Towardsthe absolutezero
physicists
nature,using
Low-temperirture
aresurpassing
Pomeranchuk
dilutionrefrigeration,
coolingandnucleardemagnetization
phenomena
hithertounknownin the universe.
to investigate
OlliV. Lounasmaa
tdes bded on thes€colsideraiions. One
Low temperature physicists are con
stantly trying to extendthe temperahrre exahple involves looking aL very weak
to expedmenialinvesti- coupli.ss. When orderihginvolvesdelrangeaccessible
sations closerad .loser to tle absolute icaie and cohplicated ansular conela
tions,asit doesi. superfluidHe3 B, iiwill
,ero. While ihe ihird law ofthernody
nadics prevenisiheir everreachins0 X. be desiroyed very €asilr by incoherent
lhet have long since surpassedNature scatieringaDdwill appearonly whenth€
herself. The tempemture of the cosmic temperatur€is so low that th€ scattering
becksroundradiation is 3 K below 3 K, mechanisn is sufficienttyreduced.
The fornation ofCooperpairsin many
we are creatihg new physics. hitherto
unknown io the universe- And this has mel,alsand allo)'s the phenomenonof
superconductivity-takes place below 23
been done without aby lese erpenditues
of manpower or equipment the nost K. So far only S wavepairinc has been
sophisti.ated weaponsat the .old frontier obseNedithe sophisticatedP wavecouplinghas not be€nfoud yet. Thisnay
ofphysics arc inexpensiv€indeed.
There are furth€r good reasonsfor he due to th€ fact thet in real metals th€
P-wave interaction is eltreheb \reak and,
continuing tle endeavor. Such funda
meDiallyihportmt propertiesof malter consequently, that still lower temperas superconductiviiy and superfluidity tures ee neededto seeit. Equallywell it
is possiblethat P wavepaidng do€snot
occuronly at low tehperaiures. lt is al
says possible that ,ew, equally inteF exist in metals at all. On the other hand,
estins phenomenawould be found if se in supeduid He! P-wave.oupiins do€s
could nake neasurementsat liill lower
It is generally believed that P wave
tempelatures. A good example is the
dis.overy,l in 19r-2,of the supeduid pairing is most likely to be found in
phasesof liquid He3 below 3 mK. (By strongly paramagn€ticmetu]s,in which
cort.ast. Hea becomessupeduid at 2.2 erchangeoflong lived spin fluctuations
K.) Nuclearcoop€.ativepheDomena,,.3("lirtuat pa.amasDons")favors triplei
over singlei pairing. Of pure metalF
that is, nuclea. felrohagnetism and nu
clearantifeuonagneusm,coDstitutean palladium is the nost promising candioth€r example;temperaturcslessthd 1 date, bui. recent calculations showlhai ihe
njcrolelvin are neededfor investisations transition temperarureis ofthe order of
10 microkelvins. Two other systems,
-Another,less spectacularbut equally Ni Rh and ZrZnr, in whichthe degreeof
important .eason for elperiments near parahasneiism can be varied by chansins
the absotutezero is dr desireto study ],hecompositionor th€ externallyapplied
hatter uder conditions at which thermal presFure,respectively,apped io be more
disorder is snall. It is then possibleio prohising candidatesfo! experihehtal
investigale,lbr erample,th€ angulardisFrom the lheoreticalpoini ofviewthe
tribution of gammarars emiited ftoh a
main interesi in P-wavesupercohdu.ti!'
radioactivesourceof ofderednuclei.
ity is that exchangeof vi.tual paratuag
nons would probably oeate d disot.opic
Generally speaking,physicsheal the phase like supeduid He3'A. But the
absolutezerc is the physicsoforder, and currents found in such superconducto$
the mo.e sultle the type of o.der i6, ihe would coupledirecily io ihe eleciromagloFer is ihe temperatureneededto seeit. netic field dd would thus be huch nore
Anthony Lessett recentlydiscussed'the easilyd€tectedthan the electricallyneuprospects1br ihlestigatihg some inter- tral currents in He3. Ore could thus
esiing phenomehaat uitralow t€hpera- study the iopoLogicalpropeiiies of the
new superfluid phasein sreai detail.
Anoiher exampl€ that LeggeNidisprolessorollhe
OlliV. Lounashaais research
Academy ol Finand and directorol the Low cusses could be called "high ene.sy
Tehperatlire Laboralofyal the HelsinkiUnl- physicsat ultralow temperarure." Cur
rent theo es of €lementary particles
PHYSCSTODAY DECEMBEB
1979
predict very $eak srmmetry violating
efiecis (see,for etanple, "Cosnolosf od
elementay panicle physics"by Miclael
S. Turner dd David N. Schranm,
lHtslcs ToDAY, Septenber, page 42),
and ore could look for such effecis in
hishly o.dered superfluids. Fo. instdce,
one couldsiudy the elechon nucteo! interaction due to nedtral .urents, whi.h
is inva.iant under time reve$al bui noi
under spatialinversion,by neasuring1-he
eleciic dipole nonent ofHe3 B; in this
liquid the Cooperpairs h
exp€ciation value of the lector produci of
the spin and orbital angular momenta,
which is a condilionrequiredto makeihe
dipole noment neasurable.
Three new methods fo. cooling io 10
nK and below have rather recently be'
comeavailable. They de He3-Headjlution refriseration,Pomeranchukcoolns,
€nd adiabatic nuclear demasnetizationA dilution rehigeraior can mainiam
temleratures asior as 2 mK continuously
and in the presenceofa quite lsge heai
leak. Poner&chuk's method,coolinsby
adiabaiic compressio. of a liquid solid
mixture of He3,is capableof producing
temperaturcs down to t hK. Nu.l€ar
demasnetization has enabled experi
melters io reach a spin temperat$e of 50
nK ed io cool coEductionelectronsin a
metal to a tedperature of 50 mic.okelvins
Fisure I showsan ermple of this type ot
I shall now desc.ibethesetechniques,
emphasizinsnuclaar refrigeration, and
exDerimentsai ihe lowest presenuyac_
c€;sibletemperatures,including sevetal
€xamplesof recent results. For mo.e
details on lechhiques, refer to mY
Dilulionreldgeration
The operatinglrinciple of ihe dih't'on
rcf.ise.ato. is based on the pecuxar
Cascadenuclearrelrigeratorco.slructedano
5laboraiory n Finlano
operatinaIn Lounaemaa
The super.ondu.tin! magnerzseemblr'(bluer
afd the radalion shieldsare belns nstareo'
The nucear spin systemol copper has beeo
cooedto50 nanokevn n this apparalus rv
rurrher
deraiLs,
seeI lures and.i","lrT"; i
does. Consequentl!, one ftay describe
the Hea ih the dilure phase as a "sdpporting m€djum" or "mechanicalvacu'
trh" for th€ "dilute gas" of active Her
We can now explain the operating
pri.ciple ol the dilutjon refrigerator by
comparingit sith ordinary evaporation.
