  We propose and optimize a vertically-loaded diamond microdisk resonator
(VLDMoRt) coupled to a nitrogen-vacancy (NV) center in diamond for efficient
collection of zero-phonon-line emission into low numerical aperture
($\text{NA}$) free-space modes. The VLDMoRt achieves a Purcell enhancement of
172 with $39\%$ of the emitted light collected within a $\text{NA}$ of 0.6,
leading to a total external spin-photon collection efficiency of 0.33. As the
design is compatible with established nanofabrication techniques and couples to
low-NA modes accessible by cryogenic free-space optical systems, it is a
promising platform for efficient spin-photon interfaces based on diamond
quantum emitters.
