The tunable quantum spin ladder Cu(Qnx)(Cl$_{(1-x)}$Br$_{x}$)$_{2}$

We report magnetic, specific heat and ESR measurements on a series of $S=1/2$ spin ladder compounds Cu(Qnx)(Cl$_{(1-x)}$Br$_{x}$)$_{2}$. Down to $T=2$ K all the observables can be described by the spin ladder model with about 1% of $S=1/2$ impurities in the background, which are present even in a nominally pure Cu(Qnx)Cl$_{2}$ and Cu(Qnx)Br$_{2}$, for the whole range of $0\leq x\leq1$. We extract ladder exchange constants $J_{l}(x)$ and $J_{r}(x)$ as well as the gap value $\Delta(x)$ by comparing the experimental data to quantum Monte-Carlo simulations. As the ESR measurements show the $g$-factor of impurities to be precisely equal to $g$-factor of the ladder spins, we suppose the impurities to be the consequence of structural defects resulting in a broken ladder ends.