"NMR DETECTION WITH THE SQUID - APPLICATION TO LIQUID 3He"

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”NMR DETECTION WITH THE SQUID - APPLICATION TO LIQUID 3He”

R. Webb

To cite this version:

R. Webb. ”NMR DETECTION WITH THE SQUID - APPLICATION TO LIQUID 3He”. Journal de

Physique Colloques, 1978, 39 (C6), pp.C6-1613-C6-1617. �10.1051/jphyscol:19786608�. �jpa-00218103�

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JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-1613

"NMR DETECTION WITH THE SQUID - APPLICATION TO LIQUID 3H e "+

R.A. Webb+

Argonne National Laboratory, Argonne, Illinois 60439, U.S.A.

Résumé.- On discute les techniques uitlisées pour réaliser une variété d'expériences de résonnance magnétique utilisant un SQUID. On traite en particulier le cas des mesures de magnétisme nucléaire de 3He liquide en champ magnétique de 3,7 à 309 Oe dans le domaine de température de 2 mK à 1,2 K effectuées avec cette technique.

Abstract.- A discussion of the techniques used for performing a variety of magnetic resonance experiments using a SQUID is presented. In particular, measurements of the nuclear magnetism of liquid

3He in magnetic fields of 3.7 to 309 Oe in the temperature range 2 mK to 1.2 K using SQUID NMR techniques will be discussed.

INTRODUCTION.- In the last twenty years nuclear magnetic resonance (NMR) measurements on both liquids and solids have greatly enhanced our unders- tanding of the low temperature bulk properties of matter. The ability to isolate and study a single nuclear spin species has provided information on

the structure of matter, reaction rates, relaxation times, chemical bonding, internal motions in solids and liquids as well as nuclear susceptibilities.

In this paper a discussion is presented of a new technique for performing NMR measurements in low fields and at ultralow temperatures using a superconducting quantum interference device (SQUID). The selectivity of an NMR experiment combined with the extreme sensitivity of the SQUID should allow new and very interesting magnetic phenomena to be in- vestigated under experimental conditions that pre- viously made a conventional NMR experiment impossible.

SQUID NMR is not new. In 1967 Silver and Zimmerman III first demonstrated that a SQUID could be used to detect the change in nuclear magnetiza-

tion of a sample during an rf absorption experiment. Later Day 121 used a SQUID to measure abso-

lute magnetization of a sample in an adiabatic fast passage experiment in the temperature range 4.2 K to 300 K. Meredith et al. /3/ used a SQUID to measure the change in the average value of the z-component of magnetization of a copper sample as the frequency of a transverse H field was swept through resonance. Only recently have expe-

Based on work performed under the auspices of the U.S. Department of Energy.

Now at IBM Thomas J. Watson Research Center, Yorktown Heights,N.Y.

riments using pulsed SQUID NMR been reported /4,5/

although the advantage of this technique over conventional methods is the most apparent. Following a single rf pulse, both the value for the sample susceptibility and the spin lattice relaxation time, T , can be obtained independent of the spin- spin relaxation time, T.. In view of some of the advantages of SQUID NMR over conventional NMR it is somewhat surprising that no widespread use of these techniques has occurred within the low temperature physics community.

In what follows, I will present a brief description of a simple experimental arrangement that allows SQUID cw NMR, pulsed NMR, adiabatic fast passage as well as static susceptibility measurements to be performed in any temperature range. As an example of the power of the SQUID NMR technique, some measurements on liquid 3He in the temperature range 1.2 K to 2 mK in magnetic fields varying from 3.7 to 309 Oe will be discussed. A detailed description of SQUID NMR techniques can be found elsewhere /6/.

APPARATUS.- The, basic experimental arrangement for performing SQUID NMR measurements is shown schema- tically in figure 1. A sample is placed in a static magnetic field H that is held very constant by means of a superconducting shield. A superconducting pickup coil, coil axis parallel to the static field, is wound around the sample. This coil is connected to a second superconducting coil that is tightly coupled to a SQUID. The SQUID will generally be operated in the flux-locked-loop configuration 111 where the output of the SQUID electronics is a voltage that is linearly proportional

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786608

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c6-1614 JOURNAL DE PHYSIQUE

Fig. 1 : Block diagram of the measuring system.

to the current in the input coil. This arrangement is standard configuration for measuring the static susceptibility of a sample. If the temperature of the sample is changed, the magnetization of the sample changes and the flux coupled to the pickup coil changes by an amount A$. But because the pickup coil is part of a totally closed superconducting loop whose flux must be maintened constant, a current I is then induced in the loop such that I(L +L ) =

A$

where L 1 and L are the inductances

1 2 2

of the pickup coil and input coil respectively.

