Impact of inter-ladder coupling in a coupled spin-1/2 two-leg ladder*

We present the zero-field specific heat and neutron scattering studies on an $S=$1/2 Heisenberg antiferromagnet to understand the nature of its spin Hamiltonian. The system is magnetically ordered below $T_{\mathrm{N}}=$2.0(1) K. The conclusion that the system is best described as coupled two-leg spin-1/2 ladders is supported by the material structure, neutron scattering measurements, and theoretical calculation.