Comment on ‘Oxygen vacancy-induced magnetic moment in edge-sharing CuO₂ chains of Li₂CuO₂’

Abstract

In a recent work devoted to the magnetism of Li 2 CuO 2 , Shu et al (2017 New J. Phys. 19, 023026) have proposed a 'simplified' unfrustrated microscopic model that differs considerably from the models refined through decades of prior work. We show that the proposed model is at odds with known experimental data, including the reported magnetic susceptibility χ(T) data up to 550K. Using an 8th order high-temperature expansion for χ(T), we show that the experimental data for Li 2 CuO 2 are consistent with the prior model derived from inelastic neutron scattering studies. We also establish the T-range of validity for a Curie-Weiss law for the real frustrated magnetic system. We argue that the knowledge of the long-range ordered magnetic structure for T<T N and of χ(T) in a restricted Trange provides insufficient information to extract all of the relevant couplings in frustrated magnets; the saturation field and INS data must also be used to determine several exchange couplings, including the weak but decisive frustrating antiferromagnetic interchain couplings.Li 2 CuO 2 takes a special place among the still increasing family of frustrated chain compounds with edge-sharing CuO 4 plaquettes and a ferromagnetic (FM) nearest neighbor (NN) inchain coupling J 1 [1]. This unique position is due to its ideal planar CuO 2 chain structure and its well-defined ordering characterized by a 3D Neél-type arrangement of adjacent chains whose magnetic moments are aligned ferromagnetically along the chains (b-axis). Li 2 CuO 2 is well studied in both experiment and theory (see e.g. [2][3][4][5][6][7][8][9][10][11]) and serves nowadays as a reference system for more complex and structurally less ideal systems. In particular, it is accepted in the quantum magnetism community that the leading FM coupling is the NN inchain coupling J 1 . (J 1 is also dominant but antiferromagnetic (AFM) in the special spin-Peierls case of CuGeO 3 [12].) There is always also a finite frustrating AFM next-nearest neighbor (NNN) coupling J 2 >0, see figure 1, left. This inchain frustration is quantified by J J 2 1 a = | |. In the present case, and in that of the related Ca 2 Y 2 Cu 5 O 10 , there are only frustrating OPEN ACCESS RECEIVED

Corrigendum: Oxygen vacancy-induced magnetic moment in edge-sharing CuO2 chains of Li2CuO2−δ (2017 New J. Phys. 19 023026)

“…, the conventional coupling constants J i based on the Hamiltonian  = J S S i j ij i j å < · must have the J i = 2 J i * relationship for a consistent comparison. The J values shown in the 4th and 5th rows of table 6 in the paper by Shu et al should be doubled, i.e., J 1 for δ ∼ 0 and 0.16 are ∼130 K and 122 K, respectively, which is also consistent to the J 1 estimation as shown in the figure 2 of reply to the comment raised by Kuzian et al [3]. In addition, strictly speaking, it is not appropriate to position J¢/ J in the J 3 /J 5 columns, because the former is for the dipole-dipole inter-chain coupling for each FM chain as a unit, and the latter is for inter-chain individual spin exchange coupling.…”

Reply to Comment on ‘Oxygen vacancy-induced magnetic moment in edge-sharing CuO2 chains of Li2CuO2-δ ’

“…Therefore, the onset of significant deviation from the high-T linear extrapolation could be used as a rough estimate to the dominant nearest neighbor coupling J nn . Experimentally, the deviation of high-T 1/χ linearity has been found to start from ∼140 K, as revealed in figure 2 via a difference plot between χ(T) data and the Curie-Weiss law with fitted parameters, which is nearly half of the J 1 value (∼230 K) fitted by Kuzian and Lorenz et al [1,3] This experimental evidence suggests that the dominant J 1 size must be in the range of ∼140 K, which is consistent with most published results (listed in table 6 of Shu 2017), especially near values calculated via highly correlated ab initio electronic structure calculations, of FM J 1 ∼142 K [12]. More accurate J 1 values can be obtained via HTSE fitting to include higher-order corrections of J/k B T in the series expansion, but a doubling of the value via HTSE fitting is unlikely [16], not to mention that the validity of J 1 must be checked to show consistency to the sign of Θ∼−Sz J i i .…”

“…Based on the results of J 1 ∼−230 K and Θ∼+50 K by applying a rigorously established Heisenberg model to the χ(T) data HTSE fitting, Kuzian and Lorenz et al speculated that all earlier published Curie-Weiss law analyses using susceptibility data in the range between ∼200-550 K are not really in the true PM regime and should be denoted as pseudo * Q [3]. In addition, they projected that the pseudo * Q converges to the true Θ only above ∼2500 K (see figure 1 in the comment of Kuzian et al) [1], i.e., all published Curie-Weiss law fitting results on Li CuO 2 2 are wrong because the fitting temperature range is too low, leading to a negative * Q ; the true Θ must be positive when using linear fitting of 1/χ(T) data above ∼2500 K. We disagree and would like to dispute with two experimental facts. First, as shown in figure 2 (as well as figure 4 in Shu 2017), the nearly perfect linearity of 1/χ(T) in the range of ∼140-550 K implies that the temperature is high enough to be unaffected by the residue effect of the spontaneous spin exchange interaction; [6] otherwise, an upward deflection of 1/χ for  T 0 would occur as a result of the competing temperature-independent AF coupling effect.…”

“…We believe that the controversy originates from the fact that the impact of the magnetic moment induced by the oxygen vacancies in d -Li CuO 2 2 was ignored in the works of Kuzian and Lorenz et al, while solid experimental evidence of an oxygen vacancy-induced magnetic moment was detailed in , as well as the conclusive identification of a magnetic moment near the oxygen sites according to the neutron scattering study by Chung et al [4] Although Kuzian et al admitted in this comment that the very question regarding the influence of oxygen vacancies on the magnetic properties of Li CuO 2 2 raised by us is 'interesting and should be studied', no new experimental evidence about this claim was provided. Instead, to defend their results of an unusually large J 1 value (nearly doubled comparing to most published results) and the positive sign of Θ obtained via the INS experiment and susceptibility data fitting, the validity of the commonly used Curie-Weiss law susceptibility data fitting protocol was challenged once again [1], as previously stated in Lorenz 2009 [3].…”

Ab initio ligand field approach to determine electronic multiplet properties

“…The one-dimensional spin-1 /2 J 1 -J 2 Heisenberg model is one prime example of frustrated magnetism, where quantum fluctuations can alter both ground state and spin correlations [34,35]. Due to its simple structure with flat CuO 2 chains, the compound Li 2 CuO 2 was considered as a model system for studies of the highly non-trivial magnetism in the edge-shared cuprates [36][37][38][39][40][41][42][43][44][45][46][47]. Almost two decades passed from the determination of the crystal and magnetic structures of Li 2 CuO 2 [36] to a reliable determination of main magnetic interactions within and between the CuO 2 chains [41,48].…”