1'he concentratedphase of nea.lt pure
Her, {here rhe active atoms are closetogeiher,.orrespondsto the liquid phasein
the evaporationrefiiseraior. The dilute
phase,in which the Hdr atoms are sepa.ated b] superfluid Hea,coresponds to
ile vapor phase in the evaporationre
f.ige.atoi. In both cases,energy is re
qui.ed to separateihe atons becauseof
ati.active torcesahongthem; so moving
holeculesupivad fiom the liquid to ihe
vapo. phaseior atoms of Hetrdownward
from the con.ehtrated to th€ dilute phase,
lowe.s the tehperature of the liquid or
concentraied phase. By constantly
pumping molecules f.om the vapor in the
evaporation reftigerator or He3 atoms
fioh the dilute phasein the dilutjon refrigeratoi-one ce producea subsi&tial
For instance, the cooling power under
idealconditionsis givenby the difference
between the heat ca.ied by He3 fron ihe
last heat eachangerDd the coolingp.o-
Q='ir(ao-ac)
wbe.€n 3 is the circulationnte of H€3,,tlD
is the enthalpy of the diluie phaseat *e
temperatureof the mixing chanber, ?M,
and ,,rc is the enthrlpy of the concen
traied phse at the temperatu€ of tbe last
heat exchanser,?N. The enthlpies cd
be deternined from the p.ope.ti€s of
liquid He3;they are proportionsl to th€
squaresof the temperatures. Putting in
the vslues for the proporiionaliiy con-
P H Y S C ST O D A Y/ D E C E M E E 1R9 7 9
l
2
t
t
2
3
Q = ,3[(e5 J/K',no])"M'2
- (13 J,4t'mol)7N'z1
For a perfect heai exchaDger,7M = ?-.
tr
Q = t3(82 J/K'nol)?M:r
;
,I
p
The coolingpower is proporiional to the
squar€ of the mixing chanber tempersItis noweasyto seeihe importanceof ture. This is $hy the externalheat leal{
the 6..1E0
solubility ofHe3 in Hea. In ah eveniually catchesup ed further.ooling
ordilary evaporation refrigeralor the siops, even though the consiant 6.470
vapor phasebecomesdepleied of n1ole- solubjlity of ger inio liquid Hea ensues
cules rathe. soon, becausethe vapor that d3 is not a function of 7M.
(schematic).pressure
dilutionrelrigeralor
CoNenliona!
Heliun dilution .ef.iseratorshar€now
decreaseserponentially wiih
Toincrease
thethermalcontactarea,thefrain tenperature, whereasin the dilution .e
been in senersl use for nore than a dechealexchanqers
arelllledwitha sinteredcopper
polver
withclearholesinthefriddle fijgerator the concentration of He3 atoms ade. During this time their cooling
orsilversponge,
factor
100
ahd
the
phase
has
indeased
by
a
of
in
th€
dilute
remains
constant
as
2
flowofhe ium-3. FiSure
1oranlnimpeded
low t€mpemiure limit has been pushed
th€ temperature is lowercd below 40 nK.
Thus, the nunber of H€3 atoN that cross from 10 to 2 hK. The dilution refriserth€ ph6e bomdny per unit time is in
aror has already fully established itseH as
the DoBi importaht iool for reseach ai
propertieselhibited b! mixiu.es of He3 dependentof temperature.
The pdncipaL paris of a dilution !e- uliralow tempe.atures, replacins adia
and He1 ai Low temperatues. Below
ebout 0.8K aliquidmiltur€ ofthese iwo friserator are schemaucallyiilustraied in batic demagnetizationof paramagnetic
isoiopesspontaneouslt sepaates iniio two fisur€ 2. Cooiinsby diluiior is achieved sslts. MdJ experiments ihat wodd hav€
components,one of the phasesbeingrich in the mixiDgchamber. The process.an been difficult or impossiblebelo{ 0.3 K
in He3and ihe oiher ich in Hea. Becaue be nade continuousby circulatinsHer in ae .ow perfo.med routihely with dilution
of its low€r density, the H€3 dch phase the systemby a pump ai room tempeia'
H€inz London firsi suggeited the
ture. Incominggasis first precooledand
floats o! top of ihe Herrich phase.
As the tedperature is loweredfurther, ljquefied in the condenser,which G at- principle of ihe dilution refrigerator in
the .elative ahounts of He3 and He4 in iachedto the He4pottuaibtainedatabout 1951ihe, iogethe. wiih Geoffrey Cldke
ihe filo phaseg.hange; b€low about 40 1.1 X. The He3 then ente6 the still end. Edc Mendoza elsborated on ihe
mK the upper, or concentmtedphaseis heat exchanger{whereiis energyis given suesestionin 1962. Pankej Das,Rudolf
practicallypure Her andihelower, or di- io evaporaieHe3 on ihe r€tum paih) at d€Bruin Oubote. and Kijn Taconis buiti
luie phse is made of 6.4 atomic perceni about 0.7 X and passesthrough a sei of the first dyostat of this twe at Leiden rn
of He3dd 93.6c'of Hea. The possibiliiy heat exchangersto cool it further before 1965;it wasableto rcach0.22K Wiih'n
a vea Boris Negaov, Nicolai Boisov 8nd
of dissolving a la.ge amount of Her in ii enten the mixing c anbe..
