Hexagonal YMnO₃

The crystal structure of hexagonal yttrium trioxomanganate has been determined at room temperature and at 180 K. It is isomorphous with LuMnO₃. The Mn displacement vector has a frustrated component in the ab plane and a ferroelectric part along the c axis. The net ferroelectricity is zero due to inversion twinning, with 1:1 twin fractions.

S1. Comment

The compounds LnMnO₃, with Ln a lanthanide, have attracted much interest in two different fields of materials science. The large ionic radius lanthanides, La, Ce—Dy, crystallize in a distorted orthorhombic perovskite structure (Yakel, 1955). The compounds have recently gained enormous interest because of the colossal magnetoresistance effect, i.e. a metal-insulator transition that changes the conductivity by many orders of magnitude at the Curie temperature (Ramirez, 1997). The Mn is octahedrally coordinated by O. The octahedra form a corner-shared three-dimensional network. The small ionic radius lanthanides, Ho—Lu, crystallize in a hexagonal structure (Yakel et al., 1963). Here, the Mn ions are co-ordinated by a trigonal bipyramid of O, forming a pseudo-layered structure by corner sharing of the trigonal basal plane O atoms. These compounds are of interest because of the combination of ferroelectric and magnetic ordering (Smolenskii & Bokov, 1964). The intermediate ionic radius of Y allows both crystal structures; under ambient conditions, the hexagonal structure is obtained. But the orthorhombic structure can be stabilized by either low temperature (Brinks et al., 1997), or high pressure synthesis (Waintal & Chevanas, 1967), or epitaxic thin film growth (Salvador et al., 1998).

The magnetic properties of hexagonal YMnO₃ were reported by Bertaut & Mercier (1963) from powder neutron diffraction experiments. They found a frustrated triangular basal plane spin structure at 4.2 K. The measurements allowed two stacking sequences for the basal planes spin structure, only one of which allows a ferromagnetic canting. Because ceramic samples showed a ferromagnetic component in the magnetization below 45 K, this stacking sequence was favoured. However, this conclusion was withdrawn when it was realised that the ferromagnetic component originates from small amounts of the impurity phase Mn₃O₄ (Bertaut et al., 1965). Despite various reports on single-crystal growth of YMnO₃ (Yakel et al., 1963; Bertaut et al., 1963), we could find in the open literature neither the crystallographic structure determination nor the temperature-dependent magnetization of phase-pure samples. Here we report the details of the refinement of the crystal structure. We will show in a separate publication the magnetic behaviour; these single crystals exhibit an antiferromagnetic anomaly at T_N = 75 K, and a large magnetic anisotropy as expected for this crystal structure (Van Aken et al., 2000).

In table 2, the metal-oxygen bond lengths are given. Both yttrium positions and the manganese position have unusual oxygen environments. In the centrosymmetric, high temperature phase, T_s = 1283 K, (Łukaszewicz & Karut-Kalicinska, 1977) the single yttrium has an eightfold co-ordination, in the form of a bicapped trigonal antiprism. In the noncentrosymmetric structure, the capping O atoms are displaced with respect to the yttrium in such a way that the Y—O bond length changes from twice 2.7 Å to 2.4 Å and 3.3 Å. Manganese is surrounded by five O atoms in a trigonal bipyramidal way. Striking is the difference in bond length between in-plane and out-of-plane bonds, respectively ≈ 2.05 Å and ≈ 1.86 Å. The origin of this difference is the orbital occupation given by the crystal-field splitting of Mn³⁺. The three-dimensional states split in a trigonal bipyramidal field according to the magnetic quantum number (Van Aken et al., 2000). This yields an empty z² orbital, which is in agreement with the shorter Mn—O distances along the c axis, than in the ab plane. It can easily be shown that the 3 d⁴ ground state is non-degenerate and thus not Jahn-Teller active.

