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A search for a heavy CP-odd Higgs boson, $A$, decaying into a $Z$ boson and aheavy CP-even Higgs boson, $H$, is presented. It uses the full LHC Run 2dataset of $pp$ collisions at $\sqrt{s}=13$ TeV collected with the ATLASdetector, corresponding to an integrated luminosity of $140$ fb$^{-1}$. Thesearch for $A\to ZH$ is performed in the $\ell^+\ell^- t\bar{t}$ and$\nu\bar{\nu}b\bar{b}$ final states and surpasses the reach of previoussearches in different final states in the region with $m_H>350$ GeV and$m_A>800$ GeV. No significant deviation from the Standard Model expectation isfound. Upper limits are placed on the production cross-section times the decaybranching ratios. Limits with less model dependence are also presented asfunctions of the reconstructed $m(t\bar{t})$ and $m(b\bar{b})$ distributions inthe $\ell^+\ell^- t\bar{t}$ and $\nu\bar{\nu}b\bar{b}$ channels, respectively.In addition, the results are interpreted in the context of two-Higgs-doubletmodels.

Search for a CP-odd Higgs boson decaying into a heavy CP-even Higgs  boson and a $Z$ boson in the $\ell^+\ell^- t\bar{t}$ and  $\nu\bar{\nu}b\bar{b}$ final states using 140 fb$^{-1}$ of data collected  with the ATLAS detector