Crystal structure and magnetism in the S = 1/2 spin dimer compound NaCu₂VP₂O₁₀

The crystal structure of the spin dimer magnet NaCu₂VP₂O₁₀ was determined using single-crystal X-ray diffraction and electron diffraction. NaCu₂VP₂O₁₀ displayed a non-centrosymmetric orthorhombic C222₁ structure with a = 6.13860 (10) Å, b = 14.4846 (3) Å and c = 8.2392 (2) Å. The layered structure comprised CuO₄ plaquettes, VO₆ octahedra and PO₄ tetrahedra. A pair of CuO₄ plaquettes formed Cu₂O₆ structural dimers through edge sharing. The Cu–Cu network formed a distorted puckered-layer structure with pseudo-one-dimensional characteristics. Maximum magnetic susceptibility was observed at ∼60 K and NaCu₂VP₂O₁₀ became non-magnetic upon further cooling. The spin gap between the spin-singlet non-magnetic ground state and triplet excited state was estimated to be 43.4 K. Thus, NaCu₂VP₂O₁₀ was assumed to be an alternating chain system with a singlet ground state of dimer origin. The V⁵⁺ ions in the VO₆ octahedra showed large off-centre displacements along the [110] direction in the primitive perovskite structure, which were attributed to the pseudo-Jahn–Teller distortion of d⁰ transition metals.

1. Introduction

Quantum-spin systems have attracted considerable attention since the discovery of characteristic quantum phenomena such as superconductivity and quantum-spin liquids (Lee, 2008; Balents, 2010). Spin dimer systems are representative materials that exhibit quantum-spin fluctuations. In such systems, magnetic ions are often coupled with antiferromagnetic exchange interactions, resulting in the formation of spin dimers. Dimers are coupled with neighbouring dimers via weak exchange interactions. With increasing interactions between dimers in low-dimensional systems, spin dimer compounds can be considered as an alternating chain system. Dimerized quantum magnets usually display an energy gap between spin-singlet non-magnetic ground and triplet excited states; furthermore, the inter- and intra-dimer interactions caused by the arrangement of magnetic ions affect the energy gap.

In the spin dimer system of Cu²⁺ (S = 1/2), dimerized Cu²⁺ often shows characteristic atomic arrangements; Cu²⁺, which possesses a 3d⁹ configuration, exhibits Jahn–Teller distortion owing to the occupied d_3z2–r2 orbital and sometimes forms a CuO₄ plaquette or distorted CuO₆ octahedron. A CuO₄ plaquette is two-dimensional because its ligands prefer planar coordination. Thus, Cu₂O₆ dimers formed by edge-sharing CuO₄ plaquettes show various arrangements which are related to interactions between Cu ions. These Cu₂O₆ dimers have been identified in compounds such as SrCu₂(BO₃)₂ (Smith & Keszler, 1991; Kageyama et al., 1999), Cu₂P₂O₇ (Effenberger, 1990; Janson et al., 2011) and BaCu₂V₂O₈ (Vogt & Müller-Buschbaum, 1990; Klyushina et al., 2016). SrCu₂(BO₃)₂ represents a typical two-dimensional orthogonal dimer system. In SrCu₂(BO₃)₂, Cu₂O₆ dimers are located orthogonally along the [110] direction in a tetragonal system and connected through BO₃ triangles. In Cu₂P₂O₇, Cu₂O₆ dimers are located parallel to the b axis in the monoclinic system. The Cu–Cu network in Cu₂P₂O₇ has a distorted two-dimensional honeycomb structure. In contrast, BaCu₂V₂O₈ has three-dimensional arrangements of Cu₂O₆ dimers and its Cu–Cu network adopts pseudo-one-dimensional screw chains along the c axis. Both arrangements of Cu₂O₆ dimers and Cu–Cu networks strongly affect quantum states. Thus, it is important to discover other examples of spin dimer systems with a finite spin gap to an excited state.

In this study, we synthesize the spin dimer compound NaCu₂VP₂O₁₀, the crystal structure of which was determined using single-crystal X-ray diffraction (XRD) and electron diffraction. The obtained crystal structure is layered, and it comprises corner-sharing Cu₂O₆ dimers, VO₆ octahedra and PO₄ tetrahedra. Magnetic susceptibility measurements of NaCu₂VP₂O₁₀ reveal that it exhibits a non-magnetic ground state and a spin gap between the ground and excited states. We clarify that NaCu₂VP₂O₁₀ is an alternating chain system and discuss the relationship between its crystal structure and magnetic properties.

2. Experimental section

2.1. Synthesis

Polycrystalline samples were synthesized by a solid-state reaction. A mixture of equal amounts of NaVO₃ and Cu₂P₂O₇ was sintered at 823 K for 20 h and then 923 K for 10 h. To grow single crystals, the sintered sample was heated at 1023 K for 2 h and then cooled to 923 K at a rate of 1 K/ h. The obtained crystals had a columnar shape with a diameter of ∼50 µm.

2.2. Electron-probe microanalysis

The chemical composition of the polycrystalline materials was measured using an electron-probe microanalyzer (JXA-8230, JEOL). The prepared samples were polished to form flat surfaces. The normalized Na:Cu:V:P ratio for the three grains was determined to be 0.87 (12):2.014 (7):1.094 (3):2.022 (9), which is close to the stoichiometric chemical composition (Na:Cu:V:P ratio of 1:2:1:2).

