Magnetic Susceptibility: Instrumentation and Applications L
L. N. Mulay” and lndumati L. Mulay Material Sciences Department (139 Materials Research Laboratory), The Pennsylvania State University, University Park, Pa. 16802
In this eighth review on magnetic susceptibility we survey important trends in instrumentation and applications, especially in the realm of analytical chemistry. The first seven reviews appeared during 1962-1974 (53,59-64). This 1976 addition covers literature from about January 1974 to December 1975. In response to an editorial plea, we have made this review more concise than the previous ones. In doing so it seemed imperative that we depict the exceptionally novel trends and eliminate those that we covered before, without, of course, implying in the least that these are no longer important. Hence, we shall not review the work on lunar samples, which was adequately covered before (62, 6 3 ) and work on transition metal complexes including the biocomplexes, which we surveyed in all reviews up to 1972 (59-63). I t should be noted that new books by Mulay and Boudreaux (55a,b) and excellent surveys on the transition metal and rare earth complexes and on molecular diamagnetism are now available and are listed in a later section. Since this review is concerned with instrumentation and analytical applications, we have focused relatively more attention on practical aspects of instrumentation and have attempted to point out the truly new trends in the hope that experimentalists will explore novel avenues of instrumentation for specific problem-oriented research and that they will not remain chained to otherwise outmoded techniques. Since the classical methods, such as the Faraday and the Gouy techniques, quite surprisingly, continue to be very reliable for the measurement of weak susceptibilities and since these are relatively less expensive than some of the modern gadgetry, we shall continue to incorporate important modifications and tricks-of-the-trade reported by ingenious workers. Unfortunately, owing to limitations of space we shall not be able to survey various temperaturecontrolling and measurement devices. Furthermore, while curtailing our usual coverage of the general field of magnetic instrumentation we have stressed applications which are expected to be of special appeal to analytical chemists. Our rationale for selecting these, is given later under the “Applications” section. We urge our readers to refer to our earlier reviews (60-64) concerning the scope of areas like solid-state science (that is chemistry and physics of solids), which is synonymous with materials science in order to appreciate their interdisciplinary role in science and technology, their relevance to societal needs, and their relationship to analytical chemistry, with special reference to the characterization of materials at the macro- and microscopic levels. GENERAL LITERATURE Abstract Services a n d New Journals. Reference should be made to our earlier reviews (60-63) concerning abstract services and review series available in the general area of magnetics. Despite the hue and cry concerning the proliferation of journals amongst its editors and, more importantly, amongst its readers, one is perplexed to find the entry of two new journals in the realm of magnetics. One entitled the “Journal of Magnetism and Magnetic Materials” edited by Freeman (33) was introduced in late 1975. I t should be noted that Freeman (34) is also the editor of another “International Journal of Magnetism”. A second journal edited by Cox ( 1 6 )is entitled “Magnetism Letters” and is designed for rapid publication of topical papers dealing with all aspects of magnetism and magnetic materials. Considering the possibility that these two new periodicals (in additions to the already existing international journal, and the IEEE transactions in magnetics) may help to consolidate to some extent the widely scattered literature in this field, most magneticists may welcome the addition of the new journals. Their future publication performance will 314R
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tell if these might substantially represent the interests of chemists, which can be always categorized, despite their diversity, under the rubric of “Magnetochemistry”. In any event, we welcome these journals with hopes within, future ahead, and with mixed blessings! Books, Reviews, and Contributed Chapters. Mulay and Boudreaux (55a) have edited an advanced treatise entitled “The Theory and Applications of Molecular Diamagnetism” and another with a similar title on “Molecular Paramagnetism” (5%).The spirit and rigor with which work on the two books was undertaken in collaboration with outstanding contributors is reflected in Mulay’s preface to each volume. We give below edited excerpts from his prefaces: “The popular quotation, ‘Brevity, the soul of wit, may become the very body of untruth’ aptly reflects the dangers and the agonies of attempting a short review of any difficult and complex subject. Researchers and teachers alike well recognize that our comprehension of such subjects may be only of the abbreviator’s preconceived notions and not of ‘the vast ramifying reality from which these notions have been arbitrarily extracted.’ We trust that Aldous Huxley’s astute observations ought to explain in part our indulgence in editing a voluminous book. Needless to say, this enterprise would not have been possible without the consent and more importantly, the tireless labors of our participating authors. We must concede that when our adventure was first conceived we thought that one could perhaps discuss, within the confines of a compact volume, important developments in molecular diamagnetism and paramagnetism, which represent but two ramifications of magnetism. However, prompted by the pressures of information explosion we soon discovered the compelling need for editing two separate volumes in these areas . . . We should point out that during the past two decades of our research and teaching activities in the magnetics area, we were dismayed to find a lack of advanced and comprehensive treatments on molecular diamagnetism and paramagnetism. We, therefore, sincerely hope that these volumes may be useful to researchers and, in a small measure, to students a t the advanced level.” The volume on diamagnetism ( 5 5 ~ contains ) the following chapters. In his very first chapter, entitled “The Realm of Magnetics, Magnetochemistry and Diamagnetism” Mulay discusses principles of not only molecular diamagnetism but also of Landau diamagnetism of conduction electrons as encountered in graphite, the extensive work on which is reviewed in a later chapter on recent advances written in collaboration with Boudreaux. Mulay has made a special effort to devote several pages to the relevance of magnetics research to societal needs. He has written a separate chapter defining various magnetic terms and has addressed himself to the vexing problems concerning the adoption of the unrationalized cgs (or so called cgsemu) units vs. the rationalized mks or the new Systemme’ International (SI) units. Hameka and Cressy give quantum mechanical foundations of diamagnetism and correlations with NMR chemical shifts. Their chapter is immediately followed by the most extensive treatment by Haberditzl on the appropriate formulations of theories of molecular diamagnetism and numerous applications. He discusses the advanced and reliable techniques of calculating molecular susceptibilities. In addition he discusses correlations with NMR chemical shifts, and interestingly the effects of magnetic fields on diamagnetic macromolecular systems. The advanced treatise on molecular paramagnetism ( 5 5 b ) includes again an appropriate introductory chapter by Mulay with even more extensive sections on the rele-
L. N. Mulay is a professor of Solid State Science in the Materials Science Department at The Pennsylvania State University since 1967 and served as chairman of the corresponding interdisciplinary program from 1967-1972. He took his PhD (1950) in physical chemistry from the University of Bombay. He held various research and teaching positions in chemistry at Northwestern and Harvard Universities before joining the faculty at Penn State in 1963 as an Associate Professor. Dr. Mulay is the author of about 130 research publications and a monograph on “Magnetic Susceptibility”. He is the coeditor of two new treatises on the “Theory and Applications of Molecular Diamagnetism and Paramagnetism” (Wiley, 1976). He is internationally recognized for his many contributions to magnetics. His research interests have centered on magnetic probes, such as susceptibility, broad-line NMR, EPR, and Mossbauer spectroscopy for the characterization and structural elucidation of solids at the macro and microscopic levels. Dr. Mulay has traveled widely and contributed to international meetings and research conferences. He is a member of several professional organizations and was chairman of the Central Pennsylvania Section of the ACS (1965). He has been a regular contributor to Analytical Chemistry’s Fundamental Review issue since 1962. lndumati L. Mulav has been a research associate and collaborator in the Materials Research Laboratory at The Pennsylvania State University since 1963 She received a BS in chemistry and MS in biochemistry (1953) from the University of Bombay She also earned an MS (Radcliffe College) in 1957 and a PhD in bioiogy (Cincinnati) and did postdoctoral research at the University of Cincinnati before joining Penn State Her main research interests include radiation genetics. trace metal analysis, EPR studies on cancer tissues, and the effect of magnetic fields on biological matter She has published several papers and reviews in these areas and contributed a chapter to a book on biomagnetism. She is a member of several professional organizations She has been a regular contributor to Analytical Chemistry’s biennial Fundamental Reviews since 1964
vance of magnetics research to societal needs and a chapter on basic magnetic terms, their definitions, and units for expressing them. In so doing, the editors have attempted to keep the two advanced treatises self-sufficient in the hope that readers would acquire the volume with the most appeal. Casey has written two chapters dealing with the classical and quantum mechanical principles of paramagnetism and the theoretical basis for the magnetic behavior of compounds containing d“ ions. Such behavior itself is reviewed in depth by Casey and Mitra, who also cover in a separate chapter the magnetic behavior of lanthanide compounds. They have stressed the anisotropic properties of these complexes. The magnetic properties of actinide compounds and the common theoretical basis for lanthanide as well as actinide compounds is given by Siddall. Hatfield has comprehensively dealt with the topic on magnetically condensed compounds, that is metal cluster complexes, which have often been described as exhibiting the so-called “intramolecular antiferromagnetism”. Several recent and selected advances in molecular paramagnetism are surveyed by Mulay and Boudreaux. Topics on magnetic materials are covered by Craik (13), by Cullity ( 1 5 ) ,and by Heck ( 4 2 ) . Several books on highly specialized topics have appeared recently. These deal with (i) physical investigations in strong magnetic fields edited by Skobel’tyan ( 7 0 ) ,(ii) magnetically ordered crystals containing impurities [Izyumov et al. (4611, (iii) experiments on simple magnetic model systems-and their status in the light of current theories( [DeJong et a1 ( 2 0 ) ] ,and (iv) “Chemisorption and Magnetization” [Selwood (68a)I.The last book should be of interest to those working on catalysis.
