high field nuclear magnetometer
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High field nuclear magnetometerApril Dutta and C. N. Archie Citation: Review of Scientific Instruments 58, 628 (1987); doi: 10.1063/1.1139228 View online: http://dx.doi.org/10.1063/1.1139228 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/58/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Torsional oscillator magnetometer for high magnetic fields Rev. Sci. Instrum. 67, 4161 (1996); 10.1063/1.1147562 A high field Faraday magnetometer for measurements under high pressure (abstract) J. Appl. Phys. 73, 5638 (1993); 10.1063/1.353622 Diaphragm magnetometer for dc measurements in high magnetic fields Rev. Sci. Instrum. 61, 848 (1990); 10.1063/1.1141452 Optically Pumped Nuclear Magnetometer Rev. Sci. Instrum. 34, 1363 (1963); 10.1063/1.1718237 HighField Optical Magnetometer Rev. Sci. Instrum. 33, 74 (1962); 10.1063/1.1717667
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High field nuclear magnetometer April Duttaa) and C. N. Archieb
)
Department of Physic~~ State University of New York at Stony Brook, Stony Brook, New York 11794
(Received 2 December 1986; accepted for publication 18 December 1986)
. A magnetometer capable of measuring changes in the nuclear magnetism of ~\He in the presence of an 8-T magnetic field is described. A key component is a type II superconducting shield (NbTi) which stabilizes the external field. Short-term sensitivity is equivalent to detecting magnetic field changes of a few parts in lOw, In applications involving large pressure changes and 3He liquid-solid phase changes, additional problems arise. Sensitivity to physical distortion of the device in some applications can generally be corrected for or exploited for pressure detection.
INTRODUCTION
Measurements of magnetic fields with SQUID-based magnetometers have occasionally achieved resolutions of better than a few parts in lOw. For example, the measurements of the change in the liquid 3He magnetization between the normal liquid and the A phase required such resolution. I However, such situations have nearly ideal ambient field environments of modest magnetic fields less than 0,05 T in mu-metal and type I superconducting shields.
Detection of nuclear-magnetic susceptibility in high magnetic fields is conveniently done by nuclear-magnetic resonance techniques provided there are no serious problems with field homogeneity, spin-lattice relaxation time, or rf heating of the sample or celL
A potential advantage of a nonresonant magnetization measurement, however, arises in the study of the nonlinear field dependence of nuclear magnetization. Extensive changes in the magnetic field and, hence, the Larmor frequency for pulsed and cw NMR introduce calibration problems associated with changes in tank circuit Q 's and gains in rf electronics. These problems can be handled to some extent with heterodyning techniques.
Nonresonant mechanical techniques have been reported with sensitivities comparable to or better than SQUID magnetometers. These measure the magnetic force2 or torque3 on the nuclear magnetization due to the presence of a large magnetic field. While these are promising developments it remains unclear whether such techniques can be applied to high-pressure liquid-solid studies of interest to us,
OUT desire to have a reasonably self-contained nuclear magnetometer serviced by readily available commercial electronics which could study a wide range of high field properties of 3He motivated the development of a S.H.E. rf SQUln~-based gradient magnetometer. Direct detection in a nonresonant way of the nuclear magnetism contribution to the total magnetic field by a sensitive magnetometer relies OIl
stability of that component of the external field that the coil system is sensitive to. We report upon several important design features which have helped to make this device have a short-term sensitivity of a few parts in 1010 of the main field which is comparable to low field devices and to one high field dilute gas (spin-polarized hydrogen) application.5 In addi-
tion, complications associated with massive pressure changes of the sample are discussed.
I. DESIGN AND CONSTRUCTION
Figure 1 depicts the magnetometer which is designed to be part of a low-temperature 3He compression cell. The pressure, temperature, and volume of the sample are monitored in situ by sensors not shown. A dilution refrigerator plus the Pomeranchuk effect allows the temperature of the cell to be reduced to below 5 mK.
The astatic pair is intended to greatly reduce fiux contribuiions from the homogeneous part of the main magnetic field. The pair is part of an adjustable superconducting fiux transformer illustrated in Fig. 2. Changes in the entrained flux are detected by a standard S.H.E. rfSQUID. Adjusting the sensitivity of the circuit by varying the distance between the coils in the dc flux transformer proves to be an expedient way to optimize the performance of the magnetometer after experiencing the actual operating conditions. Characteristics reported here result from a 10- 3 attenuation ofthe astatic coil flux change as seen by the l'fSQUID.
Detrimental magnetic field changes can result from the slow decay of the quasi persistent superconducting magnet (decay time 7~2000 days), mechanical vibrations of the cell relative to the magnet, and flux rearrangement in the magnet and elsewhere. In order to reduce these, the magnetometer coils are encased in a NbTi tube. Operating between Hel and Hc2 for this type II superconducting material results in a slight magnetic field difference between inside and out (estimated by field ramping hysteresis to be on the order of 500 G). Provided that outside field changes are less than this difference, the inside field remains constant. In practice, a few hours after a major field change, the magnetometer signal settles down with a long-term noise level considerably less than 10- 3 of the saturation nuclear magnetism ofliquid 3He.
