Torque Magnetometry

In a homogeneous external magnetic field a sample experiences a magnetic torque, if there is any anisotropy of the magnetic susceptibility and the field is not applied along principal axes. The torque τ is given by:

Here m is the magnetic moment of the sample and B is the magnetic induction. For anisotropic samples, the magnetic moment and the applied field are in general not parallel and a torque develops. In the simple case of field independent susceptibilities the induced magnetic moment is given by

where χ is the susceptibility tensor. The measured torque is therefore proportional to B² and is very favourable for high field measurements. But already at B = 1T, high resolution torquemeters exceed the sensitivity of commercial SQUID magnetometers. Torquemeters are also very useful for investigations of superconducting and ferro- or antiferromagnetic states and are one of the standard tools for studying de Haas-van Alphen oscillations in metals.

The torque is usually detected by mechanical sensors. The deflection of the mechanical system can be measured by optical, piezoresistive or capacitive methods. At the WMI, we developed a cantilever beam magnetometer with capacitive readout as shown in the Figure by an exploded view. The ground plate (8*10mm²) and the cantilever are prepared by photolitographic techniques. The sensitivity can be varied by the thickness of the cantilever beam and is up to 10^-12 Nm. The crystal under investigation can be also contacted in a four wire arrangement and torque and resistance are measured at the same time.