2.3. Powder X-ray diffraction

To determine the phase purity and estimate the basic structure of the synthesized compounds, we collected powder XRD patterns using a powder X-ray diffractometer (X'Pert Pro Alpha-1, Panalytial) equipped with a high-speed detector and Cu Kα₁ X-ray source (45 kV, 40 mA). The scanning range of diffraction angles (2θ) was 5–145°, which was adequate for indexing the diffraction peaks. We confirmed that the samples did not contain any impurity phases by comparing the measured powder XRD patterns with a simulated pattern of the refined structure model of NaCu₂VP₂O₁₀ (see Fig. S1 in the Supporting information).

2.4. Electron diffraction

Selected-area electron diffraction (SAED) measurements were performed using a transmission electron microscope (JEM-ARM200F, JEOL) operated at 200 kV. The specimen was prepared by crushing the polycrystals; the particles were deposited on a copper grid with a holey carbon support film. We determined the space group by testing the extinction rules of the sample using SAED.

2.5. Single-crystal X-ray diffraction

Diffraction data were collected using a single-crystal X-ray diffractometer (D8 VENTURE, Bruker) equipped with a complementary metal oxide semiconductor detector and Mo Kα X-ray source (50 kV, 1 mA). A single crystal with a diameter of ∼50 µm was mounted on a borosilicate glass needle using an adhesive. Lattice constants were determined using the SAINT program (Bruker, 2015) and multi-scan absorption correction was carried out using the SADABS program (Bruker, 2015). The initial structure model was calculated using the SUPERFLIP program based on the charge-flipping algorithm (Palatinus & Chapuis, 2007). Crystal structure analysis was carried out using the JANA2006 program package (Petricek et al., 2014) and the analysed crystal structure was visualized using the VESTA program (Momma & Izumi, 2011).

2.6. Magnetic susceptibility

The magnetic susceptibility of the polycrystalline materials was measured using a superconducting quantum-interference device magnetometer (MPMS, Quantum Design). Magnetization was obtained at 2–400 K in an applied field of 1 T.

2.7. Thermal analysis

The heat capacity of the polycrystalline materials was measured using a physical property measurement system (PPMS, Quantum Design). The temperature dependence of the heat capacity was measured at 2–300 K using a thermal-relaxation method. No thermal anomalies were observed in the investigated temperature range.

3. Results

3.1. Space group determination

We measured the powder XRD pattern of NaCu₂VP₂O₁₀, which could be indexed to an orthorhombic unit cell. According to the indices obtained from the powder XRD patterns, the zone axes of the incident electron beams were identified in the SAED patterns. Fig. 1 shows the SAED patterns collected under several electron beams with different incidences. In the [100] and [010] zone axis SAED patterns [Figs. 1(a) and 1(b)], only diffraction spots with indices of k = 2n and h = 2n were observed. The [001] zone axis SAED pattern [Fig. 1(c)] shows an extinction rule of h + k = 2n, which contains both k = 2n and h = 2n in the [100] and [010] zone axis SAED patterns. Such extinction rules indicate the C lattice symmetry (hkl: h + k = 2n) of the orthorhombic system. We then observed the diffraction spots of the 00l condition by tilting the specimen to remove the multiple reflections at forbidden reflection positions, which may appear in a crystal structure with screws or grid planes [Fig. 1(d)]. The reflections in the 00l condition were indexed as l = 2n, which represents a twofold screw parallel to the c axis (00l: l = 2n). The extinction rule was identical to that determined from the single-crystal XRD data, which was based on the kinematical theory of diffraction [Figs. S2(a)–S2(c)]. Analysis of the SAED patterns revealed that the space group of NaCu₂VP₂O₁₀ was C222₁ and non-centrosymmetric.

Figure 1 (a) [100] zone axis, (b) [010] zone axis and (c) [001] zone axis SAED patterns of NaCu2VP2O10. (d) 00l systematic reflections of NaCu2VP2O10.

3.2. Crystal structure determination from XRD data

Single-crystal XRD data obtained for NaCu₂VP₂O₁₀ were indexed to an orthorhombic cell, consistent with the SAED patterns. The determined unit-cell dimensions of NaCu₂VP₂O₁₀ were a = 6.13860 (10) Å, b = 14.4846 (3) Å and c = 8.2392 (2) Å. The initial structure model was determined using the charge-flipping method. This model represents nine independent sites in the unit cell. The Na site was at the Wyckoff position 4b (Na), the Cu site was at 8c (Cu), the V site was at 4b (V), the P site was at 8c (P) and the O sites were at 8c (O1–O5). We successfully refined all site-coordination and anisotropic atomic displacement parameters (U). The reliability indices were R = 2.33% and wR = 7.62%. The U values were adequate at all sites. The refined crystal structure model is shown in Fig. 2; the crystal data, structural parameters and atomic distances are summarized in Tables 1, 2 and 3, respectively.

Table 1
Crystal data and XRD conditions for NaCu₂VP₂O₁₀

Chemical formula	NaCu2VP2O10
Space group	C2221 (No. 20)
a (Å)	6.13860 (10)
b (Å)	14.4846 (3)
c (Å)	8.2392 (2)
V (Å)^3	733.58 (3)
Z	4
Dx (Mg m^−3)	3.84
2θ range	<60.94
Observed reflection	13034
Unique reflection	1110
Rint	0.0254
Collection range	−8 ≤ h ≤ 8
	−20 ≤ k ≤ 20
	−11 ≤ l ≤ 11
R (F^2 > 3σ)	0.0233
wR (F^2)	0.0762

