Oscillating sample superconducting magnetometerM. Cerdonio, F. Mogno, G. L. Romani, C. Messana, and C. Gramaccioni Citation: Review of Scientific Instruments 48, 300 (1977); doi: 10.1063/1.1135013 View online: http://dx.doi.org/10.1063/1.1135013 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/48/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetometers based on double relaxation oscillation superconducting quantum interference devices Appl. Phys. Lett. 66, 2274 (1995); 10.1063/1.113190 Superconducting magnetometer Appl. Phys. Lett. 56, 2037 (1990); 10.1063/1.103010 Superconducting magnet image effects observed with a vibrating sample magnetometer Rev. Sci. Instrum. 54, 137 (1983); 10.1063/1.1137359 On the sample holders for the superconducting magnetometer Rev. Sci. Instrum. 47, 1551 (1976); 10.1063/1.1134546 Vibrating Sample Magnetometer Rev. Sci. Instrum. 31, 207 (1960); 10.1063/1.1716932

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Oscillating sample superconducting magnetometer M. Cerdonio, F. Mogno, and G. L. Romani

Gruppo Nazionale di Struttura della Materia and Department of Physics. University of Rome. Rome. Italy

C. Messana and C. Gramaccioni

Laboratorio di Ricerche di Base. SNAM Progetti. Monterotondo. Rome. Italy

(Received 28 October 1975; in final form. 21 September 1976)

An oscillating sample version of the superconducting magnetometer has been developed which measures the volume susceptibility of water solutions. Changes in susceptibility as small as 0.3% of the diamagnetism of water, or 2 X lO- Q cgs, have been resolved in the same run over the temperature range between 30 K and room temperature on magnetically dilute solution samples of 0.1 cm3 volume. The reproducibility of the instrument between different runs in measuring the absolute value of the magnetic susceptibility is 2% of the diamagnetism of water, or 1.5 X 10-8 cgs. By the combined use of the present method and the previous version it has been possible to measure the temperature dependence of the molar density of ice between 150 K and the melting point.

I. INTRODUCTION

Over the last few years we have been developing a super­conducting magnetometer to allow high-resolution sus­ceptibility measurements over a wide temperature range on weakly magnetic, small volume samples .1-4 The main motivation is the study of solutions of biochemical, metallo-organic, and inorganic compounds containing transition metal ions. The relevant information comes from temperature-dependent small deviations of the susceptibility from the constant dominant diamagnetic background of the solution. The interest in such meas­urement has been discussed more extensively else­where. I •3 During this work2 we were confronted with two problems. One was the contribution to the detected signal from the quartz tube holding the sample: this has been eliminated recently:> by the use of ,a modification of the shape of the holder tube, which is still simple enough to allow easy handling of the sample. The other was a large magnetic noise at characteristic frequencies well below I Hz, which was probably due to desorption of residual atmospheric oxygen from the walls of the sample Dewar and which would show up when the sample Dewar was heated up to about 200 K.2

By improving details of the sample Dewar and the preliminary cleaning procedure we ended Up3 with a magnetometer with a useful range well into the room temperature region, which is of biochemical interest for studies in solution. This method. which we call here the nonoscillating mode of operation, combined with the results of Ref. 5, presently allows us to measure the total value of the molar susceptibility of a sample once the total number of moles of sample and an instru­mental constant are known (see Refs. 3 and 5 for details). To solve the same problems outlined above we also developed an oscillating sample version of basically the same instrument, which we present here. The features of this new method are different from the previous one:

300 Rev. Sci. Instrum., Vol. 48, No.3, March 1977

(I) The quartz holder contribution is effectively nulled; without even recourse to the special tube of Ref. 5. one can use a simple quartz tube closed at the bottom, much the same as commercial tubes for EPR and N MR; (2) the modulation technique. which makes the sample oscillate at a few Hz, effectively nulls comparatively large drifts and noise in the baseline. which might be still present if less care has been used in the preliminary cleaning procedures; (3) the output of the system is now proportional, through an instrumental constant, to the volume susceptibility of the sample rather than to the molar susceptibility as in the other mode of operation.

In Sec. II we present details of the method and pro­cedure in taking measurements. In Sec. III we present results of tests of the instrument on pure water and on a frozen solution of an iron dimer. Also. by a test with both modes of operation we get the experimental evi­dence for the proper calibration solution to be used in connection with the new method. In Sec. IV we briefly compare the features of the two modes of operation.

