The structural and magnetic properties of single-crystal Gd₄Ga₂O₉

The crystalline structures and magnetic and thermodynamic properties of a Gd₄Ga₂O₉ single crystal grown with the optical floating zone technique have been investigated. Gd₄Ga₂O₉ crystallizes in a monoclinic structure with the space group P2₁/c at room temperature. Temperature-dependent magnetic susceptibility measurements along the three crystallographic axes reveal a paramagnetic (PM) behavior between 2 and 300 K. A Curie–Weiss (CW) law fit was carried out and the CW temperature θ_CW and magnetic frustration parameter f were calculated; these suggest antiferromagnetic (AFM) interactions between Gd³⁺ spins and a strong magnetic frustration. The field dependence of the magnetization at 2 K further confirms the magnetic frustration characteristics. A distinct λ-shaped peak at 1.4 K in the heat capacity curves suggests a transition from the PM to AFM phase. The magnetic entropy is contributed solely by Gd³⁺ ions.

Computing details

Program(s) used to refine structure: FULLPROF.

(I)

Crystal data

Gd4Ga2O9	β = 108.496 (5)°
Mr = 912.44	V = 878.48 (15) Å^3
Monoclinic, P21/c	Z = 4
Hall symbol: -P 2ybc	Dx = 6.899 Mg m^−3
a = 7.5536 (7) Å	Cu Kα radiation, λ = 1.540560 Å
b = 10.7646 (11) Å	T = 300 K
c = 11.3923 (11) Å

Data collection

Rigaku Smartlab diffractometer	2θmin = 10.065°, 2θmax = 90.065°, 2θstep = 0.020°
Scan method: step

Refinement

Rp = 4.729	4001 data points
Rwp = 5.994	33 parameters
Rexp = 2.438	0 restraints
RBragg = 10.197

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

	x	y	z	Uiso*/Ueq
Ga1	0.206 (7)	0.167 (4)	0.130 (3)	0.028 (9)*
Ga2	0.644 (6)	0.164 (4)	0.105 (3)	0.028 (9)*
Gd1	0.524 (4)	0.106 (2)	0.7796 (18)	0.036 (2)*
Gd2	0.026 (4)	0.088 (2)	0.812 (2)	0.036 (2)*
Gd3	0.342 (4)	0.123 (2)	0.439 (2)	0.036 (2)*
Gd4	0.841 (3)	0.114 (3)	0.416 (2)	0.036 (2)*
O1	0.76545	0.25284	0.75953	0.03800*
O2	0.22462	0.22422	0.73871	0.03800*
O3	0.24920	0.01296	0.17323	0.03800*
O4	0.15619	0.19741	0.95337	0.03800*
O5	0.38483	0.24613	0.08758	0.03800*
O6	0.64410	0.22213	0.93396	0.03800*
O7	0.70511	0.02586	0.13763	0.03800*
O8	0.06635	−0.0194	0.37859	0.03800*
O9	0.51123	0.04766	0.38543	0.03800*

Geometric parameters (Å, º)