The non-equivalent Mn—O atomic distances, both within the basal plane and to the apices, have smaller differences than in isomorphous LuMnO₃. Nevertheless, the Mn ion is not located in the centre of the trigonal bipyramid. It is both displaced in the a-b basal plane, and along the c axis. The three Mn displacement vectors within the basal plane cancel each other in a triangular fashion. The displacement along the c axis is the same for all Mn ions in the unit cell. Furthermore, the yttrium ions are also non-symmetrically surrounded by the O atoms. This means that YMnO₃ is ferroelectric and an ordering temperature of ≈920 K has been reported (Smolenskii & Chupis, 1982). The macroscopic electric polarization is cancelled by an inversion twin. The origin of the ferroelectricity is not known at the moment. One possibility could be the fact that this hexagonal YMnO₃ is less dense than the perovskite YMnO₃. This could mean that there is some excess volume in the centrosymmetric HT phase. The excess volume can be reduced by rotating or deforming the oxygen polyhedra around the metal ions. This could lead to the disappearance of the inversion centre.

We conclude that YMnO₃ is ferroelectric with a frustrated displacement pattern. Both the Y and the Mn ions are shifted along the c axis. The electric polarization is cancelled by inversion twinning. Both methods for synthesis result in single crystals of the same quality.

Related literature

For related literature, see: Bertaut & Mercier (1963); Bertaut et al. (1965); Bertaut, Forrat & Fang (1963); Brinks et al. (1997); Flack (1983); Ramirez (1997); Rao & Gopalakrishnan (1997); Salvador et al. (1998); Smolenskii & Bokov (1964); Smolenskii & Chupis (1982); Van Aken, Bos, de Groot & Palstra (2000); Waintal & Chevanas (1967); Yakel (1955); Yakel et al. (1963).

S2. Experimental

Single crystals YMnO₃ were obtained using a flux method by weighing appropriate amounts of Y₂O₃ and MnO₂ with Bi₂O₃ in a 1:12 ratio (Yakel, 1963). The powders were thoroughly mixed and heated for 48 h at 1523 K in a Pt crucible. The separation of the crystals from the flux has been done by two methods (Bertaut, 1963b). 1) By increasing the temperature to 1723 K and evaporating the Bi₂O₃ flux, 2) by slowly cooling (50 K/h) through the solidification of the flux. Then the single crystals will segregate on top of the flux. Both methods have been used and the results are equal within the error of the structure determination. We report here only on crystals prepared by slow cooling.

S3. Refinement

The space group is determined to be P6₃cm, taking into consideration the unit-cell parameters, statistical analyses of intensity distributions and, where appropriate, systematic extinctions (h-hl: l ≠ 2n; 00 l: l ≠ 2n). Other space groups, that satisfy the same extinction conditions, were discarded during the refinement. Attempts to fit the data on a crystal structure with space group P63/mcm, where unsuccessful. Anisotropic displacement parameters indicated that the atoms at the mirror plane ought to be split in two positions on each side of the mirror plane.

The structure was solved by Patterson methods with SHELXS97 and subsequent difference Fourier maps. The initial co-ordinates were comparable with the isomorphous structure of LuMnO₃. The positional and anisotropic displacement parameters were refined.

All the occupied sites were checked for partial occupancy and the Y and the Mn sites were checked for mixed occupancy with Bi: partial occupancy or mixed population did not improve the refinement.

The Flack parameter (Flack, 1983) of an initial refinement indicated that the crystal was twinned. Therefore an inversion twin was added to the structure model. An initial attempt gave a twin fraction of 47 (3)%. We expect a 50%-50% distribution because this yields no net electrical polarization (Rao & Gopalakrishnan, 1997). We fixed the twin fraction at 50(-)%, which had no significant influence on any other parameter.

Computing details

For both compounds, data collection: CAD4-UNIX software (Enraf-Nonius, 1994); cell refinement: SET4 (de Boer & Duisenberg, 1984); data reduction: HELENA (Spek, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: PLATON (Spek, 1994); software used to prepare material for publication: PLATON (Spek, 1990).

Figures

	Fig. 1. Schematic view of the crystallographic structure of YMnO3. The top panel shows a view along the basal plane. Y is represented by shaded spheres, and the MnO5 clusters are represented by trigonal bipyramids. This panel highlights the two-dimensional nature of the structure. The lower panel depicts a view along the c axis of two layers to show the stacking of the bipyramids.
	Fig. 2. ORTEP(II) (Johnson, 1976) picture of the unit cell.

