Effect of magnetic and non-magnetic impurities on the spin dimers in the spin 1/2 chains of quantum magnet Sr$_{14}$Cu$_{24}$O$_{41}$

We study the effect of impurities on the two types of spin-dimers in the hybrid chain/ladder spin 1/2 quantum magnet Sr$_{14}$Cu$_{24}$O$_{41}$. Four different impurities were used, namely, the non-magnetic Zn (0.0025 and 0.01 per Cu) and Al (0.0025 and 0.01 per Cu), and magnetic Ni (0.0025 and 0.01 per Cu) and Co (0.01, 0.03, 0.05 and 0.1 per Cu). These impurities were doped in high-quality single-crystals synthesized by the floating zone method. The magnetic susceptibility of pristine Sr$_{14}$Cu$_{24}$O$_{41}$ is analyzed rigorously to confirm that at low temperatures (T $<$ 5 K), the "free" spins in the chains undergo a long-distance dimerization as proposed in a recent study [Sahling et al. Nature Phys., \textbf{11}, 255 (2015)]. The effect of impurity on these dimers is analyzed by measuring the specific heat down to T = 0.06 K. We found that even at the lower impurity concentration, the long-distance dimers are significantly severed, but the quantum entangled spin dimerized state of the chains persists. On the other hand, the other type of spin dimers that forms at relatively higher temperatures via an intervening Zhang-Rice singlet are found to be practically unaffected at the lower impurity concentration; but at 1\% doping, even these are found to be considerably severed. The effect of Co impurity turned out to be most unusual displaying a strongly anisotropic response, and with a dimerization gap that suppresses faster along the chain/ladder direction than perpendicular to it as a function of increasing Co concentration.