Ga1—O2^i	1.68 (4)	O2—O4	2.6707 (2)
Ga1—O3	1.73 (4)	O2—O5^iv	2.4192 (2)
Ga1—O4^ii	1.95 (3)	O3—Ga1	1.73 (4)
Ga1—O5	1.79 (5)	O3—Gd1^iii	2.07 (3)
Ga2—O1^i	1.93 (3)	O3—Gd2^vi	2.40 (3)
Ga2—O5	2.10 (5)	O3—O1^iii	2.9731 (3)
Ga2—O6^ii	2.05 (4)	O3—O2^i	2.9467 (3)
Ga2—O7	1.57 (4)	O3—O5	2.9893 (2)
Gd1—O1	2.48 (3)	O3—O9	2.6202 (2)
Gd1—O2	2.51 (3)	O4—Ga1^viii	1.95 (3)
Gd1—O3^iii	2.07 (3)	O4—Gd2	1.98 (2)
Gd1—O5^iv	2.64 (2)	O4—Gd3^iv	2.43 (3)
Gd1—O6	2.11 (2)	O4—O2	2.6707 (2)
Gd1—O7^iii	2.63 (3)	O4—O5^viii	1.9799 (2)
Gd1—O9^iii	2.45 (2)	O4—O7^iii	2.9390 (2)
Gd2—O1^v	2.57 (3)	O5—Ga1	1.79 (5)
Gd2—O2	2.42 (3)	O5—Ga2	2.10 (5)
Gd2—O3^vi	2.40 (3)	O5—Gd1^i	2.64 (2)
Gd2—O4	1.98 (2)	O5—Gd3^i	2.15 (2)
Gd2—O7^iii	2.29 (3)	O5—O1^i	2.9206 (3)
Gd2—O8^vi	2.19 (2)	O5—O2^i	2.4192 (2)
Gd3—O2^i	2.72 (2)	O5—O3	2.9893 (2)
Gd3—O4^i	2.43 (3)	O5—O4^ii	1.9799 (2)
Gd3—O5^iv	2.15 (2)	O6—Ga2^viii	2.05 (4)
Gd3—O6^i	2.84 (3)	O6—Gd1	2.11 (2)
Gd3—O8	2.50 (3)	O6—Gd3^iv	2.84 (3)
Gd3—O9	1.78 (3)	O6—Gd4^iv	2.36 (3)
Gd3—O9^iii	2.68 (2)	O6—O1	2.4605 (2)
Gd4—O1^i	2.22 (3)	O6—O9^iv	2.6650 (2)
Gd4—O6^i	2.36 (3)	O7—Ga2	1.57 (4)
Gd4—O8^vii	2.37 (3)	O7—Gd1^iii	2.63 (3)
Gd4—O8^iii	2.44 (2)	O7—Gd2^iii	2.29 (3)
Gd4—O9	2.51 (2)	O7—O1^i	2.7221 (2)
O1—Ga2^iv	1.93 (3)	O7—O4^iii	2.9390 (2)
O1—Gd1	2.48 (3)	O8—Gd2^vi	2.19 (2)
O1—Gd2^vii	2.57 (3)	O8—Gd3	2.50 (3)
O1—Gd4^iv	2.22 (3)	O8—Gd4^v	2.37 (3)
O1—O3^iii	2.9731 (3)	O8—Gd4^iii	2.44 (2)
O1—O5^iv	2.9206 (3)	O9—Gd1^iii	2.45 (2)
O1—O6	2.4605 (2)	O9—Gd3	1.78 (3)
O1—O7^iv	2.7221 (2)	O9—Gd3^iii	2.68 (2)
O2—Ga1^iv	1.68 (4)	O9—Gd4	2.51 (2)
O2—Gd1	2.51 (3)	O9—O3	2.6202 (2)
O2—Gd2	2.42 (3)	O9—O6^i	2.6650 (2)
O2—Gd3^iv	2.72 (2)	O9—O9^iii	2.8595 (2)
O2—O3^iv	2.9467 (3)
O2^i—Ga1—O3	119.6 (19)	Gd2—O2—O3^iv	139.6 (12)
O2^i—Ga1—O4^ii	125.9 (17)	Gd2—O2—O4	45.5 (8)
O2^i—Ga1—O5	88 (2)	Gd2—O2—O5^iv	145.9 (15)
