Orthorhombic versus monoclinic symmetry of the charge-ordered state ofNaV2O5

Abstract

High-resolution X-ray diffraction data show that the lowtemperature superstructure of α ′ -NaV2O5 has an F −centered orthorhombic 2a × 2b × 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. 61.50. Ks; 61.44.Fw; 61.66.Fn; 75.30.Fv The low dimensional transition metal oxide α ′ -NaV 2 O 5 undergoes a phase transition at a temperature of T c = 34 K. The transition is characterized by the development of both a nonmagnetic groundstate and a superstructure [1,2]. General agreement exists that the phase transition is associated with the development of charge order on the vanadium sublattice [3,4], but the mechanism of the transition has not been revealed yet.At room temperature α ′ -NaV 2 O 5 crystallizes in space group Pmmn [5][6][7]. There is one crystallographically independent vanadium atom, that is in the mixed-valence state 4.5+. The structure can be considered as built of layers of two-leg ladders V 2 O 3 , that are stacked along c, alternating with sodium atoms and additional oxygen. The lattice parameters of the basic structure at 15 K are a = 11.294Å, b = 3.604Å, and c = 4.755Å [8]. The superlattice below T c can be described by an F −centered orthorhombic 2a × 2b × 4c supercell. The superstructure was found to have symmetry F mm2, but it showed two peculiar features [8,9]: (i) In one layer ladders with zigzag charge order alternate with ladders with vanadium in the mixed-valence state, (ii) Each of the two consecutive layers contains half of the six crystallographically independent vanadium atoms, but their structures were nearly equal. This crystal structure was found to be in agreement with two other X-ray diffraction measurements [10,11].Theoretical analyses have produced models that show zigzag charge order on all ladders [3,4,[12][13][14][15][16]. However, most approaches did not consider the true supercell, and therefore they cannot be expected to reveal all aspects of the mechanism of the phase transition.Various experiments, including anomalous X-ray scat- In order to determine the true superstructure of NaV 2 O 5 , we have measured high-resolution, highsensitive synchrotron radiation X-ray diffraction. The experiment indicates that the true superlattice is F −centered on the 2a × 2b × 4c supercell. We show that an all zigzag charge order model with orthorhombic symmetry is possible assuming stacking disorder. This model is in agreement with both X-ray diffraction and NMR.X-ray diffraction experiments were performed at beamline ID10A of the ESRF in Grenoble, France. Monochromatic radiation of a wavelength of λ = 0.66057Å was selected by the 220 reflection of diamond. Bragg reflections were measured by ω−scans using a scintillation detector.N...

Ordering in two-dimensional Ising models with competing interactions

“…The model considered in the present work deals with a single plane, leaving aside the question of charge ordering along the third (stacking) direction. The phase transition in NaV 2 O 5 quadruples the unit cell in the stacking direction, and the recent X-ray experiments, carried out deep in the ordered phase [23,33] revealed peculiar stacking ordering patterns of the super-antiferroelectrically charge-ordered planes. In addition, the pressure can change these patterns and even generate a multitude of higherorder commensurate superstructures in the stacking direction (devil's staircase) [29].…”

“…So ifJ < 1 there are regions of T c where condition (32) is satisfied, then the approximation (33) applies. However at sufficiently low temperatures (T c <J/2) we inevitably enter the other regime (38) where the asymptotics (30,31) change (x < 1 → x > 1), and the function g(T c ) crosses over from (33) to (39). If, on the contrary,J is large, then condition (32) never applies, and the approximation (39) describes the whole region T c < 1/2.…”

“…(33,39) in the both regimes (32,38), the the re-entrant behavior on the phase diagram occurs at any λ = 0.…”

“…Let us point out that the conditions (32,38) determine two different regimes (x < 1 or x > 1) of the asymptotics (30,31) we apply in order to obtain g(T c ) as (33) or (39). So ifJ < 1 there are regions of T c where condition (32) is satisfied, then the approximation (33) applies.…”

“…is defined from the minimum of the function g(T c ) (33). This point corresponds to the critical temperature…”