-{fter dossing the phase boundary Mihail Libury atDubna asweil asHenrv
liquid He4 evenai ihe absolutezerc is of
at
laramount importancefor the successof ihere, the He! atohs, driven by an os Hall, Pete. lord and Keith Thompson
motic pressuregradient, proceedin re- Manchesterbuilt dilution machinesca
tbe diluiion retuisentor.
The other dejor reasonfor ihe slccess verseorder throughthe heatexchange.s, pable of rcaching much lower temperaof th€ dilutjon ref.iSerator comesfroh the alons an unbroken column of ihe dilute tures. JolD \Vheatley, mong others, hs
renakably diftereni lowtemperature superfluid phase,to the still Fhere ihe done a considerablemount of develop
rneni llork at the Unive$ity of Cslifornia
behavlor of liquid Hea and llquid He3.
Becauseofits zeronuclear$pin,an atom
Vapor is renoved from the still by ai SaDDiego. I have recently Miiten t
pumping, which is how He3 is separated shori reviewon ihe subject.6
ofHea js a boson;beloF about 0.5 K,liq
Gioryio F.ossati and his coworkersat
uid Hea is, effectiveiy in iis quanium' iiom Hea: Becausethe vapor pressureof
nechanical ground sta'ie. Veiy few Hea is almosi neslisible even at 0.? K, G.enobl€haverecentlybuilt a refrisela
lhonoN are exciied and the liquid is a more than 90E of the outcominggas is to/ that reaches2.0 mX in continuous
ihermell! ine superfluid. The lisht He3 if a suitahleorifice for reducinsthe operation;this is the lowesttempe.aturc
so fsr producedbv the diLulionmeinod
isoi.ope,
He3,hasa nuclearspin of %; it is flow of l,heHe+filh is installed.
The Grenoble sroup has worked lbr nany
the
refrigerator
fernion
and
does
noi
erhihit
The
analJsis
of
a
dilution
thus a
sort of slnple Bose condensationHea can be pui on a mo.e quantitative basis. ]'€ds and wiih goodreslli. to improte ihe
34
I
k,
F
iI
0
;,
t
tl
H
P.
a,
pertbrnlhce oI dilutior cryosiats. The
successof ahy dilurion refiseraior dete..jd. crtri rll\ on tlF rannnr tjon dnd
e t r e r r r e n t s $o t t h e h e a t e i . l r J . g e r s ,o n
Llr noble.reiiserrtor shich js srrrtar
schFDdrictt]ja tjeure
r r n en m i 4 L h a b g o I d i l j n s \ e r yf i n e
3rver powoerto hcreasethe cohiacirrer
bPis@. liqujd H. rnd ihe exclanger
oooy. rne renperrture of ti€ hert e\
ctla.Lger.sl,ageej as measlred irom rhe
d r n - o n i n s d i l u r e m r r r e j d e . e a s e jr n
r n e r o r ^ 1 1 r nsg€ q L r e r c e2. 5 . 6 . j _4 . 0 .2 7
Il.1ld20hX.
T h e c o o l j n s p . $ e re, , r s
runw qlth Bgr, cirrutrtj^, n),t2A\)
O/urion oyosrais cd easity be adapred
to vanous erp€rimental needs. A sood
eldmD\€ ls \,\e \saibNa\
re\\Eeialsr
built by Tapio Nii.ikoski.s The ;uslat
.onsi ction was diciated by the geome
try ot magnet pole pieces and by ihe
counung-auang€rnentslor experihenrs
o n s p r ni . o z e . . p o t a r i z epdr o r o nt a r g e i s .
has a very larse coolirs
lower 10 -D\V at 200 DI( wilh rr = 7
erdpt€.
Ilnre hDiral
\alue. f.r drluion re&iser.t!6;ft 20
hrcroiratf at 20 mK, 600 mic.owari at 100
n1r, rhd 2 milliwatr at 200 nX
A very imporiant use of ditution ma
chinesis the prccootingofponeianchuk
retige.ato$ and rhe vadous kihds of
nuclea..etrigerato$,whichneedstarring
iemperaturesbeiween 10 abd 30 hilli,
Poftersnchukcooting
In 1950IsaacPoneranchuk proDosed
a reiiiserato. tased on adj;baiicetiv
c o h p f e s s i l sl i q u i d H e l t o a s o t i d . y u r i
Anutrievbuilt rhe tirst toneranchuk
rehge.ator in 1965at Moscow
F l g u e 3 s } o \ , t h e p h a s ed r . g r a b o f
-.
r L e . N . r r c et h c i t h eq t o p eo f t h en e t t D s
f u r \ e i s n F g a t i \ eb e t u w0 . 3 2K A t i o :
u"idsolid mixture of He ihereturerools
r rr is cobpressed3t ieDperaturesbelow
0.32 K- Duing the process,tiquid js
c o . r , n u o u q tcJ^ r l e r i e d i r t u s o t i d . ' l . h e
b r r r p x p e rm e r t a t d i f f i c u t r \ h r h a i
compressoncannorbe achievedfron the
oltside simply by pumpi.s Dore He3ihto
Lne 1owtehperaiu.e celt, becausethe
heliuh in the connectinsiube hasio Dass
lhroush staies in the sotid region ofthe
d'agram as ii is cool€df.ontishe. teh
peraiuresithe conn€.ting rube thus
be
. m e sb l o L k e d
ffrb s.tidHer. Oreb!(
rnererufeconpre.s the cel some ottcf
i o r e x M p l e b \ s q u € e z i nist q i t h a
lJy
peraiure,I arishirg at absotuiezero.
