other possibility is solidification of the third

and the fourth layer with increasing the liquid pressure,

analogous to the liquid pressure dependent epitaxial

adsorption of solid 4He up to seven layers [7]. The adsorbed

atoms feel the pressure from the graphite substrate given as

12

Tempera

(b)

.5 .7

500

400

300

200

100

0

Solid

Mag

netiz

atio

n [a

rb. u

nits

]

12 3 4 5 6

10

0.61bar3.39bar7.35bar

12.30bar16.67bar18.14bar

(a)

.5 .7

Temperature [mK]

Fig. 1. Temperature dependence of the solid magnetization at (a) low pressures, 0.6

28.54–31.38 bar. The bar lines are guides to the eye.

follows

pðrÞ Z pL Cns

h

C3

r3C

C4

r4

� �: (1)

Here, r is the distance from the graphite surface and pL is the

pressure of bulk liquid. The second term arises from van der

Waals potential from the graphite surface where C3 (Z2.53!10K23 J nm3) and C4 (Z1.42!10K22 J nm4) are the

coefficients of van der Waals potential determined

experimentally [8]. h is a monolayer thickness and ns is

areal density which is assumed constant here. According to

Franchetti model [9], the liquid layer solidifies in the region

p(r)Ops where ps is the melting pressure of bulk liquid

(w34 bar). If we assume the monolayer thickness is 0.3 nm

and ns is equal to the maximum value for the second layer

(Z8.7 atoms nmK2), the solidification at the third and the

fourth layer position are expected to be completed at 19 and

28 bar, respectively. Thus, the present scenario seems to

reproduce the observed behavior, although it is believed

from the adsorbed film experiments that the only two layers

exist as a solid. Above 28 bar, the pressure dependence of

the magnetization is weak, and it is not clear whether the

fifth or more solid layers exist or not from the present

observation.

Based on the above-described model, the data are

analyzed at high temperatures where the Curie–Weiss

approximation is valid. In the low-pressure region below

19.35 bar, a three solid layers model is employed

MsolidðTÞ Z Cn1st

T Kq1

Cn2nd

T Kq2

Cn3rd

T Kq3

� �; (2)

where C is a Curie constant for each spin, n1st, n2nd, n3rd

are the amount of 3He atoms, and q1, q2, q3 are the Weiss

temperature for the first, the second, and the third solid

layer, respectively. According to the film experiment, he

first layer is highly compressed [1], being consistent with

the calculated pressure from Eq. (1) (p(r)O750 bar) at the

first layer position. Therefore, we assume n1stZ11.4 atoms nmK2, a maximum density observed in the

film experiment, and q1Z0 mK, independent of the liquid

pressure. In the same way, the parameters for the second

3 4 5 610

ture [mK]

19.35 bar19.61 bar24.03 bar27.62 bar

12 3 4 5 6

10Temperature [mK]

28.54 bar30.40 bar31.38 bar

(c)

.5 .7

4–18.14 bar; (b) middle pressures, 19.35–27.62 bar; and (c) high pressures,

60

50

40

30

20

10

0

n solid

[at

oms/

nm2 ]

302520151050P [bar]

n1st+n2nd+n3rd

n1st+n2nd+n3rd+n4th

n1st+n2nd

n1st+n2nd+n3rd

3rd layer

4th layer

Fig. 2. The total amount of solid 3He layer, (B) ntotalZn1stCn2ndCn3rd and

(6) ntotalZn1stCn2ndCn3rdCn4th. Vertical lines correspond to the third

and fourth layer completion. The horizontal dotted and dashed lines

indicate the amount of solid 3He corresponding to the second and third layer

completion.

5

4

3

2

1

θ [m

K]

302520151050P [bar]

θ3 θ4

3rd layer

4th layer

Fig. 3. Pressure dependence of the Weiss temperature, (B) q3 for the third

layer and (:) q4 for the fourth layer.

A. Yamaguchi et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1482–14851484

layer at SVP are estimated from those of the previous film

experiments to be n2ndZ8.7 atoms nmK2 and q2w1.5 mK

[1]. The liquid pressure dependence of these values is

unknown, but seems to be negligible. Because the first and

the second layer feel strong pressures much higher than

Sol

id M

agne

tizat

ion

[ arb

.uni

ts]

200

150

100

50

0

Sol

id M

agne

tizat

ion

[arb

.uni

ts]

121086420Temperature [mK]

pure3He

2.5 layers of4He pre-plated

3.5 layers of4He pre-plated

(a)

Fig. 4. (a) Magnetization at saturated vapor pressure for the sample with no p

magnetization for the 3.5 layers of 4He pre-plated sample under various pressure

34 bar from the graphite substrate and therefore their

densities should not be affected seriously by the liquid

pressure. Consequently, n3rd and q3 are two free

parameters which should be determined by fitting the

data between 0 and 19.35 bar to Eq. (2). Pressure

dependence of n3rd is shown in Fig. 2 as a total solid

contribution ntotalZn1stCn2ndCn3rd and the corresponding

q3 is shown in Fig. 3.

