  The immunity of Ising superconductors to external magnetic fields originates
from a spin locking of the paired electrons to an intrinsic Zeeman-like field.
The spin-momentum locking in non-centrosymmetric crystalline materials leads to
type-I Ising pairing in which the direction of the intrinsic field can be
deduced from the spin expectation values. Conversely, in centrosymmetric
crystals the electron spins locked to the orbitals can form Ising type-II pairs
consisting of spin-orbit split doublets. Due to time-reversal symmetry, the
doublets are spin degenerate, making it difficult to read the spin polarization
of bands and the direction of spin-orbit fields. Here we present an efficient
approach to determine the direction of the intrinsic field using the
spin-mixing parameter $b^2$. Using first principles calculations based on the
density functional theory, we study monolayer transition metal dichalcogenide
superconductors PdTe$_2$, NbTe$_2$, and TiSe$_2$ with the 1T structure. We
calculate $b^2$ for individual Fermi pockets and provide a general picture of
possible Ising type-II pairing within the full Brillouin zone. In order to
complement our first principles results, we use group theory to provide a
detailed picture of spin-orbit coupling and spin mixing in the relevant bands
forming Fermi pockets. We demonstrate that contrary to the anticipated effects
of spin-orbit locking, not every spin-orbit split spin doublet actively
participates in Ising pairing. Finally, by connecting the spin-mixing parameter
$b^2$ with the intrinsic out-of-plane Zeeman field we estimate the upper
in-plane critical magnetic field.
