  A study of the decays $B^0\to \mu^+\mu^-$ and $B^0_s\to \mu^+\mu^-$ has been
performed using data corresponding to an integrated luminosity of $25$
fb$^{-1}$ of $7$ TeV and $8$ TeV proton--proton collisions collected with the
ATLAS detector during the LHC Run 1. For $B^0$, an upper limit on the branching
fraction is set at ${\cal B}(B^0 \to \mu^+\mu^-) < 4.2 \times 10^{-10}$ at
$95\%$ confidence level. For $B^0_s$, the branching fraction ${\cal B}(B^0_s
\to \mu^+\mu^-) = \left( 0.9^{+1.1}_{-0.8} \right) \times 10^{-9}$ is measured.
The results are consistent with the Standard Model expectation with a $p$-value
of $4.8\%$, corresponding to $2.0$ standard deviations.
