  The structural, magnetic, and electronic properties of
NdFe$_{0.5}$Mn$_{0.5}$O$_3$ have been studied in detail using bulk
magnetization, neutron/x-ray diffraction and first principles density
functional theory calculations. The material crystallizes in the orthorhombic
$Pbnm$ structure, where both Mn and Fe occupy the same crystallographic site
($4b$).
  Mn/Fe sublattice of the compound orders in to a G-type antiferromagnetic
phase close to 250\,K where the magnetic structure belongs to ${\Gamma}_{1}$
irreducible representation with spins aligned along the crystallographic $b$
direction. This is unconventional in the sense that most of the orthoferrites
and orthochromites order in the ${\Gamma}_{4}$ representation below the
N\'{e}el temperature.This magnetic structure then undergoes a complete spin
reorientation transition with temperature in the range 75\,K$\gtrsim$ T
$\gtrsim$ 25\,K where the magnetic structure exists as a sum of two irreducible
representations (${\Gamma}_{1}$+${\Gamma}_{2}$) as seen from neutron
diffraction measurements. At 6\,K, the magnetic structure belongs entirely to
${\Gamma}_{2}$ representation with spins aligned antiferromagnetically along
the crystallographic $c$ direction having a small ferromagnetic component
($F_x$). The unusual spin reorientation and correlation between magnetic ground
state and electronic structure have been investigated using first principles
calculations within GGA+U and GGA+U+SO formalisms.