This basic arrangement with the addition of an rf coil that produces a transverse H 1 field is all that is needed to do a SQUID NMR experiment. For example, a pulsed NMR experiment is performed by applying a burst of rf power to the H1 coil at the resonance frequency, yHo, for a period of time T .

At the end of the rf pulse the nuclear magnetization will be rotated away from the direction of the static field and the SQUID not only measures this initial change in the z-component of magnetization but also continuously monitors the recovery of the average value of the magnetization as it relaxes back toward equilibrium.

A SQUID cw NMR experiment can be performed by applying a cw H 1 field of constant amplitude

to the sample and slowly sweeping the frequency of the H field through resonance. The output of

1

the SQUID electronics can be displayed on the ver- tical channel of an x-y recorder with the horizon-

tal channel driven by a voltage from the rf sweep generator which should be linearly proportional to the generator frequency. Thus a complete record of the change in z-component of magnetization of the sample is obtained as a function of frequency.

It must be emphasized here that in general the signal to noise ratio of the direction system will be severely degraded if the H field couples

1

directly to the SQUID. Such is the case if the HI field is not exactly orthogonal to the detection coil. Practically it is almost impossible to meet this requirement to the degree necessary conside- ring the SQUID detection sensitivity. The technique employed in the earlier work on SQUID NMR was to place a thin eddy current shield between the H

1 coil and the SQUID detection coil. A few of the disadvantages of this technique / 6 / are that the pickup coils must be placed on the outside of the shield which lowers the detection sensitivity and the L/R time constant of the shield can severely limit the frequency response of the system. An al- ternative ta this approach is to install a small 1 R resistor in parallel with the SQUID detection and input coils as shown in figure 1. This resistor should be thermally grounded to the lowest temperature available to minimize the Johnson noise coupled to the SQUID detection system, and the L/R time constant should be chosen so as not to dis- tort any signal on the time scale of TI. In the present work this time constant was calculated to be 2.6 x 10-~s. At low fields the effectiveness of this resistor in shunting rf currents will be di- minished. However, it is possible, at low frequen- cies, to cancel currents in the input circuit by installing a small nulling mutual inductor / 7 / whose superconducting secondary is in series with the SQUID input coil and pickup coil. However, for the results to be presented here, even in a 3.7 Oe static field, this null scheme was not used.

MEASUREMENTS.- The measurements discussed here were performed in an adiabatic demagnetization cell using CMN as the low-temperature refrigerant and has been described elsewhere 161. The sample was liquid 3 ~ e contained in a 3-mm-i.d. tower located above the main CMN cell. The H coil was a 42-turn

1

saddle coil wound on a diameter of 5 - m ~ using 0.076-11~1 Nb wire. The absolute calibration of the SQUID magnetometer was performed in the temperature range 0.3 to 1.2 K using static susceptibility

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161 as well pulsed S Q U I D NMR and S Q U I D adiabatic fast passage.

A typical pulsed S Q U I D NMR experiment in a static field of 309 Oe is shown in figure 2. At

I I I I I

0 30 60 9 0 120 150

t - s

Fig. 2 : Response of S Q U I D magnetometer following a 91" rf pulse.

time t = 0 a 25 ys burst of rf power was applied to the H coil which rotated the magnetization

I

by 91'. The initial change in magnetization was faster than the flux-locked loop could respond and it momentarily lost lock. The new lock point is in general not simply related to the old one and can- not be used for the baseline determination. How- ever, shortly after the initial magnetization change has occurred,the S Q U I D can continually track the recovery of the magnetization back toward equilibrium. The recovery of the magnetization is exponential with time and the time constant or spin lattice relaxation time was 22.5 s. Thus a complete record of the T process is obtained

1

from a single rf pulse even though the spin-spin relaxation time, T2, was 3.3 x IO-'s. The absolute value of the susceptibility can be obtained from

this trace as well. The baseline is determined by a straight line extrapolation of the end of the relaxation process back to the beginning of the trace. The absolute value of the flux coupled to the S Q U I D is determined by extrapolating the recovery curve back to the time of the end of the rf pulse. This measured flux change together with the calibration constant of the S Q U I D and know- ledge of the rotation angle is all that is needed to determine the susceptibility of the sample.

