  Oxygen-deficient layered perovskite YBaCuFeO$_{5}$ (YBCFO) is one rare
type-II multiferroic material where ferroelectricity, driven by incommensurate
spiral magnetic order, is believed to be achievable up to temperatures higher
than room temperature. A cycloidal spiral rather than helical spiral order is
essential ingredient for the existence of ferroelectricity in this material.
Motivated by a recent experimental work on Mn-doped YBCFO where the spiral
plane is observed to cant more towards the crystallographic $c$ axis upon Mn
doping at Fe sites compared to that in the parent compound, we performed a
detailed theoretical investigation using the density functional theory
calculations to understand the mechanism behind such spin reorientation. Our
total energy calculations, within GGA+U+SO approximation, reveal that Fe/Cu
spin moments indeed align more towards $c$ axis in the Mn-doped compounds than
they were in parent compound YBCFO. Largest exchange interaction (Cu-Cu in the
$ab$-plane) is observed to decrease systematically with Mn doping concentration
reflecting the lowering of transition temperature seen in experiment. Further,
the inter-bilayer Cu-Mn exchange interaction becomes ferromagnetic in the doped
compound whereas the corresponding Cu-Fe exchange was antiferromagnetic in the
parent compound giving rise to frustration in the commensurate magnetic order.
Most importantly, our electronic structure calculations reveal that in the
doped compounds because of hybridization with the d$_{z^2}$ orbital of Mn, the
highest occupied Cu orbital becomes d$_{z^2}$ as opposed to the parent compound
where the highest occupied Cu orbital is d$_{x^2-y^2}$. Therefore, we believe
that the occupancy of out of plane oriented Cu d$_{z^2}$ orbital in place of
planar d$_{x^2-y^2}$ orbital along with the frustrating exchange interaction
drive the spins to align along $c$ in doped compound.
