Finite sample size effects on the calibration of vibrating sample magnetometer

The normal procedure for calibration of the moment readings of a VSM is to use a Ni sphere of known magnetic moment to determine the moment/volt of the VSM sensing coils as measured by a lockin amplifier. The often made assumption is that when an unknown sample is placed in the VSM the same moment/volt will be produced. This assumption should be carefully checked. If the sample is a thin film and is large compared to the size of the Ni sphere, systematic errors as large as 15% can be introduced into the measurement. These systematic errors arise from the sample geometry and can be corrected by replacing the Ni sphere used for calibration with Ni thin films the same size and shape as the sample to be measured. The field from a uniform magnetized sphere is a dipole field. Large diameter thin films cannot be approximated as point dipoles. In this paper an approximation for a thin film is used to calculate the signal induced in the VSM coils. The approximation is to treat the thin film as an oblate spheroid. This approximation has the advantage that the sample can be uniformly magnetized and solutions for the external field can be simply expressed in oblate spheroidal harmonics.