A book of special significance to biologists and biochemists deals with the effects of magnetism on the living system [Davis e t al. .(17)].Eden ( 2 4 ) has covered the topic of animal magnetism and the life energy. Last of all we turn to books of special interest to the geoscientists. Barnes ( 3 ) has a title on the origin and the destiny of the earth’s magnetic field. Stacey and Banerjee ( 7 1 ) discuss the principles of rock magnetism. The “Magnetosphere of the Earth and Jupiter” is the topic of a symposium ( 3 2 ) . Shannon and Vincent ( 6 7 ) have reviewed the relationship between magnetic properties, interionic distances, and covalency in halides and chalcogenides. Schelleng (68) has written a chapter on techniques for static magnetic measurements, which he has termed “Non-Resonance Methods”. The information is mostly oriented toward metallurgical-type research. A review with about 16 references on magnetic properties of materials is presented by Steeger ( 7 2 ) .Pacault’s article (66) summarizes magnetic properties of carbon. An extensive survey entitled “Magnetic impurities in non-magnetic metals” has been published by Gruner and Zawadowski ( 3 9 ) . I t should be noted that nonmagnetic metals such as copper or gold to which small impurities of 3d metals (iron, cobalt, and nickel) have been added show fascinating electronic properties a t very low temperature. The electrical resistance of such alloys is known to increase rapidly a t cryogenic temperatures (Kondo effect). This area is of special interest to physicists and the review title should not be mistaken to represent interests of analytical chemists or metallurgists. Another review of fundamental interest is on the “Establishment of thermal equilibrium in paramagnetic crystals,” written by Gill ( 3 7 ) .
NEW T R E N D S New developments in magnetic instrumentation are proceeding primarily along the following lines. A. Use of relatively new phenomena in superconductivity (e.g., the Josephson Tunneling Effect) and the application of the SQUID. (Superconducting Quantum Interference Device). The only limitation appears to be that volume (and not per gram) susceptibilities are measured and that a separate density ( p ) determination of the sample is required. Thus, errors introduced in densit measurements are reflected in the final useful values of x a L g = x v / p ] . B. Use of superconducting magnets in otherwise routine techniques such as the classical force methods (Gouy and Faraday balances), the vibrating sample magnetometer and so on.
APPARATUS Before proceeding to survey new developments in the instrumentation based on the SQUID technique, and the classical force methods using superconducting electromagnets, and the vibrating sample magnetometers (VSM), etc., we must mention a few developments related to gas analys1s.
