  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 Neel 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 Neel
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.