. In rh€ solid-He3atomsae iied io i,heir
lathca siies and their irave fun.tions
oleflap only paniatly. Every atoD is
thus lairly independentof irs neishb.rs
a n d r h e n u c l e a sr p i ne n t r o p l . t c r a r a t u e
clusero,?1n2,whjcf correspondsto c!o_
plete disorde.. Thus. at low ?, the sotid
entropy ca be largerthanthe tiqujd enPon€ranclLuk's rechnique has beer
very iDloiiant for studies of the suDer{ i u i dp f o p e r t i c ,o f H e r . I n f a . t , D o u c l d
osh.roff Rolert Richdd\un ,nd Ddid
l-ee usedjust tl;s meihod of cootins ro
l0
30
100 300 1000
o r s c o \ e rt h € n e w , s u p e d u i d , p h a s e r .
i t g r . e1 G a , r i e r n a L i , 1 h s n n o f a D) n
TEIIIP€RA|UREINK)
provedversior of thei. cell. The device
Phase diagrad ol hetium-3 showing the 6orid
incollor{ias a h!&a$ic
ohae. rhe me(iqq cuNe Ni\iRuR arq 32K.1he
$ress\\e rsnormai Fermi liquid phase andfie supeFltuids
plifier that consists of B; Cu beltows
heliuh-3,A and heiium,3-B. Noto lhat the
conneciedby meansof a risid shafi. A
transition
iemperature
at zeropressures 1.1 moderate Hea pressure chanse
in the
mK thisis 2000rimese3srhanrhe\_pointor
t'pper chamber GhoM to the dshr in the
Fiqurel
tryur€), compressesthe lower cohpartment suticiently to solidify the entie Hei
.hdge. At a t\Tjcal r.ie oi \otrdjficshln,
zu nrtronovrc
cooling proceedsai 4
iereDcebeiweentiquid abd sotid.emains r n L c f o k e l v i n A e c .
Tle low terperaiure
p u s i t ' \ e M d l e c a L r sde? / d ? i d n e s a t i \ e L r D t r s
a b u u t1 m K
Uel.q 0.J2 It the entrupy oi solid Hel
A very rec€nt exampte of rhe use of
musi.be lafger ihan the enbopy of the P u D e . a n L l u k
c . o l j n si s p r o \ i d e db r i h e
xqurd at tenpe.atures below the nett
work !fMaurice ChapeiLiec.
rDg-curvemmrmum. Thjs indease jn Finn-BergRaqnussene Frossatr.and
on snih-Dolej2ed
entrop\ upon treezjrg is the basis for iiqrid Her.
Owing to the Fernj deeen
t s o n e r a n c h ucko o l j n g .
F r a c vt h e s u s c e p t i b i l i toyf t i q u i d H a - j s
^ ore can easilyunde.stand the reaon l o w s d s i S n i f i c a i p o l d i z a t i o D sc a n n o t
1or ihe entfopy differeDceby tookjns al b e o b t a i n e d
e\en by apptjing a hish
t h eJ t . u . i u r e so i r h e l i q u r da n dr h e s o t i d . masnet,cfreLd
ned 1 DK. In sutid He3
li fhe liquid, rh€ He" stoms rfe tueer. the susceptibiiity
is much ldce.. Ber
roam about and iheir wave funciions nad Castains
and Philippe No,ia.es
overlap extensivelyithe thernodyhamic Eugg.ett€d
that o ne ould produces pota
p r u p e r t i e s6 r e t l u s d e t e r D i . e d b j r i e
n z e dr , q ! r db j m e t t j n g s o t iH
d e 3t h a i n a d
r e r m r \ l a r F t i r s . ( T h es i t u s t r u na a n , t - preliously
been polarizedjn s masneiic
ogds tu thc conduction €teLrronsin s r e r d a t l o w
t€Dperaiues,
d e r a L . r l n F e r r r o p ) ,o f t h e t i o u r d s. . i s
ChapeiLie.
dd his coileaeues
sotidjfied
t n e r e t ^ k a l i n e i t u n c t i o no a r h e i p m about 35%ofa He3 sampti durine con-
I
.The shapeot thF meltjng curveofHeJ,
wfLr.h
rorbs the basieof tie ttrurv of
Pomeranchukcoolins, is of .ourse.-determined by the Oausius,Ctapeyron
dP sr_s.
d" vr_y"
BecauseYr - ys, ihe nota votuDe dif-
iirli:il"1,'J#1fi
i{iiii:i'.iffi
$h'3*itfu
::*!fri"nilr:i}:i
PHYSCS TODAY/ DECEMBEF1979
p.essionwhile itcooledfrom40tu 2 mX
in an externalfie1dof 2.6 tesla,thus obtai.ins a highly polarized solid. They
then reieded the pressures! fficiehl,l) so
that the solid melted dd honitored the
pola.ization via the nuclear hagneticresondce sighal. The resultsshowthat
the poldization decr€ases
exponentially
from the high iniiial value to the low ralue
characte.isticof Ferni tiquids;the group
recorded initial liquid poldizations as
high as about 20nhand relaxation times as
These and Binila obseNations bv
Gemrd Schunacher,Daniel Thoulouze.
Casiai.s, Yves Chabre,Pierre Segransm,
sd JacquesJoffrin open up the possibiliry of studies of polarizedliquid He .
Iuther, it has been 'rredici€dthat the
nelting curle E hlch lowered at hjgh
spjDpoldjzations dd thst the minimum
may complet€ly disapped. The netting
pressuremay even b€ suppressedbelow
the vapor pr€ssure,in which caseone o.
two triple points would apped in the
phasediasram of fisure 3.
Nuclearrefrigerati6n
Nicholas Xu.ti at Olford University
wa! the fi.st io se, in 195?,the technique
of adiabatic nucled demagnetization.
The basicpinciple of this i€chnique is the
sanreaslbr parahagnedcsalts,but ihere
are very sisnificant diffe.encesin practiceBecausenuclear magneticmom€nts are
aboui 2000times smsllerthan thei. electronic counierparh. it is morc difficult to
produce significant changesin ihe nucled{pin ehtropJ by external means. In
tact, one hust start with ienpe.atures
b€]ow20 hX and ns€Ietic fields in excess
of 5 T for nuclear .oolihs, whe.easfor
s0LJr0
pdamagneiic sslts ihe corrcsponding
nuhbe.s arc 1K and 1T. Fortunately,
ihe starting condilionsfor nuclee magnetization can be reachedraUrer easily
with dilution retuigeratorsand supeF
conduciing masnets. (These are the The cascadenucl€arrel.igeratorat felsl.ki.3
conditionsIor the so cslled"b.ute force" The firsl atage is made ol 600 qrams of insllal6d
nuclearcoolinsnethod. I shali alsodis- 0.s mm copper wies; the second stage is a
cusshr"efine-enhanced nuclearrefris- 2-grambundleo120000.04-mn copperwn€s.
e.ation Dd dFamic polaization, to A dilulior refrigeratoiprecoolsthewnesto l0
which different starting conditions nK. Themagnersappylelds ol8 andTTtorhe
ftsl and second stages before dehagneliztion.
aPPl,.)