Measurements on Gases. Hummel ( 4 3 ) describes an apparatus for measuring the difference in magnetic susceptibility of a sample gas and a constant susceptibility reference gas. I t consists of a magnet with at least one measuring gap delineated by pole pieces and a test container with two symmetrical chambers, one for the sample gas and the other for the reference gas. The test container is suspended resiliently in the field in the gap in such a way that a difference in the susceptibility of the gases in the two chambers tends to deflect the container from the equilibrium position when the susceptibilities are equal. Electronic means are provided for detecting the susceptibility-dependent forces tending to deflect the container, from the values of which the susceptibility of the sample gas may be calculated. Hummel ( 4 4 ) has patented another apparatus for analyzing gas mixtures which should be of some significance in air-pollution problems. An apparatus for the analysis of a gas mixture is based on measuring the electric or magnetic susceptibility without using a reference gas. A cuvette containing the gas (either flowing through or a t rest) is placed ANALYTICAL CHEMISTRY, VOL. 48, NO. 5, APRIL 1976
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in an alternating field, which gives rise to an alternating gas pressure. This is measured directly by using a receiver (e.g., a condenser microphone) and converted to an electric signal, giving a measure of the susceptibility. The cuvette is made of a material of low susceptibility. T o eliminate interferences caused by elastic deformation, the cuvette is bolted parallel to the direction of the field leaving an air space on both sides of the cuvette windows. The apparatus was used to measure SO2 in s 0 2 - N ~or SOZ-air mixtures and NH3 in “3-air mixtures. The apparatus can also be used as a detector in the chromatography of hydrocarbons. A detector for paramagnetic gases has been patented by Zysman and Davis (79). An analyzer for the partial pressure of a paramagnetic gas of increased sensitivity is described. I t consists of a gas flow chamber with a magnetic circuit with two pairs of pole pieces and an oblong diamagnetic-ceramic test body between them. The test body is coated with titanium and has channels defining a continuous conductive pattern. The torque exerted on the test body by the differential partial pressures between the two pairs of pole pieces is compensated for by the electric current in the test body surface, which is determined as a measure of the partial pressure. The Superconducting Quantum Interference Devices (SQUID). In our last review (64) we commented briefly on the SQUID devices which are employed in susceptometers (that is apparatus for measuring magnetic susceptibilities) and in gradiometers which measure the gradients in a magnetic field. Since the insertion of a specimen in a uniform magnetic field creates a “gradient”, the measurement of such gradient, that is the use of a SQUID in the gradiometer mode is said to constitute a susceptometer (52). As one would expect, considerable strides are now being made in the development of SQUID techniques for a wide range of magnetic applications. I t is indeed fortunate that Cukauskas, Vincent, and Deaver (14) have described in sufficient detail the construction and principles of operation of a superconducting “magnetometer,” that is of a “susceptometer”. The measurement of susceptibility consists of transferring energy E M of a sample to energy E R stored by a current flowing through a weakly linked superconducting (SC) ring. The signal power from the magnetometer is proportional to the energy E R and the transfer of energy is accomplished by moving the magnetized sample from a coil L1. The flux change in L1 induces a current in the superconducting circuit L1-Lp and causes a corresponding flux change in another radiofrequency (rf) coil L2 and in turn in the SC ring (with a weak link) which in turn is coupled to a L3 coil-capacitor-rf-tank circuit. L1 in practice is replaced by a “split coil” to give a so-called gradiometer configuration. With properly matched distances and coupling coefficients of unity, EM is transferred to the SC ring. E M is related to other measurable parameters by the following relation
E M = 1/8rB2V= 2rxu2H2V2 where H is the applied field, V is the volume of the sample and xu is the volume susceptibility of the sample. One must infer that it is essential to independently measure the density ( p ) of the sample to obtain xg, the per-gram susceptibility (xg = xv/p). Since, the “per-gram” and not the “volume” susceptibility is employed in all computations to arrive a t the “molar” susceptibility of a sample and the “effective” or “saturation” moments, the inability of the susceptometer to yield the “per-gram susceptibility” (as obtainable, for instance, by the Faraday technique) must be considered as a serious limitation of the SQUID susceptometer. Any errors arising from nonuniform packing of solids in a sample tube must also be investigated in great detail. The authors have generally employed thin-walled quartz tubes, 3- to 5-mm diameter or thin-walled (-0.08 mm) Mylar tubes 3- to 6-mm diameter. These small volumes permit the use of milligram samples. Cukauskas and coworkers’ (14) paper has several useful and important features. First of all the bibliography, consisting of 26 references is more than adequate for the selfeducation of a novice who may be anxious to enter the newly emerging area of SQUID techniques. Secondly, refer316R
