Title: Band filling control of the Dzyaloshinskii-Moriya interaction in weakly ferromagnetic insulators,
Abstract: We observe and explain theoretically a dramatic evolution of the
Dzyaloshinskii-Moriya interaction in the series of isostructural weak
ferromagnets, MnCO$_3$, FeBO$_3$, CoCO$_3$ and NiCO$_3$. The sign of the
interaction is encoded in the phase of x-ray magnetic diffraction amplitude,
observed through interference with resonant quadrupole scattering. We find very
good quantitative agreement with first-principles electronic structure
calculations, reproducing both sign and magnitude through the series, and
propose a simplified `toy model' to explain the change in sign with 3 d shell
filling. The model gives a clue for qualitative understanding of the evolution
of the DMI in Mott and charge transfer insulators.