Image and sample geometry effects in SQUID magnetometers

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Abstract
This review concerns the interpretation of the signal provided by SQUID magnetometers designed for measurements of magnetization and magnetic susceptibility. ‘‘Image effect’’ refers to the influence of superconducting elements in the vicinity of the sample and detection coil. Several exact and approximate methods are presented for calculation of how the device sensitivity G(r) varies with position r of a unit dipole sample in the presence of a superconducting shielding tube. In particular, the relative decrease of G(r) is approximately given by the third power of the ratio of the detection coil and shield diameters, and the effect of the shield’s finite length is found to be negligible in practical situations. A survey of complex detection coils (Helmholtz, saddle‐type, gradiometer, and second derivative coil) includes calculation of the optimum spacing of the Helmholtz pair in the presence of a superconducting cylinder. The image effects due to the properties of the SQUID circuit and the field‐dependent effects in high‐field SQUID magnetometers are also discussed. Change in the instrument calibration due to sample size, shape, and location is considered for arbitrary samples as well as for specific cases of small, medium, and very long samples. A spherical harmonic expansion of G(r) makes it possible to derive simple formulas describing sample geometry effects for medium‐sized samples with regular geometries (thin rod, cylinder, and rectangular parallelepiped). The results are compared to published experimental data.