602 IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-21, NO. 2, MARCH 1985

AN ABSOLUTE SQUID MAGNETOMETER.

by J.C.Gallop & W.J.Radcliffe

Nat ional Physical Laboratory Teddington, Middx. TW11 OLW

England

Abst rac t

A prototype free precession magnetometer is

descr ibed which uses a SQUID t o d e t e c t t h e p recess ing nuc lea r magne t i sa t ion o f a sample of He.

The e x p e c t e d s e n s i t i v i t y is compared wi th t ha t o f a s imple SQUID . Other advantages t o be gained from

t h i s low noise absolute magnetometer are a l s o d iscussed .

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1. I n t r o d u c t i o n A SQUID is o n l y a b l e t o m e a s u r e d i r e c t l y t h e

change i n magne t i c f l ux l i nk ing it and cannot d e t e r m i n e t h e a b s o l u t e v a l u e o f f l u x d e n s i t y o r of

changes i n it. The pape r desc r ibes a pro to type magnetometer which avoids t h i s l i m i t a t i o n w h i l e

a t t a i n i n g t h e v e r y h i g h s e n s i t i v i t y of a SQUID. The d e v i c e c o n s i s t s o f a f r e e p r e c e s s i o n 3He

magnetometer i n which the f r equency o f t h e

precess ing nuc lear magnet i sa t ion is de tec ted wi th a

SQUID. This i s i n some s e n s e s a cryogenic analogue o f t h e well known p ro ton f r ee p recess ion

magnetometer, used widely for ambient f ield measurements a t s i tes with low magne t i c f i e ld

grad ien ts . 2. Detect ion of nuclear magnet isat ion with a SQUID

If a s i n g l e n u c l e u s wi th s p i n I and magnetic

d i p o l e moment m is p l a c e d i n a SQUID r i n g we may ask

what will be the f lux change dB which r e s u l t s . d!J will va ry w i th t he pos i t i on o f t he nuc leus w i th in

t h e r i n g b u t t o s i m p l i f y matters l e t u s assume t h a t

t he nuc leus moves r ap id ly t h roughou t t he volume o f

t h e r i n g o n a time scale s h o r t compared with the

inverse upper f requency limit o f t h e SQUID e l e c t r o n i c s . Then it i s e a s y t o see t h a t t h e

a d d i t i o n a l f l u x is j u s t g i v e n by

dfl = AyoM Ap m/V where A is t h e c r o s s s e c t i o n a l area o f t h e r i n g , its

i n t e r i o r c y l i n d r i c a l volume being V , and M is t h e magne t i sa t ion , t ha t i s t h e magnetic moment p e r u n i t volume. I n a d d i t i o n we may c a l c u l a t e t h e e n e r g y change dU a s s o c i a t e d w i t h t h e i n t r o d u c t i o n o f a

s i n g l e d i p o l e i n t o t h e r i n g :

dU = (dgf)2/2L pom2/2V

Manuscript received September 10, 1984

where L is the r i ng i nduc tance and we have assumed t h e i n d u c t a n c e r e l a t i o n s h i p for a l o n g t u b e i n

a r r i v i n g a t t h e f i n a l e x p r e s s i o n . The r a the r s imp le dependence of dU o n t h e r i n g volume a l l o w s t h e

ques t ion to be asked: what i s t h e minimum number of s p i n s whose p r e s e n c e i n t h e r i n g c o u l d j u s t b e

de tec ted? If we a l low a measurement bandwidth o f 1Hz and assume t h a t a SQUID is a v a i l a b l e which has a

r e s o l u t i o n , set by t h e u n c e r t a i n t y p y i n c i p l e , h J/Hz (where h i s P lanck ' s cons t an t ) w i th a r i n g volume of

lmm3 t h e n f o r a t y p i c a l n u c l e a r d i p o l e moment m-10-26 t h e minimum d e t e c t i o n s e n s i t i v i t y would

correspond t o lo7 a l i g n e d s p i n s . Rather recent ly Ketchen e t a1.l have demonstrated a p lanar SQUID

susceptometer with a very small sensing volume, s u i t a b l e f o r m i c r o n s i z e d p a r t i c l e s , and with a

noise performance comparable with the uncertainty p r i n c i p l e limit. Even i f we e x t r a p o l a t e t h i s

achievement somewhat and assume t h a t a sens ing

volume of lpm3 could be produced a t least lo3 n u c l e i

would be required . So i t i s not reasonable t o t h i n k of SQUIDs as b e i n g a b l e i n t h e f o r s e e a b l e f u t u r e t o

d e t e c t s i n g l e n u c l e a r s p i n s by t h i s method (al though it m i g h t j u s t b e p o s s i b l e t o d e t e c t a s i n g l e

e lec t ronic magnet ic d ipole moment 1.