(290K) Yttrium manganese oxide

Crystal data

MnO3Y	Unit cell parameters (Duisenberg, 1992) and orientation matrix were determined from a least-squares treatment of SET4 (de Boer & Duisenberg, 1984) setting. Reduced cell calculations did not indicate any higher metric lattice symmetry and examination of the final atomic co-ordinates of the structure did not yield extra symmetry elements (Spek, 1988; Le Page 1987, 1988)
Mr = 191.85	Dx = 5.135 Mg m^−3
Hexagonal, P63cm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 6c -2	Cell parameters from 22 reflections
a = 6.1387 (3) Å	θ = 29.8–39.7°
c = 11.4071 (9) Å	µ = 28.07 mm^−1
V = 372.27 (4) Å^3	T = 293 K
Z = 6	Platelet, black
F(000) = 528	0.15 × 0.15 × 0.02 mm

Data collection

Enraf Nonius CAD-4F diffractometer	658 reflections with I > 2σ(I)
Radiation source: fine focus sealed Philips Mo tube	Rint = 0.041
Perpendicular mounted graphite monochromator	θmax = 40.0°, θmin = 3.6°
ω/2θ scans	h = 0→11
Absorption correction: analytical (Meulenaer & Tompa, 1965)	k = −11→0
Tmin = 0.053, Tmax = 0.511	l = −20→20
3385 measured reflections	3 standard reflections every 180 min
865 independent reflections	intensity decay: no decay, variation 0.5%

Refinement

Refinement on F^2	Primary atom site location: Patterson
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.037	w = 1/[σ^2(Fo^2) + (0.0717P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.107	(Δ/σ)max < 0.001
S = 1.12	Δρmax = 3.11 e Å^−3
865 reflections	Δρmin = −1.17 e Å^−3
32 parameters	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
1 restraint	Extinction coefficient: 0.025 (3)

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional co-ordinates. All e.s.d.'s are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
Y1	0.00000	0.00000	0.27122 (12)	0.0038 (2)
Y2	0.33333	0.66667	0.23041 (3)	0.0041 (1)
Mn1	0.00000	0.3352 (4)	−0.00312 (12)	0.0058 (2)
O1	0.00000	0.3083 (12)	0.1596 (7)	0.0080 (13)
O2	0.00000	0.3587 (10)	−0.1659 (6)	0.0049 (10)
O3	0.00000	0.00000	−0.0249 (12)	0.0053 (16)
O4	0.33333	0.66667	0.0155 (11)	0.0090 (14)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Y1	0.0035 (3)	0.0035 (3)	0.0044 (4)	0.0018 (2)	0.0000	0.0000
Y2	0.0021 (2)	0.0021 (2)	0.0081 (3)	0.0011 (1)	0.0000	0.0000
Mn1	0.0073 (3)	0.0060 (3)	0.0047 (3)	0.0037 (6)	0.0000 (2)	0.0006 (2)
O1	0.008 (3)	0.010 (2)	0.0052 (16)	0.0040 (13)	0.0000	−0.0012 (14)
O2	0.005 (2)	0.0038 (15)	0.0060 (14)	0.0023 (10)	0.0000	0.0003 (12)
O3	0.004 (2)	0.004 (2)	0.008 (4)	0.0020 (10)	0.0000	0.0000
O4	0.008 (2)	0.008 (2)	0.011 (3)	0.0039 (10)	0.0000	0.0000

Geometric parameters (Å, º)

