Adiabatic nuclear demagnetization: Two sophisticated experiments

8

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collaborators, today,

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whom

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students

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r'eo, o g n i t i o r ~ ,

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been

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}ornmuntty

internation~i

tlLaniemi

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important th<

[]Orl()r

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Ph~'mor' t :4 1

temper'atuPe

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higm

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order

of

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~tllle KlJrti1: ' plon~:<:rir]b] ~'xper irr:mnt (]t.mor~,:;trtth.d in t h i s tier,

talk

exolain

perfoPmed

ill

I sha!],

~l'ter .~

two O t a n i e m i nueie~r

brief

experimerlts,

demagnetization

intr'c,d~<,

the

feasibility

Fecentiy

that

wfficient

cr'yostat:~:

0378-4363/84/$03.00 © Elsevier S c i e n c e Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division}

batic

of' r]u(?le~lr ( o o i i n g , t',.~Krlger it '~ ~rl

demagnetization

r~ql]ires

by v6ry

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O. ld Lounasmaa / Adiabatic nuclear demagnetization

starting conditions. Indeed, when high field superconducting solenoids and dilution refrigerators became available a decade later, nuclear demagnetization soon developed into an important technique for refrigeration to the submillikelvin region of temperature. The discovery of the superfluid phases in liquid 3He made the development of nuclear refrigeration techniques both important and urgent. There was a clearly defined need to reach temperatures below I mK. In Otaniemi, construction of our first nuclear demagnetization cryostat was started in 1968 and the machine was put to work in 1970. In nuclear demagnetization experiments it is quite a different matter to cool the nuclear spins only, or the conduction electrons and the lattice as well. The situation becomes even more complicated if an external specimen, such as 3He, must also be refrigerated. The temperature of the nuclear spin system has been reduced in Otaniemi to 30 nanokelvins. The lowest conduction electron temperature, I believe, is 13 ~K, reached by George Pickett and his coworkers. The

9

Lancaster group also holds the record for cooling superfluid 3He; they have reached 125 ~K. In all these and many other nuclear refrigeration experiments, copper was used as the working material. Another favorite substance is PrNi 5. The hyperfine enchanced nuclear refrigeration technique was developed by Klaus Andres while he was working at Bell Laboratories. Very large machines were later built at JGlich and in Tokyo. GYROSCOPIC MEASUREMENTS ROTATION

ON

But it is now time to move on to the first of the two Otaniemi experiments which I promised to describe. Our ROTA cryostat has been employed, since 1981, for measurements on superfluid 3He in rotation, up to angular velocities near 2 rad/s. ROTA is a joint project with the Institute of Physics of the Georgian Academy of Sciences and with the Landau and the Kapitza Institutes of the USSR Academy of Sciences. So far our main effort on rotating superfluid 3He

OPTICAL DATA

:-R

RM

DILS

Fig. I. Schematic

SUPERFLUID 3He-B IN

illustration of the ROTA cryostat.

O. I

10

l.()Hndwnaa

.

hliahalic nttclcar ddmd,~Hcl[Zat/O~?

Eigure

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[ Fig.

his

2.

Photograph

involved

described

by

L, r e a k . the

] f'iow

in t:t~e ZIHe,

[)Vit[']#

paso

More

by

John

w i th

sessions done

Gait,me[ i

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1

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dilution

COPPER WIRE BUNDLE

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of

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d~,i

VESPEL ROD

EXPERIMENTAL SPACE

CONICAL" PRESSED CON

kUs

;ENTRIC

,

the a p p a r a t u s ; all <~i~ :r.ronie r o t a t e w i t h the (ryostat .

is

by [>~tL'c

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operated a

RINGS

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Fig.

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] ] ~ ~!rf-;!t;

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refriger~bor

it' :n - I r ' ]

ZINC HEAT SWITCH

)rt

a dilution refrigerator, a copper nuclear a n d c o m p u t e r i z e d m e a s u r e m e n t @l@(2tl'oni,;,%.

cryoadsorption

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~I

SOL;;

CONICAL PRESSED CONTACT

Sessiorl today.

The

~ W,

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by d i S O L i S S i ~ i

11.

Pr~K% ]

at

I:,i i: t J

gyr'< socop~e ~ : x p e r i

obtained

diagram

During rotation connected from the

be

at C o r n e l S ,

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group

t' [y

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afternoon.

