Correlated disorder and crystal structure of β-VOSO₄

Pauflerite β-VOSO₄ has recently been identified as a one-dimensional S = ½ Heisenberg system, of interest both from a fundamental point of view and a potential material for future spintronics applications. The observation of diffuse scattering in a synthetic β-VOSO₄ provides a microscopic interpretation of the underlying correlated disorder, which is linked to the inversion of the short–long V—O distance pairs along VO₆ chains, forming a local defect state. Direct Monte Carlo modeling indicates that such defects form thin layers with a positive inter-layer correlation, forming small domains with inverted vanadyl bonding patterns. Two-dimensional defects in anisotropic magnetic systems may perturb, or even destroy, long-range magnetic ordering leading to unusual interactions. In particular, the lack of inversion symmetry in the defect layers opens up the possibility for the Dzyaloshinskii–Moriya interaction (DMI) and, consequently, chiral magnetism localized in the defect planes. The defect β-VOSO₄ structure, therefore, opens up new possibilities for the study of low-dimensional magnetic systems.

Computing details

Program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014).

(I)

Crystal data

O5SV	Dx = 3.283 Mg m^−3
Mr = 163.00	Synchrotron radiation, λ = 0.69027 Å
Orthorhombic, Pnma	Cell parameters from 2031 reflections
a = 7.3908 (1) Å	θ = 3.9–32.9°
b = 6.2864 (1) Å	µ = 3.21 mm^−1
c = 7.0981 (1) Å	T = 293 K
V = 329.79 (1) Å^3	Cube-like, green
Z = 4	0.05 × 0.03 × 0.02 mm
F(000) = 316

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	663 independent reflections
Radiation source: synchrotron	644 reflections with I > 2σ(I)
Synchrotron monochromator	Rint = 0.031
Detector resolution: 5.8140 pixels mm^-1	θmax = 32.9°, θmin = 3.9°
Absorption correction: multi-scan CrysAlisPro 1.171.40.67a (Rigaku Oxford Diffraction, 2019) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	h = −10→10
Tmin = 0.298, Tmax = 1.000	k = −9→9
2591 measured reflections	l = −10→10

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0372P)^2 + 0.3329P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.025	(Δ/σ)max < 0.001
wR(F^2) = 0.069	Δρmax = 0.87 e Å^−3
S = 1.15	Δρmin = −0.75 e Å^−3
663 reflections	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
44 parameters	Extinction coefficient: 0.024 (4)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
V1	0.33361 (18)	0.2500	0.26749 (7)	0.00686 (19)	0.979 (5)
V2	0.391 (8)	0.2500	0.253 (3)	0.00686 (19)	0.021 (5)
S1	0.37713 (7)	0.7500	0.36813 (7)	0.00697 (14)
O1A	0.3747 (2)	0.56303 (18)	0.24372 (15)	0.0116 (2)
O1B	0.5447 (2)	0.7500	0.4805 (2)	0.0135 (3)
O1C	0.2157 (2)	0.7500	0.4904 (2)	0.0127 (3)
O2	0.1265 (2)	0.2500	0.3323 (2)	0.0125 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
V1	0.0044 (5)	0.00812 (17)	0.0080 (2)	0.000	−0.00067 (15)	0.000
V2	0.0044 (5)	0.00812 (17)	0.0080 (2)	0.000	−0.00067 (15)	0.000
S1	0.0062 (2)	0.0079 (2)	0.0068 (2)	0.000	−0.00018 (14)	0.000
O1A	0.0158 (5)	0.0079 (4)	0.0110 (5)	−0.0004 (4)	0.0004 (3)	−0.0017 (3)
O1B	0.0080 (6)	0.0227 (7)	0.0099 (6)	0.000	−0.0031 (5)	0.000
O1C	0.0086 (6)	0.0201 (7)	0.0093 (6)	0.000	0.0020 (5)	0.000
O2	0.0087 (7)	0.0164 (7)	0.0125 (7)	0.000	0.0003 (5)	0.000

Geometric parameters (Å, º)

