Magnetic transition of solid 3He observed by polarized neutrons

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Magnetic transition of solid 3He observed by polarized

neutrons

Angélique Benoit, J. Flouquet, D. Rufin, J. Schweizer

To cite this version:

Angélique Benoit, J. Flouquet, D. Rufin, J. Schweizer. Magnetic transition of solid 3He observed

by polarized neutrons.

Journal de Physique Lettres, Edp sciences, 1982, 43 (12), pp.431-436.

�10.1051/jphyslet:019820043012043100�. �jpa-00232072�

Magnetic

transition

of

solid

3He

observed

_by

_polarized

neutrons

A. Benoit

_(*),

J.

_{Flouquet (*),}

D. Rufin

_(*)

and J. Schweizer

_(**)

(*) Centre de Recherches sur les Très Basses Températures, C.N.R.S., B.P. 166 X, 38042 Grenoble

Cedex, France

(**)

Département

de Recherche Fondamentale, C.E.N.G., B.P. 85 _X, 38041 Grenoble _Cedex, France

and Institut

_{Laue-Langevin,}

B.P.156 X, 38042 Grenoble Cedex, France

(Re.Cu le }er mars 1982, accepte le 23 avril 1982)

Résumé. 2014 On décrit des _mesures de transmission de neutrons

polarisés

sur une cible de 3He solide

faiblement

_polarisée.

Des

_{températures}

de 0,45 mK sont obtenues. Sur la courbe de fusion, ce résultat

permet

d’envisager

de réaliser des

_{expériences neutroniques}

en dessous de la

_température

d’ordre

magnétique.

On estime la résistance de

_Kapitza.

Abstract. 2014 Measurements of the transmission of

polarized

neutrons _through a

_{weakly polarized}

solid 3He target are

_{reported. Temperatures}

down to 0.45 mK have been reached. This

_permits

experimentation

on the

_melting

curve below the _temperature of the _magnetic transition. The

_Kapitza

resistance is estimated.

Classification

Physics Abstracts 67.80

A

_major

contribution to the

_{understanding}

of the

_{magnetic properties}

of solid

3He

will be the observation of

_magnetic

reflections in a neutron diffraction

_{experiment [1].}

The first

_problem

is to cool a

3He

_solid

_target

in the presence of a neutron

beam,

since the neutron

_absorption

cross section

_(y)

of

3He

nuclei is

high : a -

3 000 b for a

wavelength

of 1

A

[2].

In the same

_spirit

as Passel and Schermer

[3]

who have measured the

_{magnetization}

of absorbed

3He

nuclei on zeolite

by studying

transmission of a

_polarized

neutron

beam,

we have set _up an

experiment

with a

_{weakly polarized}

solid

3He

_target. Since the

_{susceptibility}

has been measured

previously

as a function of

_temperature

and of molar

volume,

these measurements

_{give, in}

_situ,

the

_temperature

of a

3He

solid

_target

in a neutron beam.

1. Considerations.~ - The basic idea for the

experiment

is that the neutron

_capture

occurs

only

for the

_singlet

state built _up

_by

the nuclear

_{spin I}

=

1/2

and _s =

1/2

of

3He

and of the

neutron. The neutron

_capture

_may occur

_only

for

antiparallel spin

_components of the neutron

and 3He.

_It

with

_respect

to the

_spin

_component of the neutron, n+ and n- are the number of

3He

nuclei of a

_target

of an area S of

parallel

and

_{antiparallel spin}

_component, the transmission of

No

neutrons is

_equal

to :

L-432 JOURNAL DE PHYSIQUE - LETTRES

[The

factor 2 takes into account the fact that the

_absorption

cross section is

_given

for random

spin

orientation]. Using

an

_absorption

_{parameter a}

defined

_by

where

_A,

V and x are

_{respectively Avogadro’s}

number,

the molar volume and the thickness of the _target, N can be written as a function of the

3He

magnetization

M normalized to the

satura-tion

_Mo

11

cx can be determined

_{by simple}

transmission

_experiments

at

_higher

_{temperatures.}

The

_flipping

ratio

(R)

between the normalized number of transmitted neutrons with _up and down

_polarization

is

_given

_{by :}

This

_quantity

will lead to a

_{magnetization}

measurement.

For a

_given

_target,

a is

_proportional

to

V -1.

The measurement of the neutron transmission

at

_high

_temperature

_gives

the

_density

of the

3He

solid.

_By

_{performing experiments}

under well known

conditions,

a molar volume

_gauging

can be

performed.