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can

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GRAPHITE SPA

the

photorraph

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instruments

showr~ per

nuclear

stage

in

~he

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MIXING CHAMBER

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Eeppy's

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!.'xpiltiN

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Rudniok's

collaborated,

work

Krustus

technique

[r>2nts ,

w0rk

m{:daur{xmenl

properti~s

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by

NHR Hatti

shall

gyroscopic

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proper

h~liurn

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purity

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O. V. Lounasmaa /Adiabatic nuclear demagnetization

11

ly carried out in the following way:

The sample

was first cooled at rest well below the superfluid transition temperature. The cryostat was then rotated, at a p r e p a r a t i o n angular velocity £ , for about I min and then halted. During 5 minutes following the stop, the vibrational amplitude in the @-direction was recorded. The cryostat was then rotated in the opposite sense at the same speed and halted again. The average response to the two opposite r o t a t i o n s is our basic datum. We have made extensive m e a s u r e m e n t s of the angular m o m e n t u m at eight different pressures from 3 to 29 bar and at temperatures from 0.8 mK to T . c Figure 5 shows our data at 8 bar. We note that the L vs. ~ -curve separates into three regions: I)

For ~

~ ~ = 0.23 rad/s, L = 0; this is the c regime. 2) For a between ac and 2ac,

reversibl~

FLANGES WITH

L = (L c /~c p)(C - ~c )- 3) When ~ > 2C c, L = L cis the limit of the reversible region and L e e is the maximum p e r s i s t a b l e angular momentum. In regions 2 and 3 irreversible vortex formation occurs.

I

I

I

/

"~6

I

I

°--I

I

I

tl,

•

c

,44

oc

v J

2

I

I

Fig. 4. The ac-gyroscope.

The foot is thermally

0.2

connected to the nuclear stage. Top view of the toroidai flow channel is shown below. ducting solenoid; the whole drive system was placed inside a niobium shield. Capacitive detectors were used for m o n i t o r i n g the ~-motion.

0.4

I

0.6 0.8 ~p (r ad/s)

I

I

I

1.0

1.2

1.4

Fig. 5. The persisted orbital angular m o m e n t u m L in the ring as a function of the p r e p a r a t i o n angular velocity ~_ (= highest speed at which the cryostat was r~tated before it was stopped). P = 8 bar.

When the ring is driven about 8 at the resonant frequency of the ~-mode, a sinusoidal response results in the ~-direction, provided that there is an angular m o m e n t u m in the ring, caused by circulating superfluid. The r e s p o n s e is proportional to the m e c h a n i c a l Q-value of the ~-mode and to the angular m o m e n t u m L of the superflow in the ring. In our device Q = 20000 w h i c h is thus the a m p l i f i c a t i o n factor that one obtains in an ac-system by operating it at .resonance. M e a s u r e m e n t s of the angular m o m e n t u m were usual-

Much is already known about vortices in superfluid 3He as will become clear from the invited talk by Grigori Volovik in the afternoon today. When the cryostat is a c c e l e r a t e d above ~ it c becomes favorable to create vortices, probably in the form of rings, with their diameter of the order of the interstitial space. The rings expand, are cut to pieces, and become pinned to powder particles. It is this pinned vorticity that is r e s p o n s i b l e for the observed persistent angular momentum after the cryostat has been

12

O. F. Lounasrnaa I Adiabatic mtclear demagnetization

brought

Filled

to rest.

ments A careful was made

check for p o s s i b l e weak d i s s i p a t i o n in 3He-B at 8 bar pressure. In these

experiments first

the

created

cryostat

maximum in

angular

the

ring

at a p r e p a r a t i o n

momentum

by

slight

shift

boundary.

rotating

the

critical

larger

than

mm/s,

is o b s e r v e d

whereas

field

B-phase

angular

momentum

experimental

continuously

was again measured.

accuracy

there was no decay the

relaxation

excess

of

viscosity tude

450

lower

the same

of

I0%

hours

than

for

This

and

gives

for

a value

in

implies

in 3He B a

12 orders

of magni-

the normal

Fermi

liquid

velocity

at

temperatures.

The critical v e l o c i t y of the s u p e r f l u i d can, of course, be calculated from the measured eritiea[

An

A

much

more

c

temperature but a weak function varies between 4 and 6 mm/s.

interesting

situation

exists

the B-phase splits into two separate with different critical velocities.

