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Abstract

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) 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 the 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 $3d$ shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

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