Scanning Squid Microscopy

Kirtley, J. R.; Wikswo, John P.

doi:10.1146/annurev.matsci.29.1.117

Cited by 161 publications

(87 citation statements)

References 85 publications

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“…A more concrete definition of R j (h) for h ∈ BM O may in fact be obtained upon additively renormalizing (11), replacing for instance the right hand side with…”

Section: The Spaces Hmentioning

confidence: 99%

Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions

Baratchart¹,

Hardin²,

Lima³

et al. 2012

Inverse Problems

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Abstract. Recently developed scanning magnetic microscopes measure the magnetic field in a plane above a thin-plate magnetization distribution. These instruments have broad applications in geoscience and materials science, but are limited by the requirement that the sample magnetization must be retrieved from measured field data, which is a generically nonunique inverse problem. This problem leads to an analysis of the kernel of the related magnetization operators, which also has relevance to the "equivalent source problem" in the case of measurements taken from just one side of the magnetization. We characterize the kernel of the operator relating planar magnetization distributions to planar magnetic field maps in various function and distribution spaces (e.g., sums of derivatives of L p (Lebesgue spaces) or bounded mean oscillation (BMO) functions). For this purpose, we present a generalization of the Hodge decomposition in terms of Riesz transforms and utilize it to characterize sources that do not produce magnetic field either above or below the sample, or that are magnetically silent (i.e., no magnetic field anywhere outside the sample). For example, we show that a thin-plate magnetization is silent (i.e., in the kernel) when its normal component is zero and its tangential component is divergence-free. In addition, we show that compactly supported magnetizations (i.e., magnetizations that are zero outside of a bounded set in the source plane) that do not produce magnetic fields either above or below the sample are necessarily silent. In particular, neither a nontrivial planar magnetization with fixed direction (unidimensional) compact support nor a bidimensional planar magnetization (i.e., a sum of two unidimensional magnetizations) that is nontangential can be silent. We prove that any planar magnetization distribution is equivalent to a unidimensional one. We also discuss the advantages of mapping the field on both sides of a magnetization, whenever experimentally feasible. Examples of source recovery are given along with a brief discussion of the Fourier-based inversion techniques that are utilized.

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“…A more concrete definition of R j (h) for h ∈ BM O may in fact be obtained upon additively renormalizing (11), replacing for instance the right hand side with…”

Section: The Spaces Hmentioning

confidence: 99%

Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions

Baratchart¹,

Hardin²,

Lima³

et al. 2012

Inverse Problems

View full text Add to dashboard Cite

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“…The development of high spatial resolution magnetic measurements of meteorites and lunar rocks will be one avenue to realize this goal. These measurements can come from new techniques, e.g., scanning SQUID microscopy (Kirtley, 1999;Rochette et al, 2009) and magnetic tunnel junction microscopy (Lima et al, 2013). It will also be important to more completely measure the spatial and temporal characteristics of the current geomagnetic field through satellite missions, similar to the ESA's SWARM that was successfully launched in November, 2013.…”

Section: Wwwfrontiersinorgmentioning

confidence: 99%

Grand challenges in geomagnetism and paleomagnetism

Kodama

2013

Front. Earth Sci.

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“…SQUID microscopy is a powerful technique for imaging weak magnetic field distributions with the highest field sensitivity. A SQUID microscope allows samples of about 100 µm to be scanned at room temperature (Kirtley and Wikswo 1999;Chatraphorn et al 2000;Ono and Ishiyama 2004;Fong et al 2005). An important use of this technique is the study of geological samples (Fong et al 2005;Baudenbacher et al 2002Baudenbacher et al , 2003Wang et al 2014;Weiss et al 2000Weiss et al , 2007aOda et al 2011).…”

Section: Introductionmentioning

confidence: 99%

Scanning SQUID microscope system for geological samples: system integration and initial evaluation

Oda

Kawai

Miyamoto

et al. 2016

Earth Planets Space

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We have developed a high-resolution scanning superconducting quantum interference device (SQUID) microscope for imaging the magnetic field of geological samples at room temperature. In this paper, we provide details about the scanning SQUID microscope system, including the magnetically shielded box (MSB), the XYZ stage, data acquisition by the system, and initial evaluation of the system. The background noise in a two-layered PC permalloy MSB is approximately 40-50 pT. The long-term drift of the system is approximately ≥1 nT, which can be reduced by drift correction for each measurement line. The stroke of the XYZ stage is 100 mm × 100 mm with an accuracy of ~10 µm, which was confirmed by laser interferometry. A SQUID chip has a pick-up area of 200 μm × 200 μm with an inner hole of 30 μm × 30 μm. The sensitivity is 722.6 nT/V. The flux-locked loop has four gains, i.e., ×1, ×10, ×100, and ×500. An analog-to-digital converter allows analog voltage input in the range of about ±7.5 V in 0.6-mV steps. The maximum dynamic range is approximately ±5400 nT, and the minimum digitizable magnetic field is ~0.9 pT. The sensor-to-sample distance is measured with a precision line current, which gives the minimum of ~200 µm. Considering the size of pick-up coil, sensor-to-sample distance, and the accuracy of XYZ stage, spacial resolution of the system is ~200 µm. We developed the software used to measure the sensor-to-sample distance with line scan data, and the software to acquire data and control the XYZ stage for scanning. We also demonstrate the registration of the magnetic image relative to the optical image by using a pair of point sources placed on the corners of a sample holder outside of a thin section placed in the middle of the sample holder. Considering the minimum noise estimate of the current system, the theoretical detection limit of a single magnetic dipole is ~1 × 10 −14 Am 2 . The new instrument is a powerful tool that could be used in various applications in paleomagnetism such as ultrafine-scale magnetostratigraphy and single-crystal paleomagnetism.

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Scanning Squid Microscopy

Cited by 161 publications

References 85 publications

Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions

Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions

Grand challenges in geomagnetism and paleomagnetism

Scanning SQUID microscope system for geological samples: system integration and initial evaluation

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