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Magnetic ordering induced by interladder coupling in the spin-1/2 Heisenberg two-leg ladder antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$

We present specific-heat and neutron-scattering results for the \emph{S}=1/2 quantum antiferromagnet (dimethylammonium)(3,5-dimethylpyridinium)CuBr$_4$. The material orders magnetically at \emph{T}$_N$=1.99(2)\,K, and magnetic excitations are accompanied by an energy gap of 0.30(2) meV due to spin anisotropy. The system is best described as coupled two-leg spin-1/2 ladders with the leg exchange $J_{\rm leg}$=0.60(2)~meV, rung exchange $J_{\rm rung}$=0.64(9)~meV, interladder exchange $J_{\rm int}$=0.19(2)~meV, and an interaction-anisotropy parameter $λ$=0.93(2), according to inelastic neutron-scattering measurements. In contrast to most spin ladders reported to date, the material is a rare example in which the interladder coupling is very near the critical value required to drive the system to a Néel-ordered phase without an assistance of a magnetic field.