Figure

6

illustrates

which

the phase

the boundary

between

diagram the

7.1

from

zero

the

field

has

the critical

to 6.3 mm/s when

!:h{~

to 4 mT.

equally

striking

the

large

new

latent

parable measured

heat,

of t h e

feature

phase

separation

1.5

to that of the latent

~J/mole,

transitiLm

curve

which

is the is com-

the B + A transition. W<" heat from w a r m up curves;

two examples are shown in Fig. 7, wh~r~ the temperature of the 3tie sample has been pLotte< as a function of time. The latent he~t i: manifested

7

[ -0.6~ '

by the plateau

in the warm-up

<:urve.

i

~p=1.20 rodls o~

above

I~ bar: regions into

from

the

from 5.2 to !%

effect:

decreases

of

triples

l the m a g n e t i c

and o p p o s i t e

is increased

across

angular momentum. We found that at pressures below 14 bar the o b s e r v e d critical v e l o c i t y is independent of of pressure: v

ii,

crosses

of 4 m']; a

our

the L-data,

of the s u p e r f l o w

is at least

the

Within

in

of the signal.

time

which

for 48 hours,

4 mT field

in R e g i o n

in Region

in

our rrt,:asur!~ while

in the position

the

velocity

a much smaller

field

in a magn(~t]e field

However,

2~ . The a p p a r a t u s was then brought to rest and c L was measured. After having kept the eryostat the

% <~r~ f r o m

Fig.

external

are data obtained

was

velocity

in

circles

made at zero

of 3He

two regions

i

:.

°

4 o6a m-

"

5 mm

g -0.9

064

of d i f f e r e n t critical v e l o c i t i e s has been drawn. Rather u n i m a g i n a t i v e l y we call the "outer" area time

Region

I and

ample,

at 23 bar

I is 7.1

the "inner"

mm/s,

area Region

the critical

while

II.

velocity

in R e g i o n

il v

e

For ex-

in Region

- 5.2 mm/s.

Fig. 7. Warm-up d i f f e r e n t values

curves of ~ ;

ct tile g y r o s c o p e ~t. two iu this experim~nt ~ :

18 bar and B = 4 sT. PThe FLateau, caus
,

i

l

SOLID

The new phase scopie

3O

20 Q_

NORMAL FER~4I LIQUID

~ I 15

I 2 T (mK)

The phase d i a g r a m of 3He, Fig. 6. two regions i and II of d i f f e r e n t structures.

is,

observed in

vortex

irl

o~,r" vyro-

general

appear

similar to that found earlier by our at 29 bar and r e c e n t l y e x t e n s i v e l y over' the entir,a pressure range. 'Yh~: NMR frequency shift and the disin the c r i t i c a l w~!oeity arc: b<~th

transition. I again refer talks by K r u s i u s and Vo]ovik.

I 25

showing

its

rotation-induced, but the t r a n s i t i o n t e m p e r a t u r e is independent of the speed at which the eryoslat was rotated. It thus seems that in both eases we are dealing with the same vortex eor'e

B-PHASE ~

boundary,

experiments

rance, very NMR group investigated jump in the continuity

10

by th~

the core

to the f o r t h c o m i n g

O. V. Lounasmaa / Adiabatic nuclear demagnetization

13

mixing chamber CASCADE NUCLEAR REFRIGERATION DIAGRAM OF COPPER

AND THE B-S PHASE

tin heat switch The second example that I shall discuss is our work on spontaneous nuclear ordering in copper; this research has been going on in Otaniemi since 1974 [3]. Over the years many persons have been involved in our experiments and in their theoretical interpretation. Our latest achieve-

Pt-wire-NMR thermometer first nuclear stage below the crosssection

ments on nuclear ordering in copper will be discussed in more detail during an invited talk by Matti Huiku this afternoon. Some of the theoretical aspects will be described by Aarne Oja in a post-deadline paper. We all know that electronic magnetism shows a wide spectrum of different ordering phenomena, extending from room temperature and above in iron to a few millikelvins in CMN. Because nuclear magnetic moments are over a thousand times smaller than their electronic counterparts