(Thisis the workingendol the apparalusshown
The hain advstag€ of nuclearcooling
is the very lowtemperatufe thatone can
rea.h. Nuclei order sponianeously, denagnetizationthen coolsthe smple to
owins to their mutual dipote dipole in- a finsl tenperai.ureZr given by
teractions, Fell belo$ I nicrokelvin.
Becace spontareous ordering i6 ihe limit
r, = 1. Il,, +tt
IJ,
of any cooling process,temperaturesin
the sub-hic.olelvin resiob can be reached where b is ihe effeciivefield of the inter,
by nucl€d demagneii2ation.For cerium action betseen the nuciei. Thus, for er:
magnesiumnitrat€, shich is theweakesi ahple, ifw€ start wii,bBi = 8 T, ?i = 16
pdamagneiic sali. th€ orderingiemper
DK, ad we linish with Bf = 0, and the
ature is slishtly below2 nK.
material has b = 0.3 mT then the final
The techDiqueofnuclear cootinscon, temperatue of the sampleis 0.6 hic.o
sists ofmagnetizing tne sampleisotheF kelvin.
mally. raising the hasnetic field fion 0 to
Ai ve.y low temperat'Ies ii nakes
Br at ihe (low) iniriai temperatu.e ?i.
senseto distinsuish bet{een the ten
One then isolates1,hesmple and reduces peratureof th€ nuclearspins,?.. and the
the external field to Br. T|e adiabati. temperatu.eof the conductionelecifons,
38
PHYSICSTODAY/ DECEMBER1979
?,. The nuclei reach i,lernal equilibri.
um among thehselves in the slin sljn
.elaxationtime rr, and the nuclearspins
and conduction elect ons equilibrat€ {ith
respectio ea.h othei in the spin laitice
relaxationtine,rr. Atverylowt€mper
aturest2 ishuch shorterthd rr, sothat
the spins reach thermal equilibiium
amolg themsehesvery repidly Fhile only
lloely equilibraiins with the rehailder
of the syst€m- Nucleardehagnetizaiion
cools ?", leavins 7e more or lessunaffected. One must thus wait for times
larser than il for the cold nucl€i to cool
the remainde. of the syslem. For mo6t
metalsrr is the orderof secondsat l0mKi
for jDsulators 11is days or elen Feeks. it
G lhus cl€arthat onemust useneials for
brut€lbrce nuclearreft igeration.
The snall 11 in netals is due to conduction elecironsthat act as inierhredi
aies betwe€nthe nuclearspins and the
laltice. Only electroni near the Fe.ni
surfaceconhibutej their nutuber is proportional to ?e, making rr propo.tionsl to
i/7", that is,
rlTe = x
she.e { is calledthe Koninga consiaht.
In practj.e ohly copp€rand indium have
been used for brute-force nuclear oagUnavoidably,exieinal heat leaksinto
the conduciion electron syslem. This
heat flow has an important effect on
equilibriun between7. and ?". lf the
rate, Q, at which the heat floBs in is too
ldge, the spin lattice relaxation proc€ss
is not sufficjently rapid for cooling the
conductionel€chonsad€quately,and the
difference between the electron and nu
clear temperatureswill be iarge. Quan
pttx|)
Ta_1=
T"
L@2 + b2)
where p0 is the p€rmeability of fie€ space
ald I is the nuclearCurie constant.
Nuhe.ical calculationsshow thal in
mahl cases to keopthe sanple cold tor
sufficienily long tiDes or to obiair sig
nificant refriseraiionof conductionelectroDs o. an ext€.nal specim€n one
should not carry the nucles demagDeiization all th€ way to Br = 0 but shooLd
stop atsome intermediatefield. In particular, one reachesthe lowest 7. b!'-de'
Br(opt) = r/porQTT
In tlis case?./T, = 2
The most importat useofnuclearre
friseratorsso far has heenthe coolingof
liquid He3. Ai l€asi a dozen such.rto
siats arc nos ih operation;they have ar
readyse.vedfo. alarye number ofexcjt
ing measurebents. One difficuliy €n
counter€d jn these erpedments i6 tbe
Xapitza ihermal boundary resistance
beilreer liquid He3 and a sr,lid bodr,.
i,uclill' this difficuliy can be partielly
orercomebecause
ihe nuclea spinsofHer
are coulled to Lhenagr€ti. ihpu tieson
A srouprworkirgatthe HetsinkiUri
the copDersurlaces,which oarkedly re
ve$ir,!
of lechnologjhasreceDrt!.
.on
.luc€s the ihcrmal resisiance. tn 19t8
stfu.ted a c4,oslat, ltiih tlro nu.lea.
Osh€rolf and \'Iikko Paatanen at Beu
d e m a 8 n F h z l r i unn. g s n t e r x h . g r . s e
Laloratoies were aLle to use this techr
i s . I n { h r c h i h p r p i n so f , p p e r i L i t p i
n i q u et o c o o l l u r el i q u i d H e r t o 0 . 2 g n K ,
have
beencooledto ?" - 50 nK. This is
the loilesr tempefature yet rea.hed for
ttre
Lowest
tempe.ature ever produced.
liquid Her. Severatorhe. taboiaroiies
rhe apparatusG illustrated in fisures 1
boih in the US and in Eufope, have atso
beenable to cool supeduid Hesio betow
The secondnuclearstase.which is also
0 . 5n X .
the
specimen,
is cooledby the fi$i ructed
With mixture! ofHe3 and Hel rhe sii
retngerator fo 0.2 mK in a fietd of ? T;
uation is nuch nofe difficuti b€causea
uDder these conditions the equilibriuh
layer o1noD-hasretic He4ou alt sufaces
huclear-spir polarizarion is over 99o/o.
p r e \ e n t ! m . g n € t i . b o u n d d r )c o u p t r . g .
