X-ray spectrum of a pinned charge density wave

We calculate the X-ray diffraction spectrum produced by a pinned charge density wave (CDW). The signature of the presence of a CDW consists of two satellite peaks, asymmetric as a consequence of disorder. The shape and the intensity of these peaks are determined in the case of a collective weak pinning using the variational method. We predict divergent asymmetric peaks, revealing the presence of a Bragg glass phase. We deal also with the long range Coulomb interactions, concluding that both peak divergence and anisotropy are enhanced. Finally we discuss how to detect experimentally the Bragg glass phase in the view of the role played by the finite resolution of measurements.Comment: 13 pages 10 figure

X-ray anomalous scattering investigations on the charge order in α′\alpha^\prime-NaV2_2O5_5

Anomalous x-ray diffraction studies show that the charge ordering in $\alpha^\prime$-NaV$_2$O$_5$ is of zig-zag type in all vanadium ladders. We have found that there are two models of the stacking of layers along \emph{c-}direction, each of them consisting of 2 degenerated patterns, and that the experimental data is well reproduced if the 2 patterns appears simultaneously. We believe that the low temperature structure contains stacking faults separating regions corresponding to the four possible patterns.Comment: Submitted to Phys. Rev. Lett., 4 pages, 4 eps figures inserted in the tex

Zigzag Charge Ordering in alpha'-NaV2O5

23Na NMR spectrum measurements in alpha'-NaV2O5 with a single- crystalline sample are reported. In the charge-ordered phase, the number of inequivalent Na sites observed is more than that expected from the low-temperature structures of space group Fmm2 reported so far. This disagreement indicates that the real structure including both atomic displacement and charge disproportionation is of lower symmetry. It is suggested that zigzag ordering is the most probable. The temperature variation of the NMR spectra near the transition temperature is incompatible with that of second-order transitions. It is thus concluded that the charge ordering transition is first-order.Comment: 4 pages, 5 eps figures, submitted to J. Phys. Soc. Jp

Watching the birth of a charge density wave order: diffraction study on nanometer-and picosecond-scales

Femtosecond time-resolved X-ray diffraction is used to study a photo-induced phase transition between two charge density wave (CDW) states in 1T-TaS$_2$, namely the nearly commensurate (NC) and the incommensurate (I) CDW states. Structural modulations associated with the NC-CDW order are found to disappear within 400 fs. The photo-induced I-CDW phase then develops through a nucleation/growth process which ends 100 ps after laser excitation. We demonstrate that the newly formed I-CDW phase is fragmented into several nanometric domains that are growing through a coarsening process. The coarsening dynamics is found to follow the universal Lifshitz-Allen-Cahn growth law, which describes the ordering kinetics in systems exhibiting a non-conservative order parameter.Comment: 6 pages, 5 figure

Exact diagonalisation study of charge order in the quarter-filled two-leg ladder system NaV2O5

The charge ordering transition in the layer compound NaV2O5 is studied by means of exact diagonalization methods for finite systems. The 2-leg ladders of the V-Trellis lattice are associated with one spin variable of the vanadium 3d-electron in the rung and a pseudospin variable that describes its positional degree of freedom. The charge ordering (CO) due to intersite Coulomb interactions is described by an effective Ising-like Hamiltonian for the pseudo-spins that are coupled to the spin fluctuations along the ladder. We employ a Lanczos algortihm on 2D lattice to compute charge (pseudo-spin) and spin-correlation functions and the energies of the low lying excited states. A CO-phase diagram is constructed and the effect of intra-ladder exchange on the CO transition is studied. It is shown that a phase with no-longe range order (no-LRO) exists between the in-line and zig-zag ordered structures. We provide a finite-size scaling analysis for the spin excitation gap and also discuss the type of excitations. In addition we studied the effect of bond-alternation of spin exchange and derived a scaling form for the spin gap in terms of the dimerization parameter.Comment: 9 pages with 9 EPS figures and 1 table, To be appeared in Phys. Rev. B (2001

