Past exam of the condensed matter physics major option course of the University of Oxford / 2019 / 5 / e / Solution

Measure magnetization along $z$ at low temperature and use a small field to select a single weak-ferromagnetic domain. After domain alignment, subtract the approximately linear field-induced susceptibility background to obtain the spontaneous weak moment, using the extrapolated intercept of that branch rather than a multidomain zero-field average.

There are four iron ions per orthorhombic cell. If the spontaneous magnetization density is $M_z$ and the cell volume is $V_{\mathrm{cell}}$, the ordered moment and dimensionless spin component per ion areHere spin components are expressed in units of $\hslash$ as in the source Hamiltonian. Alternatively normalize the magnetic moment to the measured number of iron ions. A field too large to preserve the small-canting structure would not measure the zero-field component directly. For high-spin Fe${}^{3+}$ with $S=5/2$ and $g\simeq 2$, the angle above corresponds to approximately $0.026{\mu }_B$ per iron ion.