  Two-dimensional (2D) materials with nodal-loop band crossing have been
attracting great research interest. However, it remains a challenge to find 2D
nodal loops that are robust against spin-orbit coupling (SOC) and realized in
magnetic states. Here, based on first-principles calculations and theoretical
analysis, we predict that monolayer MnN is a 2D nodal-loop half metal with
fully spin polarized nodal loops. We show that monolayer MnN has a
ferromagnetic ground state with out-of-plane magnetization. Its band structure
shows half metallicity with three low-energy bands belonging to the same spin
channel. The crossing between these bands forms two concentric nodal loops
centered around the $\Gamma$ point near the Fermi level. Remarkably, the nodal
loops and their spin polarization are robust under SOC, due to the protection
of a mirror symmetry. We construct an effective model to characterize the fully
polarized emergent nodal-loop fermions. We also find that a uniaxial strain can
induce a loop transformation from a localized single loop circling around
$\Gamma$ to a pair of extended loops penetrating the Brillouin zone.
