Substellar members of young ($lesssim$150 Myr) moving groups are valuable benchmarks to empirically define brown dwarf evolution with age and to study the low-mass end of the initial mass function. We have combined Pan-STARRS1 (PS1) proper motions with optical$-$IR photometry from PS1, 2MASS and $textit{WISE}$ to search for substellar members of the AB Dor Moving Group within $approx$50 pc and with spectral types of late-M to early-L, corresponding to masses down to $approx$30 M$_{Jup}$ at the age of the group ($approx$125 Myr). Including both photometry and proper motions allows us to better select candidates by excluding field dwarfs whose colors are similar to young AB~Dor Moving Group members. Our near-IR spectroscopy has identified six ultracool dwarfs (M6$-$L4; $approx$30$-$100 M$_{Jup}$) with intermediate surface gravities (INT-G) as candidate members of the AB Dor Moving Group. We find another two candidate members with spectra showing hints of youth but consistent with field gravities. We also find four field brown dwarfs unassociated with the AB Dor Moving Group, three of which have INT-G gravity classification. While signatures of youth are present in the spectra of our $approx$125 Myr objects, neither their $J-K$ nor $W1-W2$ colors are significantly redder than field dwarfs with the same spectral types, unlike younger ultracool dwarfs. We also determined PS1 parallaxes for eight of our candidates and one previously identified AB Dor Moving Group candidate. Although radial velocities (and parallaxes, for some) are still needed to fully assess membership, these new objects provide valuable insight into the spectral characteristics and evolution of young brown dwarfs.
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