In this corrigendum, we present corrections to the paper 'Oxygen vacancy-induced magnetic moment in edgesharing CuO 2 chains of Li 2 CuO 2−δ ' (2017 New J. Phys. 19 023206) by Shu et al. Equation (7) shown in the paper is wrong due to copying error, which has been corrected following the referenced source with modification. The J 1 values for Li 2 CuO 2−δ (δ ∼ 0 and 0.16) shown in table 6 should be doubled for a consistent comparison based on the definition of used Hamiltonian.(1) Correction to equation (7): Equation (7) shown in the paper by Shu et al is wrong [1], the correct one with proper units must follow the original form of equation (3) in [2] by Takeda et al with an added z J   term as z J z J Ng 1 2 . AbstractLi 2 CuO 2 is a typical charge transfer insulator with CuO 2 chains that are composed of edge-shared CuO 4 plaquettes. The existence of oxygen vacancies for single crystals prepared under various oxygen partial pressures has been confirmed by the chemical and thermogravimetric analyses. The puzzling discovery of extra magnetic moment near the oxygen site by earlier neutron scattering studies has been verified by a thorough Curie-Weiss law analysis of spin susceptibilities, and resolved quantitatively with a molecular orbital model of edge-sharing CuO 2 chains containing oxygen vacancies.where ¢ = z 2 and  = z 4 correspond to the coordination numbers for ¢ J and  J , respectively, as shown in figure 9(b). With the defined = ¢  A J J ratio, the best fitting parameters of χ(T) for δ∼0.16 and 0 are summarized in table 5. The signs of --¢  J J J indicate that the intra-chain coupling (J) is FM, inter-chain coupling within the ab-plane ( ¢ J ) is FM, and the inter-chain coupling along the diagonal direction (  J ) is AF, which is consistent to the neutron diffraction results as illustrated in figure 9(a) [2, 6]. These fitted intra-chain and interchain coupling constants are comparable to those obtained using the J 1 -J 2 -J c model and molecular quantum chemistry calculation also [14,23]. Figure 9. (a) The magnetic couplings J i (i=1-6) for the antiferromagnetically FM chains in Li 2 CuO 2 . The spin structure is plotted based on the neutron diffraction results proposed by Sapina et al [2] and Chung et al [6]. (b) A simplified inter-chain coupling model of FM chains projected in the ac-plane is shown, where ¢ J and  J roughly correspond to the averages of J 3 4 and J 5 6 shown in (a), respectively. Table 5. The intra-chain (J) and inter-chain ( ¢ J ,  J ) couplings for Li 2 CuO 2−δ single crystal samples of δ∼0.16 and 0 are extracted from the fitting of temperature-dependent spin susceptibility data with equation (7). The nearest-neighbor ¢ J and the next-nearest-neighbor  J are depicted in figure 9(b) with defined ratio of = ¢  A J J . It is interesting to find that the fitted value of = ¢  A J J (table 5) is nearly equal to the ratio of  ¢ d d J J as 7 Å Å ( )  = ¢ ~=  ¢ A J J d d 5.240 3.662 1.431, 9 J J +50 * Defined˜( ) = J J 1 5 and˜( ) = J J 2 6 but missed both J 3 and J 4

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In this reply to the comment on 'Oxygen vacancy-induced magnetic moment in edge-sharing CuO 2 chains of d -Li CuO 2 2 ' (2017 New Journal of Physics 19 023206), we have clarified several key questions and conflicting results regarding the size of the intra-chain nearest neighbor coupling J 1 and the sign of the Weiss temperature Θ defined in the Curie-Weiss law of χ(T)=χ • +C/(T−Θ). Additional data analysis is conducted to verify the validity of the Curie-Weiss law fitting protocol, including the negative sign and size of Θ based on the high-temperature linear temperature dependence of 1/χ(T) for T>J 1 and m  1 g SH k T B B. The consistency between the magnetic antiferromagnetic (AF) ground state below T N and the negative sign of Θ in the high-temperature paramagnetic (PM) state is explained via the reduction of thermal fluctuation for a temperature-independent local field due to magnetic interaction of quantum nature. A magnetic dipole-dipole (MDD)-type interaction among FM chains is identified and proposed to be necessary for the 3D AF magnetic ground state formation, i.e., the Heisenberg model of an exchange-type interaction alone is not sufficient to fully describe the quasi-1D spin chain system of Li CuO 2 2 . Several typical quasi-1D spin chain compounds, including Li CuO , CuAs O , Sr Fe O 2 2 2 4 3 2 5 , and CuGeO 3 , are compared to show why different magnetic ground states are achieved from the chemical bond perspective.