The relationship bitseen rotation angle and the rf power applied to the HI coil can be determined by measuring the change in flux coupled to the S Q U I D as a function of rf power. Figure 3 shows

T I P ANGLE,

degree

0 90

180

I I

12- PULSED NMR

-

HOE 3 0 9 GAUSS

10-

P

=

26.2 BAR

-

T = I S m K

R F VOLTAGE, volts p.p.

Fig. 3 : Maximum change in flux coupled to the S Q U I D as a function of the applied rf voltage to the HI coil for a time T = 24.5 ys.

one typical calibration, where the extrapolated flux change immediately following a 24.5 us rf pulse is plotted as a function of the voltage applied to the rf coil. The solid curve is a fit to

the data assuming only that AM = % ( I

-

case), where 9 is the rotation angle and

%

is the equilibrium magnetization at this field temperature. It must be remembered that the maximum pulse width 'r, just as in the case of conventional NMR, is deter-

mined by either the inhomogeneity in H or the intrinsic linewidth of the sample.

An example of one of the reai advantages of S Q U I D pulsed NMR is shown in figure 4 where fcur typical traces of the recovery of the magnetization of superfluid 3 ~ e are 181 shown at a temperature of 2 mK for four different rotation an- gles. Relaxations that exhibit exponential, linear, and square-root time dependences are observed and easily studied using a single rf pulse independent of the dephasing time, T2.

A typical cw NMR experiment on liquid 3 ~ e at 15 mK is shown in figure 5. This trace was obtained by sweeping the frequency of the H field

1

through resonance in the time shown. The baseline shows a slight upward drift and is due to a temperature dependent paramagnetic background and

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c6-1616 JOURNAL DE PHYSIQUE

Fig. 4 : Four examples of the recovery of the magnetization of superfluid 3 ~ e in a 180 Oe sta-

tic field. The time scale for the 90' and 120° data is 0.5 ms/cm and for the 150" and 180" data is 2.0 ms/cm.

t-min

0

Ho = 309 GAUSS T = 14.9 rnK P.16.4 BAR

Fig. 5 : Tracing of a typical cw NMR experiment on liquid 3 ~ e .

imperfect temperature control of the cell. Remem- ber, the S Q U I D will respond to all changes in flux coupled to the detection coil. The two peak resonance curve is due to the peculiar nature of the gradient in magnetic field H over the detection volume and is the major disadvantage of S Q U I D NMR.

This gradient in H arises because of the presence of the superconducting detection coil. The Nb

shield traps an integral number of flux lines, and the field H at any cross section of the sample sould be H = d@/dAeff, where @ is the total flux threading the cylinder and Aeff is the cross sec- tional area of the Nb shield minus the area of any superconducting material in the cross section con- sidered. The superconducting pickup coil has a fini- te length but is sensitive to magnetization changes occurring outside the ends of the coil. Thus it is expected that a two peak resonance curve should be observed because of the nearly discontinuous change in Hn on going from the region just outside the coil to the region inside the detection coil. For a small sample this inhomogeneity can be substan- tially reduced by using a split-Helmholtz design for the S Q U I D pickup coil, with the ends of the coil kept away from the sample. For a long sample, the use of superconducting shims or some other sui- table technique may be required to cancel most of the change in effective area occurring near the ends of the coil.

The maximum change in magnetization as a function of the square of the HI field observed during a S Q U I D cw NMR experiment is shown in figure 6. The solid curve drawn through the data is

Ho

= 309 gauss T=18mK P = 23 bar TI = 29 s T2 = 3.3 X s

Fig. 6 : Maximum change in magnetization occurring during a cw NMR experiment on 3 ~ e as a function of the square of the H I field. The solid curve is a fit to the data.

given by 191

AMZ ( Y H ~ ) ~ T ~ T ~ - -

%

I+(YH,)~T,T,

where T was used as an adjustable parameter while 2

H I and T were determined independently. The value 1

for T2 was 3.3 x s and is in agreement with the estimate of T one can make from the observed

2

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width of the curve displayed in figure 5.