Thefe is no heat swiich bet*een the 'wo
lr.e po!fbl€ drrpr.€.|.wlricl has beeo
nu.lee strges.so one hasro demagredze
tded but so fa. unsuccessfully,is first to
ine Bpecrhe! and carry out the actual
cool pure liquld H€r by nuclearreftieer
ea!€rimenls in a tihe shorr in conparison
ation and then dilute ii with Her.
wrth 7r to reduce lossesof poiarization
Liquid nixiures ofHe3 ed Hel a ow
due to relaration. In zeroeriern:t fiFld
temp€mtures,ee ertiemely interesting.
7r rs about 20 hin. \l'e obtainedthe ex
Heo becomesa superfluid at veN tow
pedmenial information aboufthe nucled
tehperatures by a pai.ing heclmish
spin systen ofcopper,ln fieids fron 0 io
analogousto that rcsponsiblefor suDer1i mT, from nnr measurementsdon€
conductivity iD the Bardeen Coo;e.wiih
Josephsondevices(SQUID8).
Schrieffer ileory.
The conpar;ble
We fouhd the tehperaiure ?" in the
iheort' ior helium predictsthat for ditute
second stage aftei demasneijzaiionbv
soluti.ns of Her in Hea the Dairihs ivill
enploying dircctlv the second law of
produceS states.likethe C""p* p"i*in
therhodraamicsasappliedro asystemin
superconductors;
at high con.eni.ations.
= dQ/dS. We
thermal equilhdum:
hoiveler, the siable paiN should be in
brought a heat inpuNdO
" io rhe huclearPaiales, as they are in pure He3.
spiD systeh by applying a snall rfputse
The long .anse.oherencep.operriesof
at the hr peaLabsorpiionfrequercvod
the supeduidphases can producetdgeobiain^eddS b\ mFasuins ihe potdzascrle effecis from atomic phenomena.
Becausethe atomic phenomenath€mAft€r consiruciingthe entropydiagrm
selvesare tro small io measuredir€ctlv.
of copper ve found thai the mea$,red
the supedlLridsare very att.aclive ex
temperatureswerelessrhan thosecalcupe.imental ioois for exdihing them, as
laied for an interactingparamagneiF,ith
Legsettdiscussesin his reviewarricle.4
a constanilocalfield. tr'ofinstece, at ai
One slmple exampleis the vert' smau
entropyof0..l5 4 in 4 the measuredte$
orbilal magneticmoment po.bassociated
perature is 50 nK insteadofthe 110nX
\rith lhe rotation of a homonuclea. di
that one calculatesfrom I locaLfield 0.34
atomicmoleclrle. 'Ihe magneticmoment
mT. By analogt'with elecironichasne is obviously directed alons rhe orbital
iism, a plot ofihe invene statjcsusc€Dti
aDgularmomeniuD vector. Howeve.,in
bility
as a fuhction of tenperarLrre
M o.diDdy dialomic sas ihe hotecutar
sLrsg€ststhat the nuclee spins prefer
a\es of.oiation are oriented completely
ahltte omasnetjc order, with a Weiss
ar mndom, €ren ii a hish field, because
t
Tlre
.uclear
rerrigeraror
ot
An.lres
at Be[ Lab_ e m p e r a i u . eo f 1 5 0 . K .
/ldb is so small ihat it is undeteciable.
On the other hahd. we found no ctear
The hyperJine
structureot th.,a
The situation is radically differenr in oratories.rr
praseodymum
chdngr in the entropy diagrah o. in the
nickel
greaUy
crysra
enha.ces
the anGotropicsupe luid phasc He3-A. the etreclivefietd
at rhe nucte,therebyalso nmr daia indicaiing a iransition to ihe
In this casewe heveCooperpairs.vhich enhancrnq
thecooinadle lo adabaitcnuc4r
o..lered state. This nighi be due to ex
.ray be considcred as giant diatoDic demagneUzaton
Ths apparalus
hascooted p e r i h e n t a lr n a c c u r a c r e sI t. r s s l s on o s .
nolecuies. Bui, in conlrast to an ordi- helium-3
to 1 mitttketvin.
Fcu.e6
s i l , l e $ c t i h e n u c l e dsr p r n . y s i e n$ 6 n o i
ndrJgas,thepairsautohaticallycondense
a b l et o h r l e r h e t r a n s i t i . . r o \ v r r st o r h e
Dto the same state ("tsose cond.ns,- He! is an
elception owiDgio the sirong fatnerraprddemrrnerjzaiior) or lhat rtrF
tion"), sothai the aresofrotatioh are ail quahiun-hechanicai
exchanse force.) actual N6el Lemperetureis belos 50 nX.
in ihe samedireciion. The snall orbitdl Thus, to invesiigate
nuclearcooperative In elecironicaniiferromaenetsthe ratio
hasnetrc moments then add up coher phenomena,
such as ruclear fe.roDas
of Weiss to N6el tehper;tures is often
€ntly, we havea maoos.opic etYeci,and nettsh and
aniifenomasnetism in a considerabtylarger than 1. tn any case_
tne systembehavesas averyweaktiquid m€ta1,onenust bring ihe
temperaiureof theseexpetmehts showthai thenuclear
ferronagnet. Douglas Paulson ;nd
the _sjstem io the .anokehin .egjon. spjn s)'stemof coppef clearly faro$ dn
Wh?stLevlD
ha\ e acruallydetef ed rro,bin ]-ucrrrryrt $ not neces6aryto cooi the
H e - A , t l r e \ D F a . u r e dt h e a n i s o h o p \o f ohoL€specimen,cnlv the nuctear
spins.
zero sound attenuation in a nuclear re- The conductionelect.onsnav
renaL at Hype{ine enhancement
ftige.ation cryostat. This is the fi|sL ob- a considerabh hisher temperature
beAroiher iechnique of nuct€a.cooiins.
servaiion of a senuinely chenical efect in causethe spin lattice relaxation
tine 11, "hypofinp oha.tFd rr lear refrigera
heliun, the fornation of "nolecLrtes.',
e \ e n I n d m e t a l j s s u f t i . i e . i l \ , l o n ed r i
rron lrGrp Fnrllbe ne \Er}sarLesful.
