Phase of the induced torque: application to potassium

Abstract

The phase of the induced torque with respect to an AC magnetic field used to create the torque was calculated for three sets of sample conditions: a sphere with free-electron conductivity, a sphere with open orbits and an ellipsoid with free-electron conductivity. The phase of the induced torque of a free-electron sphere depends on two dimensionless parameters, a/ delta , the ratio of sample radius to skin depth, and omega c tau , the product of the cyclotron frequency and scattering time. The phase increases with increasing magnetic field between two limits placed symmetrically about omega c tau =2. The phase in a sphere with open orbits increases with increasing magnetic field when only closed orbits are excited and remains in the low-field condition when open orbits are excited. Therefore there are phase dips in the magnetic field directions where there are open orbits. The phase for an ellipsoid is more complex. The phase at low magnetic fields and in symmetry directions closely follows that of a sphere. However, at higher magnetic fields there is fourfold symmetry. In high magnetic fields, there are phase spikes in symmetry directions for which the phase increases rapidly over a narrow range of magnetic field directions. This theory of the phase of the induced torque was compared with measured results for potassium. The agreement between theory and experiment is good for samples showing ellipsoidal properties and for the structure torque identified as due to open orbits.