II. EXPERIMENTAL SETUP AND MEASUREMENT METHOD

The instrument measures the change in magnetic flux when the sample oscillates perpendicularly to the plane of one of a system of two astatic pickup coils and parallel to the applied magnetic field (Fig. I). The magnet is superconducting and is operated in the persistent mode at typical fields of few tens of oersteds. The pickup coil is the primary of a superconducting dc trans­former; the secondary of the transformer is coupled to a SQUID superconducting magnetometer6 which is sensi­tive to a fraction of the flux quantum <Po = 2 x 10- 1

"

Wb. The whole assembly is immersed in liquid helium at 4.2 K. The pickup coils are a few turns. of 50 Mm o.d. niobium wire. with 10 mm o.d. in a planar configura­tion. The sample fills the bottom of a quartz tube of 6.0

Copyright © 1977 American Institute of Physics 300

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lOKHZU

tm5HZ \, IV \ /

-=- \/ - "

PICK-UP COILS

[j', , \ '

(

i \

SQUID

ELECTRONICS

o SQUID

RATIO

METER

FIG. I. Schematic of the detection setup in the oscillating mode of operation.

mm o.d. and 5.2 mm i.d., to a height of I close to the tube diameter d. The sample is suspended in a stainless steel Dewar; the tip of this Dewar, made of high purity silver, extends through the pickup coils; the sample temperature can be regulated at any desired value be­tween 4.2 and 350 K with the aid of platinum thermome­ters and manganin heaters. Details have been given previously.3

The sample is supported by a ferrite rod at room temperature attached to it and this rod is levitated and put in oscillation at about 5 Hz by a coaxial magnet (see Fig. I). A second ferrite rod is used to generate a reference signal proportional to the oscillation ampli­tude. This rod modulates the mutual inductance between two coils, one of which is fed with a stable 10 kHz signal. The 5 Hz amplitude-modulated 10 kHz carrier from the other coil is amplified and demodulated to give a dc signal proportional to the rms amplitude of oscillation of the sample. The signal from the SQUID magnetometer is fed to a lock-in amplifier, which uses as reference signal the 5 Hz oscillation amplitude signal, and yields a dc signal proportional to the rms change in flux. Finally, a ratiometer gives the ratio D of the rms magnetic flux change to the rms oscillation amplitude.

The sample can be either only moved through the two astatic pickup coils (see for details Ref. 3), as in the earlier moving sample mode of operation, or it can be put in oscillation at 5 Hz and at the same time slowly moved through the pickup coils.

For comparison we show in Fig. 2 the output N of the instrument in moving the sample through the pickup

301 Rev. Sci. Instrum., Vol. 48, No.3, March 1977

coils without any oscillation superimposed, and in Fig. 3 the ratio D obtained as described above with an oscilla­tion amplitude of a few millimeters. The oscillation amplitude is always kept small in respect to the width of the sample contribution to the signal [Fig. 2, curve (a)]. Apparently curves (a) and (b) of Fig. 3 are the derivatives with respect to position of the corresponding curves of Fig. 2. It can be noticed from a comparison of curves (a) and (b) in Fig. 2 that the quartz holder gives a large contribution which superimposes on the sample contri­bution to form the total signal. By contrast it can be appreciated that the two smaller peaks, the "sample" peaks, of Fig. 3, curve (a), occur at a position where the quartz holder signal is negligible, as shown by curve (b). We have taken the height D of the "sample" peaks as a measure of the susceptibility. At each temperature we determine the value D at one of the two "sample" peaks by scanning the immediate vicinities of the chosen peak.

We have found that for a number of different tubes of similar dimensions and for samples with I = d, the residual holder contribution at the sample peak is less than 1% of the height of the sample peak D.

III. TESTS OF THE INSTRUMENT

The instrument has been tested with a few samples of pure, deionized, deoxygenated water of different total volumes. The reproducibility between different helium runs for the same sample has been found to be of the order of 2% of the sample susceptibility. On the other hand, the resolution in detecting small susceptibility changes in the same run is less than I % (see also Fig. 6 below). Experimental data for samples tested in different helium runs are shown in Fig. 4(a). The range of sample volumes explored is between a minimum of 0.098 cm3

for one sample in the liquid state and a maximum ofO. 141 cm3 for another sample in the frozen state. For compari­son, in Fig. 4(b) we show experimental data for a similar sample taken with the previous, nonoscillating method of Refs. 3 and 5. Both Figs. 4(a) and 4(b) were obtained for the same coil geometry, sample tube, and similar sample dimensions. Because, for the same run, resolu­tion is better than the run-by-run reproducibility, we present the data as follows: in both cases measurements in the same experimental run are given relative to the datum Do at temperatures above the melting point of water. Values of Do for different samples agree within the reproducibility.