O3—Ga1—O4^ii	114.3 (17)	Gd3^iv—O2—O3^iv	66.5 (7)
O3—Ga1—O5	116 (2)	Gd3^iv—O2—O4	53.5 (7)
O4^ii—Ga1—O5	64 (2)	Gd3^iv—O2—O5^iv	114.4 (10)
O1^i—Ga2—O5	92.9 (16)	O3^iv—O2—O4	112.432 (13)
O1^i—Ga2—O6^ii	125.7 (15)	O3^iv—O2—O5^iv	66.874 (9)
O1^i—Ga2—O7	101.8 (18)	O4—O2—O5^iv	162.125 (19)
O5—Ga2—O6^ii	93.6 (16)	Ga1—O3—Gd1^iii	137 (3)
O5—Ga2—O7	128 (2)	Ga1—O3—Gd2^vi	111 (3)
O6^ii—Ga2—O7	115.3 (19)	Ga1—O3—O1^iii	167 (3)
O1—Gd1—O2	107.8 (9)	Ga1—O3—O9	98 (2)
O1—Gd1—O3^iii	81.1 (10)	Gd1^iii—O3—Gd2^vi	111 (2)
O1—Gd1—O5^iv	69.5 (8)	Gd1^iii—O3—O1^iii	55.4 (10)
O1—Gd1—O6	64.2 (8)	Gd1^iii—O3—O2^i	129.9 (12)
O1—Gd1—O7^iii	164.4 (9)	Gd1^iii—O3—O5	105.3 (11)
O1—Gd1—O9^iii	105.3 (8)	Gd1^iii—O3—O9	61.8 (9)
O2—Gd1—O3^iii	170.6 (10)	Gd2^vi—O3—O1^iii	56.0 (9)
O2—Gd1—O5^iv	56.0 (8)	Gd2^vi—O3—O2^i	107.0 (11)
O2—Gd1—O6	88.7 (8)	Gd2^vi—O3—O5	143.0 (13)
O2—Gd1—O7^iii	71.6 (9)	Gd2^vi—O3—O9	114.7 (12)
O2—Gd1—O9^iii	109.1 (8)	O1^iii—O3—O2^i	148.02 (2)
O3^iii—Gd1—O5^iv	131.9 (8)	O1^iii—O3—O5	159.52 (2)
O3^iii—Gd1—O6	92.8 (9)	O1^iii—O3—O9	88.765 (11)
O3^iii—Gd1—O7^iii	99.1 (10)	O2^i—O3—O5	48.096 (7)
O3^iii—Gd1—O9^iii	70.2 (9)	O2^i—O3—O9	73.703 (9)
O5^iv—Gd1—O6	106.6 (7)	O5—O3—O9	86.828 (11)
O5^iv—Gd1—O7^iii	119.2 (8)	Ga1^viii—O4—Gd2	128 (2)
O5^iv—Gd1—O9^iii	81.6 (7)	Ga1^viii—O4—Gd3^iv	106 (3)
O6—Gd1—O7^iii	100.3 (8)	Ga1^viii—O4—O2	159 (2)
O6—Gd1—O9^iii	161.7 (7)	Ga1^viii—O4—O5^viii	54.1 (17)
O7^iii—Gd1—O9^iii	89.3 (8)	Ga1^viii—O4—O7^iii	105 (2)
O1^v—Gd2—O2	90.9 (9)	Gd2—O4—Gd3^iv	124.4 (17)
O1^v—Gd2—O3^vi	73.3 (9)	Gd2—O4—O2	60.7 (10)
O1^v—Gd2—O4	85.8 (8)	Gd2—O4—O5^viii	150.5 (13)
O1^v—Gd2—O7^iii	169.0 (9)	Gd2—O4—O7^iii	51.0 (9)
O1^v—Gd2—O8^vi	91.3 (8)	Gd3^iv—O4—O2	64.3 (8)
O2—Gd2—O3^vi	160.4 (10)	Gd3^iv—O4—O5^viii	57.3 (8)
O2—Gd2—O4	73.8 (9)	Gd3^iv—O4—O7^iii	110.4 (10)
O2—Gd2—O7^iii	79.2 (10)	O2—O4—O5^viii	107.679 (17)
O2—Gd2—O8^vi	84.3 (9)	O2—O4—O7^iii	64.608 (9)