Table 2
Structural parameters and atomic displacement parameters of NaCu₂VP₂O₁₀

Site	Wyckoff position	g	x	y	z	Ueq (Å^2)
Na	4b	1	0	0.46651 (11)	1/4	0.0198 (5)
Cu	8c	1	0.15209 (6)	0.11957(3)	0.10586 (4)	0.01583 (12)
V	4b	1	0	0.86680 (4)	1/4	0.0072 (2)
P	8c	1	0.34633 (11)	0.16200 (4)	0.45456 (7)	0.0066 (2)
O1	8c	1	0.0438 (4)	0.39928 (14)	0.5749 (2)	0.0119 (5)
O2	8c	1	0.1072 (3)	0.06005 (13)	0.8811 (2)	0.0107 (5)
O3	8c	1	0.1107 (4)	0.2370 (2)	0.9171 (2)	0.0153 (6)
O4	8c	1	0.2228 (3)	0.34868 (13)	0.1330 (2)	0.0104 (5)
O5	8c	1	0.3418 (3)	0.37507 (14)	0.8450 (2)	0.0117 (5)
Site	U11	U22	U33	U12	U13	U23
Na	0.0207 (9)	0.0159 (7)	0.0229 (9)	0	0.0051 (8)	0
Cu	0.0051 (2)	0.0363 (2)	0.0061 (2)	0.00172 (14)	0.00042 (13)	0.00126 (13)
V	0.0071 (3)	0.0092 (3)	0.0051 (3)	0	−0.0001 (2)	0
P	0.0046 (3)	0.0099 (3)	0.0054 (3)	−0.0002 (2)	0.0007 (2)	0.0002 (2)
O1	0.0042 (9)	0.0168 (8)	0.0146 (10)	−0.0010 (6)	−0.0016 (7)	−0.0029 (7)
O2	0.0124 (9)	0.0109 (8)	0.0088 (8)	−0.0002 (6)	−0.0005 (7)	0.0009 (7)
O3	0.0162 (10)	0.0167 (9)	0.0131 (10)	−0.0043 (7)	0.0024 (8)	−0.0056 (7)
O4	0.0076 (9)	0.0191 (8)	0.0046 (8)	−0.0006 (7)	−0.0020 (6)	0.0000 (6)
O5	0.0053 (9)	0.0244 (9)	0.0054 (8)	−0.0026 (8)	0.0008 (7)	0.0006 (6)

Table 3
Atomic distances (Å) in NaCu₂VP₂O₁₀

Na–O1	2.861 (2)	(×2)		V–O2	1.649 (2)	(×2)
Na–O1	2.434 (2)	(×2)		V–O3	2.147 (2)	(×2)
Na–O2	2.670 (2)	(×2)		V–O4	1.973 (2)	(×2)
Na–O4	2.388 (2)	(×2)		〈V–O〉	1.9230
〈Na–O〉	2.5883
				P–O1	1.522 (2)
Cu–O1	1.904 (2)			P–O3	1.516 (3)
Cu–O2	2.060 (2)			P–O4	1.538 (2)
Cu–O5	1.949 (2)			P–O5	1.561 (2)
Cu–O5	1.972 (2)			〈P–O〉	1.5343
〈Cu–O〉	1.9713

Figure 2 Crystal structure model of NaCu2VP2O10. Atom colours: Na (green), Cu (blue), V (yellow), P (pink) and O (red). Ellipsoids are set at a 90% probability level.

The average bond distances of 〈Na–O〉, 〈Cu–O〉, 〈V–O〉 and 〈P–O〉 in the crystal structure of NaCu₂VP₂O₁₀ were 2.5883, 1.9713, 1.9230 and 1.5343 Å, respectively, which are in good agreement with the bond distances estimated by combinations of the effective ionic radii of the respective ions of 2.58, 1.97, 1.94 and 1.57 Å (Shannon, 1976). The valence of each site was estimated using the bond valence sum (BVS) method, which is used to calculate valence from experimental parameters and bond distances (Brese & O'Keeffe, 1991). The calculated BVS values of the Na, Cu, V and P sites were 1.07, 1.84, 5.08 and 4.84, respectively. The average bond distances and BVS values were appropriate, which suggests that the structure analysis was successfully performed. As shown in Fig. 2, Cu ions display characteristic highly anisotropic ellipsoids along the b direction. In general, Cu ions in CuO₄ plaquettes prefer the anisotropic displacement perpendicular to the CuO₄ plane because there are no apical oxygen ions (Effenberger, 1990; Smith & Keszler, 1991). Furthermore, NaCu₂VP₂O₁₀ has enough space for Cu ions to fluctuate along the b direction. The anisotropic ellipsoids of the Cu ions can be interpreted from crystallographic considerations. The Flack parameter, which is an index of the ratio of inversion structure, was determined to be 0.018 (14) (Flack & Bernardinelli, 1999). Therefore, the measured single crystal is regarded as a monodomain crystal with respect to the inversion twin.