The data of Fig. 4(b) are consistent with the data given by Cabrera,1 in particular in crossing the melting point, and extend the range to lower temperatures, giving the temperature dependence of the molar susceptibility of ice relative to the value for water at 289 K. The absolute value of X.U, evaluated from the calibration given in Ref. 3, is identical within 1% to the absolute value given in Ref. 7. The data of Fig. 4(a) show a much larger varia­tion with temperature, especially at the melting point, where there is a large density change of water. This behavior suggests that an appropriate calibration rela-

Superconductlng magnetometer 301

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4

~

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4 5 6 7 8 9 10 SAMPLE POSITION X (em)

tion for the new oscillating mode of operation might be the following:

(I)

with a calibration constant Z independent of the temperature-dependent density of the sample.

To test the validity of this hypothesis, we plot in Fig. 5 the quantity p(T)/po = D(T)N oIDoN(T) as extracted from the data of Figs. 4(a) and 4(b). Assuming the validity of the appropriate calibration relation for the two

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4 5 6 7 8 9 10 SAMPLE POSITION X (em)

302 Rev. Sci. Instrum., Vol. 48, No.3, March 1977

11

11

(a) water 0.11 gr

(b) quartz holder

H = 31 oersted

T = 280 DK

FIG. 2. X - Y recording of the output of the magnetometer versus sample position in the moving sample mode of operation. Curve (a). water sample in quartz holder; curve (b). quartz holder alone.

versions as given in Ref. 5 and in Eq. (1) above, the ratio p(T)/po should represent the temperature variation of the density of the frozen water sample peT) relative to the density Po in the liquid state. The small density changes above melting are smaller than our resolution and neglected. For comparison the solid curve in Fig. 5 shows the temperature dependence of the density of ice I given by Kel1. 8 It should be noted that whenever water is slowly frozen at low pressure as we do, one invariably gets polycrystalline ice I. The agreement is very good,

(a) water 0.11 gr

(b) quartz holder

H =31 oersted

T = 2800K

FIG. 3. X - Y recording of the output of the ratiometer (see Fig. I) versus sample position in the oscillating mode of operation. Curve (a), water sample in quartz holder; curve (b), quartz holder alone.

Superconducting magnetometer 302

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FIG. 4. (a) Output D(T) of the ratio meter in the oscillat­ing mode of operation rela­tive to the value Do meas­ured above the melting point in the same run, for samples of pure, deoxygenated, de­ionized water of different weight and for different runs of the same sample. Sample holder quartz tube of 0.52 cm i.d. for all measurements; (b) (0), output N( n of mag­netometer in the nonoscillat­ing mode of operation rela­tive to the value No at T = 289 K, sample mass 0.120 g; (e), molar susceptibility of water relative to the value at 20°C (adapted from Ref. 7).

tOOf-

0.95f-

0.00-

0.85f-

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water

I

100

o 0.130 9 .0 O.lll 9

• 0.122 9

t:, 0.098 9

.. 0.126 9

I 50

o

so we conclude that, for the new oscillating sample version, relation (1) is an adequate calibration relation for "short" samples, that is, when I = d, which expands on freezing. It should be emphasized that the instrumental constant Z is independent of sample density and also of sample height, in the limits of the range of volumes scanned, when the sample cross section is kept constant.

303 Rev. Sci. Instrum., Vol. 48, No.3, March 1977

I I

200 250

(a)

.4Ca6. 0 •

• o

T(Of()

I 300

WATER o this work-method of refs. [3] and [5J

• from ref. [7J

o .. ~

I I 1 I 150 200 250 300

(b)

Another test has been made to show the capability of the instrument in resolving very small susceptibility changes between different temperatures in the course of the same run. In Fig. 6 we show preliminary data7 of the antiferromagnetic behavior of the oxobridged dimer [(Fe BDEDA)20(H20h] (S04h' H20. We observe a small temperature-dependent contribution superim­posed on a large diamagnetic background. In the low-

Superconductlng magnetometer 303

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plTI eo ---~-.--------- ·_--1 -I

