  Valleytronics, that uses the valley index or valley pseudospin to encode
information, has emerged as an interesting field of research in two-dimensional
(2D) systems with promising device applications. Spin-orbit coupling (SOC) and
inversion symmetry breaking leads to spin-splitting of bands near the energy
extrema (valleys). In order to find a new 2D material useful for valleytronics,
we have designed hexagonal planar monolayers of cadmium chalcogenides (CdX, X =
S, Se, Te) from the (111) surface of bulk CdX zinc blende structure. Band
structure study reveals valence band local maxima at symmetry point K and its
time reversal conjugate point K$\textquotesingle$. Application of SOC initiates
spin-splitting in the valleys that lifts the energy degeneracy and shows strong
valley-spin coupling character. We have substituted two Cd atoms in the planar
monolayers by Sn atoms which increases the spin-splitting significantly. The
structural, dynamic, mechanical and thermal stability of all the monolayers has
been confirmed. Values of formation energies indicate that it may be feasible
to synthesize the Sn-doped CdSe and CdTe monolayers using bottom-up approach.
Zeeman-type spin-splitting is observed in the valley region and Rashba
spin-splitting is observed at the $\Gamma$ point for Sn-doped CdSe and CdTe
monolayers. Berry curvature values are more in all the Sn-doped monolayers than
the pristine monolayers. These newly designed monolayers are thus found to be
suitable for valleytronics applications. Sn-doped monolayers show band
inversion deep in the valence and conduction bands between Sn~$s$ and $p$ and
X~$p$ states but lack topological properties.
