Tetragonal Mn2Au is a metallic antiferromagnet with high Néel temperature well above 1000 K. The collinear magnetic sublattice with broken inversion symmetry in company with stable in-plane anisotropy in this material favors to control it via the Néel spin–orbital effect and spin-Hall effect. In this paper, we study the spin–orbital torque induced Néel order dynamics in the heavy-metal(HM)/Mn2Au system based on coupled Landau–Lifshitz-Gilbert-Slonczewski equations. We demonstrate robust picosecond switching of the Néel order of the Mn2Au in the presence of two charge currents, and close resemblance of the Néel order switching of the HM/Mn2Au bilayer to short-term plasticity and long-term potentiation observed in the biological synapses. Orders in magnitude reduction of the power consumption in the Pt/Mn2Au bilayer comparing with the ferromagnetic tunnel junction is demonstrated also. The ultra-high speed terahertz dynamics, ultra-lower power consumption accompanying with feasible electrical manipulation make HM/Mn2Au system a promising candidate in memory storage and neuromorphic computing applications. [ABSTRACT FROM AUTHOR]