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ence is made to a novel technique, previously described by Day (18) to observe especially broad-line NMR absorption spectra using essentially the same magnetometer apparatus. Day’s technique involves the measurement of magnetization of a sample as the frequency of an applied transverse rf is varied. When the conditions of adiabatic fast passage are satisfied, the total magnetization reverses direction as the applied frequency is swept through the resonant frequency. Thus the microscopic changes in the magnetization of nuclear moments are recorded and not the absorption of the rf power, as is done in the classical NMR spectrometers. The authors (14) cite examples of magnetic resonance absorption for protons (HI) in water and in Delvin (an acetyl resin), and for fluorine (FI9) in Teflon. Thus their SQUID magnetometer may be said to constitute a dual purpose susceptometer and a NMR spectrometer. An additional virtue of their NMR measurement capability is that it automatically provides a means for measuring the actual applied magnetic field from the (superconducting) magnet a t the specimen; thus the NMR spectrometer acts as a gaussmeter. It should be obvious from the previous discussion that the sensitivity of the magnetometer is very high since it is capable of measuring the magnetizations (and hence the susceptibilities) of nuclei in a sample. Their reported measurements exemplify a challenging situation indeed. The total susceptibility (which has been apparently mislabeled as “magnetization” by the authors) for water measured a t 4 K and a t 100 Oe is stated to be X T = -0.686 X cgs units and the calculated nuclear paramagnetism xn for protons in water a t 4 K is quoted as xn = +0.024 X cgs units. Subtracting this contribution from X T is said to yield X H 0 = -0.710 X cgs, which is approximately the susceptikility for water a t room temperature (300 K). The authors allude to measurements on Co(I1) carbonic anhydrase and to (differential) measurements of susceptibility on an aqueous solution of K4Fe(CN)6 and on water only and indicate that they were able to thus measure the susceptibility of K4Fe(CN)6 complex alone. Unfortunately no precise values for the susceptibilities are reported. Furthermore, no results for the temperature dependence of susceptibility of the Fe(II1) are reported, which makes it difficult to assess the actual working performance of their instrumentation. The authors stress the high sensitivity attainable with their SQUID magnetometer; for instance, a volume susceptibility change of cgs units is measurable in a field of 100 Oe; since high stabilized fields up to 30 kOe are available in superconducting magnets, a sensitivity of AX = cgs units is said to be possible and is said to compare well with static techniques of Brill (9) and discussed by Mulay (54). They point out that perhaps sensitivity is not the primary virtue of their susceptometer, but a more important feature is the response time. With the usual 30-MHz operating frequency it should be possible to observe “instantaneous” changes in magnetization a t frequencies up to many kilohertz and even to a few megahertz. Thus the susceptometer may be useful for studying fast relaxation rates in photoexcited states or mixing experiments as encountered in biochemical studies (14). Duret and coworkers (23) describe an ultra high frequency (uhf) superconducting magnetometer utilizing a new thin film sensor. Readers interested in the SQUID techniques will find their paper interesting in many ways. The attainment of uhf up to 350-MHz pumping frequency, the use of a particular rf gives rise to an improved signal-tonoise ratio, and a sensitivity of 2 X low4@/Hz is easily obtained. Here @ is the flux quantum equal to 2.07 X Wb = 2.07 G-cm2. The thin film (2000 A) SQUID is made by vacuum depositing niobium on a fused quartz cylinder (72-mm diameter). I t is inexpensive to fabricate and has a higher critical temperature, readily established critical current (0.5 to 1.5 FA with a *O.l FA accuracy). The advantages of their thin film microbridge SQUID are compared with those of a conventional Zimmermann’s point contact SQUID (78). The paper is well written and the construction of the entire magnetometer, including vapor deposition synthesis of the SQUID are given in detail. Another simple low noise uhf SQUID magnetometer is outlined by Clark and Jackel (12). An x-band uhf of 450 MHz is used with a two-hole Zimmerman SQUID (78) con-
