Topological Analysis of the Experimental Electron Density in Multiferroic Antiferromagnet Ba2MnGe2O7

In the field of magnetoelectric coupling, especially via the spin-dependent metal–ligand
d-p
hybridization mechanism found in multiferroic Ba
₂
${M}$
Ge
₂
O
₇
(
${M}$
= Mn, Co), detailed knowledge of the microscopic structural parameters is essential, also for the theoretical modeling. In this article, we report a systematic structural study of Ba
₂
MnGe
₂
O
₇
single crystal under varying temperatures between 110 and 673 K using non-destructive
in situ
single crystal synchrotron radiation diffraction. The maximum entropy method (MEM) was applied to the X-ray diffraction data for the determination of the deformation in the electron density and the orbital hybridization between the
3d
of Mn and
2p
of O in the Mn–O bond. Within this entire temperature range, the structure was described in a single crystallographic space group
$P\bar {4}2_{1}m$
and no structural phase transition has been detected. Interestingly, the forbidden reflections, which arise from multiple diffractions so-called “Renninger effect,” were observed at all temperatures without any symmetry lowering. The changes in the structural parameters [bond-lengths, bond-angles, anisotropic displacement parameters, and electron density distributions (EDDs) of the atoms] with temperature are revealed, helping to understand some aspects comprising orbital hybridization in multiferroic Ba
₂
MnGe
₂
O
₇
.