Y1—O1	2.281 (7)	Y2—O2^viii	2.300 (4)
Y1—O2^i	2.316 (6)	Y2—O1^ix	2.275 (5)
Y1—O3^i	2.326 (14)	Y2—O2^v	2.300 (6)
Y1—O1^ii	2.281 (7)	Y2—Y2^x	3.5442 (3)
Y1—O2^iii	2.316 (5)	Y2—Y2^xi	3.5442 (3)
Y1—O1^iv	2.281 (8)	Y2—Y2^xii	3.5442 (3)
Y1—O2^v	2.316 (6)	Mn1—O1	1.863 (8)
Y2—O1	2.275 (6)	Mn1—O2	1.862 (7)
Y2—O2	2.300 (4)	Mn1—O3	2.073 (3)
Y2—O4^vi	2.451 (13)	Mn1—O4	2.052 (3)
Y2—O1^vii	2.275 (8)	Mn1—O4^x	2.052 (4)
O1—Y1—O2^i	77.20 (17)	Y2^xii—Y2—O1^vii	86.65 (16)
O1—Y1—O3^i	123.93 (19)	O1^ix—Y2—O2^viii	77.6 (2)
O1—Y1—O1^ii	91.9 (2)	O2^viii—Y2—O2^v	95.9 (2)
O1—Y1—O2^iii	164.1 (3)	Y2^x—Y2—O2^viii	39.61 (14)
O1—Y1—O1^iv	91.9 (2)	Y2^xi—Y2—O2^viii	135.38 (14)
O1—Y1—O2^v	77.2 (2)	Y2^xii—Y2—O2^viii	93.36 (13)
O2^i—Y1—O3^i	71.96 (17)	O1^ix—Y2—O2^v	169.8 (3)
O1^ii—Y1—O2^i	77.2 (2)	Y2^x—Y2—O1^ix	86.65 (16)
O2^i—Y1—O2^iii	110.86 (14)	Y2^xi—Y2—O1^ix	146.85 (18)
O1^iv—Y1—O2^i	164.1 (3)	Y2^xii—Y2—O1^ix	38.85 (15)
O2^i—Y1—O2^v	110.86 (19)	Y2^x—Y2—O2^v	93.36 (16)
O1^ii—Y1—O3^i	123.9 (2)	Y2^xi—Y2—O2^v	39.61 (17)
O2^iii—Y1—O3^i	71.96 (17)	Y2^xii—Y2—O2^v	135.38 (15)
O1^iv—Y1—O3^i	123.9 (2)	Y2^x—Y2—Y2^xi	120.00 (1)
O2^v—Y1—O3^i	71.96 (17)	Y2^x—Y2—Y2^xii	120.00 (1)
O1^ii—Y1—O2^iii	77.2 (2)	Y2^xi—Y2—Y2^xii	120.00 (1)
O1^ii—Y1—O1^iv	91.9 (2)	O1—Mn1—O2	179.4 (3)
O1^ii—Y1—O2^v	164.1 (3)	O1—Mn1—O3	91.8 (4)
O1^iv—Y1—O2^iii	77.20 (16)	O1—Mn1—O4	86.6 (4)
O2^iii—Y1—O2^v	110.9 (2)	O1—Mn1—O4^x	86.6 (4)
O1^iv—Y1—O2^v	77.2 (2)	O2—Mn1—O3	87.6 (4)
O1—Y2—O4	69.2 (2)	O2—Mn1—O4	93.7 (4)
O1—Y2—O2^vi	169.8 (2)	O2—Mn1—O4^x	93.7 (4)
O1—Y2—O1^vii	108.1 (2)	O3—Mn1—O4	120.13 (16)
O1—Y2—O2^viii	77.1 (2)	O3—Mn1—O4^x	120.13 (12)
O1—Y2—O1^ix	108.1 (2)	O4—Mn1—O4^x	119.49 (15)
O1—Y2—O2^v	77.6 (2)	Y1—O1—Y2	103.4 (3)
Y2^x—Y2—O1	38.85 (13)	Y1—O1—Mn1	129.0 (3)
Y2^xi—Y2—O1	86.65 (11)	Y1—O1—Y2^x	103.4 (3)
Y2^xii—Y2—O1	146.85 (15)	Y2—O1—Mn1	107.9 (3)
O2^vi—Y2—O4	120.94 (15)	Y2—O1—Y2^x	102.3 (3)
O1^vii—Y2—O4	69.2 (2)	Y2^x—O1—Mn1	107.9 (3)
O2^viii—Y2—O4	120.94 (15)	Y1^xiii—O2—Mn1	103.6 (2)
O1^ix—Y2—O4	69.21 (19)	Y2^xiii—O2—Mn1	122.8 (2)
O2^v—Y2—O4	120.94 (16)	Y2^xiv—O2—Mn1	122.8 (3)
Y2^x—Y2—O4	90.00 (1)	Y1^xiii—O2—Y2^xiii	101.5 (2)
Y2^xi—Y2—O4	90.00 (1)	Y1^xiii—O2—Y2^xiv	101.5 (2)
Y2^xii—Y2—O4	90.00 (1)	Y2^xiii—O2—Y2^xiv	100.8 (2)
O1^vii—Y2—O2^vi	77.6 (2)	Y1^xiii—O3—Mn1	96.9 (4)
O2^vi—Y2—O2^viii	95.9 (2)	Mn1—O3—Mn1^ii	118.58 (19)
O1^ix—Y2—O2^vi	77.1 (2)	Mn1—O3—Mn1^iv	118.58 (19)
O2^vi—Y2—O2^v	95.9 (2)	Y1^xiii—O3—Mn1^ii	96.9 (4)
Y2^x—Y2—O2^vi	135.38 (16)	Y1^xiii—O3—Mn1^iv	96.9 (4)
Y2^xi—Y2—O2^vi	93.36 (14)	Mn1^ii—O3—Mn1^iv	118.58 (19)
Y2^xii—Y2—O2^vi	39.61 (13)	Y2—O4—Mn1	95.9 (4)
O1^vii—Y2—O2^viii	169.8 (3)	Y2—O4—Mn1^vii	95.9 (4)
O1^vii—Y2—O1^ix	108.1 (3)	Y2—O4—Mn1^ix	95.9 (4)
O1^vii—Y2—O2^v	77.1 (2)	Mn1—O4—Mn1^vii	118.94 (17)
Y2^x—Y2—O1^vii	146.85 (18)	Mn1—O4—Mn1^ix	118.94 (18)
Y2^xi—Y2—O1^vii	38.85 (17)	Mn1^vii—O4—Mn1^ix	118.94 (18)
O4—Y2—O1—Y1	134.7 (2)	O4—Mn1—O1—Y1	−120.1 (3)
O4—Y2—O1—Mn1	−4.45 (17)	O4—Mn1—O1—Y2	4.98 (19)
O1—Y2—O4—Mn1	3.87 (15)	O1—Mn1—O4—Y2	−4.42 (17)
O3—Mn1—O1—Y1	0.0 (3)	O2—Mn1—O4—Y2	176.13 (15)
O3—Mn1—O1—Y2	125.06 (17)	O3—Mn1—O4—Y2	−94.5 (5)

