  Precision measurements of Schiff moments in heavy, deformed nuclei are
sensitive probes of beyond Standard Model $T,P$-violation in the hadronic
sector. While the most sensitive limits on Schiff moments to date are set with
diamagnetic atoms, polar polyatomic molecules can offer higher sensitivities
with unique experimental advantages. In particular, symmetric top molecular
ions possess $K$-doublets of opposite parity with especially small splittings,
leading to full polarization at low fields, internal co-magnetometer states
useful for rejection of systematic effects, and the ability to perform
sensitive searches for $T,P$-violation using a small number of trapped ions
containing heavy exotic nuclei. We consider the symmetric top cation
$^{225}$RaOCH$_3^+$ as a prototypical and candidate platform for performing
sensitive nuclear Schiff measurements and characterize in detail its internal
structure using relativistic ab initio methods. The combination of enhancements
from a deformed nucleus, large polarizability, and unique molecular structure
make this molecule a promising platform to search for fundamental symmetry
violation even with a single trapped ion.
