Effects of quantum impurity spins on the magnetic properties of zigzag and linear spin chains

We investigated the magnetic ground state and low-energy excitations of the spin chains compounds SrCuO${}_2$ (zigzag chains) and Sr${}_2$CuO${}_3$ (linear chains) in the presence of quantum impurities induced by lightly doping ($\leq 1 %$)withZn$^{2+}$($S = 0$),Co$^{2+}$($S =1/2$)andNi$^{2+}$($S = 1$) impurities at the Cu${}^{2+}$ site. We show that the ground states and the nature of low-lying excitations (i.e., gapped or gapless) depend on the spin state and symmetry of the defects. For Ni doped chains a spin gap is observed but for Zn and Co doping the excitations remain gapless. Co-doped chains exhibit magnetic order with critical temperatures significantly enhanced compared to those of the pristine compounds. In the specific case of 1 % Co impurities, the linear chains exhibit long-range order below 11 K, while the zigzag chain is characterized by a quasi-long range ordered phase below 6 K with correlation lengths of about 12$\mathit{\text{a}}$ and 40$\mathit{\text{c}}$ units along the crystal axes $\mathit{\text{a}}$ and $\mathit{\text{c}}$, respectively. The different magnetic behaviours of these two compounds with comparable intra- and interchain couplings underpin the role of spin frustration in the zigzag chains.