3.3. Magnetic susceptibility

Fig. 3 shows the temperature dependence of the magnetic susceptibility measured at 1 T using a single-phase polycrystalline NaCu₂VP₂O₁₀ sample. The maximum magnetic susceptibility was observed at ∼60 K and the magnetic susceptibility became close to zero upon further cooling. The Curie–Weiss fitting using χ(T) = C/(T − θ) + χ₀ for the high-temperature region (>200 K) represents the Weiss temperature of θ = −41.9 K and Curie constant of C = 4.04 × 10⁻¹ emu K/ mol Cu. The inset in Fig. 3 shows the temperature dependence of 1/χ, which represents a straight line owing to Curie paramagnetism in the high-temperature region. Both the effective magnetic moment of μ_eff = 1.80μ_B and the g factor of 2.07 are decent values for Cu²⁺ (S = 1/2) compounds. Fitting for the magnetic susceptibility using the isolated spin dimer model (Bleaney & Bowers, 1952) resulted in failure (Fig. S3). Alternatively, the data can be fitted in the full range using an alternating Heisenberg chain model (Johnston et al., 2000) using the expression χ(T) = N_Ag²μ_B²/k_BJ × χ^*(α, T) + C_imp/(T − θ_imp) + χ₀. Here, N_A, μ_B and k_B are Avogadro number, Bohr magneton and Boltzmann constant, respectively. The exchange parameter J, alternation parameter α ( = J′/J), C_imp, θ_imp, and χ₀ are the fitting parameters. When α = 0 and α = 1, the function represents the isolated spin dimer and the uniform chain models, respectively. A small impurity Curie–Weiss contribution, which appeared because of magnetic impurities or defects of Cu²⁺ in NaCu₂VP₂O₁₀, was observed below ∼5 K. We obtained a Weiss temperature of θ_imp = −2.38 K and Curie constant of C_imp = 3.72 × 10⁻³ emu K/ mol Cu, corresponding to 0.99% of nearly free S = 1/2 impurities; χ₀ represents the temperature-independent term of −2.35 × 10⁻⁵ emu/ mol Cu. We obtained J = 99.3 K, α = 0.72 and a g factor of 2.12 in the S = 1/2 alternating chain model. This α value indicates that there are non-negligible interactions between the dimers. Using the relationship Δ ≃ J(1 − α)^3/4(1 + α)^1/4, we estimated that the spin gap Δ was 43.4 K. In the thermal analysis, the heat capacity indicated that there were no anomalies below 100 K (Fig. S4). This result suggests that the long-range magnetic order did not evolve and that changes in the magnetic susceptibility were not related to a conventional phase transition. The crystal structure and magnetic susceptibility of NaCu₂VP₂O₁₀ indicated that it is a spin-gap system.

Figure 3 Temperature dependence of the magnetic susceptibility χ of NaCu2VP2O10. Red open symbols represent raw data. The blue solid and black dashed lines show the fitting curves of the alternating chain and Curie–Weiss models. The inset shows the temperature dependence of 1/χ.

4. Discussion

Fig. 4(a) shows the crystal structure model of NaCu₂VP₂O₁₀. The layered structure consisted of Cu₂O₆ dimers, VO₆ octahedra and PO₄ tetrahedra, which were connected through corner sharing. The Na ions were located between the polyhedral layers. As shown in Figs. 1(a) and 1(c), the weak diffuse streak scattering along the [010] direction indicates the presence of stacking faults in the layered structure. The Cu₂O₆ dimers were almost parallel to the ac plane in each layer. Fig. 4(b) depicts the partial structure of one polyhedral layer viewed from the [010] direction. These layers were composed of two-layer units [Figs. 4(c) and 4(d)]. The two-layer units were related to the twofold screw parallel to the c axis, which was constrained by the symmetry of the crystal structure. Each layer unit was connected by corner-sharing VO₆ octahedra and PO₄ tetrahedra. Fig. 4(c) displays one of the polyhedral layer units, in which the Cu₂O₆ dimers were connected to two VO₆ octahedra and four PO₄ tetrahedra. The Cu₂O₆ dimers lay in a line approximately parallel to the [101] direction. The PO₄–VO₆–PO₄ polyhedral clusters alternated with Cu₂O₆ dimers to fill the space. In the other polyhedral layer unit, Cu₂O₆ dimers lay in a line almost along the [10 ] direction [Fig. 4(d)].

Figure 4 Crystal structure models of (a) NaCu2VP2O10 viewed from the a axis, (b) the local structure of a single layered structure, (c) the upper layer unit and (d) the lower layer unit.

Fig. 5(a) displays the VO₆ octahedron in NaCu₂VP₂O₁₀. The VO₆ octahedron showed anisotropic V–O bond distances. In particular, the V–O2 bond distance of 1.649 Å was shorter than that of the other bonds in the VO₆ octahedron. Furthermore, the V–O2 bond distance was not in good agreement with the effective ionic radius of V⁵⁺ in sixfold coordination {r[V⁵⁺(6)] + r[O²⁻(6)]} of 1.94 Å (Shannon, 1976); this bond distance suggests that hybridization occurred between V⁵⁺ and O²⁻. Fig. 5(b) also shows anisotropic bond distances, which indicate the large off-centre displacement of V ions. The pseudo-Jahn–Teller effect occurs in the d⁰ transition-metal octahedra when the empty d orbitals of the metal form hybrid orbitals with the filled p orbitals of the ligands (Bersuker, 2013; Kunz & Brown, 1995; Halasyamani & Poeppelmeier, 1998; Urushihara et al., 2019). Therefore, V⁵⁺ ions with a d⁰ configuration can display the pseudo-Jahn–Teller effect. It has been reported that in some vanadium oxides, V⁵⁺ ions in VO₆ octahedra show off-centre displacements in the [110] or [100] direction in simple cubic perovskites (Zavalij & Whittingham, 1999; Halasyamani, 2004). In NaCu₂VP₂O₁₀, V⁵⁺ ions in the VO₆ octahedra also exhibit an off-centre displacement in the [110] direction in the simple cubic perovskite notation. Here, we defined that the direction of the V—O4 bonds is the [001] direction in the simple cubic perovskite. V⁵⁺ moves toward the edge of O2 ions connected to the Cu₂O₆ dimer, as shown in Fig. 5(b). The off-centre displacement would arise from the Coulomb repulsion between the higher valence V⁵⁺ and P⁵⁺ ions and pseudo-Jahn–Teller distortion. In potassium vanadium selenite K(VO₂)₃(SeO₃)₂, V⁵⁺ ions also represent an off-centre displacement along the [110] direction in the simple cubic perovskite notation (Harrison et al., 1995). Two of the six V–O bond distances in the VO₆ octahedron are much shorter than those expected based on the effective ionic radius. These shorter V—O bonds could be owing to the off-centre displacement towards the octahedral edge, which is accompanied by hybridization between V⁵⁺ and O²⁻, as with NaCu₂VP₂O₁₀ compounds.