.94

.93 • • I

. 92 4

4 ,~

.91

.90 I I I 100 150 200 250 300

T (OJ()

FIG. 5. Data points (6, &, D .• , O .• ) temperature dependence of the molar density piT) of the same samples of Fig. 4(a) relative to the value Po at 289 K as extracted from the data of Figs. 4(a) and (b); full curve--: temperature dependence p( T)lpo for ice I as reported by Kell in Ref. 6.

temperature region this contribution shows a simple Curie behavior, which can be easily attributed to the paramagnetism of dissolved oxygen plus a few percent of the total iron present being in a free high-spin form. We have fitted this low-temperature part of the data with the solid line shown in Fig. 6. The overall scatter of the data from the linear Curie law interpolation is of the same order as the reading error of each datum point. We take this quantity, about 0.3% of the diamagnetism of water or 2 x 10-9 cgs, as the resolution of our instrument for the same run.

At higher temperatures an additional temperature­dependent "paramagnetic" contribution shows up. This

0.7

0.70

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behavior would be typical of a contribution from intra­molecular antiferromagnetism in the dimer. with a coupling constant of the order J/K/I =, -)50 K. We believe that this is what we arc observing. and indeed. it compares very well with the coupling constant J / K/I = -133 K already found in the solid form of the same dimerY This comparison will be quantitatively analyzed elsewhere. lo Here we only want to show that such a small temperature-dependent contribution to X"m" can be resolved easily by our method.

IV. DISCUSSION

In this section we discuss further our particular choice for the calibration relations of Eq. (I) and con­sider the difference between the two modes of operation.

In relating N or D to the sample susceptibility in each of the two modes of operation, with and without oscilla­tion. care has to be taken in regard to the change in density of the sample. As we intend to use the instrument in a wide temperature range, at least 100°C below room temperature, it is obviously convenient to use a calibra­tion formula in which the calibration constant is inde­pendent of sample density. Let us first consider the previous mode of operation (Ref. 3), with the modifica­tion given in Ref. 5.

We recall here the calibration relation given in Ref. 3 as modified in Ref. 5.

11.6 mM in Fe (m)

pH=6

H = 38 oersted

20 25

FIG. 6. Volume susceptibility versus inverse temperature (K-') for a solutio~ 1':6 mmol in 3+Fe of the antiferromagnetic oxobridged dimer [(Fe BPEDA)20(H20hJ (SO.h· H20. (BPEDA = N .N'-bis-(2-picolifl-ethylenedIamme.l

304 Rev. Sci. Instrum., Vol. 48, No, 3, March 1977 Superconducting magnetometer 304

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where H is the external applied field, 11; is the total number of moles of the i component of the sample of molar susceptibility XW, and ~ is an instrumental con­stant independent of the amount of sample and its density. Relation (2) has been found adequate experi­mentally within the experimental error of about 1% and can be easily deduced from basic principles if one assumes the validity of the so-called "short" sample approximation as given in Ref. 6(b). In this sense, read­ing relation (2), we say that the previous version of the instrument measures the total value of the molar susceptibility.

Let us now consider the present oscillating sample version. We have already seen in Sec. III that the combination of calibration constant and susceptibility given by relation (I) keeps the calibration constant independent of density and the amount of sample present, provided that we put in relation (I) the volume susceptibility Xcml. In this sense we say that our oscillat­ing sample magnetometer measures the total value of the volume susceptibility.

We believe there is a simple physical argument which leads us to expect the validity of relation (1) with Z density independent under the specified condi­tions. Roughly, we have

D = KN/~x, (3)

where K is a numerical constant and ~ is the width of the bell-shaped sample contribution in the nonoscillating mode of operation [see Fig. 2, curve (a)]. This result, with the appropriate numerical constant, will apply to any reasonable bell-shaped sample contribution, as, for instance, an isosceles triangle, a Gaussian, or a Lorent­zian. Let us then consider that the quartz tube used as sample holder will expand with temperature much less than the frozen solutions we are dealing with. We can assume to a first approximation that the sample cross section diameter will not change with temperature be­cause the sample is more plastic than the quartz and will not deform the tube; thus, the height of the sample will be proportional to its volume. It is also reasonable to assume that the width ~x will be proportional to the sample height; thus, width ~x becomes proportional to the volume of the sample. If, with this in mind, we combine Eqs. (2) and (3), we recover relation (I) above with Z proportional to the sample cross section. If we keep this last parameter constant, as we do, then Z comes out to be volume and density independent. ll

Obviously this is only a plausibility argument, but as relation (I) is experimentally obeyed, under our condi­tions, to within our run by run reproducibility, we expect it to give an adequate approximation which should be deducible from a careful a priori calculation. This problem involves the detailed calculation of the distribution of the magnetic field at the pickup coil as given by the sample at any distance and, due to the relative size of sample and pickup coils, must be done numerically. We hope to perform this calculation in the near future.