A relatively rapid increase of ntotal and the weak

dependence of q3 with a large value between 0 and 10 bar

should be attributed to the growth of the low-density third

layer, while a weak dependence of ntotal and a rapid drop of

q3 between 10 and 18.35 bar is possibly due to the

compression of the third layer.

In the higher-pressure region than 19.35 bar, a similar

analysis is made by assuming the growth of the fourth layer

and adding the term n4th/(TKq4) to Eq. (2). The first and

second layer parameters are assumed to be the same as in the

above analysis. As for the third layer parameters, the values

obtained at 19 bar are employed, n3rd of 8.1 atoms nmK2

and q3 of 1.6 mK. The results for n4th and q4 are shown in

Figs. 2 and 3. The increase of ntotal is similar to the third

layer region. The difference of ntotal between 0 and 28 bar is

almost the same with the ntotal at 0 bar, supporting our

assumption that the third and the fourth layer are added to

the two original solid layers. q4 does not show any particular

pressure dependence, being nearly constant, in contrast to

the large pressure dependence of q3 near the third layer

completion. Moreover, the value of q4 is large and

independent of the fourth layer completion. A possible

cause of this behavior is weaker adsorption potential at the

fourth layer position than at the third layer. Therefore, the

normal motion of 3He atoms to the substrate is enhanced

between the solid layer and the liquid. This situation is

favorable for investigating a liquid mediated RKKY type

interaction.

350

300

250

200

150

100

50

05 6 7 8 9

12 3 4 5 6 7 8 9

10Temperature [mK]

0.22 bar8.21 bar

10.03 bar19.85 bar

(b)

re-plating and those pre-plated with 2.5 and 3.5 layers of 4He. (b) Solid

s.

A. Yamaguchi et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1482–1485 1485

What happens for the 4He pre-plated samples? Fig. 4(a)

shows the temperature dependence of magnetization for

pure 3He, 2.5 and 3.5 layers of 4He pre-plated samples at

saturated vapor pressure, where the magnetization arising

from the bulk 3He liquid is already subtracted. The

magnetization are reduced by substitution of 3He in the

first and second layer with solid 4He. The 2.5 layers of 4He

is not sufficient to suppress the formation of solid 3He layer

probably in the third layer [10]. The 3.5 layers of pre-plating

eliminates most of surface magnetization except for very

small amount of solid-like magnetization, which is probably

due to 3He atoms trapped at the heterogeneities with much

deeper absorption potential than the flat area. Fig. 4(b)

shows the magnetization data for the 3.5 layers of 4He pre-

plate sample under various pressures. With increasing liquid

pressure a magnetization obeying a Curie–Weiss law

gradually grows in the same way as for pure liquid 3He.

The pressure-induced magnetization is attributable to the

formation of solid 3He layer in the fourth layer. The fitting

the high temperature data to a Curie–Weiss law gives the

Weiss temperature, qw3 mK. Both the Weiss temperature

and the simultaneously obtained Curie constant correspond-

ing to the number of 3He atoms have relatively weak

dependence on the liquid pressure, which is similar to that

for the fourth layer of pure sample.

In summary, the third and the fourth layer grow as a solid

with increasing liquid pressure. In our knowledge, it is

the first experimental evidence that more than two 3He

layers solidify on graphite surface. The upper solid layers

show a strong ferromagnetic tendency that depends on

liquid pressure.

Acknowledgements

This work was partly supported by a grant-in-aid

Scientific Research from Ministry of Education, Science,

Sports, and Culture of Japan.

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[3] Grafoils is a product of GrafTech Int. Ltd.

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[5] D.P. Grimmer, et al., J. Low Temp. Phys. 26 (1997) 19.

[6] H. Ramm, et al., J. Low Temp. Phys. 2 (1970) 539.

[7] S. Ramesh, et al., Phys. Rev. Lett. 49 (1982) 47.

[8] F. Joly, et al., Surf. Sci. 264 (1992) 419.

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