The a b o v e d i s c u s s i o n i l l u s t r a t e s that SQUIDs have g r e a t s e n s i t i v i t y compared with other techniques

such as nmr f o r d e t e c t i n g n u c l e a r m a g n e t i s a t i o n . It should be clear from t h e simple argument above that

the s e n s i t i v i t y is independent o f f lux dens i ty B i n

which the s p i n s are s i t u a t e d , u n l i k e nmr, except

i n s o f a r as t h a t f l u x d e n s i t y is used t o produce a spin a l ignment . The e s s e n t i a l f e a t u r e s o f a n a b s o l u t e SQUID magnetometer are as f o l l o w s . F i r s t t a k e a sample of nuclear spins, produce some degree

o f p o l a r i . s a t i o n , t h e n p l a c e t h e s p i n s i n a magnetic f i e l d t o be sensed, and measure the freely

p recess ing nuc lea r magne t i sa t ion d i r ec t ly w i t h a

SQUID. Commercially available SQUIDs have a r a t h e r

l imi ted f requency response , to a round 30kHz, SO t h a t such a magnetometer w i l l o n l y o p e r a t e i n low a p p l i e d

f i e l d s , up t o -1mT. However, un l ike p ro ton magnetometers whose s e n s i t i v i t y fa l l s o f f r a p i d l y

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0018-9464/85/0300-0602$01.0001985 IEEE

603

below about lOpT, our device will c o n t i n u e t o work,

i n p r i n c i p l e w i t h the same s e n s i t i v i t y , i n z e r o

f i e l d .

There is l i t t l e c h o i c e i n s e l e c t i n g the n u c l e a r

s p i n s p e c i e s f o r u s e i n t h e magnetometer. It is important that t h e sp ins shou ld be i n t h e l i q u i d o r gaseous s t a t e i n o r d e r t h a t atomic motion should be r ap id enough t o a l low d ipo le -d ipo le i n t e rac t ions between s p i n s t o be averaged t o zero over one per iod

of t h e Larmor precession (so called motional narrowing). Although a r e -en t r an t c ryos t a t

conta in ing a room tempera tu re l i qu id or gas could be

employed t h i s would lead t o higher Johnson noise as well as a much more complicated low temperature

apparatus. Only t h e two isotopes of hel ium and

atomic hydrogen remain gaseous o r l i q u i d i n t h e

ope ra t ing t empera tu re r ange of SQUIDS. Atomic

hydrogen a t a reasonab le dens i ty p re sen t s s eve re

experimental problems and 'He possesses no nuc lear

moment s o that He is t h e only reasonable choice. A

degree of s p i n p o l a r i s a t i o n may be produced i n 3He by two d i f f e r e n t methods. Brute force p o l a r i s a t i o n i n a large magnetic f i e l d is the s implest , , providing

a f r a c t i o n a l p o p u l a t i o n d i f f e r e n c e o f a r o u n d 1 i n 10 a t 3K for r e a d i l y a v a i l a b l e f ie lds . O p t i c a l

pumping is capable of producing up t o 708 p o l a r i s a t i o n b u t t h i s apparent advantage is offset

by the fact that i t can on ly be carried o u t i n gas a t a maximum p r e s s u r e o f "lmbar. Thus b r u t e f o r c e

p o l a r i s a t i o n o f l i q u i d 3He can produce roughly the same nuclear magnet i sa t ion as o p t i c a l pumping at the

maximum a l lowable dens i ty . In v iew of t h e s impler n a t u r e o f the equipment required t h e former

technique has been used for t h e work described here. 3. Prototype.HE-SQUID Magnetometer

The e x i s t i n g system has been developed for the specific purpose of examining t h e magnitude and

uni formi ty o f a t rapped f i e ld w i t h i n a superconduct ing tube. Th i s work forms part of a

project t o measure the f l u x quantum and t o develop a p o s s i b l e quantum cur ren t s t anda rd 3,4. Figure 1

shows a schematic diagram of the pro to type magnetometer. A small b u l b i n t o which about lcm3 of

l i q u i d %e can be condensed is coupled by a normal metal f lux t r ans fo rmer t o t h e s i g n a l co i l o f a two-hole 20MHz SQUID. The n u c l e a r s p i n s are polarised by p lac ing t h e bulb a t the cent re . of a

small supercOnducting solenoid providing a modest f ie ld o f -5OmT. T h i s p rocess takes a t least 30 mins.

