Synchrotron-radiation study of the two-leg spin-ladder (VO)₂P₂O₇ at 120 K

Oxovanadium phosphates constitute a family of compounds with a versatile crystallochemistry that results in an intricate magnetochemistry. This diversity is due to the accessibility of several oxidation states of vanadium, the ability of phosphate and vanadium polyhedra to form a large variety of complex network structures, and the involvement of phosphate groups in the spin transfer between V ions. Vanadyl pyrophosphate, (VO)₂P₂O₇, has been extensively studied by chemists, because this compound is known to be a very efficient catalyst for selective oxydation of n-butane to maleic anhydride (Centi et al., 1988). This process is of considerable industrial importance, as it is presently the only (heterogeneously catalyzed) alkane oxidation performed on a large scale. Recently, (VO)₂P₂O₇ has attracted much attention from solid-state physicists due to its low-dimensional magnetic properties. It represents a quantum magnetic spin system of V⁴⁺ ions (3 d¹ configuration, spin S = 1/2), whose antiferromagnetic superexchange interactions give rise to a non-magnetic singlet ground state accompanied by a singlet-triplet energy gap (Barnes et al., 1993; Eccleston et al., 1994). From a crystallographic point of view, (VO)₂P₂O₇ has been widely considered to be a prototype of a two-leg spin ladder system. S = 1/2 spin ladders are of interest as an intermediate stage between one-dimensional spin chains and two-dimensional spin lattices, and it has been proposed that hole-doped spin ladders may exhibit superconductivity (Dagotto et al., 1992; Dagotto & Rice, 1996). The magnetism of (VO)₂P₂O₇ has been interpretated in a number of ways, which have been reviewed in detail by Johnston et al. (2001). Initially, magnetic susceptibility measurements and inelastic neutron scattering data were discussed in terms of a two-leg spin ladder model (Barnes & Riera, 1994; Eccleston et al., 1994) and an alternating spin chain model (Johnston et al., 1987; Barnes & Riera, 1994). Subsequent inelastic neutron scattering studies revealed that the magnetic properties are dominated by alternating spin chains, because the dispersion of magnetic excitations was found to be inconsistent with a spin ladder (Garrett, Nagler, Barnes & Sales, 1997; Garrett, Nagler, Tennant et al., 1997). Recently, high-field magnetization measurements, NMR and Raman scattering studies proved the co-existence of two magnetic subsystems associated with two different spin-gap energies (Kikuchi et al., 1999; Yamauchi et al., 1999; Kuhlmann et al., 2000).

Several studies of the crystal structure of (VO)₂P₂O₇ at room temperature have been published. Initial diffraction experiments with X-rays and electrons suggested orthorhombic symmetry with space group Pcam or Pca2₁ (Gorbunova & Linde, 1979; Bordes & Courtine, 1979), but the final R values from the structure refinement were unsatisfactory. Subsequent single-crystal X-ray structure analyses gave acceptable R values, but contradictory results: Ebner & Thompson (1991) reported space group Pca2₁ with disorder on the V sites, while Nguyen et al. (1995) found space group P112₁ with a pseudo-orthorhombic translation lattice, as indicated by a monoclinic angle of 89.975 (3)°. The P112₁ structure model seems to be doubtful, since it presents extremely distorted non-positive definite thermal vibration ellipsoids for several V and P sites, but also unusually large isotropic displacement parameters for two O sites that are shared by opposing PO₄ tetrahedra in the P₂O₇ groups. Recent diffraction studies with X-rays, neutrons and electrons on (VO)₂P₂O₇ powder samples showed systematic extinctions which are consistent with space group Pca2₁, and led to a structure model with exceptionally large isotropic displacement parameters for a number of O sites in the P₂O₇ groups also (Hiroi et al., 1999). Crystallographic disorder in (VO)₂P₂O₇ was often detected in X-ray and electron-diffraction patterns as diffuse scattering (Bordes & Courtine, 1979; Hiroi et al., 1999) and peak-broadening effects due to the introduction of stacking faults (Nguyen et al., 1996). Several studies revealed the ability of (VO)₂P₂O₇ to accomodate various disordered or polytypic structures generated by interlayer vacancies (Thompson et al., 1994) and O defect sites (Gai & Kourtakis, 1995; Gai, 1997). On the other hand, the structure of (VO)₂P₂O₇ is capable of preserving mixed-valence V⁴⁺/V⁵⁺ pairs associated with interstitial O sites in the P₂O₇ sublattice (López-Granados et al., 1993). Very recently, a high-pressure phase treated at 2–3 GPa was found to crystallize in the orthorhombic space group Pnab, with a unit cell half the size of that of the ambient-pressure phase (Azuma et al., 1999; Saito et al., 2000).