Figure 5 Local structure models of (a) a VO6 octahedron, (b) a corner-sharing octahedron and (c) a Cu2O6 dimer of NaCu2VP2O10.

Fig. 5(c) shows the local structure around the Cu₂O₆ dimer. The Cu–O2 bond distance was slightly longer than the other Cu–O bond distances. The green and red dashed lines represent ∠O5—Cu—O2 and ∠O5—Cu—O1 bond angles, which were determined to be 156.4° and 172.7°, respectively. The O2 ions are offset from the prescribed position of the planar CuO₄ plaquette. This also suggests that O2 ions strongly connect with V⁵⁺, and the bonding state is different from that of other O ions connected to P⁵⁺. Thus, NaCu₂VP₂O₁₀ is expected to exhibit complicated interactions between Cu ions because of Cu—O—V—O—Cu superexchange interactions.

Fig. 6 shows the Cu–Cu networks, which are arrangements of magnetic ions. The Cu ions form a puckered-layer structure, which has also been observed in other two-dimensional materials such as black phospho­rus (Brown & Rundqvist, 1965; Liu et al., 2014). As shown in Figs. 6(a) and 6(b), the first-nearest-neighbour connection is the Cu pairs in Cu₂O₆ dimers, which have a distance of 3.021 Å. The dimer bridging angle ∠Cu—O5—Cu is 100.8° [Fig. 5(c)]; therefore, it is reasonable to suppose that the intradimer exchange interaction is antiferromagnetic (Crawford et al., 1976). The second-nearest-neighbour Cu–Cu connection distance was 3.874 Å and the third-nearest-neighbour connection distance was 4.887 Å. Figs. 6(c)–6(e) display the single layer Cu–Cu network viewed from different directions. The armchair and zigzag directions are along the c and a axes, respectively. For a prototypical puckered-layer structure, such as that of black phospho­rus, two connections in the layer have the same distances. In contrast, the connections in NaCu₂VP₂O₁₀ have different distances, which correspond to the first- and third-nearest-neighbour connections. Therefore, the Cu–Cu network displays a highly distorted puckered-layer structure. As a result, the Cu–Cu network can be regarded as a pseudo-one-dimensional system; that is, the Cu–Cu chains along the armchair direction correlate with each other. Thus, NaCu₂VP₂O₁₀ represents a new type of spin dimer compound with a pseudo-one-dimensional system.

Figure 6 (a) Crystal structure model of NaCu2VP2O10. Na ions are omitted. (b) Cu–Cu network and local structures of a single layer of the Cu–Cu network along the (c) [010], (d) [100] and (e) [001] directions. Large and small Cu ions represent the atomic positions at the front and back, respectively. The red, green and blue dashed lines indicate the first-, second- and third-nearest-neighbour Cu–Cu bond distances, respectively.

5. Conclusions

In this study, we synthesized the spin dimer compound NaCu₂VP₂O₁₀. Using selected-area electron diffraction, the space group of NaCu₂VP₂O₁₀ was revealed to be C222₁. The crystal structure of NaCu₂VP₂O₁₀ consisted of a layered structure containing Cu₂O₆ dimers, VO₆ octahedra and PO₄ tetrahedra. Furthermore, temperature-dependent magnetic susceptibility measurements revealed that NaCu₂VP₂O₁₀ has a non-magnetic ground state and spin gap. V⁵⁺ in the VO₆ octahedra exhibited off-centre distortion caused by the pseudo-Jahn–Teller effect. The hybridization between V and O2 led to complicated interactions via the Cu—O—V—O—Cu path. The crystal structure and magnetic susceptibility results suggest that NaCu₂VP₂O₁₀ is a new quantum-spin system owing to dimerized Cu²⁺.

Supporting information

Computing details

Data collection: APEX2 (Bruker, 2015); cell refinement: SAINT (Bruker, 2015); data reduction: SAINT (Bruker, 2015); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: JANA2006 (Petříček et al., 2014); molecular graphics: VESTA (Momma & Izumi, 2011).

(I)

Crystal data

Cu2NaO10P2V	F(000) = 808
Mr = 423	Dx = 3.840 Mg m^−3
Orthorhombic, C2221	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: C 2c 2	Cell parameters from 13034 reflections
a = 6.1386 (1) Å	θ = 2.8–30.5°
b = 14.4646 (3) Å	µ = 7.56 mm^−1
c = 8.2392 (2) Å	T = 298 K
V = 731.58 (3) Å^3	Block, yellow
Z = 4	0.06 × 0.06 × 0.03 mm

Data collection

Bruker CCD diffractometer	1122 independent reflections
Radiation source: X-ray tube	1110 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.025
φ and ω scans	θmax = 30.5°, θmin = 2.8°
Absorption correction: multi-scan SADABS v2014/5 (Bruker, 2014)	h = −8→8
Tmin = 0.462, Tmax = 0.593	k = −20→20
13034 measured reflections	l = −11→11