O3^vi—Gd2—O4	115.4 (9)	O5^viii—O4—O7^iii	99.659 (12)
O3^vi—Gd2—O7^iii	117.3 (10)	Ga1—O5—Ga2	122 (4)
O3^vi—Gd2—O8^vi	84.5 (9)	Ga1—O5—Gd1^i	102 (3)
O4—Gd2—O7^iii	86.7 (9)	Ga1—O5—Gd3^i	126 (3)
O4—Gd2—O8^vi	157.8 (8)	Ga1—O5—O1^i	119 (3)
O7^iii—Gd2—O8^vi	92.6 (9)	Ga1—O5—O4^ii	62 (2)
O2^i—Gd3—O4^i	62.2 (8)	Ga2—O5—Gd1^i	94 (2)
O2^i—Gd3—O5^iv	101.1 (7)	Ga2—O5—Gd3^i	105 (2)
O2^i—Gd3—O6^i	71.3 (7)	Ga2—O5—O2^i	131 (3)
O2^i—Gd3—O8	96.9 (7)	Ga2—O5—O3	91 (2)
O2^i—Gd3—O9	93.9 (11)	Ga2—O5—O4^ii	121 (2)
O2^i—Gd3—O9^iii	170.5 (6)	Gd1^i—O5—Gd3^i	100.3 (13)
O4^i—Gd3—O5^iv	50.9 (8)	Gd1^i—O5—O1^i	52.6 (7)
O4^i—Gd3—O6^i	91.1 (8)	Gd1^i—O5—O2^i	59.2 (8)
O4^i—Gd3—O8	93.3 (9)	Gd1^i—O5—O3	108.9 (9)
O4^i—Gd3—O9	152.0 (11)	Gd1^i—O5—O4^ii	145.1 (11)
O4^i—Gd3—O9^iii	127.2 (8)	Gd3^i—O5—O1^i	113.4 (10)
O5^iv—Gd3—O6^i	73.1 (8)	Gd3^i—O5—O2^i	119.4 (13)
O5^iv—Gd3—O8	121.5 (8)	Gd3^i—O5—O3	145.8 (12)
O5^iv—Gd3—O9	128.7 (11)	Gd3^i—O5—O4^ii	71.8 (10)
O5^iv—Gd3—O9^iii	86.4 (7)	O1^i—O5—O2^i	97.493 (14)
O6^i—Gd3—O8	163.5 (8)	O1^i—O5—O3	98.664 (12)
O6^i—Gd3—O9	65.9 (11)	O1^i—O5—O4^ii	161.97 (2)
O6^i—Gd3—O9^iii	105.8 (7)	O2^i—O5—O3	65.030 (9)
O8—Gd3—O9	104.7 (11)	O2^i—O5—O4^ii	94.232 (13)
O8—Gd3—O9^iii	84.0 (7)	O3—O5—O4^ii	73.999 (9)
O9—Gd3—O9^iii	76.8 (11)	Ga2^viii—O6—Gd1	119 (2)
O1^i—Gd4—O6^i	65.0 (10)	Ga2^viii—O6—Gd3^iv	85.3 (19)
O1^i—Gd4—O8^vii	105.3 (10)	Ga2^viii—O6—Gd4^iv	120 (3)
O1^i—Gd4—O8^iii	164.3 (9)	Ga2^viii—O6—O1	157 (2)
O1^i—Gd4—O9	94.7 (9)	Ga2^viii—O6—O9^iv	111.6 (19)
O6^i—Gd4—O8^vii	168.2 (10)	Gd1—O6—Gd3^iv	103.2 (15)
O6^i—Gd4—O8^iii	103.1 (9)	Gd1—O6—Gd4^iv	119.1 (18)
O6^i—Gd4—O9	66.4 (9)	Gd1—O6—O1	65.1 (9)
O8^vii—Gd4—O8^iii	85.2 (9)	Gd1—O6—O9^iv	110.1 (10)
O8^vii—Gd4—O9	122.8 (9)	Gd3^iv—O6—Gd4^iv	95.5 (16)
O8^iii—Gd4—O9	89.1 (8)	Gd3^iv—O6—O1	116.4 (13)
Ga2^iv—O1—Gd1	103 (2)	Gd4^iv—O6—O1	54.8 (9)
