Electronic and magnetic properties of the HfO₂ monolayer engineered by doping with transition metals and nonmetal atoms towards spintronic applications

Doping two-dimensional (2D) materials is a vitally important method to modulate their electronic and magnetic properties. In this work, doping with transition metals (TM = Mn and Fe) and nonmetal atoms (X = B and C) is proposed to engineer the magnetism in the HfO₂ monolayer. The pristine monolayer is an intrinsically nonmagnetic insulator with a large band gap of 4.85 (6.43) eV as calculated using the PBE (HSE06) functional. Doping with Mn and Fe atoms induces monolayer magnetization with total magnetic moments of 3.00 and 4.00<i>μ</i> _B, respectively. Herein, Mn- and Fe-3d electrons produce mainly magnetic properties and regulate the electronic nature by forming new mid-gap energy states. Similarly, the 2p orbital of impurities plays a key role in determining the electronic and magnetic properties of B- and C-doped systems. Mn and B doping leads to the emergence of magnetic semiconductor nature, while the half-metallicity is obtained by doping with Fe and C atoms. Further, the substitution of the Hf-O pair with the TM-X pair is also studied. In these cases, both TM and X impurities induce the system magnetism, exhibiting an antiparallel spin orientation. Consequently, pair-atom-doped systems have smaller total magnetic moments in comparison with single-atom-doped systems. Interestingly, doping with all four Mn-B, Mn-C, Fe-B, and Fe-C pairs induces a magnetic semiconductor nature, where spin-dependent energy gaps are determined by the doping-induced multiple mid-gap energy states. When incorporated into the HfO₂ monolayer lattice, transition metals lose charge, while nonmetal impurities act as charge gainers. This study demonstrates the effectiveness of the doping method to engineer the magnetism in the HfO₂ monolayer for spintronic applications.