  We have simulated the magnetic Bragg scattering in transmission electron
microscopy in two antiferromagnetic compounds, NiO and LaMnAsO. This weak
magnetic phenomenon was experimentally observed in NiO by Loudon. We have
computationally reproduced Loudon's experimental data, and for comparison we
have performed calculations for the LaMnAsO compound as a more challenging
case, containing lower concentration of magnetic elements and strongly
scattering heavier non-magnetic elements. We have also described thickness and
voltage dependence of the intensity of the antiferromagnetic Bragg spot for
both compounds. We have considered lattice vibrations within two computational
approaches, one assuming a static lattice with Debye-Waller smeared potentials,
and another explicitly considering the atomic vibrations within the quantum
excitations of phonons model (thermal diffuse scattering). The structural
analysis shows that the antiferromagnetic Bragg spot appears in between (111)
and (000) reflections for NiO, while for LaMnAsO the antiferromagnetic Bragg
spot appears at the position of the (010) reflection in the diffraction
pattern, which corresponds to a forbidden reflection of the crystal structure.
Calculations predict that the intensity of the magnetic Bragg spot in NiO is
significantly stronger than thermal diffuse scattering at room temperature. For
LaMnAsO, the magnetic Bragg spot is weaker than the room-temperature thermal
diffuse scattering, but its detection can be facilitated at reduced
temperatures.