Charge Order Driven spin-Peierls Transition in NaV2O5

We conclude from 23Na and 51V NMR measurements in NaxV2O5(x=0.996) a charge ordering transition starting at T=37 K and preceding the lattice distortion and the formation of a spin gap Delta=106 K at Tc=34.7 K. Above Tc, only a single Na site is observed in agreement with the Pmmn space group of this first 1/4-filled ladder system. Below Tc=34.7 K, this line evolves into eight distinct 23Na quadrupolar split lines, which evidences a lattice distortion with, at least, a doubling of the unit cell in the (a,b) plane. A model for this unique transition implying both charge density wave and spin-Peierls order is discussed.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Long-range modulation of a composite crystal in a five-dimensional superspace

Citation: Guerin, L., Mariette, C., Rabiller, P., Huard, M., Ravy, S., Fertey, P., . . . Toudic, B. (2015). Long-range modulation of a composite crystal in a five-dimensional superspace. Physical Review B, 91(18), 7. doi:10.1103/PhysRevB.91.184101The intergrowth crystal of n-tetracosane/urea presents a misfit parameter, defined by the ratio gamma = c(h)/c(g) (c(host)/c(guest)), that is very close to a commensurate value (gamma congruent to 1/3). High-resolution diffraction studies presented here reveal an aperiodic misfit parameter of gamma = 0.3369, which is found to be constant at all temperatures studied. A complex sequence of structural phases is reported. The high temperature phase (phase I) exists in the four-dimensional superspace group P6(1)22(00 gamma). At T-c1 = 179(1) K, a ferroelastic phase transition increases the dimension of the crystallographic superspace. This orthorhombic phase (phase II) is characterized by the five-dimensional (5D) superspace group C222(1)(00 gamma)(10 delta) with a modulation vector a(o)* + c(m)* = a(o)* + delta . c(h)*, in which the supplementary misfit parameter is delta = 0.025(1) in host reciprocal units. This corresponds to the appearance of a modulation of very long period (about 440 +/- 16 angstrom). At T-c2 = 163.0(5) K, a 5D to 5D phase transition leads to the crystallographic superspace group P2(1)2(1)2(1)(00 gamma)(00 delta) with a very similar value of delta. This phase transition reveals a significant hysteresis effect

High frequency ESR investigation on dynamical charge disproportionation and spin gap excitation in NaV_2O_5

A significant frequency dependence of the ESR line width is found in NaV_2O_5 between 34-100 K and the line width increases as the resonance frequency is increased from 95 GHz to 760 GHz. The observed frequency dependence is qualitatively explained in terms of the dynamical charge disproportionation. The present results show the essential role of the internal charge degree of freedom in a V-O-V bond. We have also proposed the existence of the Dzyaloshinsky-Moriya interaction in the low temperature charge ordered phase considering the breaking of the selection rule of ESR realized as the direct observation of the spin gap excitation.Comment: 9 figures submitted to J. Phys.Soc. Jp

Orthorhombic versus monoclinic symmetry of the charge-ordered state of NaV2O5

High-resolution X-ray diffraction data show that the low-temperature superstructure of alpha-NaV2O5 has an F-centered orthorhombic 2a x 2b x 4c superlattice. A structure model is proposed, that is characterized by layers with zigzag charge order on all ladders and stacking disorder, such that the averaged structure has space group Fmm2. This model is in accordance with both X-ray scattering and NMR data. Variations in the stacking order and disorder offer an explanation for the recently observed devils staircase of the superlattice period along c.Comment: REVTEX, 4 pages including 2 figures, shortened, submitted to PR

Spin-Peierls transition in NaV2O5 in high magnetic fields

We investigate the magnetic field dependence of the spin-Peierls transition in NaV$_2$O$_5$ in the field range 16T-30T. The transition temperature exhibits a very weak variation with the field, suggesting a novel mechanism for the formation of the spin-Peierls state. We argue that a charge ordering transition accompanied by singlet formation is consistent with our observations.Comment: 4 pages, 3 figures, final version to appear in Phys. Rev. B (RC