This design specifically shields the coils from field sources outside the shielding. Contributions from epoxies and plastics (significant hydrogen component) and normal metals elsewhere in the experimental cell are, thereby, greatly reduced. The nonmagnetic quartz former is made from commercially available tubing and rod.
628 Rev. Sci. Instrum. 58 (4), April 1987 0034·6748/87/040628-04$01.30 @ 1987 American Institute of Physics 628
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o NbTi
t;J Quortz
1?'?1 Epoxy ii§ Stycost 1266
Gradient Coii
/Calibrating / Primary Coil
5mm ~----------~
FIG. 1. The high field nuclear magnetometer is protected from small changes in the magnetic field (vertically oriented) by the type n NbTi superconducting shield. This device is epoxied into the upper wall of a lowtemperature "'He compression cell.
II, CAL.IBRATION
Sensitivity calibration is performed by the "calibrating primary coil" depicted in Fig. 1. We have calculated the mutual inductance between this coil and the astatic pair as well as the induced flux in the astatic pair due to a homogeneously magnetized material occupying the open volumes depicted in Fig. 1. The main contribution clearly comes from the cylindrical volume enclosed by the lower coil of the astatic pair. Note that it is important to include the effect of shielding currents in the superconducting tube.6
Equivalent surface current formalism for the magnetized material allows all the calculations to be determinations of mutual inductances between coaxial coils. A convenient way to express the results of these calculations is to let the coils representing the 3He magnetization have the same winding density N /1 as for the primary coil, then the ratio of sample mutual inductance to primary coil mutual inductanceisJlf 3S lMps = 0.251 ± 10%. Thecurrentwhichcorresponds to full polarization in the coil system representing the 3He is then np] IN where n is the number density for the 3He and fl is the nuclear-magnetic moment. The short-term (t<.10 s) primary current resolution (at constant sample pressure) corresponds to to-· 5 of the 3He saturation magnetization which in turn implies a field change detection precision near four parts in 1010.
In addition to allowing for nuclear-magnetization measurements in magnetic fields up to 8 T and as a function of temperature, some of our applications require the magne-
629 Rev. ScI. Instrum., Vol. 58, No.4, April 1987
resistors
magnetometer r astatic coil pair
primary
FIG. 2. Schematic of the wiring servicing the primary and secondary coils of the magnetometer. Only the probe depicted in Fig. 1 and the twisted pairs leaving it are in high field. The dc fiux transformer is in the helium bath along with the rf SQUID. The limiting resistors for the calibrating primary arc heat sunk to the still of a dilution refrigerator. All these components except the twisted pa.ir coming from room temperature to the resistors are encased in superconducting shields.
tometer to function accurately in the presence of substantial pressure changes (8P~ 1 to 10 bar).
This complicates the calibration procedures since the finite compressibility (K~2.gx 10--0 bar-- 1 ) of the quartz implies that pressure changes affect the area of the quartz former and hence the magnetic flux if; entrained by the astatic pair. For a homogeneous main field and perfectly wound astatic pair, flux changes in the lower coil are compensated by corresponding changes in the upper coil. Even small imperfections in this arrangement lead to significant effects when compared to the nuclear magnetism. The flux change in one loop of the lower coil due to a pressure change 8Pin a magnetic field H is
0"- = ~ aHldjp Of' 3
where a is the area of the loop. This mimics a sample magnetization change 8m given approximately by
f.tilm ~o<p/a.
For a pressure change of 1 bar in 8 T this equals 0.15 g or about 4% of the saturation nuclear magnetization. Consequently, the residual ofimperfect cancellation must be compensated for.
In addition, studies indicate that there is an effective sample volume dependence to our magnetometer signal. We speculate that cell distortion and tilting of the magnetometer resulting from compressing/decompressing the sample in situ is responsible for this. Our calibration procedure compensates for this effect as well. 7
Compensation calibrations for pressure and volume changes are conducted near 1 K where magnetization contributions from the nuclear magnetism and diamagnetism of 3He are small. For several different amounts of the sample, the cell is compressed and decompressed and the volume,
Nuclear magnetometer 629
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pressure, and magnetization signals are recorded. Quadratic fits to these studies remove the pressure and volume dependences from the magnetometer signal to better than 1 % of the saturation nuclear magnetization over a to-bar pressure span relevant to our application. Measurements involving less violent pressure changes can expect correspondingly better compensation.
