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 $S=1\mathrm{/}2$ 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 $S=1\mathrm{/}2$ 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 $0\leq x\leq1$\mathrm{.}Weextractladderexchangeconstants$J_{l}(x)$and$J_{r}(x)$ as well as the gap value $\mathrm{\Delta }(x)$ 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.