Pick-up systems for vibrating sample magnetometers-a theoretical discussion based on magnetic multipole expansions

It is quantitatively analysed how the voltage induced in a pick-up coil is related to arbitrarily (i.e. non-uniformly) magnetized samples, arbitrarily large vibration amplitude and arbitrary direction of vibration. The influence of errors in the position and in the vibration direction of the sample on the measured magnetization is discussed, and a well known criterion, commonly used to minimize sample position errors, is generalized. The authors propose compensated coil pairs, which are insensitive to either spurious vibrations or to power line pick-up. They also outline a system which realizes a true vector measurement of the three dipole moments as well as a measurement of three of the five quadrupole moments.