A critical test of these pressure and volume compensations is conducted by compressing a high-temperature sample (T ~ 0.3 K), thereby converting unpolarized liquid to unpolarized solid. Solid strain conceivably could produce different cell distortions than compensated for by the allliquid studies. In practice irreproducible magnetization anomalies of the order of a few percent of the solid saturation magnetization are observed. The tendency for plastic deformation of solid 3He apparently prevents pressure differences across the cell greater than about 0.1 bar during all but sudden conversions.8
III. DISCUSSION
Use of the magnetometer requires accurate simultaneous measurements of pressure, volume and magnetometer signals. Such ability was available during our studies of the production of moderately spin-polarized 3He solid by the freezing onow-temperature liquid in an 8-T magnetic fieldY Figure 3 shows the sample pressure and the compensated magnetization signal during one relatively rapid compression in a magnetic field of 8 T at low temperatures (below 20 mK).
This particular compression is chosen for discussion because several features appeared during this experiment which illustrate strengths, weaknesses, and observations of this magnetometer. The volume rate of change is nearly constant throughout the time period except for a pause near the very beginning.
Solid 3He is nearly paramagnetic except at the low temperatures and fields: therefore, the solid magnetization m is given approximately by
m = flll tanh (pH /kB T),
34
d
\ '-
.8 33.5 Z \~ • \ \
\ \
) t f
o
10
~ /'-. ..1"./30
i ...... .l 4
/ 0 33
e 32.5
0L--l.--
IL.O---'---2-'-O---'---3-'-O-----L---l
Time (minule)
FIG. 3. Pressure and corrected magnetization during a low-temperature conversion of un polarized 'He liquid to a moderate nuclear-spin polarized solid in the presence of an S-T magnetic field. Letters refer to particular events during the compression. See the text for details.
630 Rev. Sci. instrum., Vol. 58, No.4, April 1987
wherefl/kB = 0.78 mK/T. By contrast, the liquid is a Pauli magnet (degenerate Fermi liquid). As a consequence, the magnetization in units of the solid saturation magnetization (pn) can change from 3.5% (liquid equilibrium value in 8 T at high pressure) to greater than 60% during the compression caused phase change. Several features of the compression should be noted.
Discontinuities in the magnetization signal (feature a) are due to flux jumps in the rf SQUID. Unlocking of the SQUID in feedback mode is frequent and spontaneous immediately after a major field ramp but after several hours, momentary unlocking is usually due to exceeding the feedback limit of the device. In any case, provided such "resets" are infrequent their unique signature allows the data to be corrected.
Feature b corresponds to the sample pressure reaching the melting pressure. Due to conversion ofliquid to the 5% denser solid, the rate of pressure increase suddenly decreases.
The apparent reversal of the magnetization just before the major increase (feature c) is not well understood. In light of the high-temperature liquid-solid conversion studies, this is probably due to the small but nonzero solid flow stress discussed previously.
Solid apparently forms in the magnetometer during the final half of the compression (between features c and e) but before full solid production occurs, as indicated in the pressure trace by a sudden increase in slope (feature f ). The pressure leveled off at feature d due to the cooling power from liquid to solid conversion becoming equal to the heat leak. This is near 5 mK
Increased noise in the signals later in the compression (after feature d) is likely due to crushing of solid and the resulting heating and recovery. Our current compressions are performed at considerably slower rates thereby avoiding these noise features and producing considerably higher solid spin polarizations.
The device dependence on sample pressure and volume is both a nuisance and suggestive of future applications. On the one hand, the device cannot accurately track the magnetization during rapid pressure changes (dP /dT:;.O.l barfs) because of systematic errors introduced by the pressure and volume corrections caused by time lags in the sensors.
On the other hand, a particularly promising application is as a sensitive pressure gauge of high dynamic range and small dead volume. The current device has a short-term pressure resolution of 10--4 bar with a range which is untested but must certainly be greater than a few hundred bars . Considerable improvement can be gained by using a simple coil wound on a quartz rod sitting in a field stablized type II superconducting shield. Such a device would be a robust gauge for high field low-temperature experiments with a ratio of range to sensitivity greatly superior to the often used capacitive strain gauges. 10
ACKNOWLEDGMENT
This work was supported by the National Science Foundation through Grant No. DMR 8218993.
Nuclear magnetometer 630
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• ) Present address: Harvard Medical School, NMR Lab, 22! Longwood Avenue, Boston, Massachusetts 02115.
h) Present address: Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York, 105<}8.
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631 Rev. Sci. lostrum., Vol. 58, No.4, April 1987
.' ••••••• :.:.;.;.~.,. ........... y.:o; ••••••• ; •••••• v; •••••••• -•• ' ••••••••••••••• -.-•••• /.
ed in San Diego, CA . 'J. T. M. Walraven and I. F. Silvera, Physica 107"8, 517 (1<}81). oR. P. Giffard, R. A. Webb, and J. C. Wheatley, J. Low Temp. Phys. 6, 533( 1972).
7Cell distortion should involve only two independent degrees of freedom since the liquid-solid state of the sample is thermodynamically well specified by two variables, such as cell volume and pressure.
SM. B. Manning, M. J. Moeller, and C. Elbaum, Phys. Rev. B 33, 1634 (1986).
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Nuclear magnetometer 631
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