We report inelastic neutron scattering measurements of the magnetic excitations in Ba2CuTeO6, proposed by ab initio calculations to magnetically realize weakly coupled antiferromagnetic two-leg spin-1 2 ladders. Isolated ladders are expected to have a singlet ground state protected by a spin gap. Ba2CuTeO6 orders magnetically, but with a small Néel temperature relative to the exchange strength, suggesting that the interladder couplings are relatively small and only just able to stabilize magnetic order, placing Ba2CuTeO6 close in parameter space to the critical point separating the gapped phase and Néel order. Through comparison of the observed spin dynamics with linear spin wave theory and quantum Monte Carlo calculations, we propose values for all relevant intra-and interladder exchange parameters, which place the system on the ordered side of the phase diagram in proximity to the critical point. We also compare high field magnetization data with quantum Monte Carlo predictions for the proposed model of coupled ladders. arXiv:1806.04052v2 [cond-mat.str-el] 7 Dec 2018 FIG. 1. (Color online) Schematic phase diagram of two-leg spin-1 2 AFM ladders as a function of the in-plane interladder exchange coupling J [see Fig. 2(b)]. Below a critical coupling J c , the ground state is an overall singlet with a spin gap ∆. The J = 0 state is schematically illustrated in the inset in the strong rung limit (Jrung J leg ), showing the Cu 2+ ions (blue circles) and spin singlet bonds (black ovals). For J > J c , AFM Néel order is expected below a finite temperature TN for nonzero interplane coupling J3D. Ba2CuTeO6 has been proposed to be located close to the quantum critical point, on the ordered side of the phase diagram. 21,22