  Layered materials that exhibit magnetic ordering in their pristine form are
very rare. Several standard approaches, such as adsorption of atoms,
introduction of point defects, and edge engineering, have been developed to
induce magnetism in two-dimensional materials. In this way, we investigate the
electronic and magnetic properties of monolayer TiS$_2$ doped with 3$d$
transition metals (TMs) atoms in both octahedral 1T and trigonal prismatic 1H
structures using first-principles calculations. In its pristine form, TiS$_2$
is a non-magnetic semiconductor. The bands near the Fermi energy primarily
exhibit $d$ orbital characters, and due to the presence of ideal octahedral and
trigonal arrangements, they are well separated from other bands with $p$
character. Upon substituting 3$d$-TM atoms in both structures, a variety of
electronic and magnetic phases emerge, including magnetic semiconductor,
magnetic half-metal, non-magnetic metal, and magnetic metal. Chromium exhibits
the largest magnetic moment in both the 1T and 1H structures. The 1T structure
shows a slightly higher magnetic moment of 3.419 $\mu_B$ compared to the 1H
structure 3.138 $\mu_B$, attributed to the distorted octahedral structure of
the 1T structure. Unlike pristine TiS$_2$, the deficiency in saturation of
neighboring S atoms in the presence of impurities leads to the proximity of
energy levels of $d$ and $p$ states, resulting in unexpectedly sizable magnetic
moments. Another interesting case is Cobalt, which leads to a magnetic moment
of approximately 0.805 $\mu_B$ in the 1H structure, while the Co exhibits a
non-magnetic state in the 1H structure. These materials demonstrate a high
degree of tunability and can be optimized for various magnetic applications.
