CARBON POWDER MAGNETIZATION THERMOMETRY FOR VERY LOW TEMPERATURES

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CARBON POWDER MAGNETIZATION

THERMOMETRY FOR VERY LOW

TEMPERATURES

C. Bastuscheck, R. Buhrman, B. Sarma, D. Mast, J. Ketterson, W. Halperin

To cite this version:

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JOURNAL D E PHYSIQUE

Colloque C6, supplkment

au

no 8, Tome 39, aotit

1978, page C6-1164

CARBON POWDER M A G N E T I Z A T I O N THERMOMETRY FOR VERY LOW TEMPERATURES

f

+

C.M. Bastuscheck and R.A. Buhrman, B.K. ~arma', D.B. ~ a s t ' , J.B. K e t t e r s o n

,

and W.P. ~ a l ~ e r i n ' Department of Applied Physics and MateriaLs Science Center Come22 University, Ithaca, New York, 44853, U.S.A.

Department of Physics and Astronomy and

MateriaZs

Research Center Northwestern University, Evanston, IZZimis 60201, U.S.A.

Rdsum6.- Nous avons d t u d i d l ' a i m a n t a t i o n s t a t i q u e d'un n o i r de carbone amorphe (Carbolac I ) en f o n c t i o n de l a tempdrature en vue d ' u t i l i s e r ce matdriau comme thermomstre 1 b a s s e tempdrature. Nous trouvons que l ' a i m a n t a t i o n s u i t une l o i de C u r i e au-dessus de 10 mK. Les mesures, e f f e c t u s e s dans une s d r i e de champs magnstiques, s u g g s r e n t un systsme paramagn&tique de s p i n 1 a y a n t un f a c t e u r g dgal

1

2.

Abstract.- We have i n v e s t i g a t e d t h e temperature dependent s t a t i c m a g n e t i z a t i o n of an amorphous c a r - bon b l a c k (Carbolac I ) f o r use a s a low temperature secondary thermometer. We f i n d t h a t t h e magne- t i z a t i o n obeys C u r i e ' s law above 10 mK. Measurements performed i n a number of magnetic f i e l d s a r e c o n s i s t e n t w i t h a s p i n 1 paramagnetic system w i t h a g - f a c t o r of 2.

I t has been a long s t a n d i n g requirement i n u l t r a - l o w temperature work t h a t c a r e be e x e r c i s e d i n t h e s e l e c t i o n of a s u i t a b l e secondary thermometer. Since t h e r e i s now c o n s i d e r a b l e i n t e r e s t i n t h e pro- p e r t i e s of s u p e r f l u i d 3 ~ e and s o l i d 3 ~ e i n t h e tem- p e r a t u r e range e x t e n d i n g t o 0.5 mK t h e thermometry requirements have become more e x a c t i n g . I d e a l l y t h e thermometer should respond a s r a p i d l y a s t h e helium sample can t h e r m a l l y e q u i l i b r a t e , have a low s p e c i - f i c h e a t , and g e n e r a t e a continuous r e c o r d of t h e temperature which should be determined w i t h h i g h p r e - c i s i o n . Although we s h a l l n o t a d d r e s s o u s e l v e s t o t h e c a l i b r a t i o n of t h e thermometer which can be .performed by comparison w i t h t h e v a r i o u s aspe'cts of t h e 3 ~ e phase diagram ; i t i s convenient i f t h e secondary thermometer f o l l o w some well-defined physi- c a l law. The temperature dependent m a g n e t i z a t i o n of t h e amorphous carbon b l a c k , Carbolac I , (Cabot Cor- p o r a t i o n ) s a t i s f i e s a l l of t h e above requirements i n t h e temperature range i n v e s t i g a t e d i n t h i s work e x t e n d i n g t o 7

&.

We have used SQUID magnetometers i n t h r e e se- p a r a t e experiments t o determine t h e temperature and magnetic f i e l d dependence of t h e m a g n e t i z a t i o n of Carbolac I. I n t h e f i r s t of t h e s e , performed a num- b e t of y e a r s ago, t h e m a g n e t i z a t i o n of cerium magne- sium n i t r a t e

(CMN)

and t h a t of t h e carbon powder were d i r e c t l y compared i n t h e mixing chamber of a

d i l u t i o n r e f r i g e r a t o r over t h e temperature range 40 mK t o 0.6 K i n v a r i o u s magnetic f i e l d s between 0.1 and 6.0 m t e s l a

.