Our investigations were motivated by the fact that all previously published crystal structure data of the ambient-pressure phase of (VO)₂P₂O₇ do not provide accurate enough values for the spin-orbital interaction energies (Koo & Whangbo, 2000). Their knowledge is indispensable to conclude unambiguously which of the alternating spin chains has a larger energy gap, and which of the bridged and edge-sharing spin dimers has a stronger spin exchange interaction in the chains. The complications in earlier studies may be attributed to sample preparation conditions, poor crystal quality, and limited experimental accuracy. The present structure determination from low-temperature synchrotron X-ray data measured on a high-quality single-crystal confirms the Pca2₁ space-group assignment. Moreover, the structure refinement provides reliable anisotropic displacement parameters for all atoms, and improves the accuracy of the atomic coordinates, as given by Hiroi et al. (1999) and Gorbunova & Linde (1979), by one order of magnitude.

The asymmetric unit of (VO)₂P₂O₇ in Pca2₁ contains four V sites, four P sites and 18 O sites. Along the a axis, the crystal structure consists of infinite two-leg ladders of vanadyl cations, (VO)²⁺, which are separated by pyrophosphate anions, (P₂O₇)^4-. All V atoms show a (4 + 1) square-pyramidal coordination to five O atoms, consisting of four equatorial V—O distances ranging from 1.940 (3) to 2.083 (4) Å and one short axial V—O distance varying between 1.594 (3) and 1.612 (4) Å. In the [100] direction and nearly opposite the strong V═O bond of the vanadyl group, the V atoms are also weakly coordinated to the apical O atom belonging to the neighbouring VO₅ pyramid, with a long V—O distance ranging from 2.250 (4) to 2.341 (3) Å. Along the c axis, the unit cell of (VO)₂P₂O₇ comprises two alternating crystallographically inequivalent chains built of pairs of edge-sharing VO₅ square pyramids. They are arranged in such a way that in every VO₅ pair the V═O bonds are in trans positions, as each axial O atom is located alternately above or below the basal plane. The VO₅ double pyramids in the V1–V2 chain are bridged by tilted PO₄ double tetrahedra involving P1 and P2 [with a P1···P2 separation of 3.0112 (18) Å], while those in the V3–V4 chain are linked by untilted PO₄ double tetrahedra involving P3 and P4 [with a P3···P4 separation of 3.0873 (19) Å]. Each equatorial O atom of the VO₅ pairs shares a corner with one PO₄ group (Fig. 1). The P—O distances range from 1.487 (4) to 1.583 (3) Å, and the O–P–O bond angles within the PO₄ tetrahedra vary between 104.1 (2) and 116.9 (2)°. The P1–O6—-P2 and P3—O5—P4 bridging angles are 144.50 (18) and 157.20 (17)°, respectively. Both values fall within the typical range found for P₂O₇ groups. The shortest non-bonding V···V distances in [001] direction (i.e. along the rungs of the ladder) are d(V3···V4) = 3.2047 (12) Å and d(V1···V2) = 3.2282 (12) Å. Those in the [100] direction (i.e. along the legs of the ladder) are much longer and approximately given as a/2 = 3.85 Å. Bond-valence calculations were carried out with the program VALENCE (Brown, 1996), using bond-valence parameters according to Brese & O'Keeffe (1991). The bond-valence sums agree very well with the expected valence states V⁴⁺ and P⁵⁺ (Table 2), and exclude the presence of mixed-valence V⁴⁺/V⁵⁺ pairs for the measured crystal. The equivalent isotropic displacement parameters of O atoms are found to be significantly larger than those of V and P atoms, and the principal mean-square atomic displacements of several O sites show a pronounced anisotropy (Fig. 2). The thermal motion of these O atoms could not reasonably well described by a split-atom model.

At T = 300 K, the lattice parameters of (VO)₂P₂O₇ have been determined as a = 7.7285 (3), b = 9.5842 (4) and c = 16.5962 (6) Å. Assuming a simple linear behaviour, the coefficients of linear thermal expansion in the temperature range between 300 and 120 K are estimated as α_a=2.0 × 10 ^-5 K^-1, α_b = 3.8 × 10 ^-6 K^-1 and α_c = 4.6 × 10 ^-6 K^-1. This indicates a strong anisotropic thermal expansion, taking place mainly in the direction parallel to the legs of the ladder. The value obtained for α_a is comparable to that one resulting from Raman scattering experiments (Kuhlmann et al., 2001).