SQUID adiabatic fast passage is a cw NMR technique used to invert the magnetization vector by applying a large HI field and quickly sweeping the frequency of the rf field through resonance. With a single passage through resonance both the value for twice the magnetization as well as the spin lattice relaxation time can be obtained. The conditions for an adiabatic fast passage in a SQUID NMR experiment are /6/

where AH is the inhomogeneity in H

.

^{The first}

part of the inequality insures that the magnetization vector will be reversed adiabatically 191, and the second part insures that the full resonance curve will be traversed in a time short compa- red to T1. A typical adiabatic fast passage experiment on 3 ~ e is shown in figure 7. Only the pas-

t - s

0 0.5 1.0 1.5 2 .O

I I I I I \

tional NMR experiment increases with decreasing frequency /6/ or decreasing magnetic field. Figure 8 demonstrates an example of the extreme sensitivity of the SQUID for detection of nuclear magne tism in low fields. A tracing of a pulsed SQUID

I I 4 I

PULSED NMR 3 ~ e

Ho= 3 7 GAUSS

812

P = 2 6 B A R - I O X I O - ~ ~

0 1 fo= 12.1 kHz

TI = 2 7 sec

Fig. 8 : Tracing of a pulsed NMR experiment on li- quid 3 ~ e for a nominal 180' pulse in a static field of 3.7 Oe.

NMR experiment in 3.7 Oe is shown following an 180° spin rotation. The signal to noise ratio for this trace was better than 100/1 and the measuring bandwidth was 10 Hz.

Ho=309 GAUSS SQUID NMR should prove to be a very power-

8

P-16.4 BAR

0.5

ful complement to convention NMR. Its main advan- T =

15.3

mK

HI=7.2

X

loT2 GAUSS

tages will be for studies of T. processes in the presence of very fast dephasinL times, measurements

$

of absolute susceptibilities and measurements in

Z

very low magnetic fields. It should be mentioned here that electron spin resonance experiments are also possible using a SQUID in the same measure-

f

-MHz

References

Fig. 7 : Tracing of a typical adiabatic fast pas-

sage experiment on liquid 3 ~ e . /I/ Silver,A.H. and Zimerman,J.E., Appl. Phys. Lett.

10 (1967) 142

-

sage through resonance is shown and not the reco- /2/ Day,E.P., Phys. Rev. Lett.

9

(1972) 540 /3/ Meredith,D.J., Pickett,G.R. and Symko,O.G., very of the magnetization back toward equilibrium.

J. Low Temp. Phys.

2

(1973) 607 The absolute magnetization scale was determined

/4/ Webb,R.A., Phys. Rev. Lett.

38

(1977) 1151 independently using only the calibration constant

/5/ Sager,R.E., Kleinberg,R.L., Warkentin,P.A. and of the SQUID 161. In a conventional NMR experiment Wheatley,J.C., Phys. Rev. Lett.

2

(1977) 1343 the passage through resonance generally must be 161 Webb,R.A., Rev. Sci. Instrum.

48

(1977) 1585 made ont the time scale of T2, but /9/ because /7/ Giffard,R.P., Webb,R.A. and Wheatley,J.C., J.

the SQUID is measuring the magnetization of the Low Temp. Phys.

6

(1971) 533

181 Webb,R.A., Phys. Rev. Lett.

60

(1978) 883 sample directly T I is the appropriate time scale.

This is a real advantage in many applications. /9/ Abragam,A., The Principles of Nuclear Magnetism (Clarendon Press, Oxford) 1961

In genera' the Of the detection sen-

/lo/ Deaver,B.S., Bucelot,T.J. and Finley,J.J., to be sitivity of a SQUID NMR experiment to a conven- published in the AIP Proceedings of the Confe-

rence on Future Trends in Superconductive Elec- tronics, Charlottesville,Virginia (1978)