For most substances,as I have hen
u . l e t d i o k e e p r h e i u r l F J r s p i n c This nethod has beeh devetopedsince
{
x
LLoned.spontadeous nuclear orderins r n g n c d l o n ge n l u g h t . p e r f o r mr h €
e r . 1 9 6 7m a i n l r b y K l a u s A n d r e se . d h i s c o
occumwell beloir t hic.okelvin. (Sotid
wo.keis at the BeLlLaLo.atories.'1
PHYSTCS
TODAY/ DECEMEER
197s
39
In .ertain paramasneti. lanthanide
alloysin whichthe fare earthion.c.upies
a sinslet sround nate split by rhe .r)'sral
lield ("Van Vleck alloys"), an applied
magneiicfield nires €xcited stetesiaith
i,hesround state. '1'heextemalfield i,bus
indu.es a large electronic poiari2al,ion,
which, in iurn, enhancesthe field ai the
sit€sof the ree-earl.h nlclei.
ln i,he best specihens, wHch afe ini.ermetalliccompouhdsof praseodlDiuh,
ihe lieLd is boostedby a facior varlins
The enhancedfi€ld allows one to iehove a comparablyenhancedfraction of
the spin .ntropy. \lith an initial magnetic field of2 T and an initialtempefa
iure of 20 nX, the eni,ropyof PrNis is
reducedby 2570.The stad.iDscondiiions
for demasletization aie thu! excellent.
Fo. copper the correspondirs entropy
redudion is only 0.14'ro. CoDpounds
such aq PfNis thus provide a very large
cooling ca!a.itl
during and after
demagnetization. UnfoiLLrnaiell;.thes€
compounosere nor easy [o prepare necaus€they husibe extfenely purein }oih
conposjtion and slr!.ture. Even traces
of nagnetically oidered impudty phases
may leadto irreversibilitiesthatwipe out
the entire nu.lear coolins effect. Other
drawbacksof ihese sp.cjmens are their
otten poor the.mal conductivit]' and the
fact rhat spontaneousnuclear orde.i!g,
which setsthe lowtemperaiure limit obtainable by ihe h}'peifire'enhanced nu,
.led coolins method. occurssonewhere
above 0.5 mK, depending on l,h€ com
Figure 6 sbows the apparaius that
Andres is cunently using. He has, for
exanpl€,cooledsuperfluidHe3to 1.0mX.
A g.oup worling et the Unlversiiy of
Nlinnesotahas recently obseNedu nu
clear magnetic order in PrCu6 at 2.5
nK.
Jan Huiskanp's sroup in Leiden has
lbr some tihe ope.ated a cascadehuclear coolinscryosiatbasedonthe same
principle. The first siage js made of
Prcud and ihe secondof indium. lran!
Pobell and his cowo.ke.sat the KeDforschungselageJtlich in West Germany
hav€recentlycompletedareftigeraior in
whichthe fiJsi nucled stageis madeof 1.8
ke of PrNis and the secondof 0.6 ks of
copper. \Vithout a beai load, PrNii, denagnetized froh 6 T, reached0.48mKi
this is thelowesi iemperaturesofarproduced br ihe ht"erfine-enhanced nu
clearcoolingmethod. TheirsecondstaF€
produced a record .onduction electron
temperature ol 50 microkelvins. The
sroup headedbyXazuo Ono etiheihsiitut€ of Solid State Phr_sicsjn Tokyo has
rec€ntlJ obtained a nuclear spin temperature of 111mic.okelvins in a sinilar
D y n a m i cp o l a r i z a t i o n
A group at Saclay,headedby Anatole
Abragan ard Mau.ice Goldman.ha! for
40
FHYSICSIODAY / DECEMEEF1979
Nuclear ant eromagnellc slrlctures in thiuh hydrideat pos ive and negariveabsoturetemperatureswh6nthe exlerna f eld is para elto a ll00ldrecton oithe crystal.2 Blackandopen
r ' r o r . ' e o e . e r ' l i r ' i u - - /n c p . . d p o i o l . . e s p e r ' n " J
manr,rears st!died spontaneousnuclear
orderingin insulators,noiablyin caLiuh
Uuoride. Their eiperihenial methodof
coolingis drnami. polarizationby means
of i.le "soljd effeci," followed bt' adiabai.ic
?he specinrenis a small CaF, crystal
iDr,o{hich Tm:- ions wereintroducedas
electrcni. nagnetic impudtie! ai a coD
centration of 10 parts per million. An
He3 refrige.ator first .oo1sihe sp€cimen
io 0.7 X in a lield of 2-7T. Under ihese
conditions the poLdization of r,heiluorine
mrclei is alhost zero, ilhereas the elec
i".onic nomeDts of Thr+ a.e almost
conpleteiy polari,ed. This is, ofcourse,
due to the fact that the eled.onic magnetic hohents are aboui ih.ee ordersof
maghitude larser ihan lhe nuclear noNext. ihe systcm is supplied with mi
crowaee radiai,ion whose ansulai he
quen.y oe - o,. is equaltothe difference
in l,h€Larnor frequ€nci€sof the Tm,+
electronicand the fluodne nuclear homents (the nLrclearspin of celciun is
,erol. The hicrowavesinduce flip,flop
transitions, in which an €lectroric homent originaily pointing up (in rhe di
rection of the external fieldl flips dowh
aDd a neighboringnuclearmoment oliginallypointingdoFn simultdeouslt tuns
up. Owing to its shoft relaxdtion tihe
with rhe lattice. ihe electonic moment
will quickl) .elurn to its oiiginsl dir€ction
atier the ilip flop, shereas the nucleus,
becaus€rr is lery loDsin insularors,will
.eiain its ne$ ori€ntation. Ihe ifml+
ihpurity then perfo.ms a new flip-flop
processilith dother lluorinenucleus,and
so on. This is th€ "solid effe.t."
Th€ end .esult, jD theory. js i,iat ihe
nuclearand electronicpolarizaiioDsivill
beconeequal In Fracii.eihere ar€some
losses,but ihe Saclat sioup has achie!€d
nuclear poladzatjons in €xcessof 90%
aiter .1houF of mic.owaveirradieiioh.
