Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section B / 21 / c / Solution

Weak ferromagnetism from canted antiferromagnetic order is the consistent model. Importantly, the plot has different magnetization scales: the left axis belongs to Mn and Fe; the right belongs to Co and Ni. Approximate low-temperature field-cooled readings are 40, 50, 450 and 390 G cm${}^3$ mol${}^{-1}$, respectively. Dividing by 5585 givesThese moments are tiny compared with fully aligned moments of about 5.09, 4.40, 4.25 and 2.47 ${\mu }_B$, calculated using the Curie-derived $g$ values below. A conventional ferromagnet of the full high-spin ions would have much larger spontaneous magnetization; a simple bipartite array of identical metal sites also supplies no obvious unequal sublattice moments for ferrimagnetism. Opposed large sublattice moments with a small transverse uncompensated component reconcile the net response with negative $\Theta$.

If the 10 Oe field has aligned the weak-ferromagnetic domains, $M_{\mathrm{weak}}=gS{\mu }_B\sin \alpha$ estimates sublattice canting angles of roughly 0.08°, 0.12°, 1.1° and 1.6°. These are illustrative, not precision structure determinations: the low field may not fully align the domains, and the readings are graphical. Bulk magnetization strongly supports this model but does not uniquely establish every spin direction; magnetic neutron diffraction would test the microscopic arrangement.