Orbital ordering and quasi-two-dimensional magnetism in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi><mml:msub><mml:mi mathvariant="normal">MnF</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo> </mml:mo><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo>,</mml:mo><mml:mi>Rb</mml:mi><mml:mo>)</mml:mo></mml:math> : A first-principles study

Strongly correlated systems with the interplay of electronic, charge, spin, and orbital degrees freedom have, in recent times, received a surge interest because their rich physics, novel physical properties, potential applications. In present work, we study structural, magnetic, electronic properties ordering layered perovskite-type $A\mathrm{Mn}{\mathrm{F}}_{4} (A=\mathrm{K},\mathrm{Rb})$ from first principles. A detailed analysis both compounds reveals an interesting nodal-line-like dispersion at $\ensuremath{\sim}0.4$ eV below Fermi level hinges Brillouin zone. Magnetic reflect quasi-two-dimensional magnetism these compounds, very weak exchange interaction between layers. Our results report robust in-plane ferromagnetic spin order $A\mathrm{Mn}{\mathrm{F}}_{4}$ ($A$=K, Rb) critical temperatures estimated to be around 30--60 K. We also find anti-ferro-orbital within $ab$ plane ferro-orbital out favoring $C$-type compounds.