  A search new phenomena giving rise to pairs of opposite electrically charged
muons with impact parameters in the millimetre range is presented, using 139
fb$^{-1}$ of $\sqrt{s} = 13$ TeV $pp$ collision data from the ATLAS detector at
the LHC. The search targets the gap in coverage between existing searches
targeting final states with leptons with large displacement and prompt leptons.
No significant excess over the background expectation is observed and exclusion
limits are set on the mass of long-lived scalar supersymmetric muon-partners
(smuons) with much lower lifetimes than previously targeted by displaced muon
searches. Smuon lifetimes down to 1 ps are excluded for a smuon mass of 100
GeV, and smuon masses up to 520 GeV are excluded for a proper lifetime of 10
ps, at 95% confidence level. Finally, model-independent limits are set on the
contribution from new phenomena to the signal-region yields.