The nicroilale poweris then cui off and
the He3refrige.atorcoolsrhe CaFrspecimen to 0.3 K. It is importaht io note
that anucleafpolarizationof90ooat 2.i T
correspoldsio at€mperaiure7n = 1nK.
Th€ siarting conditions for ruclcar
demagbei.izaiion,
which is the n€xl srep,
areihus excellent. The end temp€rature
reachedin the nuclea.spinsis about 300
DK. The lattice slays at 0.il K, but rhis
Anoi.he.f€ature of the Saclayexperi
ften|s is the possibility of produ.ins
negative absolute tempe.atures ih ihe
nuclear spin systeh. hradiating the
specimenwith micioilavesat a tuequency
ofoe + o"$i1l induceflip,flip. insieadof
flip flop, transitioDs: the resuli is i,hai
the nuclei hecone pola.ized oppositetc
ihe externslfield. This meansrhdt after
demagnetizalionthe syst.m will reacha
nesative absolute tempe.atue ?" of -300
Calcim fluoride behar€squite differentl] at posiiive and negativetemp€ratures. Suscepiibility data show ihat ai
positive ?i the systeh .eDains para
hagneric down to 300nK, while ai !ega
tive 'I" there is a magneticftansitio!appar€ntly to an antiferromagnetic
sl,ate wirh a \6el lemperatureof -600
The Saclaygrouphas recentll provenl
nuclear antile..omagnetisn in l.lH.
Figur€ ? shows ihe order€d sfuu.tures
predictedby i.hemee field \Veissiheory.
The expedn.ntal neihod is the sameas
ihat aheady etplained for CaFr. Ho*
ever,in theseexperimeni-s.
the exi.ernal
field*as 6.5?dd a dilurion relrigerantr
precool€dthe sample io 50 nX. Afier
ih.ee daysof mi.rosave iuadiation and
befor€ demagneiization,ihe Lil nLrcle'
rvere80%pola.ized and the t.oI.on !olarizationsas 95%. Neutron dilta.iion
siudies lorh at posii.ive and regaijte
iemperaturesshowedan erira Br.gs re-
llecrion characierisiic of anijierromag
T h e . € c e n i . s u c c e s so et nsu c t € a r r e l r i s ,
eiatron prcmie further progress ir
reacnrnglon tempe.atues. It thus ap
pea.s that wnile Pomeranchukcootine
r n r v r e m a r nr b p o r t a n th s p e o a le a s e s .
ouDno. .el gerrtion and n!ct€sr
dehagneti2ation
ivill be the main iootsf.r
tuLure research_ Comptere diturion
cryostais are. in fact, alreadv commer
cially alailable.
The €xamplesof erpedmehiat resulrs
ihai I hare discussedin rtis reviewdem
n " t r a t eI I o ! e , t h a i i h e i pi s a B F a r d e a t
n r r D n o ; n e n r l l t Jr h p o r t d . t D h \ s i c sr s
leech lobe doheinrhemili , nnro and
!anokelrrn .egions of temDer,tIrrF
Nlany of the Dewphenohena io be dis
cove.edwill probabtyinvotvemac.oscopic
q u a n t l h . o h e r e n @ I t a p p e d Bi.n i a c t ,
o o r nr r o mt h F e x p e i m e . t a ]a o d r h e o f e r _
rcalpoints ofview, rhat lolr-Lemperarure
pnysr.snasoncedsan enteredanewa.d
exciring era on the road io absotute
But, ofcourse,we can neverreachihat
goal. This should noN discouraeeus.
The thid law of thernodynmicils no
mnorance to progress. If sohe new
lnenomelon occursai a temperaiue rhat
nasprevrouslynot been.eached.it is at_
sal's possible,boih in p.inciple ahd in
practr.e,to employ ihis phenohenon io
srepdo$nluriier and reachthis oasjs.f
,nterest. Only ri nothhs hs!p€n.. if
r n e r e) q! n t y , d e s e r rb e t q e e nu u r l o s e c r
r€mperaiurc and the absoturezero we
cannoNprogressluriher. bur rhere js ro
scientificihleiest for ir either.
L D D_-O\ho.fr R C R.l,rrdson.Ir N.
L e t t 2 8 . 8 S 5( r 9 i t r .
L Y . R o m e lV . B o u r f u d .U L B a ,c h e t aI t .
Prot P l\liriel p Roubpau,O.Aienei,
vL.Lodrfu A Abrdsm pht!.Re\ Lef..
4 1 .1 5 ? 2( 1 9 ? 8 ) .
3. C J. Ehnhotnj, J. P. Ekstrnn, J f. Jac
q u i n l r M 1 . L l J o n e f , O .\ I o u n a s r r r l
J K S,ini th\\ fie\ tetr 1:, riu.z
,1.A. J Lecsetr, J. physiaue 39.
C6 116,1
(19?81.
i O \ l - o u r d . m a JF
, f p e n ? e a t o rF r d r
rt^ ud M Lhall BPlor , x qlJncmi(
fre- Londu & Nctryirk 19irl
r O \ L o u n B . s d a ,. 1 . p h y , I 1 2 .
bi,a
r19i9)
T G. F.ossiti, J. phrsiqu. t9, C6 t5t8
(1978i.
8. T. O. Nii l.sli, Pra. 6th tntetndt
ctlaeeni: Lneineeti.e Canl , tpc Soence
ard Te.hology Pres (19t6)rpase102.
9 Nl. Clap€llier. c }.rossari.F.B. Rasnus
s.n, Phrs. Re1..Latr. ,1:.90,1(19?u)
L0 D. N. Paulsor,J. C \!hoartey, plrs.Rev
L e i i . , 1 0 , 5 5{71 9 i 8 ) .
rt. Ii. Andres Cr!oserics 18,,1.r3i19?8).
1 1 .J B r h , r k J K i e r . T N t J n h ! ,r ! .
\ ! e , h d o n n .P h . , . R p \ . T p f t $ . 3 . 0
l]9791
Ithacop-resents
a fewchoicr
wordsaboutpreamps.