Spin dynamics of coupled spin ladders near quantum criticality in Ba2CuTeO6

We report inelastic neutron scattering measurements of the magnetic excitations in ${\mathrm{Ba}}₂{\mathrm{CuTeO}}₆$, proposed by ab initio calculations to magnetically realize weakly coupled antiferromagnetic two-leg spin-$\frac{1}{2}$ ladders. Isolated ladders are expected to have a singlet ground state protected by a spin gap. ${\mathrm{Ba}}₂{\mathrm{CuTeO}}₆$ orders magnetically, but with a small N\'eel temperature relative to the exchange strength, suggesting that the interladder couplings are relatively small and only just able to stabilize magnetic order, placing ${\mathrm{Ba}}₂{\mathrm{CuTeO}}₆$ close in parameter space to the critical point separating the gapped phase and N\'eel 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.