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

(180K) Ytrrium Manganese oxide

Crystal data

MnO3Y	Unit cell parameters (Duisenberg, 1992) and orientation matrix were determined from a least-squares treatment of SET4 (de Boer & Duisenberg, 1984) setting. Reduced cell calculations did not indicate any higher metric lattice symmetry and examination of the final atomic co-ordinates of the structure did not yield extra symmetry elements (Spek, 1988; Le Page 1987, 1988)
Mr = 191.85	Dx = 5.151 Mg m^−3
Hexagonal, P63cm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 6c -2	Cell parameters from 22 reflections
a = 6.1277 (5) Å	θ = 29.8–39.8°
c = 11.411 (1) Å	µ = 28.16 mm^−1
V = 371.06 (5) Å^3	T = 180 K
Z = 6	Platelet, black
F(000) = 528	0.15 × 0.02 × 0.02 mm

Data collection

Enraf Nonius CAD-4F diffractometer	658 reflections with I > 2σ(I)
Radiation source: fine focus sealed Philips Mo tube	Rint = 0.040
Perpendicular mounted graphite monochromator	θmax = 39.9°, θmin = 3.6°
ω/2θ scans	h = 0→11
Absorption correction: analytical (Meulenaer & Tompa, 1965)	k = −11→0
Tmin = 0.065, Tmax = 0.510	l = −18→20
3336 measured reflections	3 standard reflections every 180 min
853 independent reflections	intensity decay: no decay, variation 0.5%

Refinement

Refinement on F^2	Primary atom site location: Patterson
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.037	w = 1/[σ^2(Fo^2) + (0.0717P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.109	(Δ/σ)max < 0.001
S = 1.09	Δρmax = 2.31 e Å^−3
853 reflections	Δρmin = −1.36 e Å^−3
32 parameters	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
1 restraint	Extinction coefficient: 0.018 (2)