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0016I^2)
R[F > 3σ(F)] = 0.023	(Δ/σ)max = 0.015
wR(F) = 0.076	Δρmax = 1.66 e Å^−3
S = 1.74	Δρmin = −0.87 e Å^−3
1122 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
76 parameters	Extinction coefficient: 100 (200)
0 restraints	Absolute structure: 462 of Friedel pairs used in the refinement
0 constraints	Absolute structure parameter: 0.018 (14)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Na	0	0.46651 (11)	0.25	0.0198 (5)
Cu	0.15209 (6)	0.11957 (3)	0.10586 (4)	0.01583 (12)
V	0	0.86680 (4)	0.25	0.00715 (16)
P	0.34633 (11)	0.16200 (4)	0.45456 (7)	0.00661 (16)
O1	0.0438 (4)	0.39928 (14)	0.5749 (2)	0.0119 (5)
O2	0.1072 (3)	0.06005 (13)	0.8811 (2)	0.0107 (5)
O3	0.1107 (4)	0.23698 (15)	0.9171 (2)	0.0153 (6)
O4	0.2228 (3)	0.34868 (13)	0.1330 (2)	0.0104 (5)
O5	0.3418 (3)	0.37507 (14)	0.8450 (2)	0.0117 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na	0.0207 (9)	0.0159 (7)	0.0229 (9)	0	0.0051 (8)	0
Cu	0.00505 (19)	0.0363 (2)	0.00610 (19)	0.00172 (14)	0.00042 (13)	0.00126 (13)
V	0.0071 (3)	0.0092 (3)	0.0051 (3)	0	−0.0001 (2)	0
P	0.0046 (3)	0.0099 (3)	0.0054 (3)	−0.0002 (2)	0.0007 (2)	0.00014 (19)
O1	0.0042 (9)	0.0168 (8)	0.0146 (10)	−0.0010 (6)	−0.0016 (7)	−0.0029 (7)
O2	0.0124 (9)	0.0109 (8)	0.0088 (8)	−0.0002 (6)	−0.0005 (7)	0.0009 (7)
O3	0.0162 (10)	0.0167 (9)	0.0131 (10)	−0.0043 (7)	0.0024 (8)	−0.0056 (7)
O4	0.0076 (9)	0.0191 (8)	0.0046 (8)	−0.0006 (7)	−0.0020 (6)	0.0000 (6)
O5	0.0053 (9)	0.0244 (9)	0.0054 (8)	−0.0026 (8)	0.0008 (7)	0.0006 (6)

Geometric parameters (Å, º)