305 Rev. Sci. Instrum., Vol. 48, No.3, March 1977

A few comments are in order here comparing the performance of the two methods. Both have been used to cover the same temperature interval between about 30 K and a little over room temperature; in this range the capability in resolving small changes in susceptibility is similar for the present version compared to the previ­ous one. Also the run-by-run reproducibility is similar in the two versions. There is no intrinsic limitation to further expanding the useful temperature range. The in­creased vibrational noise, which we observe when the sample is below 30 K and which compels us to reduce the resolution below the limits quoted above, is the result of our particular setup and can be avoided by increasing the mechanical stability of the sample Dewar.

We consider the two versions to be complementary; indeed, the central point about measurements of mag­netic susceptibility on such a wide temperature range is that the density of sample may not be known accurately enough. This is certainly true for solutions of chemical and biochemical compounds. We have shown that com­bined measurements with the two versions of the instru­ment can give the temperature dependence of the molar susceptibilities of the sample alone, which is the property of interest, and as a side bonus also the temperature dependence of the density. Whenever the temperature dependence of the density of a sample is not a problem, the present version might be more con­venient if the demands of care in keeping the apparatus clean from paramagnetic impurities, such as atmos­pheric oxygen, are too stringent with the other method.

The need for an instrument with performance similar to the present one for the study of very weakly magnetic samples, like biochemical compounds, has been already discussed in Refs. I and 3. However, note that this instrument makes it possible to investigate intramolecu­lar antiferromagnetism in moderately dilute solutions. The sample concentration, close to 5 mM in dimer, and the total amount of material needed, less than I /-Lmol of dimer, are accessible to present biochemical purification methods. Moreover the instrument scans a temperature range which is highly significant for these studies because the coupling constants are expected to fall in the range of few hundred kelvins for many relevant cases.

ACKNOWLEDGMENTS

We wish to thank B. Pispisa for his kind permission to reproduce data from our work in collaboration prior to publication. We are indebted to M. Berardo and E. Gori for their continuous and skilled technical assistance.

I M. Cerdonio. R. H. Wang. G. R. Rossmann, and J. E. Mercereau, in Pmc. Low Temp. Phys. Conf LT 13 (1972), edited by E. Timmerhaus (Plenum, New York, 1974).

2 M. Cerdonio and C. Messana, IEEE Trans. Magn. M-ll, 728 (1975). 3 M. Cerdonio, C. Cosmelli, G. L. Romani, C. Messana, and

C. Gramaccioni, Rev. Sci. Instrum. 47, I (1976).

Superconducting magnetometer 305

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I A preliminary account of this work has been given by M. Cerdonio. C. Cosmelli. F. Mogno, and G. L. Romani. in Loll' Tcmperaturc Physi('s LTl4, Vol. IV, edited by M. Krusius and M. Vuorio (North Holland-American Elsevier, Helsinki, 1975), p. 258.

c, M. Cerdonio. C. Messana. and C. Gramaccioni. Rev. Sci. Instrum. 47,1551 (1976).

" For recent reviews of superconducting quantum interference devices see, for instance, (a) J. Clarke. Proc. IEEE 61, 8 (1973), and (b) R. P. Giffard, R. A. Webb, and J. C. Wheatley, J. Low Temp. Phys. 6, 5-6 (1972).

306 Rev. Sci. Instrum., Vol. 48, No.3, March 1977

, B. Cabrera. J. Chern. Phys. 38, 1(1941). H G. S. Kell. Chem. Phys. Lett. 30, 2Tl (1975). " B. Pispisa (private communication).

10 M. Cerdonio. F. Mogno, B. Pispisa. G. L. Romani. and S. Vitale. Inorg. Chern. (to be published).

II This argument may not apply to a ,.,ituation where the ,ample would contract rather than expand on freezing, e.g .. many solid materials. We are indebted to the referee for pointing out this possibility to us. However. such a situation is very unlikely for water solutions of chemicals and biochemicals.

Superconducting magnetometer 306

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