sisting of oxidized point contact niobium SQUID rings. Advantage is taken of the distributed impedance of the cavity to combine the functions of resonator, impedance transformer, and a shielding can in one structure. Constructional details are given for the 450-MHz SQUID system resonator along with a scheme for signal detection and rf current vs. voltage characteristics. Johnson (47) has derived equations for designing a tricoil electromagnet. We review i t here because of its relevance to possible future superconducting solenoid applications for susceptibility measurements. As mentioned later Stewart (73) and several other workers now use such solenoids with gradient coils in conjunction with a Faraday balance. Johnson (47) has considered an assembly of three coaxial coils A, B, A’ (A is identical with A’) which are coaxially situated. He has shown that, if the spacing between adjacent coils (AB and BA’) is a, if each coil contains equal number of ampere turns, if the radius of end coils (A and A’) is a, and if the radius of the center coil is a 5al4, the second derivative of the axial flux density is found to vanish a t the center of the assembly, that is a t the center coil B. Thus this tricoil electromagnet produces a relatively constant axial magnetic flux density over its entire length 2a. Comparison is made of this tricoil arrangement with the classic Helmholtz coil pair. James Clark Maxwell had considered a somewhat similar arrangement for use in a galvanometer almost a century ago! In his arrangement the end coils had different ampere turns than the center coil and the spacings between coils were different than those derived by Johnson. Vibrating Sample Magnetometers (VSM). General Comments. In our past reviews (64) we catalogued several vibrating sample magnetometers (VSM) and similar apparatus according to the major purpose for which an individual equipment was designed and described by the author. For instance, we referred to a paper by Hudgens (cf. 64) describing a rotating sample magnetometer for measuring diamagnetic susceptibilities of samples. We should like to emphasize that such cataloguing was obviously done for organizational convenience and we did not mean to imply that an apparatus designed for, say paramagnetic, susceptibilities could not be used at all for measurements on other types of materials. I t should be obvious that a change-influx type apparatus designed to measure paramagnetic emu/gram) will be capable of susceptibilities (of measuring much higher susceptibilities, as encountered in, say, ferro-, ferri- or superparamagnetic systems. It is important to note that most homemade or commercial instruments can be modified to measure even weaker susceptibilities, for instance even diamagnetic susceptibilities which emu/gram. In other words, with range around -1 X sufficient ingenuity it should be possible to increase the sensitivity of a vibrating sample magnetometer, as described originally by Foner (29) to facilitate the measurements of diamagnetic susceptibilities. We surveyed such instruments in our last review (64). Improving the Sensitivity of a V S M . Foner (30) has discussed the above situation in a brief note appropriately entitled, ‘‘. . . how to increase the sensitivity of a vibrating sample magnetometer”. He cites example of unfair comparisons in the literature made between the VSM and the force methods such as the Faraday method and the confusion which occasionally arises between the (physicists) terminology of the specific “moment” (meaning magnetization M , expressed generally as emu/gram) and the specific “susceptibility x”, which is also expressed in emu (or cgsu)/ g. I t should be noted that M = xH, where H is the field applied during a magnetic measurement. Thus, a “moment” of say emu/g, measured a t a field of lo4 G, in reality corresponds to a susceptibility, x, of x = 10-lO emu/g. Hence, the sensitivity of a VSM when expressed in terms of the “moment” (at a given field) would always look smaller than the corresponding “susceptibility”, if the experimenter is not careful enough to note the simple yet important difference between the definitions of the two parameters. Foner points out with reference to his original paper (29) that the sensitivity of a VSM can be increased by several orders of magnitude by moving the detector coils closer to the sample; conversely the sensitivity decreases when the coils are moved farther apart, but the working
volume of the sample is increased. This flexibility has made it difficult to categorically state the limiting sensitivity of a VSM. Foner (30) suggests that the sensitivity can be increased further by (i) increasing the filling factor (ratio of the sample volume to the effective detection coil volume) especially in the case of small samples with very low “moments”, that is low “magnetizations” or weak “susceptibilities”, and (ii) by cooling the detector coils. The cooling of detection coils, say to liquid helium temperature (4.2 K), reduces the “Johnson” noise, that is the “intrinsic electronic” noise which is always present in any electronic circuit. Experimentally it may be cumbersome to maintain the coils a t low cryogenic temperatures; however, when accomplished the sensitivity can be increased by a factor of 100. Various