  The structural, electronic, and magnetic properties of 3$d$ transition metal
(TM) atoms (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) adsorbed germanene are
addressed using density functional theory. Based on the adsorption energy, TM
atoms prefer to occupy at the hollow site for all the cases. The obtained
values of the total magnetic moment vary from 0.97 $\mu_B$ to 4.95 $\mu_B$ in
case of Sc to Mn-adsorption, respectively. A gap of 74 meV with a strongly
enhanced splitting of 67 meV is obtained in case of Sc-adsorption, whereas
metallic states are obtained in case of Ti, Cr, Mn, Fe, and Co. Non-magnetic
states are realized for Ni, Cu, and Zn-adsorption. Moreover, semiconducting
nature is obtained for non-magnetic cases with a gap of 26 to 28 meV.
Importantly, it is found that V-adsorbed germanene can host the quantum
anomalous Hall effect. The obtained results demonstrate that TM atoms and
nearest neighbour Ge atoms are ferro-magnetically ordered in the cases of V,
Mn, Fe, Co, Ni, Cu, and Zn, while anti-ferromagnetic ordering is obtained for
Sc, Ti, and Cr. In addition, the effects of the coverage of all TM atoms on the
electronic structure and the ferro-magnetic and anti-ferro-magnetic coupling in
case of Mn are examined. The results could help to understand the effect of TM
atoms in a new class of two-dimensional materials beyond graphene and silicene.
