Origin of ferromagnetic interactions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>NaMnCl</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> : How the response theory reconciles with Goodenough-Kanamori-Anderson rules

The on-site Coulomb repulsion $U$ is the key ingredient for describing magnetic properties of Mott insulators, leading to a popular belief that many limitations density-functional theory based methods can be cured by artificially incorporating such interactions localized electrons in model form. layered antiferromagnet $\mathrm{Na}\mathrm{Mn}{\mathrm{Cl}}_{3}$ reveals quite different story: while on Mn sites controls strength antiferromagnetic superexchange interactions, an equally important parameter Stoner coupling ${\mathcal{I}}_{\mathrm{Cl}}$ ligand sites. latter responsible large ferromagnetic contributions interatomic exchange which nearly cancel effect interactions. Although behavior anticipated from phenomenological Goodenough-Kamanori-Anderson rules, quantitative description ligand-related remains disputable. Considering as example, we discuss how they generally taken into account linear response regain dependence ${\mathcal{I}}_{\mathrm{Cl}}$. problem complicated fact that, filled Cl $3p$ shell, parameters are sensitive assumptions.