Na—Na^i	4.2321 (5)	Cu—V^i	3.0834 (4)
Na—Na^ii	4.2321 (5)	Cu—O1^vii	1.904 (2)
Na—Cu^iii	3.2975 (11)	Cu—O2^xi	2.0604 (17)
Na—Cu^iv	3.2975 (11)	Cu—O3^xi	2.317 (2)
Na—V^v	3.3912 (7)	Cu—O5^vii	1.9722 (17)
Na—V^vi	3.3912 (7)	Cu—O5^viii	1.9488 (19)
Na—P^iii	3.4245 (13)	V—O2^i	1.6486 (16)
Na—P^vii	3.2047 (10)	V—O2^ix	1.6486 (16)
Na—P^iv	3.4245 (13)	V—O3^i	2.147 (2)
Na—P^viii	3.2047 (10)	V—O3^ix	2.147 (2)
Na—O1^i	2.4335 (19)	V—O4^iii	1.9732 (18)
Na—O1^ix	2.4335 (19)	V—O4^iv	1.9732 (18)
Na—O2^vii	2.6700 (18)	P—O1^xii	1.522 (2)
Na—O2^viii	2.6700 (18)	P—O3^vii	1.516 (3)
Na—O4	2.3881 (19)	P—O4^xiii	1.5380 (18)
Na—O4^x	2.3881 (19)	P—O5^vii	1.5608 (18)
Cu—Cu^x	3.0213 (5)
Na^i—Na—Na^ii	153.52 (5)	O1^ix—Na—O4	138.18 (7)
Na^i—Na—Cu^iii	59.713 (17)	O1^ix—Na—O4^x	113.15 (6)
Na^i—Na—Cu^iv	101.35 (3)	O2^vii—Na—O2^viii	163.43 (8)
Na^i—Na—V^v	95.588 (9)	O2^vii—Na—O4	62.82 (6)
Na^i—Na—V^vi	95.588 (9)	O2^vii—Na—O4^x	104.54 (6)
Na^i—Na—P^iii	106.86 (4)	O2^viii—Na—O4	104.54 (6)
Na^i—Na—P^vii	52.66 (2)	O2^viii—Na—O4^x	62.82 (6)
Na^i—Na—P^iv	48.07 (2)	O4—Na—O4^x	88.96 (7)
Na^i—Na—P^viii	150.71 (4)	Na^vi—Cu—Cu^x	96.727 (13)
Na^i—Na—O1^i	40.56 (4)	Na^vi—Cu—V^i	125.557 (18)
Na^i—Na—O1^ix	113.23 (6)	Na^vi—Cu—O1^vii	46.92 (5)
Na^i—Na—O2^vii	115.26 (4)	Na^vi—Cu—O2^xi	97.47 (5)
Na^i—Na—O2^viii	68.85 (4)	Na^vi—Cu—O3^xi	143.61 (6)
Na^i—Na—O4	76.73 (4)	Na^vi—Cu—O5^vii	69.76 (5)
Na^i—Na—O4^x	123.80 (5)	Na^vi—Cu—O5^viii	125.79 (5)
Na^ii—Na—Cu^iii	101.35 (3)	Cu^x—Cu—V^i	124.085 (14)
Na^ii—Na—Cu^iv	59.713 (17)	Cu^x—Cu—O1^vii	135.34 (5)
Na^ii—Na—V^v	95.588 (9)	Cu^x—Cu—O2^xi	128.60 (5)
Na^ii—Na—V^vi	95.588 (9)	Cu^x—Cu—O3^xi	117.38 (6)
Na^ii—Na—P^iii	48.07 (2)	Cu^x—Cu—O5^vii	39.32 (5)
Na^ii—Na—P^vii	150.71 (4)	Cu^x—Cu—O5^viii	39.88 (5)
Na^ii—Na—P^iv	106.86 (4)	V^i—Cu—O1^vii	100.29 (5)
Na^ii—Na—P^viii	52.66 (2)	V^i—Cu—O2^xi	29.72 (4)
Na^ii—Na—O1^i	113.23 (6)	V^i—Cu—O3^xi	44.08 (6)
Na^ii—Na—O1^ix	40.56 (4)	V^i—Cu—O5^vii	162.41 (6)
Na^ii—Na—O2^vii	68.85 (4)	V^i—Cu—O5^viii	84.21 (5)
Na^ii—Na—O2^viii	115.26 (4)	O1^vii—Cu—O2^xi	87.18 (7)
Na^ii—Na—O4	123.80 (5)	O1^vii—Cu—O3^xi	97.05 (8)
Na^ii—Na—O4^x	76.73 (4)	O1^vii—Cu—O5^vii	96.94 (7)
Cu^iii—Na—Cu^iv	95.64 (4)	O1^vii—Cu—O5^viii	172.70 (7)
Cu^iii—Na—V^v	72.503 (11)	O2^xi—Cu—O3^xi	71.83 (7)
Cu^iii—Na—V^vi	150.66 (2)	O2^xi—Cu—O5^vii	156.46 (6)
Cu^iii—Na—P^iii	56.25 (2)	O2^xi—Cu—O5^viii	94.16 (7)
Cu^iii—Na—P^vii	107.851 (13)	O3^xi—Cu—O5^vii	130.09 (7)
Cu^iii—Na—P^iv	56.41 (2)	O3^xi—Cu—O5^viii	90.19 (8)
Cu^iii—Na—P^viii	118.184 (13)	O5^vii—Cu—O5^viii	79.02 (7)
Cu^iii—Na—O1^i	34.85 (6)	Na^iii—V—Na^xiv	129.67 (4)
Cu^iii—Na—O1^ix	75.49 (6)	Na^iii—V—Cu^ii	72.468 (8)
Cu^iii—Na—O2^vii	145.83 (6)	Na^iii—V—Cu^xv	104.292 (11)
Cu^iii—Na—O2^viii	50.67 (3)	Na^iii—V—O2^i	50.65 (6)
Cu^iii—Na—O4	134.80 (4)	Na^iii—V—O2^ix	95.08 (7)
Cu^iii—Na—O4^x	104.69 (4)	Na^iii—V—O3^i	90.63 (7)
Cu^iv—Na—V^v	150.66 (2)	Na^iii—V—O3^ix	125.71 (6)
Cu^iv—Na—V^vi	72.503 (11)	Na^iii—V—O4^iii	43.61 (5)
Cu^iv—Na—P^iii	56.41 (2)	Na^iii—V—O4^iv	146.82 (5)
Cu^iv—Na—P^vii	118.184 (13)	Na^xiv—V—Cu^ii	104.292 (11)
Cu^iv—Na—P^iv	56.25 (2)	Na^xiv—V—Cu^xv	72.468 (8)
Cu^iv—Na—P^viii	107.851 (13)	Na^xiv—V—O2^i	95.08 (7)
Cu^iv—Na—O1^i	75.49 (6)	Na^xiv—V—O2^ix	50.65 (6)
Cu^iv—Na—O1^ix	34.85 (6)	Na^xiv—V—O3^i	125.71 (6)
Cu^iv—Na—O2^vii	50.67 (3)	Na^xiv—V—O3^ix	90.63 (7)
Cu^iv—Na—O2^viii	145.83 (6)	Na^xiv—V—O4^iii	146.82 (5)
Cu^iv—Na—O4	104.69 (4)	Na^xiv—V—O4^iv	43.61 (5)
