  Using the first-principles and Monte Carlo methods, here we systematically
study magnetic properties of monolayer octagonal-tetragonal phosphorus with 3d
transition-metal (TM) adatoms. Different from the puckered hexagonal black
phosphorus monolayer (phosphorene or $\alpha$-P), the octagonal-tetragonal
phase of 2D phosphorus (named as ot-P or $\epsilon$-P in this article) is
buckled with octagon-tetragon structure. Our calculations show that all TMs,
except the closed-shell Zn atom, are able to strongly bind onto monolayer
$ot$-P with significant binding energies. Local magnetic moments (up to 6
$\mu$B) on adatoms of Sc, Ti, V, Cr, Mn, Fe and Co originate from the exchange
and crystal-field splitting of TM 3d orbitals. The magnetic coupling between
localized magnetic states of adatoms is dependent on adatomic distances and
directions. Lastly, the uniformly magnetic order is investigated to screening
two-dimensional dilute ferromagnets with high Curie temperature for
applications of spintronics. It is found that ot-P with V atoms homogeneously
adsorbed at the centre of octagons with a concentration of 5% has the most
stable ferromagnetic ground state. Its Curie temperature is estimated to be 173
K using the Monte Carlo method.
