Structural invariance upon antiferromagnetic ordering in geometrically frustrated swedenborgite, CaBaCo₂Fe₂O₇

Centimetre-sized single crystals of high-quality CaBaCo₂Fe₂O₇ were synthesized by the optical floating zone technique. The metal-to-metal stoichiometry and oxygen content were confirmed by spectroscopy and thermal reduction experiments. The hexagonal symmetry P6₃mc (No. 186) well describes the powder X-ray and neutron diffraction as well as single-crystal neutron diffraction at all measured temperatures. This symmetry is also consistent with optical second harmonic generation data obtained between 10 and 295 K. However, a satisfactory structure description from single-crystal neutron diffraction data needs an oxygen split position. Specific heat, magnetic susceptibility and powder neutron diffraction data indicate a magnetic phase transition at T_N = 159 K to an antiferromagnetic ground state, but with a persisting hexagonal symmetry and intrinsic geometric frustration.

Computing details

(I)

Crystal data

BaCaCo2Fe2O7	Z = 4
Mr = 519	F(000) = 654
Trigonal, P31c	Dx = 9.386 Mg m^−3
Hall symbol: P 3;-2c	X-ray radiation, λ = 0.87 Å
a = 6.4 Å	µ = 0.04 mm^−1
c = 10.35 Å	T = 3 K
V = 367.14 Å^3	× × mm

Data collection

1693 measured reflections	θmax = 45.4°, θmin = 4.5°
582 independent reflections	h = −10→0
566 reflections with I > 3σ(I)	k = −8→10
Rint = 0.031	l = 0→16

Refinement

Refinement on F^2	1 constraint
R[F^2 > 2σ(F^2)] = 0.043	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0004I^2)
wR(F^2) = 0.121	(Δ/σ)max = 0.038
S = 4.58	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
582 reflections	Extinction coefficient: 460 (50)
61 parameters	Absolute structure: 23 of Friedel pairs used in the refinement
0 restraints

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ca	0.333333	0.666667	0.3716 (3)	0.0049 (6)
Ba	0.333333	0.666667	0.0000 (3)	0.0081 (7)
Co	0.3416 (2)	0.1708 (3)	0.1846 (2)	0.0051 (5)	2.12 (3)
Fe	0	0	0.4392 (2)	0.0031 (3)	0.890 (12)
O1	0.5074 (7)	0.4920 (7)	0.7165 (5)	0.0137 (13)	0.5
O1'	0.4829 (7)	0.5170 (7)	0.7684 (6)	0.0152 (12)	0.5
O2	0	0	0.2516 (3)	0.0057 (5)
O3	0.0992 (8)	0.7875 (7)	0.5005 (3)	0.0097 (13)	0.5
O3'	0.2117 (7)	0.9002 (8)	0.5005 (3)	0.0098 (13)	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ca	0.0065 (7)	0.0065 (7)	0.0016 (10)	0.0033 (4)	0	0
Ba	0.0104 (8)	0.0104 (8)	0.0037 (12)	0.0052 (4)	0	0
Co	0.0039 (5)	0.0039 (6)	0.0068 (6)	0.0015 (5)	0.0007 (6)	0.0003 (4)
Fe	0.0036 (4)	0.0036 (4)	0.0022 (6)	0.0018 (2)	0	0
O1	0.0091 (15)	0.0107 (15)	0.024 (2)	0.0072 (12)	−0.0034 (17)	0.0033 (18)
O1'	0.0062 (13)	0.0069 (14)	0.033 (2)	0.0035 (11)	−0.0026 (15)	0.0028 (15)
O2	0.0060 (5)	0.0060 (5)	0.0051 (9)	0.0030 (3)	0	0
O3	0.0146 (17)	0.0144 (16)	0.0060 (12)	0.0117 (15)	0.0029 (10)	0.0004 (10)
O3'	0.0116 (15)	0.0196 (18)	0.0053 (12)	0.0132 (15)	−0.0014 (10)	−0.0034 (10)

Bond lengths (Å)

Ca—Ba	3.846 (4)	Ba—O3^xi	2.840 (6)
Ca—Ba^i	3.9267 (15)	Ba—O3'^xii	2.845 (3)
Ca—Ba^ii	3.9267 (15)	Ba—O3'^xiii	2.845 (6)
Ca—Ba^iii	3.9267 (15)	Ba—O3'^xiv	2.845 (6)
Ca—O1^iv	2.384 (6)	Co—O1^iv	1.898 (5)
Ca—O1^v	2.384 (6)	Co—O1^xiv	1.901 (7)
Ca—O1^vi	2.384 (6)	Co—O1'^iv	1.939 (5)
Ca—O1'^iv	2.300 (6)	Co—O1'^xiv	1.939 (7)
Ca—O1'^v	2.300 (6)	Co—O2	2.0164 (17)
Ca—O1'^vi	2.300 (6)	Co—O3^x	1.947 (4)
Ca—O3	2.404 (6)	Co—O3'^x	1.947 (4)
Ca—O3^vii	2.404 (6)	Fe—O2	1.942 (4)
Ca—O3^viii	2.404 (5)	Fe—O3^xv	1.876 (6)
Ca—O3'	2.405 (6)	Fe—O3^vii	1.876 (5)
Ca—O3'^vii	2.405 (5)	Fe—O3^xvi	1.876 (6)
Ca—O3'^viii	2.405 (6)	Fe—O3'^xv	1.874 (6)
Ba—O1^iv	2.851 (6)	Fe—O3'^vii	1.874 (6)
Ba—O1^v	2.851 (6)	Fe—O3'^xvi	1.874 (5)
Ba—O1^vi	2.851 (6)	O1—O1'	0.603 (8)
Ba—O3^ix	2.840 (3)	O3—O3'	0.721 (5)
Ba—O3^x	2.840 (6)

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