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 $J_\bot = (1.09 \pm 0.01)$meVand$J_| = (0.296 \pm 0.005)$ meV, accurately describes the data. The experimental limit on the effective inter-ladder exchange constant is $\mathrm{\mid }{J}_{\mathrm{i}\mathrm{n}\mathrm{t}}^{\mathrm{e}\mathrm{f}\mathrm{f}}\mathrm{\mid }\lesssim 0.006$ meV, and the limit on total diagonal, intra-ladder exchange is $\mathrm{\mid }{J}_F+J_{F^{\mathrm{\prime }}}\mathrm{\mid }\le 0.1$ meV. Including the effects of copper to bromide covalent spin transfer on the magnetic form-factor, the experimental ratios of intra-ladder bond energies are consistent with the predictions of continuous unitary transformation.