Reply to Comment on ‘Oxygen vacancy-induced magnetic moment in edge-sharing CuO₂ chains of Li₂CuO_2-δ ’

Abstract

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.

Comment on `Oxygen vacancy-induced magnetic moment in edge-sharing CuO$_{2}$ chains of Li$_{2}$CuO$_{2}$'

“…3 of Ref. [38]). Moreover, they state: "Finally, the polynomial HTSE fitting can always achieve high goodness-of-fit for nearly any curve without abrupt turns via higher order parameter adjustment within a limited temperature range".…”

“…(iv) In section 4.5 of [38], Shu et al erroneously claim that i<j J ij S i S j = 1 2 i,j J ij S i S j and doubt that we properly interpret our exchange values. We may mention that in the notations of Eq.…”

“…This is in contrast to the SLT-model, which does not account for these data. (i) In their "Corrigendum" [37] submitted later on but published nevertheless shortly before our Comment and the Authors's Reply [38], Shu et al have recognized that their equation ( 7) is wrong. In the proposed corrected equation, they use the notations of Ref.…”

“…(ii) Unfortunately, in the Reply [38], Shu et al repeat their erroneous statement that a positive value of Θ CW would be allowed only for a system with an FM ground state (see the end of p. 5). Just for illustration, let us consider the case of a simple cubic magnetic lattice with a large NN FM interaction along the x-direction and a tiny NN AFM coupling along the y-and z-directions.…”

“…(iii) On pages 5,6 of Ref. [38], Shu et al erroneously claim that HTE (they call it "HTSE") would be an approximation to the Curie-Weiss law (see the paragraph below Fig. 3 of Ref.…”