Neutron diffraction and bulk measurements are used to determine the nature of the low-temperature ordered state in ${\mathrm{LiCu}}_2{\mathrm{O}}_2$, a $S=1/2$ spin-chain compound with competing interactions. The spin structure is found to be helimagnetic, with a propagation vector $(0.5,\zeta ,0)$, $\zeta =0.174$. The nearest-neighbor exchange constant and frustration ratio are estimated to be $J_1=5.8\mathrm{meV}$ and $J_2/J_1=0.29$, respectively. For idealized quantum spin chains, these parameter values would signify a gapped spin-liquid ground state with commensurate spin correlations. The observed temperature dependence of the magnetic propagation vector in ${\mathrm{LiCu}}_2{\mathrm{O}}_2$ is attributed to a competition between incommensurate helimagnetism in the classical spin model and commensurability in the quantum case. It is also proposed that long-range ordering in ${\mathrm{LiCu}}_2{\mathrm{O}}_2$ is facilitated by intrinsic nonstoichiometry.

The quasi-one-dimensional helimagnet $\mathrm{Li}{\mathrm{Cu}}_2{\mathrm{O}}_2$ was studied by single crystal inelastic neutron scattering. The dispersion relation of spin wave excitations was measured in the vicinity of the principal magnetic Bragg reflection. A spin wave theoretical analysis of the data yields an estimate of the relevant exchange constants and explains the mechanism of geometric frustration that leads to helimagnetism. It is found that the simple antiferromagnetic $J_1\text{−}{J}_2$ model that was previously proposed is inadequate for $\mathrm{Li}{\mathrm{Cu}}_2{\mathrm{O}}_2$. The experimental findings are generally in a qualitative agreement with first principles calculations of [A. A. Gippius, E. N. Morozova, A. S. Moskvin, A. V. Zalessky, A. A. Bush, M. Baenitz, H. Rosner, and S.-L. Drechsler, Phys. Rev. B 70, 020406 (2004)], though certain important discrepancies remain to be explained.

A new brownmillerite-type compound Sr₂Al_1.07Mn_0.93O₅ was synthesized. The crystal structure was determined using electron diffraction and high resolution transmission electron microscopy and refined from X-ray powder diffraction data (space group Imma, a = 5.4358(1) Å, b = 15.6230(4) Å, c = 5.6075(1) Å, R_I = 0.036, R_P = 0.023). The structure is characterized by a disordered distribution of the tetrahedral chains in L and R configuration and a partial occupation of the octahedral position by the Mn³⁺ and Al³⁺ cations. The relationships between the crystal structures of Sr₂Al_1.07Mn_0.93O₅ and its A₂B′MnO₅ analogues (A = Ca, Sr, B′ = Al, Ga) and the structural reasons for the different types of tetrahedral chain ordering in brownmillerites are discussed. The temperature dependences of the magnetic susceptibility and specific heat reveal that the compound is antiferromagnetically ordered below T_N = 105 K.

A Reply to the Comment by S.-L. Drechsler et al.