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional co-ordinates. All e.s.d.'s are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
Y1	0.00000	0.00000	0.27175 (12)	0.0024 (2)
Y2	0.33333	−0.33333	0.22989 (4)	0.0024 (1)
Mn1	0.3344 (4)	0.0000 (8)	−0.00312 (12)	0.0041 (2)
O1	0.3090 (12)	0.00000	0.1596 (7)	0.0036 (11)
O2	0.3610 (11)	0.00000	−0.1660 (6)	0.0051 (13)
O3	0.00000	0.00000	−0.0236 (15)	0.0056 (16)
O4	0.33333	−0.33333	0.0168 (11)	0.0050 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Y1	0.0021 (3)	0.0021 (3)	0.0030 (4)	0.0010 (2)	0.0000	0.0000
Y2	0.0010 (2)	0.0010 (2)	0.0051 (3)	0.0005 (1)	0.0000	0.0000
Mn1	0.0036 (3)	0.0053 (3)	0.0039 (3)	0.0026 (6)	0.0003 (2)	0.0000 (2)
O1	0.0046 (18)	0.001 (2)	0.0042 (17)	0.0006 (10)	−0.0023 (13)	0.0000
O2	0.0045 (16)	0.007 (3)	0.0046 (16)	0.0034 (13)	0.0011 (13)	0.0000
O3	0.005 (2)	0.005 (2)	0.007 (4)	0.0026 (12)	0.0000	0.0000
O4	0.0031 (18)	0.0031 (18)	0.009 (2)	0.0016 (9)	0.0000	0.0000

Geometric parameters (Å, º)