due t o t h e l o n g s p i n - l a t t i c e r e l a x a t i o n time (T ) for 3He (up t o 1500s i n t h e l i q u i d a t 3K) . Next the

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4

1

Superconductin8 shield -

Warising coils

Ewcuated regton

.Liquid 4He

Helmholtz coils

*Precision cylinder

Figure 1. Schematic diagram o f prototype HE-SQUID

magnetometer.

sample bulb and SQUID assembly are moved down i n t o the f i e l d reg ion of i n t e r e s t . A 90'. p u l s e is a p p l i e d

t o a c o i l wound on the b u l b o r t h o g o n a l l y t o the f l u x

t r a n s f o r m e r , i n o r d e r t o t i p t h e n u c l e a r s p i n s i n t o the p lane a t r igh t a n g l e s t o t h e f l u x d e n s i t y B i n the tube. The precessing magnet isat ion produces an

o s c i l l a t o r y f l u x c h a n g e i n the t ransformer, and

hence a t t h e SQUID, a t t h e Larmor frequency w=8B ' (see f i g u r e 2) . . Following a c e r t a i n amount of

f i l t e r i n g t h e SQUID output is Pea d i r e c t l y i n t o a counter which times a number of p e r i o d s o f t h e

o s c i l l a t i o n , g i v i n g a d i r e c t l y c a l c u l a b l e v a l u e for

w. The long T, va lue may now be used t o advantage

s ince a l though t h e free p r e c e s s i o n s i g n a l disappears

i n a c h a r a c t e r i s t i c time Tq , which is t h e magnetic

f i e ld inhomogeneity broadening time, the s i g n a l may

be r e s t o r e d by apply ing a 180' p u l s e which produces a s p i n echo s o t h a t more measurements of w can be

made, over a total time o f the o r d e r of T1. The bulb may be moved t o a new p o s i t i o n i n between 180'

Pulses provided the magnetic f i e l d g r a d i e n t i s small . Figure 3 shows, a sequence of 30 such ' sp in

echoes ' , extending over a time o f Imin. F i n a l l y t h e

i

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n u c l e a r s u s c e p t i b i l i t y , B is t h e p o l a r i s i n g f i e l d , P

A is t h e c r o s s s e c t i o n a l a r e a o f the pick-up c o i l and t i s the t ime ava i lab le for measurement . On t h e

o the r hand the minimum d e t e c t a b l e f i e l d change w i t h

t h e SQUID is

dBs $,/A Thus t h e r a t i o o f t h e s e two s e n s i t i v i t i e s is s e e n t o

be r=dBH/dB = 1/8XB t

For l i qu id 3He a t 3K t i t h a p o l a r i s i n g f i e l d o f O.lT, r is g r e a t e r t h a n 1 for measuring times grea te r than l sec . so tha t under these condi t ions the abso lu t e ve r s ion of t h e SQUID magnetometer is

expec ted to be more s e n s i t i v e t h a n a simple SQUID.

P

F igure 2. Beat s i g n a l between IkHz reference and

SQUID ou tpu t , showing f r e e p r e c e s s i o n s i g n a l . ( T o t a l

scan time l s , bandwidth of d e t e c t o r 40Hz).

bulb is r e t u r n e d t o t h e s u p e r c o n d u c t i n g s o l e n o i d t o

r e p o l a r i s e t h e s p i n s . The a im of the p ro jec t i s t o

produce a very uniform f ie ld region within’ a

superconduct ing tube , where no f lux l ines l eave through the tube wal l s . The homogeneity of t h e

t r a p p e d f i e l d may be improved by carefu l cool ing of the tube th rough i t s t r ans i t i on t empera tu re . It has

so f a r been poss ib l e t o p roduce s igna l s which decay

with a T2 time of 10 s e c , r e p r e s e n t i n g a n a x i a l

f ie ld un i formi ty o f a round 0.3nT/mm f o r a mean va lue of B of 30pT.

*

The peak s i g n a l d e t e c t e d a t t h e SQUID i s up t o

O.1fl0 i n a m p l i t u d e , t h e t o t a l e q u i v a l e n t f l u x n o i s e i n t h e SQUID be ing t yp ica l ly Th i s

s i g n a l t o n o i s e r a t i o means tha t h igh accuracy can

be achieved from a s i n g l e measurement of w, t h e

present p rec is ion be ing “ImHz i n lkHz, corresponding t o a f i e l d s e n s i t i v i t y of 30pT, i n a measurement

time of l0msec. This precision could be improved by i n c r e a s i n g t h e p o l a r i s i n g f i e l d o r reducing the

SQUID no i se , which i s primari ly of mechanical or igin a t p r e s e n t .