first-order and second-order effects in increasing sensitivity are also discussed (30). The most important “first-order” parameter is the distance r between the sample and the nearest windings. Sensitivity increases as l / r 3 ; hence by reducing r from -1.5 cm to, say, 0.15 cm, the sensitivity can be increased by lo3. In doing this the coil volume is also reduced, which increases the filling factor, and this in turn increases the signal-to-noise ratio and hence the sensitivity of the apparatus. For reasonable coil geometries, the detailed arrangements of the coil windings, orientation, etc., do help to increase the sensitivity by less than an order of magnitude, and these effects fall under the “second-order effects” category. Foner (30) gives a convincing example of an experiment in which the sensitivity of a VSM was increased to permit a measurement of emu for a 1-g sample change in susceptibility, Ax at a field of lo4 G. In continuation of his earlier publication (30),Foner (31) has discussed further improvements in the sensitivity of his VSM. General geometric scaling factors for VSM detection coils are discussed and their importance in increasing sensitivity is pointed out. In particular, parameters such as the number of turns in the coaxial detector coil, its radius and total resistance, and the effect of the Johnson noise are considered. Analysis of signals from a sample placed in a conventional electromagnet giving a field ( H ) of 10 kOe and in a superconducting magnet with H = 50 kOe is given. In general test results demonstrated a IO3 to lo4 increase in VSM described by Foner (29). Thus at 10 kOe for a 1-g emu/g-Oe. Foner sample the sensitivity limit is A x = points out that his sensitivity surpasses that achieved by any force method or any other technique such as the sensitive SQUID technique described by Cukausaks (14) and reviewed above. The SQUID technique gives a limiting resoemu a t 100 Oe, whereas Foner’s tests lution of 7 X (31) a t 20 kOe yield 10 times this sensitivity at -200 times their applied field. The most practical advantage of the VSM is that it yields the magnetizations or susceptibilities on a “per gram” basis and not as “per unit volume”. Readers are urged to refer to our earlier reviews (59-64) which describe a wide variety of designs for detector coils and other successful efforts at improving the sensitivity of vibrating sample or vibrating coil magnetometers. Theory of V S M . An insight into the theory and working limitations of the VSM as first described by Foner (29) may be gained from a paper by Foiles and McDaniel (28), who discuss the dipole approximation for a VSM. These authors stress that standard procedures employed in the use and calibration of a VSM rely upon the sample being a pure magnetic dipole and report measured deviations from a pure dipole behavior in right circular cylinders having a diameter to length ratio of -15. In most VSM’s a sample of pure nickel with a spontaneous (saturation) magnetization (or a similar ferromagnetic metal) is employed as a standard and the “moments” (that is “magnetizations” and hence “susceptibilities”) are determined relative to the known moment of the standard (for nickel, 0 = 54.39 emu/ g). These authors point out that “Foner (29) explicitly recognized the potential problem of sample size and conducted limited tests on paramagnets having irregular shapes; (his) moments agreed to within f l %and thus the pure dipole approximation (i.e., output signal is directly proportional to volume independent size) was obeyed. However, the maximum linear dimension of these samples was 3 mm and no information was given concerning the detection coil configuration used for these tests”. These observations
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prompted the authors (28) to test various configurations of a sample (in the form of a short piece of aluminum wire) and of detector coil systems. The point of interest here is that, while various ferro-, ferri-, and paramagnetic samples with permanent magnetic dipole moments ( p expressed in Bohr Magnetons per gram-atom) do conform to the “magnetic dipole” approximation, metals, such as aluminum, do not. (For instance, metals like copper are diamagnetic; others like sodium, potassium, etc., show an “induced feeble paramagnetism” arising from itinerant electrons; this feeble paramagnetism, which is independent of temperature, is known as the Pauli paramagnetism). The authors (28) were interested in the electrical and magnetic properties of binary alloys which display atomic-order disorder transitions; for the first, a sample in the form of a wire is indeed useful, since electrical resistivity measurements are desired. For a comparison of magnetic properties of the same sample, they felt it necessary to use the same cylindrical (wire) sample in a magnetometer. From the ensuing considerations and experimental tests, which are elegantly presented, the authors conclude the following. (i) For right circular cylinders of finite dimensions, the pure dipole approximation is valid to within f l %as lon as the cylinder length is