Cu^iv—Na—O4^x	134.80 (4)	Cu^ii—V—Cu^xv	172.67 (2)
V^v—Na—V^vi	129.67 (5)	Cu^ii—V—O2^i	38.29 (5)
V^v—Na—P^iii	95.843 (17)	Cu^ii—V—O2^ix	134.66 (6)
V^v—Na—P^vii	91.14 (3)	Cu^ii—V—O3^i	48.64 (6)
V^v—Na—P^iv	126.91 (2)	Cu^ii—V—O3^ix	138.60 (7)
V^v—Na—P^viii	59.129 (18)	Cu^ii—V—O4^iii	102.24 (5)
V^v—Na—O1^i	103.84 (6)	Cu^ii—V—O4^iv	78.76 (5)
V^v—Na—O1^ix	116.05 (6)	Cu^xv—V—O2^i	134.66 (6)
V^v—Na—O2^vii	139.12 (5)	Cu^xv—V—O2^ix	38.29 (5)
V^v—Na—O2^viii	28.52 (4)	Cu^xv—V—O3^i	138.60 (7)
V^v—Na—O4	102.41 (6)	Cu^xv—V—O3^ix	48.64 (6)
V^v—Na—O4^x	34.74 (4)	Cu^xv—V—O4^iii	78.76 (5)
V^vi—Na—P^iii	126.91 (2)	Cu^xv—V—O4^iv	102.24 (5)
V^vi—Na—P^vii	59.129 (18)	O2^i—V—O2^ix	100.21 (8)
V^vi—Na—P^iv	95.843 (17)	O2^i—V—O3^i	84.38 (9)
V^vi—Na—P^viii	91.14 (3)	O2^i—V—O3^ix	174.16 (9)
V^vi—Na—O1^i	116.05 (6)	O2^i—V—O4^iii	93.50 (8)
V^vi—Na—O1^ix	103.84 (6)	O2^i—V—O4^iv	96.27 (8)
V^vi—Na—O2^vii	28.52 (4)	O2^ix—V—O3^i	174.16 (9)
V^vi—Na—O2^viii	139.12 (5)	O2^ix—V—O3^ix	84.38 (9)
V^vi—Na—O4	34.74 (4)	O2^ix—V—O4^iii	96.27 (8)
V^vi—Na—O4^x	102.41 (6)	O2^ix—V—O4^iv	93.50 (8)
P^iii—Na—P^vii	159.05 (4)	O3^i—V—O3^ix	91.28 (9)
P^iii—Na—P^iv	68.67 (3)	O3^i—V—O4^iii	86.99 (8)
P^iii—Na—P^viii	91.375 (16)	O3^i—V—O4^iv	82.35 (8)
P^iii—Na—O1^i	66.59 (5)	O3^ix—V—O4^iii	82.35 (8)
P^iii—Na—O1^ix	23.07 (6)	O3^ix—V—O4^iv	86.99 (8)
P^iii—Na—O2^vii	99.71 (4)	O4^iii—V—O4^iv	164.75 (7)
P^iii—Na—O2^viii	93.97 (4)	Na^vi—P—Na^xiii	79.27 (3)
P^iii—Na—O4	161.02 (5)	Na^vi—P—O1^xii	38.81 (7)
P^iii—Na—O4^x	103.46 (4)	Na^vi—P—O3^vii	130.35 (8)
P^vii—Na—P^iv	91.375 (16)	Na^vi—P—O4^xiii	117.60 (6)
P^vii—Na—P^viii	109.10 (4)	Na^vi—P—O5^vii	68.61 (6)
P^vii—Na—O1^i	92.57 (4)	Na^xiii—P—O1^xii	63.17 (7)
P^vii—Na—O1^ix	151.69 (6)	Na^xiii—P—O3^vii	131.46 (8)
P^vii—Na—O2^vii	87.58 (4)	Na^xiii—P—O4^xiii	45.31 (6)
P^vii—Na—O2^viii	82.82 (4)	Na^xiii—P—O5^vii	117.24 (6)
P^vii—Na—O4	27.25 (4)	O1^xii—P—O3^vii	112.97 (12)
P^vii—Na—O4^x	93.52 (6)	O1^xii—P—O4^xiii	108.28 (9)
P^iv—Na—P^viii	159.05 (4)	O1^xii—P—O5^vii	107.27 (10)
P^iv—Na—O1^i	23.07 (6)	O3^vii—P—O4^xiii	109.85 (9)
P^iv—Na—O1^ix	66.59 (5)	O3^vii—P—O5^vii	110.02 (10)
P^iv—Na—O2^vii	93.97 (4)	O4^xiii—P—O5^vii	108.31 (10)
P^iv—Na—O2^viii	99.71 (4)	Na^ii—O1—Cu^xiii	98.24 (8)
P^iv—Na—O4	103.46 (4)	Na^ii—O1—P^viii	118.13 (12)
P^iv—Na—O4^x	161.02 (5)	Cu^xiii—O1—P^viii	135.99 (10)
P^viii—Na—O1^i	151.69 (6)	Na^xiii—O2—Cu^xvi	107.64 (7)
P^viii—Na—O1^ix	92.57 (4)	Na^xiii—O2—V^ii	100.83 (8)
P^viii—Na—O2^vii	82.82 (4)	Cu^xvi—O2—V^ii	111.99 (8)
P^viii—Na—O2^viii	87.58 (4)	Cu^xvi—O3—V^ii	87.28 (10)
P^viii—Na—O4	93.52 (6)	Cu^xvi—O3—P^xiii	123.41 (10)
P^viii—Na—O4^x	27.25 (4)	V^ii—O3—P^xiii	149.23 (13)
O1^i—Na—O1^ix	74.18 (7)	Na—O4—V^vi	101.65 (7)
O1^i—Na—O2^vii	117.04 (7)	Na—O4—P^vii	107.44 (9)
O1^i—Na—O2^viii	77.02 (7)	V^vi—O4—P^vii	135.91 (11)
O1^i—Na—O4	113.15 (6)	Cu^xiii—O5—Cu^xii	100.80 (8)
O1^i—Na—O4^x	138.18 (7)	Cu^xiii—O5—P^xiii	127.25 (11)
O1^ix—Na—O2^vii	77.02 (7)	Cu^xii—O5—P^xiii	128.06 (10)
O1^ix—Na—O2^viii	117.04 (7)

Symmetry codes: (i) −x, −y+1, z−1/2; (ii) −x, −y+1, z+1/2; (iii) x−1/2, y+1/2, z; (iv) −x+1/2, y+1/2, −z+1/2; (v) x−1/2, y−1/2, z; (vi) x+1/2, y−1/2, z; (vii) −x+1/2, −y+1/2, z−1/2; (viii) x−1/2, −y+1/2, −z+1; (ix) x, −y+1, −z+1; (x) −x, y, −z+1/2; (xi) x, y, z−1; (xii) x+1/2, −y+1/2, −z+1; (xiii) −x+1/2, −y+1/2, z+1/2; (xiv) x+1/2, y+1/2, z; (xv) x, −y+1, −z; (xvi) x, y, z+1.