V1—O2	1.599 (2)	V2—O2	2.04 (6)
V1—O1A	1.9983 (12)	S1—O1A	1.4702 (11)
V1—O1A^i	1.9983 (12)	S1—O1A^v	1.4702 (11)
V1—O1C^ii	1.9999 (17)	S1—O1B	1.4730 (16)
V1—O1B^iii	2.0022 (16)	S1—O1C	1.4755 (16)
V1—O2^iv	2.277 (2)	O1B—V2^iii	1.95 (2)
V2—O2^iv	1.84 (6)	O1B—V1^iii	2.0022 (16)
V2—O1B^iii	1.95 (2)	O1C—V1^vi	1.9999 (17)
V2—O1A	1.973 (3)	O1C—V2^vi	2.03 (2)
V2—O1A^i	1.973 (3)	O2—V2^vii	1.84 (6)
V2—O1C^ii	2.03 (2)	O2—V1^vii	2.277 (2)
O2—V1—O1A	99.79 (6)	O1B^iii—V2—O2	88.1 (17)
O2—V1—O1A^i	99.79 (6)	O1A—V2—O2	87.1 (17)
O1A—V1—O1A^i	159.96 (11)	O1A^i—V2—O2	87.1 (17)
O2—V1—O1C^ii	96.23 (9)	O1C^ii—V2—O2	83.0 (18)
O1A—V1—O1C^ii	86.83 (3)	O1A—S1—O1A^v	106.16 (9)
O1A^i—V1—O1C^ii	86.83 (3)	O1A—S1—O1B	109.59 (7)
O2—V1—O1B^iii	99.96 (9)	O1A^v—S1—O1B	109.59 (7)
O1A—V1—O1B^iii	90.41 (4)	O1A—S1—O1C	110.10 (7)
O1A^i—V1—O1B^iii	90.41 (4)	O1A^v—S1—O1C	110.10 (7)
O1C^ii—V1—O1B^iii	163.81 (10)	O1B—S1—O1C	111.17 (10)
O2—V1—O2^iv	178.61 (4)	S1—O1A—V2	140.9 (6)
O1A—V1—O2^iv	80.16 (6)	S1—O1A—V1	137.59 (7)
O1A^i—V1—O2^iv	80.16 (6)	V2—O1A—V1	12.6 (17)
O1C^ii—V1—O2^iv	82.37 (7)	S1—O1B—V2^iii	136.9 (17)
O1B^iii—V1—O2^iv	81.43 (8)	S1—O1B—V1^iii	149.48 (12)
O2^iv—V2—O1B^iii	95 (2)	V2^iii—O1B—V1^iii	12.6 (17)
O2^iv—V2—O1A	92.7 (17)	S1—O1C—V1^vi	136.55 (11)
O1B^iii—V2—O1A	92.8 (6)	S1—O1C—V2^vi	149.0 (16)
O2^iv—V2—O1A^i	92.7 (17)	V1^vi—O1C—V2^vi	12.4 (16)
O1B^iii—V2—O1A^i	92.8 (6)	V1—O2—V2^vii	144.0 (7)
O1A—V2—O1A^i	172 (3)	V1—O2—V2	0.8 (6)
O2^iv—V2—O1C^ii	93.7 (16)	V2^vii—O2—V2	144.73 (16)
O1B^iii—V2—O1C^ii	171 (3)	V1—O2—V1^vii	145.14 (10)
O1A—V2—O1C^ii	86.8 (7)	V2^vii—O2—V1^vii	1.2 (7)
O1A^i—V2—O1C^ii	86.8 (7)	V2—O2—V1^vii	145.9 (6)
O2^iv—V2—O2	176.7 (12)

Symmetry codes: (i) x, −y+1/2, z; (ii) −x+1/2, −y+1, z−1/2; (iii) −x+1, −y+1, −z+1; (iv) x+1/2, y, −z+1/2; (v) x, −y+3/2, z; (vi) −x+1/2, −y+1, z+1/2; (vii) x−1/2, y, −z+1/2.