Neutron scattering evidence for isolated spin-1/2 ladders in (C$_5$D$_{12}$N)$_2$CuBr$_4$

Inelastic neutron scattering was used to determine the spin Hamiltonian for the singlet ground state system of fully deuterated BPCB, (C$_{5}$D$_{12}$N)$_{2}$CuBr$_{4}$. A 2-leg spin-1/2 ladder model, with $J_\bot = (1.084 \pm 0.005)$ meV and $J_\| = (0.321 \pm 0.008)$ meV, accurately describes the data. The experimental limit on the effective inter-ladder exchange constant is $|J_{\rm int}^{\rm eff}|\lesssim 0.006$ meV, and the limit on diagonal, intra-ladder exchange is $|J_F|\leq 0.1$ meV. The experimental ratios of intra-ladder bond energies are consistent with the predictions of continuous unitary transformations calculations.