Jing

and because the interaction goes as the magnetic moment squared, analogous phenomena can be expected in a simple nuclear spin system only at submillikelvin temperatures. In

this

ation shield tetal shield

region it is meaningful to speak about

two distinct temperatures, the nuclear spin temperature T and the conduction electron temn perature T . The nuclei reach thermal equilibe rium among themselves very quickly, in a time characterized by the spin-spin relaxation process. The approach to equilibrium between nuclear spins and conduction electrons, in contrast, is governed by the spin-lattice relaxation time, which is much longer. According to Korringa's law, the spin-lattice relaxation time is inversely proportional to the conduction electron temperature. As a result, the nuclei, at sufficiently low temperatures, become thermally isolated from their surroundings. For example, in copper at 50 uK, the spin-lattice relaxation time is several hours. In the experiments that I shall discuss we are directly concerned with the nuclear spin temperature only. However, a low conduction electron temperature is indirectly important: It guarantees an efficient thermal isolation of the nu-

]1 solenoid iple ,=r support

Fig. 8.

The

YKI cascade

nuclear

refrigerator

two copper nuclear stages, all three working in series. In the latest version of our device, the first nuclear stage was made of a piece of bulk copper, with vertical grooves to reduce eddy current heating. The first stage contains effectively 10 moles of the refrigerant. Fig. 9 is a photograph of the cold parts of the apparatus.

clear spin system. For these experiments we have constructed a cascade nuclear demagnetization apparatus, which is schematically illustrated in Fig. 8. Our cryostat consists of a dilution refrigerator and

The copper specimen itself was employed as the second nuclear stage; it was connected to the first stage by welding, without any heat switch. By demagnetizing the first stage slowly from 8 T to 0.1 T, the conduction electron temperature

O. I'.

14

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O. V. Lounasmaa /Adiabatic nuclear demagnetization

15

retical calculations and our experimental measurements of s u s c e p t i b i l i t y as a function of temperature in the paramagnetic region both indicate that the ordered phase is antiferromagnetic. Figure

11

displays the entropy vs. temperature

plot for copper nuclear spins in zero field and at temperatures below 120 nanokelvins. The data show quite a bit of scatter but the transition, however~ is clearly documented. The critical

k

temperacure T = 60 nK, and the m e a s u r e m e n t s c extend down to about 30 nK. These are the lowest

Fig. 12. The single crystal copper specimen. The dimensions of the slab are 0.5 mm, 5 mm, and 20

temperatures ever reached. From the discontinuous drop in entropy at the first order transition one obtains 0.1 pJ/mole for' the latent heat.

mm in the x-, y-, and z-directions,

0.8

I

'

I

'

I

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16./.~

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z.O

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,

I

60

80

,

I

lO0

is stopped at 0.15 mT, the

,

120

In

T (nK) Fig. II. The nuclear spin entropy of copper, units of R£n4, as a function of temperature. single crystal specimen

demagnetization

susceptibility behaves during warm-up somewhat differently: the y-component increases approximately the same way as in zero field, but the z-component has changed a lot. The initial increase is almost 15% but the maximum is lower than for the x- and y-components.

/

Our

to warm-up in a different external field. Let us look at the figure more closely. In all cases, the x-component of the susceptibility is almost constant, until the paramagnetic region is reached in about 5 min. In zero field, the z-component displays a small increase after demagnetization, whereas the y-component shows an increase of about 10%. Presumably, if we could start the measurements at still lower temperatures, the y-component would be even smaller at first.

Io

U'l

respectively.

in

is a h a l f - g r a m slab

of copper; the sample was mounted, in relation to the external magnetic field B, as shown in Fig. 12. Separate transverse and longitudinal SQUID systems were connected to two astatically wound signal coils, m e a s u r i n g in the xy-plane and in the z-direction, respectively. Three different excitation coils, along the x-, y-, and z-axes, were used. Figure 13 shows some of our experimental results: the static susceptibility, as a function of time after the end of demagnetization, is plotted as measured in the three mutually orthogonal directions; each picture corresponds

a

final

field

of 0.20 mT the situation

is

again different: the y-component shows a 3% increase, while the z-component decreases rapidly with time. The e x p e r i m e n t a l l y observed differences, as illustrated in these three graphs, d e m o n s t r a t e that the spin arrangement of copper changes with the magnetic field. In fact, we believe that there are three clearly different antiferromagnetic (AF) phases. The first picture, corresponding to AFt, shows that in zero field the spins are aligned with the y-axis, i.e. perpendicular to the x- and z-directions. This conclusion is based on the w e l l - k n o w n fact that s u s c e p t i b i l i t y perpendicular to sublattice magnetization stays centant below Tc, while susc e p t i b i l i t y parallel to sublattice m a g n e t i z a t i o n decreases as the temperature is reduced. Differences of susceptibility in the x- and y-directions must be due to the flat-slab geom-

