Parameterized tight-binding models of ferromagnetic bilayer manganites

Half-metallic behavior in materials has been a subject of extensive research due to its potential for applications in spintronics. Ferromagnetic manganites have been seen as a good candidate, and aside from a small minority-spin pocket observed in La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ ($x =$ 0.38), transport measurements show that ferromagnetic manganites essentially behave like half metals. Here we develop robust tight-binding models to describe the electronic band structure of the majority as well as minority spin states of ferromagnetic, spin-canted antiferromagnetic, and fully antiferromagnetic bilayer manganites. Both the bilayer coupling between the MnO$_{\mathrm{2}}$ planes and the mixing of the \textbar $x^{2} - y^{2}$ \textgreater\ and \textbar 3$z^{2}$ $- r^{}$ \textgreater\ Mn 3d orbitals play an important role in the subtle behavior of the bilayer splitting. Effects of $k_{z}$ dispersion are included.