SECTION 9.3. THE VIBRATING-SAMPLE MAGNETOMETER 87where is the magnetic moment of a small sample located in an area where the field
gradient has a constant value.
For various types of magnetically ordered materials, in particular, it is desirable to
measure the magnetization as a function of the field strength In such cases, one may
use an apparatus as schematically shown in Fig. 9.2.1, where a homogeneous magnetic
field along the vertical or z-direction is generated by a solenoid. This field aligns the
moment of the sample in the z-direction, and if the magnetization of the sample is field-
dependent, the field applied will increase the magnitude of For measuring the size of
at each field strength by means of the force (Eq. 9.2.1), one needs an auxiliary
field gradient which can be generated by means of a set of gradient coils that are
specially designed for producing a homogeneous gradient at the site of the (small) sample.
The force is measured, for instance, by an automatic balance. The force can be calibrated
by measuring a standard sample of pure Ni, having a well-known magnetization.
9.3. THE VIBRATING-SAMPLE MAGNETOMETERThe vibrating-sample magnetometer (VSM) is based on Faraday’s law which states
that an emf will be generated in a coil when there is a change in flux linking the coil. Using
Eqs. (8.9) and (8.10), we may write for a coil with n turns of cross-sectional area a:If the coil is positioned in a constant magnetic field, one has