4. Comparison of HE-SQUID and SQUID magnetometers. It is i n s t r u c t i v e t o compare t h e s e n s i t i v i t y o f t h i s

absolute magnetometer with t h a t of a convent iona l S Q U I D device , wi th a s e n s i n g c o i l o f t h e same volume

as the sample bulb. I f t h e e f f e c t i v e f l u x n o i s e i n each SQUID i s the same, an, t h e minimum d e t e c t a b l e

f i e l d change dBH for the hel ium system becomes dBH Ib,/b!XB A t

where 8 i s t h e g y r o m a g n e t i c r a t i o f o r 3He, X i s t h e P

Noise i n t h e n u c l e a r s p i n system i t s e l f is r a r e l y

d iscussed . The spin system i s f a r from equilibrium

when measurements a r e b e i n g made so t h a t it is no t

r e a l i s t i c t o d e f i n e a sp in t empera ture for much of

the t ime. One source o f no ise is t h e random

f l u c t u a t i o n s i n t h e e v o l u t i o n o f t h e n u c l e a r

magnet i sa t ion fo l lowing po lar i sa t ion . The decay of sp in po la r i sa t ion w i th time i s governed by t h e

r e l axa t ion t ime TI and f o r N t o t a l s p i n s t h e v a r i a n c e i n n ( t ) , t h e time dependent excess of up

sp ins over down s p i n s , is expected to be of order (Nt/T,)’l2 . Such a f l u c t u a t i o n would cor respond to

an equiva len t f lux no ise

as = poi#1CNt/T11’/2 Using t h e above parameters with T1=lOOOs and t - 1 s t h e rms noise per uni t bandwidth becomes

a’, - Wb/(Hz)1/2 f a r below t h e i n t r i n s i c f l u x n o i s e f o r any e x i s t i n g

SQUID.

F igure 3. Sequence of 30 spin echoes extending over

a period of lmin. (Dots ind ica te t iming of 180’ pulses . The echo maxima occur between these).

605

With the prototype system mechanical noise dominates although Johnson noise in the normal metal pick-up coil is only about a factor of two smaller. For general applications of such ,a magnetometer the pick-up coil could be made from a superconductor in which case the .latter source of noise would not be present.

Apart from the absolute nature of the HE-SQUID magnetometer there is an additional advantage over a plain SQUID. In most sensitive low frequency field sensing applications l/f noise in SQUIDs begins to dominate white noise below some frequency in the range lOHz to 1kHz. If the HE-SQUID can be operated in an ambient field which corresponds to a Larmor precession frequency above this range the low frequency field changes to be sensed appear as side bands of the Larmor 'carrier' frequency and l/f noise will not dominate.

In view of the small size of the nuclear spin sample, and the high signal to noise ratio it has already proved possible to operate the magnetometer in a field gradient of around 0.3fT/mm, in the earth's field, which is approaching a factor of 10 2

higher than the limiting value for a typical proton magnetometer which requires around llitre of water to provide a sufficiently large signal.

5. Conclusions

The primary aim of this .paper is to point out that the high sensitivity associated with SQUIDs can be made available in an absolute free precession magnetometer. The minimum number of nuclear spins required is calculated and shown to be mu?h less than any conventional detection system would require. Work is underway to demonstrate a practical system and results obtained with a prototype magnetometer are presented which demonstrate that high sensitivity with a relatively small sample is possible, allowing operation' in relatively high magnetic field gradients. A possible way 'of avoiding l/f noise in SQUID niagnetometers is suggested. The availability of low noise planar d.c SQUIDs would allow further development of the basic concepts outlined here.

References

1. M.B.Ketchen, T.Kopley and H.Ling, "Miniature SQUID susceptometer" Appl. Phys. Lett. 44 pp. 1008-10 1984.

2. A.Abragam "The Principles of Nuclear Magnetism" Oxf:ord, Oxford University Press, 1961.

3. J.C.Gallop and W.J.Radcliffe, "A proposed high precision measurement of the electron Compton wavelengthft, J.Phys.B 11 pp L93-98 1978

4. J.C.Gallop and W.J.Radcliffe, "A superconducting quantum current standard?", NPL Report QU67 1984