Y1—O1	2.285 (8)	Y2—O2^viii	2.295 (4)
Y1—O2^i	2.323 (6)	Y2—O1^ix	2.268 (8)
Y1—O3^i	2.335 (17)	Y2—O2^v	2.295 (5)
Y1—O1^ii	2.285 (7)	Y2—Y2^x	3.5378 (3)
Y1—O2^iii	2.323 (7)	Y2—Y2^xi	3.5378 (3)
Y1—O1^iv	2.285 (7)	Y2—Y2^xii	3.5378 (3)
Y1—O2^v	2.323 (6)	Mn1—O1	1.863 (8)
Y2—O1	2.268 (5)	Mn1—O2	1.866 (7)
Y2—O4	2.432 (13)	Mn1—O3	2.062 (4)
Y2—O2^vi	2.295 (7)	Mn1—O4	2.052 (3)
Y2—O1^vii	2.268 (6)	Mn1—O4^xii	2.052 (3)
O1—Y1—O2^i	77.1 (2)	Y2^xii—Y2—O1^vii	146.83 (15)
O1—Y1—O3^i	124.1 (2)	O1^ix—Y2—O2^viii	78.0 (2)
O1—Y1—O1^ii	91.7 (2)	O2^viii—Y2—O2^v	95.6 (2)
O1—Y1—O2^iii	163.7 (3)	Y2^x—Y2—O2^viii	134.98 (17)
O1—Y1—O1^iv	91.7 (2)	Y2^xi—Y2—O2^viii	93.67 (15)
O1—Y1—O2^v	77.10 (17)	Y2^xii—Y2—O2^viii	39.57 (13)
O2^i—Y1—O3^i	72.20 (17)	O1^ix—Y2—O2^v	169.5 (3)
O1^ii—Y1—O2^i	77.1 (2)	Y2^x—Y2—O1^ix	146.83 (18)
O2^i—Y1—O2^iii	111.1 (2)	Y2^xi—Y2—O1^ix	38.73 (17)
O1^iv—Y1—O2^i	163.7 (3)	Y2^xii—Y2—O1^ix	86.74 (16)
O2^i—Y1—O2^v	111.1 (2)	Y2^x—Y2—O2^v	39.57 (15)
O1^ii—Y1—O3^i	124.05 (19)	Y2^xi—Y2—O2^v	134.98 (15)
O2^iii—Y1—O3^i	72.20 (17)	Y2^xii—Y2—O2^v	93.67 (15)
O1^iv—Y1—O3^i	124.05 (19)	Y2^x—Y2—Y2^xi	120.00 (1)
O2^v—Y1—O3^i	72.20 (17)	Y2^x—Y2—Y2^xii	120.00 (1)
O1^ii—Y1—O2^iii	77.10 (17)	Y2^xi—Y2—Y2^xii	120.00 (1)
O1^ii—Y1—O1^iv	91.7 (2)	O1—Mn1—O2	179.8 (4)
O1^ii—Y1—O2^v	163.7 (3)	O1—Mn1—O3	91.7 (5)
O1^iv—Y1—O2^iii	77.1 (2)	O1—Mn1—O4	86.0 (4)
O2^iii—Y1—O2^v	111.09 (14)	O1—Mn1—O4^xii	86.0 (4)
O1^iv—Y1—O2^v	77.1 (2)	O2—Mn1—O3	88.5 (5)
O1—Y2—O4	69.29 (19)	O2—Mn1—O4	93.9 (4)
O1—Y2—O2^vi	169.5 (3)	O2—Mn1—O4^xii	93.9 (4)
O1—Y2—O1^vii	108.2 (2)	O3—Mn1—O4	120.26 (16)
O1—Y2—O2^viii	76.9 (2)	O3—Mn1—O4^xii	120.26 (16)
O1—Y2—O1^ix	108.2 (3)	O4—Mn1—O4^xii	119.10 (17)
O1—Y2—O2^v	78.0 (2)	Y1—O1—Y2	103.3 (2)
Y2^x—Y2—O1	86.74 (16)	Y1—O1—Mn1	128.8 (4)
Y2^xi—Y2—O1	146.83 (18)	Y1—O1—Y2^xii	103.3 (2)
Y2^xii—Y2—O1	38.73 (15)	Y2—O1—Mn1	108.0 (3)
O2^vi—Y2—O4	121.18 (17)	Y2—O1—Y2^xii	102.5 (3)
O1^vii—Y2—O4	69.3 (2)	Y2^xii—O1—Mn1	108.0 (3)
O2^viii—Y2—O4	121.18 (15)	Y1^xiii—O2—Mn1	102.8 (3)
O1^ix—Y2—O4	69.3 (2)	Y2^xiii—O2—Mn1	123.2 (2)
O2^v—Y2—O4	121.18 (15)	Y2^xiv—O2—Mn1	123.2 (2)
Y2^x—Y2—O4	90.00 (1)	Y1^xiii—O2—Y2^xiii	101.3 (2)
Y2^xi—Y2—O4	90.00 (1)	Y1^xiii—O2—Y2^xiv	101.3 (2)
Y2^xii—Y2—O4	90.00 (1)	Y2^xiii—O2—Y2^xiv	100.9 (3)
O1^vii—Y2—O2^vi	78.0 (2)	Y1^xiii—O3—Mn1	96.5 (5)
O2^vi—Y2—O2^viii	95.6 (2)	Mn1—O3—Mn1^ii	118.7 (2)
O1^ix—Y2—O2^vi	76.9 (3)	Mn1—O3—Mn1^iv	118.7 (2)
O2^vi—Y2—O2^v	95.6 (2)	Y1^xiii—O3—Mn1^ii	96.5 (5)
Y2^x—Y2—O2^vi	93.67 (18)	Y1^xiii—O3—Mn1^iv	96.5 (5)
Y2^xi—Y2—O2^vi	39.57 (18)	Mn1^ii—O3—Mn1^iv	118.7 (2)
Y2^xii—Y2—O2^vi	134.98 (16)	Y2—O4—Mn1	96.4 (3)
O1^vii—Y2—O2^viii	169.5 (2)	Y2—O4—Mn1^vii	96.4 (3)
O1^vii—Y2—O1^ix	108.2 (2)	Y2—O4—Mn1^ix	96.4 (3)
O1^vii—Y2—O2^v	76.9 (2)	Mn1—O4—Mn1^vii	118.79 (19)
Y2^x—Y2—O1^vii	38.73 (13)	Mn1—O4—Mn1^ix	118.79 (17)
Y2^xi—Y2—O1^vii	86.74 (11)	Mn1^vii—O4—Mn1^ix	118.79 (18)
O4—Y2—O1—Y1	134.8 (2)	O4—Mn1—O1—Y1	−120.22 (8)
O4—Y2—O1—Mn1	−4.2 (2)	O4—Mn1—O1—Y2	4.7 (2)
O1—Y2—O4—Mn1	3.65 (19)	O1—Mn1—O4—Y2	−4.2 (2)
O3—Mn1—O1—Y1	0.00 (17)	O2—Mn1—O4—Y2	175.6 (2)
O3—Mn1—O1—Y2	124.9 (2)	O3—Mn1—O4—Y2	−93.8 (6)

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