This has been realized

using

the

pressure versus volume relation of the

liquid

3He

phase [4]

where the pressure of the _target can be measured outside at room

_temperature.

By

observing

the

_change

in the neutron transmission with

V,

the molar volume of the solid

phases

can be determined. In our

_experiment,

the _accuracy reaches 0.5

_%.

It can be increased

using higher

count rates.

2.

_Experiment.

-

Using

a dilution

_refrigerator

of our own

_design

in

_conjunction

with a

copper nuclear

demagnetization

stage, we are able to achieve _very low

_temperature

_{(T ~}

0.3

_mK).

The

_experiment

was set _up on the neutron diffractometer of the Melusine reactor of CEN

labo-ratory of Grenoble. The _target is fashioned with 700

A

_powder

of silver sintered on two _copper

plates

of

_respective

thicknesses 1 mm and 0.3 mm. The

_target

is

_squeezed

between two aluminium

pieces.

The 800 Oe

_polarizing

field is achieved

_by

a

_{permanent magnet}

_{(Fig. 1).}

The curve of the

_gauging

of the molar volume is shown in

figure

2.

Using

these

data,

the pressure

is increased in the _{target up} to the chosen

_density.

The volume is

_continuously

measured

_during

the

_{cooling procedure}

which leads to the solid

_phase.

After a

_precooling

time of 48 hours down

to 10

mK,

further

_cooling

is achieved with the

_{demagnetization}

of _copper down a final field of 2 kOe. A lowest

_temperature

of 0.3 mK is reached

_by

_{the copper lattice. The} beam _{is open} after

a

delay

of 12 hours. The number of neutrons

_falling

onto the

_sample

is

_No

= 1.2 x

104

_n/s.

For a

_counting

time of 300 s, the

uncertainty

on R is 1.5

_0/00.

3. Results. -

According

to the

_strength

of the

_magnetic

Gruneiscn

coefficient,

Sm ~ " ~7 [5],

the Curie-Weiss

_temperature

and the transition

_temperature

decrease with the molar volume.

Figure

3

_reports,

in

_arbitrary

_units,

the

_{susceptibility}

data

_{corresponding}

to the two molar volume measured of 23.1

cm3

and 24.2

cm3.

Figure

4 shows the

_{corresponding}

_flipping

ratio as a function of the time of the neutron

irra-diation.

In the

_experiment

at the molar volume of 23.1

_cm3,

the maximum

_flipping

ratio was observed

immediately

after the neutron beam was

_opened.

_Thus,

this

_sample

did not _pass

_through

the

magnetic phase

transition at 0.45 mK. On the other

hand,

for the

_sample

at 24.2

_cm3,

where the

suscep-Fig.

1. - View of the low

temperature

experimental

set _{up. MC, S, CD, CC, HD, Hp} and T are

_respectively

the

_mixing

chamber _{filled up with silver} sintered _powders, the

_{superconducting}

switch, the copper

demagne-tization _stage, the

_compensating

coils, the _{demagnetization} magnet, the

_polarizing

_{permanent magnet} and

the _target.

tibility

shows

_clearly

that

_experiments

below

_{T N}

can be maintained

during

a time of At = 50 min. after the

_opening

of the neutron beam. The factor of 2 observed between the

_{susceptibility}

mea-sured at t = 0

( T

TN)

and the

susceptibility

maximum

(T

=

TN)

is in excellent

_agreement

with the

_{thermodynamic}

measurement of Hata et al.

_[5].

This proves that the

temperature

of the

target is lower than

TN before

the

_opening

of the neutron beam.

The observed time variation of M via the measurement of R is related to the available

_magnetic

entropy.

The initial linear increase of R can be understood

_by

a slow conversion of the ordered

phase

to the

_{paramagnetic phase}

at the

_ordering

_temperature.

After

_TN,

the slow decrease of R

down to

_equilibrium

is due to the fact that solid

3 He

reaches its maximum R Ln2 well above

TN

[6].

The

_heating

_power

Q3He

_{produced by}

the neutron

_capture

on

3 He

atoms can be estimated from the results obtained on the

_melting

curve.

_According

to the _entropy

_drop

AS - 0.4 R

_Log

2

L-434 JOURNAL DE PHYSIQUE - LETTRES

Fig.

2. - Observed check of the

linearity

of _{Log No/N} versus the inverse of the molar volume V. The full

circles are the values measured for the volumes of the

_{liquid phases.}

_{The open circle shows} how, in the solid

_phase,

the volume is deduced from the measurement of _Log

_No/N.