Ga2^iv—O1—Gd2^vii	130 (2)	Gd4^iv—O6—O9^iv	59.5 (9)
Ga2^iv—O1—Gd4^iv	111 (2)	O1—O6—O9^iv	85.399 (9)
Ga2^iv—O1—O3^iii	130 (2)	Ga2—O7—Gd1^iii	115 (3)
Ga2^iv—O1—O5^iv	45.9 (14)	Ga2—O7—Gd2^iii	138 (3)
Ga2^iv—O1—O6	127 (2)	Ga2—O7—O4^iii	143 (3)
Gd1—O1—Gd2^vii	94.1 (17)	Gd1^iii—O7—Gd2^iii	104.6 (19)
Gd1—O1—Gd4^iv	110.3 (17)	Gd1^iii—O7—O1^i	108.2 (10)
Gd1—O1—O5^iv	57.8 (8)	Gd1^iii—O7—O4^iii	91.9 (11)
Gd1—O1—O6	50.7 (8)	Gd2^iii—O7—O1^i	110.6 (11)
Gd1—O1—O7^iv	126.6 (11)	O1^i—O7—O4^iii	151.031 (18)
Gd2^vii—O1—Gd4^iv	106.0 (18)	Gd2^vi—O8—Gd3	117.1 (15)
Gd2^vii—O1—O3^iii	50.7 (8)	Gd2^vi—O8—Gd4^v	111.3 (18)
Gd2^vii—O1—O5^iv	132.5 (11)	Gd2^vi—O8—Gd4^iii	135.5 (16)
Gd2^vii—O1—O6	100.0 (12)	Gd3—O8—Gd4^v	99.4 (17)
Gd2^vii—O1—O7^iv	135.5 (11)	Gd3—O8—Gd4^iii	91.9 (15)
Gd4^iv—O1—O3^iii	115.8 (14)	Gd4^v—O8—Gd4^iii	94.8 (16)
Gd4^iv—O1—O5^iv	119.0 (11)	Gd1^iii—O9—Gd3	131 (2)
Gd4^iv—O1—O6	60.3 (10)	Gd1^iii—O9—Gd3^iii	91.7 (11)
Gd4^iv—O1—O7^iv	78.7 (10)	Gd1^iii—O9—Gd4	99.2 (14)
O3^iii—O1—O5^iv	93.858 (11)	Gd1^iii—O9—O3	48.0 (7)
O3^iii—O1—O6	66.969 (9)	Gd1^iii—O9—O6^i	136.7 (10)
O3^iii—O1—O7^iv	163.69 (2)	Gd1^iii—O9—O9^iii	115.7 (10)
O5^iv—O1—O6	90.145 (13)	Gd3—O9—Gd3^iii	103.2 (18)
O5^iv—O1—O7^iv	71.616 (9)	Gd3—O9—Gd4	128 (2)
O6—O1—O7^iv	118.988 (13)	Gd3—O9—O3	88.0 (13)
Ga1^iv—O2—Gd1	111 (3)	Gd3—O9—O6^i	76.6 (14)
Ga1^iv—O2—Gd2	139 (3)	Gd3—O9—O9^iii	66.1 (12)
Ga1^iv—O2—Gd3^iv	97 (2)	Gd3^iii—O9—Gd4	86.2 (14)
Ga1^iv—O2—O4	139 (3)	Gd3^iii—O9—O3	127.1 (9)
Ga1^iv—O2—O5^iv	47.6 (19)	Gd3^iii—O9—O6^i	116.2 (9)
Gd1—O2—Gd2	104.5 (19)	Gd4—O9—O3	126.6 (10)
Gd1—O2—Gd3^iv	96.7 (14)	Gd4—O9—O6^i	54.1 (8)
Gd1—O2—O3^iv	114.1 (10)	Gd4—O9—O9^iii	108.6 (11)
Gd1—O2—O4	101.6 (12)	O3—O9—O6^i	116.649 (13)
Gd1—O2—O5^iv	64.8 (8)	O3—O9—O9^iii	123.017 (19)
Gd2—O2—Gd3^iv	98.6 (14)	O6^i—O9—O9^iii	105.771 (12)

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