  A search for decays of the Higgs boson into a pair of new spin-zero
particles, $H \to aa$, where the $a$-bosons decay into a $b$-quark pair and
muon pair, is presented. The search uses 36.1 fb$^{-1}$ of proton-proton
collision data at $\sqrt{s}=13$ TeV recorded by the ATLAS experiment at the LHC
in 2015 and 2016. No significant deviation from the Standard Model prediction
is observed. Upper limits at 95% confidence level are placed on the branching
ratio $(\sigma_H / \sigma_{SM}) \times B(H\to aa\to bb\mu\mu)$, ranging from
$2\times 10^{-4}$ to $10^{-3}$ in the $a$-boson mass range of 20-60 GeV.
Model-independent limits are set on the visible production cross-section times
the branching ratio to the $bb\mu\mu$ final state for new physics,
$\sigma_{vis}(X) \times B(X\to bb\mu\mu)$, ranging from 0.1 fb to 0.73 fb for
$m_{\mu\mu}$ between 18 and 62 GeV.
