Problem of Spin Arrangements in MnO and Similar Antiferromagnets

The magnetic dipolar energy is computed for ordering of the second kind with the four antiferromagnetic sublattices of a facecentered cube making arbitrary spin directions with respect to one another, and this energy is shown to be of the same form in the sublattice direction cosines as is the calculated powder neutron-diffraction pattern. (The dipolar energy is also calculated for ordering of the third kind and shown to lead to a spin arrangement in disagreement with powder neutron-diffraction results on $\beta$ MnS.) The observed neutron patterns in MnO and $\alpha$ MnS agree with minimum dipolar energy, but many spin arrangements can satisfy this and the spins are constrained only to certain regions. Other sources of anisotropy in ${\mathrm{Mn}}^{++}$ salts are shown to be much weaker. A model is introduced in which the spins are constrained by dipolar and exchange forces to point parallel to (111) planes and constrained by the weaker anisotropy to a threefold set of easy axes within these planes. Nagamiya's small-field approximation for the field dependence of the powder susceptibility of a uniaxial antiferromagnet is extended to all values of the applied field, and a similar calculation is made for the powder susceptibility of our MnO model. Comparison with experimental data indicates that the weak within-plane anisotropy is ∼3×${10}^4$ ergs/${\mathrm{cm}}^3$ which is to be contrasted with the theoretical out-of-plane dipolar anisotropy of ${10}^7$ ergs/${\mathrm{cm}}^3$. A rough theory of antiferromagnetic resonance for our model seems to explain the partial paramagnetic-like absorption observed below the Néel point.