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.

By analyzing the NMR line shape, the transformation of a spatially spin-modulated magnetic structure in BiFeO₃ into an ordinary spatially uniform structure of the LaFeO₃ orthoferrite in Bi_1−x La_xFeO₃ solid solutions is studied. The measurements are made using a spin-echo technique at temperatures of 77 and 4.2 K on ceramics with compositions x=0, 0.1, 0.2, 0.61, 0.9, and 1.0 enriched by the ⁵⁷Fe isotope. It is shown that the spin-modulated structure disappears near the concentration x=0.2, which corresponds, according to the published data, to the phase transition with a change in the unit-cell symmetry R3c → C222. A formula is obtained describing the NMR absorption line shape for the spin-modulated structure with account of local line-width. Theoretical spectra adequately describe the evolution of the experimental spectrum in the concentration range 0≤x≤0.2. Highly nonuniform local magnetic fields in the intermediate compositions make it impossible to detect NMR signals in a sample with x=0.61. A uniform magnetic structure characterized by a single narrow line arises in the range of existence of a phase with the symmetry Pnma typical of the pure orthoferrite LaFeO₃.

We report on ${}^{6,7}\mathrm{Li}$ nuclear magnetic resonance measurements of the spin-chain compound ${\mathrm{LiCu}}_2{\mathrm{O}}_2$ in the paramagnetic and magnetically ordered states. Below $24\mathrm{K}$ the NMR line shape shows a clear signature of incommensurate (IC) static modulation of the local magnetic field consistent with an IC spiral modulation of the magnetic moments. ${}^7\mathrm{Li}$ NMR reveals strong phason-like dynamical fluctuations extending well below $24\mathrm{K}$. A series of phase transitions at 24.2, 22.5, and $9\mathrm{K}$ is observed. Local density approximation based calculations of exchange integrals reveal a large in-chain frustration leading to a magnetical spiral.

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 prominent band centered at $\sim 1000–1300{\mathrm{cm}}^{-1}$ and associated with resonant enhancement of two-phonon Raman scattering is reported in multiferroic $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ thin films and single crystals. A strong anomaly in this band occurs at the antiferromagnetic Neel temperature, $T_N\sim 375°\mathrm{C}$ . This band is composed of three peaks, assigned to $2A_4$ , $2E_8$ , and $2E_9$ Raman modes. While all three peaks were found to be sensitive to the antiferromagnetic phase transition, the $2E_8$ mode, in particular, nearly disappears at $T_N$ on heating, indicating a strong spin-two-phonon coupling in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ .

Optical properties of single-crystal monoclinic CuO in the range $70–6000\hspace{0.5em}{\mathrm{cm}}^{-1}$ were studied at temperatures from 7 to 300 K. Normal reflection spectra were obtained from the (001) and (010) crystal faces thus giving separate data for the $A_u$ and $B_u$ phonon modes excited in the purely transverse way (TO modes). Mode parameters, including polarizations of the $B_u$ modes not determined by the crystal symmetry, were extracted by the dispersion analysis of reflectivity curves as a function of temperature. Spectra of all the components of the optical conductivity tensor were obtained using the Kramers-Kronig method recently extended to the case of the low-symmetry crystals. The number of strong phonon modes is in agreement with the factor-group analysis for the crystal structure currently accepted for the CuO. However, several “extra” modes of minor intensity are detected; some of them are observed in the whole studied temperature range, while existence of others becomes evident at low temperatures. Comparison of frequencies of “extra” modes with the available phonon dispersion curves points to possible “diagonal” doubling of the unit cell $\{\mathbf{a},\mathbf{b},\mathbf{c}\overrightarrow{\}}\{\mathbf{a}+\mathbf{c},\mathbf{b},\mathbf{a}-\mathbf{c}\}$ and formation of the superlattice. The previously reported softening of the $A_u^3$ mode $\left(\sim 400\hspace{0.5em}{\mathrm{cm}}^{-1}\right)$ with cooling at $T_N$ is found to be $\sim 10\%$ for the TO mode. The mode is very broad at high temperatures and strongly narrows in the antiferromagnetic phase. We attribute this effect to strong resonance coupling of this mode to optical or acoustic bimagnons and reconstruction of the magnetic excitations spectrum at the Néel point. A significant anisotropy of ${\epsilon }^{\infty }$ is observed: it was found to be 5.9 along the $\mathbf{b}$ axis, 6.2 along the [101] chains, and 7.8 along the $\left[101¯\right]$ chains. The transverse effective charge $e_{\mathrm{T}}^{*}$ is more or less isotropic; its value is about two electrons.