Fig.

3. -

Temperature variation of the

_{susceptibility}

_x. In full and dotted lines

_respectively

for Y = 24.2 cm3

and 23.1 cm3

_(see

reference

_[5]).

at

_TN

_[6]

and the measured time At below which the condition T

_TN

is

_realized,

a value

Q(3He)

= 8 _x

10- 10 W

is derived

through

the relation :

.

The energy loss

Q

of the

_charged

_{particles (proton}

and

_{triton) produced by}

the nuclear reaction

is

Q ~

1.3 x

10 - 9

W.

_Using

tables of atomic

_stoppin~

cross sections

_[7],

80

%

of this energy may be absorbed in silver. The

comparable

values of

6(~He)

and Q

may show either

parasitic

Fig.

4. - Time

dependence

of the

_flipping

ratio measured for V = 24.2 cm3 (full circle) and for V = 23.1 cm3

(open circle).

The time

_{origin corresponds}

to the

_opening

of the neutron beam.

heating coming

with the beam

_(y-rays,

fast

_neutrons)

or an overestimate of the role of the silver

powder.

Extrapolating

to infinite

time,

an

equilibrium

value of T ~ 2 mK seems to be reached.

Thus,

the

_Kapitza

resistance

_RK

between

3H~

and the silver

_powder

can be estimated from the

tempe-rature difference bT and the

_heating

Q(3He)

At T ~ 2

_mK,

the derived value of 6 x

105 m2

_K/W

is in excellent _agreement with the deter-mination of 5 x

105 m2

_K/W

_recently

_{reported by Mamiya et}

al.

_[8]

which is deduced

by

indirect relaxation time measurements. The concordance between the two results reinforces the interest of

_confirming

the anomalous

_temperature

_dependence

of

_{RK ~ T°~9}

found above

_TN

in refe-rence

_[8].

This _poses a basic

question

concerning

the mechanism which is involved.

4. Conclusion. - The

reported

results _prove the

_feasibility

of

_studying

solid

3He

_by

neutrons at _very low

_{temperatures,}

_notably

below

_TN.

Since

_Bragg

diffraction lines have been observed in similar conditions with

_signal

to

_background

ratio of five and

_good

statistics in 10

min.,

the

probability

of

_observing

the

_magnetic

structure is

_{high [9].}

This

_experiment

shows

_clearly

that

solid 3He

can be cooled down below 10 mK in a

_high

magne-tic field in order to

_polarize

neutrons.

The authors are indebted to the ILL

_{Laue-Langevin}

Institute for

_{performing experiments}

on the D5

_polarized

neutron

_{spectrometer.}

Previous measurements

_performed

on D1B and D4

at ILL and on

_D2

at the Siloe reactor of CEN of Grenoble have been very

helpfull.

We are

_greatful

for the

_stimulating

discussions with and the

_help

of Dr. D.

_Brochier,

Dr. P.

Convert,

Dr. P. Burlet and Dr. J.

_{Rossat-Mignod.}

Two of us

_(A.B.

and

_J.F.)

thank the «

_Physique

des Solides »

_laboratory

of

_Orsay

for

_allowing

us to use a dilution

_{refrigerator previously}

built in

_Orsay.

L-436 _JOURNAL DE PHYSIQUE - LETTRES

References

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[2] NIELSEN, J. Als. and _{DIETRICH, O., Phys.} Rev. B 133

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925.

[3]

PASSEL, L. and SCHERMER, R. I.,

Phys.

Rev. 150 ₍₁₉₆₆₎ 149.

[4]

GRILLY, E. R., J. Low _Temp.

_Phys.

4

₍₁₉₇₁₎

615.

[5]

HATA, T., YAMASAKI S., TANAKA, Y., KODAMA, T. and _SHIGI, T.,

Physica

107B ₍₁₉₈₁₎ 201.

[6]

HALPERIN, W. P., RASMUSSEN, F. B., ARCHIE, C. N. and _RICHARDSON, R. _C., J. Low _{Temp. Phys.} 31

(1978) 617.

[7]

WHALING, W., Handbuch der

_{Physik (Springer Verlag),}

Ed.

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S.

_Flugge,

XXXIV _{(1958), p.193.}

[8]

MAMIYA, T., SAWADA, A., FUKUYAMA, H., HIRAO, Y. and _{MASUDA, Y., Physica} 108B ₍₁₉₈₁₎ 847.