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We present specific-heat and neutron-scattering results for the \emph{S}=1/2quantum antiferromagnet (dimethylammonium)(3,5-dimethylpyridinium)CuBr$_4$. Thematerial orders magnetically at \emph{T}$_N$=1.99(2)\,K, and magneticexcitations are accompanied by an energy gap of 0.30(2) meV due to spinanisotropy. The system is best described as coupled two-leg spin-1/2 ladderswith the leg exchange $J_{\rm leg}$=0.60(2)~meV, rung exchange $J_{\rmrung}$=0.64(9)~meV, interladder exchange $J_{\rm int}$=0.19(2)~meV, and aninteraction-anisotropy parameter $\lambda$=0.93(2), according to inelasticneutron-scattering measurements. In contrast to most spin ladders reported todate, the material is a rare example in which the interladder coupling is verynear the critical value required to drive the system to a N\'eel-ordered phasewithout an assistance of a magnetic field.

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