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the

z axes

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in

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tL > w t i , :

10

n

field.

r"i)~ r , ;

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.;t

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ru, c ~ : ( t

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i:.

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B=O15 mT

i, 0

I %-

en%

:'

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:

b2z

ion

'upper',

, I H ~ j f C r r ( ][r,t] ~[]k~

080

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.o 090

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:.

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third

- 1 ~,L4t'(

::,

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][r'~'ct]

*,,":molt,

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f,h]!

t, h e

try*

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: t i<,[:,

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~).1:. m':

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i-ml, itud_ri::l t![d

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:imJ

±SIC:

3,Trrlonstr

/ 4--'

Li:{:

Lhp

il 8

;.aF:p]L.

)UV

pi<'ture

t

I

x_. ~ -).:-~ ~

()!l

n

potnb

[k4' ti,

in

,

0

'L l~i I 0.2

...

I 0.4

, 06

SIRl.n4

diffe:'-

pr'oposcd

shown

AFI

0

flu

for

{m)h

[~'tg.

th<

r.~m(

three

arlLi£errom3~:Rp%ic

ctoris

,~ t z r s :

lq.

The

B L', d t ~ r > m l or'de'

:,1"

copper

irl

pr~as(,s, tr,mz~J'

i~>:)

i,

]r

~h
~,,

shaJov4~,J

~'4

i'~o,cr*<<:,

O. V. Lounasmaa / Adiabatic nuclear demagnetization

shielding prevented absorptive component of bility. Consequently, magnitude of the heat late the temperature dQ/dS.

us from measuring the the magnetic susceptiwe could not find the input needed to calcufrom the second law T =

In actual fact, the experimental situation on nuclear ordering in copper is more complicated than I have had time I;o explain. I again refer to Matti Huiku's invited talk for more details.

possible to stay far below I mK for days or even weeks. REFERENCES

I.

2.

It must be admitted, of course, that our entropy diagram of copper is still rather provisional and that the proposed structures of the phases must be verified more directly. This can be done, we hope, by neutron diffraction techniques. 3. CONCLUSION From these two examples, and from many other experiments to be presented at LT-17, it is clear that nuclear demagnetization has become a versatile method for performing many different kinds of measurements at submillikelvin temperatures. In Nicholas Kurti's experiment, almost thirty years ago, the nuclei warmed up to the starting temperature in two minutes. It is now

17

For

recent

reviews,

see N. Kurti, Physica

109&110B (1982) 1737; K. Andres and O.V. Lounasmaa, Prog. in Low Temp. Phys. 8 (1982) 221. J.P. Pekola, J.T. Simola, K.K. Nummila, and O.V. Lounasmaa, Phys. Rev. Lett. 53 (1984) 70; J.P. Pekola, J.T. Simola, P.J. Hakonen, M. Krusius, O.V. Lounasmaa, K.K. Nummila, G. Mamniashvili, R.E. Packard, and G.E. Volovik, Phys. Rev. Lett. 53 (1984) 584; J.P. Pekola and J.T. Simola, J. Low Temp. Phys. (to be published). M.T. Huiku and M.T. Loponen, Phys. Rev. Lett. 49, (1982) 1288; M.T. Huiku, T.A. Jyrkki~, and M.T. Loponen, Phys. Rev. Lett. 50 (1983) 1516; M.T. Huiku, T.A. Jyrkki6, M.T. Loponen, and O.V. Lounasmaa, AIP Conf. Proc. No. 102 (1983), p. 441; M.T. Huiku, T.A. Jyrkki6, J.M. Kyyn~r~inen, A.S. Oja, and O.V. Lounasmaa, Phys. Rev. Lett. 53 (to be published); for a list of papers prior to 1982, see O.V. Lounasmaa, Physica 109&110B (1982) 1880.