Crystal structure, magnetic susceptibility, and specific heat were measured in the normal cubic spinel compounds MnSc2S4 and FeSc2S4. Down to the lowest temperatures, both compounds remain cubic and reveal strong magnetic frustration. Specifically the Fe compound is characterized by a Curie-Weiss (CW) temperature ThetaCW = -45 K and does not show any indications of order down to 50 mK. In addition, the Jahn-Teller ion Fe2+ is orbitally frustrated. Hence, FeSc2S4 belongs to the rare class of spin-orbital liquids. MnSc2S4 is a spin liquid for temperatures T>TN approximately 2 K.

We present a detailed study of complex dielectric constant and ferroelectric polarization in multiferroic LiCuVO 4 as function of temperature and external magnetic field. In zero external magnetic field, spiral spin order with an ab helix and a propagation vector along the crystallographic b direction is established, which induces ferroelectric order with spontaneous polarization parallel to a. The direction of the helix can be reoriented by an external magnetic field and allows switching of the spontaneous polarization. We find a strong dependence of the absolute value of the polarization for different orientations of the spiral plane. Above 7.5 T, LiCuVO 4 reveals collinear spin order and remains paraelectric for all field directions. Thus this system is ideally suited to check the symmetry relations for spiral magnets as predicted theoretically. The strong coupling of ferroelectric and magnetic order is documented and the complex (B,T) phase diagram is fully explored.

We report on magnetic resonance studies within the magnetically ordered phase of the quasi-onedimensional antiferromagnet LiCuVO 4 . Our studies reveal a spin reorientational transition at a magnetic field H c1 Ϸ 25 kOe applied within the crystallographic ab plane in addition to the recently observed one at H c2 Ϸ 75 kOe ͓M. G. Banks et al., J. Phys.: Condens. Matter 19, 145227 ͑2007͔͒. Spectra of the antiferromagnetic resonance along low-frequency branches can be described in the framework of a macroscopic theory of exchange-rigid planar magnetic structures. These data allow us to obtain the parameter of the anisotropy of the exchange susceptibility together with a constant of the uniaxial anisotropy. Spectra of 7 Li nuclear magnetic resonance ͑NMR͒ show that, within the magnetically ordered phase of LiCuVO 4 in the low-field range H Ͻ H c1 , a planar spiral spin structure is realized with the spins lying in the ab plane, in agreement with neutron-scattering studies of Gibson et al. ͓Physica B 350, 253 ͑2004͔͒. Based on NMR spectra simulations, the transition at H c1 can well be described as a spin-flop transition, where the spin plane of the magnetically ordered structure rotates to be perpendicular to the direction of the applied magnetic field. For H Ͼ H c2 Ϸ 75 kOe, our NMR spectra simulations show that the magnetically ordered structure exhibits a modulation of the spin projections along the direction of the applied magnetic field H.

We have performed NMR experiments on the quasi one-dimensional frustrated spin-1/2 system LiCuVO4 in magnetic fields H applied along the c-axis up to field values near the saturation field Hsat. For the field range Hc2 < H < Hc3 (µ0Hc2 ≈ 7.5 T and µ0Hc3 = [40.5 ± 0.2] T) the 51 V NMR spectra at T = 380 mK exhibit a characteristic double-horn pattern, as expected for a spinmodulated phase in which the magnetic moments of Cu 2+ ions are aligned parallel to the applied field H and their magnitudes change sinusoidally along the magnetic chains. For higher fields, the 51 V NMR spectral shape changes from the double-horn pattern into a single Lorentzian line. For this Lorentzian line, the internal field at the 51 V nuclei stays constant for µ0H > 41.4 T, indicating that the majority of magnetic moments in LiCuVO4 are already saturated in this field range. This result is inconsistent with the previously observed linear field dependence of the magnetization M (H) for Hc3 < H < Hsat with µ0Hsat = 45 T [L. E. Svistov et al., JETP Letters 93, 21 (2011)]. We argue that the discrepancy is due to non-magnetic defects in the samples. The results of the spin-lattice relaxation rate of 7 Li nuclei indicate an energy gap which grows with field twice as fast as the Zeeman energy of a single spin, therefore, suggesting that the two-magnon bound state is the lowest energy excitation. The energy gap tends to close at µ0H ≈ 41 T. Our results suggest that the theoretically predicted spin-nematic phase, if it exists in LiCuVO4, can be established only within the narrow field range 40.5 < µ0H < 41.4 T .

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