We found a p r e c i s e l i n e a r re- l a t i o n s h i p between t h e m a g n e t i z a t i o n s f o t h e two ma- t e r i a l s s i m u l t a n e o u s l y determined w i t h two SQUID f l u x d e t e c t o r s . These r e s u l t s were s u b s e q u e n t l y ex- tended t o below 12

mK

i n a n o t h e r c r y o s t a t , where two SQUIDS were used w i t h one a s t h e n u l l d e t e c t o r i n a mutual i n d u c t a n c e b r i d g e and t h e o t h e r a s a , . f l u x de-

t e c t o r . The r e s u l t s of t h i s lower temperature work, performed i n e a r t h ' d magnetic f i e l d , a r e shown i n f i g u r e 1 where t h e carbon powder m a g n e t i z a t i o n i s p l o t t e d a s a f u n c t i o n of i n v e r s e CMN magnetic tem- p e r a t u r e , T$. A l l measurements were taken w i t h t h e r e f r i g e r a t i o n c i r c u l a t i o n stopped t o avoid t h e r -

disequilibri;. , , . ,

,

. ' x

' ,

r e s e a r c h was supported by t h e Research Corpo- TICMN ( K-I)

1

r a t i o n and t h e N a t i o n a l Science Foundation through _{Fig. 1} 5 0 100 150 : The m a g n e t i z a t i o n of carbon obeys C u r i e ' s g r a n t s

DMR

76-80847, DMR 76-05181, and

DMR

77-098 _law ₌_{( 2 , 6}

+ 0. 15) 10-6,T

(K).

79.

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Fig. 2

:

A universal curve

tion as a function of HIT.

function for

J = 1

and g

=

The effect of circulation at 35

?.I

moles s-'

is shown by the crosses in the figure. Data obtai-

ned in a warmup after a single-cycle experiment

from

1 1 mK

to 7

mK

are shown, but thought to be not

in equilibrium.

The 0.023

gm

carbon powder sample was packed

to 20

%

by volume in a 0.32 cm diameter by 0.64 cm

long chamber. The recrystallized, sieved, CMN fil-

led an idnetical volume to 50

%.

Using mutual induc-

tance bridge measurements and known coil geometry

/I/ in conjonction with a calibrated germanium re-

sistance thermometer we found the susceptibility of

the CMN to be

XCm =

(2.9

+

0.15) x I O - ~ / T

(K) in

excellent agreement with previous work /I/. Similar-

ly the carbon powder susceptibility was found to be

X

=

(2.6

f

0.15) x I O - ~ / T

(K) where the precision

of this measurement with the mutual inductance

bridge was 0.04 %

at 50

mK (1

s detection filter).

Of course, this precision becomes proportionately

better at lower temperatures.

To investigate the nature of the carbon pow-

der magnetization extensive measurements were per-

formed in the mixing chamber of a third cryostat

for applied magnetic fields

:

6.1, 11.6, 43.0, 64.0

and 86.0 mtesla. In this work the magnetization was

determined.with

a SQUID flux detector in the tempe-

rature range 18

mK

to 0.1 K as indicated by a nio-

bium shielded carbon resistance thermometer cali-

brated using CMN magnetization measurements and a

calibrated germanium resistance thermometer. It was

found, as shown in figure 2, that all the data fell

on

a

universal curve when plotted as function of

HIT, as might be expected for a non interacting

for the carbon magnetiza-

This fits

a

Brillouin

2. spin system. This magnetization data was fit tc

a

Brillouin function

M

=

Mo B3(x),

where x =

g ! ~ ~ J n / k ~ ~

and where the saturation magnetization Mo, the spin

3,

and the g-factor were treated as parameters. It

was found that J

= 1

and g

=

2 provided the only ac-

ceptable fit to the data. For comparison the Bril-

louin funcitons for

J =

'I2

arid

3/2

,

g

=

2 are also

shown in the figure.

An extensive literature exists on physi- and

chemisorbed molecular oxygen adsorbed to amorphous

carbon. It is probable that molecular oxygen with

spin

1

is contributing to our measurements. This

would correspond roughly to 5 oxygen molecules per

carbon particle of a 9

mm

diameter. Measurements of

the ESR absorbtion at g

=