Journal of Inorganic Materials ›› 2019, Vol. 34 ›› Issue (10): 1047-1054.DOI: 10.15541/jim20190003
Special Issue: MAX相和MXene材料; 副主编黄庆研究员专辑
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WANG Zhong1,2,ZHA Xian-Hu2,WU Ze1(),HUANG Qing2,DU Shi-Yu2()
Received:
2018-12-29
Revised:
2019-02-11
Published:
2019-09-23
Online:
2019-05-29
Supported by:
CLC Number:
WANG Zhong, ZHA Xian-Hu, WU Ze, HUANG Qing, DU Shi-Yu. First-principles Study on Electronic and Magnetic Properties of Mn-doped Strontium Ferrite SrFe12O19[J]. Journal of Inorganic Materials, 2019, 34(10): 1047-1054.
Fig. 1 The unit cell of SrFe12O19 (a) The green ball denotes the Sr atom, the small grey ball denotes the O atom; (b) The blue, red, purple, magenta, and blue-green balls represent the Fe atoms in 12k, 4f2, 4f1, 2a, and 2b sites, respectively. The spin directions for different Fe3+ are labeled with different colors (black and red)
Spin direction of Fe ions in SrFe12O19 | a/nm | c/nm | Energy/(eV?(unit cell)-1) | Moment/(μB?(unit cell)-1) | ||||
---|---|---|---|---|---|---|---|---|
2a | 2b | 4f1 | 4f2 | 12k | ||||
+ | + | + | + | + | 0.5730 | 2.257 | 0 | 25.00 |
- | + | + | + | + | 0.5690 | 2.239 | 0.5900 | 48.00 |
+ | - | + | + | + | 0.5740 | 2.266 | 0.1300 | 44.00 |
+ | + | - | + | + | 0.5770 | 2.264 | 0.3200 | 39.00 |
+ | + | + | - | + | 0.5870 | 2.324 | 0.4600 | 59.00 |
+ | + | + | + | - | 0.5820 | 2.300 | -1.160 | -7.000 |
- | - | + | - | + | 0.5840 | 2.269 | 1.040 | 43.00 |
- | - | - | + | + | 0.5790 | 2.245 | -0.6800 | 28.00 |
+ | + | - | - | + | 0.5860 | 2.310 | -2.820 | 40.00 |
0.5880a | 2.304a |
Table 1 Lattice parameters, relative total energies and magnetic moments of SrFe12O19 in different magnetic configurations
Spin direction of Fe ions in SrFe12O19 | a/nm | c/nm | Energy/(eV?(unit cell)-1) | Moment/(μB?(unit cell)-1) | ||||
---|---|---|---|---|---|---|---|---|
2a | 2b | 4f1 | 4f2 | 12k | ||||
+ | + | + | + | + | 0.5730 | 2.257 | 0 | 25.00 |
- | + | + | + | + | 0.5690 | 2.239 | 0.5900 | 48.00 |
+ | - | + | + | + | 0.5740 | 2.266 | 0.1300 | 44.00 |
+ | + | - | + | + | 0.5770 | 2.264 | 0.3200 | 39.00 |
+ | + | + | - | + | 0.5870 | 2.324 | 0.4600 | 59.00 |
+ | + | + | + | - | 0.5820 | 2.300 | -1.160 | -7.000 |
- | - | + | - | + | 0.5840 | 2.269 | 1.040 | 43.00 |
- | - | - | + | + | 0.5790 | 2.245 | -0.6800 | 28.00 |
+ | + | - | - | + | 0.5860 | 2.310 | -2.820 | 40.00 |
0.5880a | 2.304a |
Atom | Wyckoff site | Coordinates of atoms | Magnetic moment (GGA) | Magnetic moment (GGA+U) |
---|---|---|---|---|
Sr | 2d | 1/3, 2/3, 3/4 | 0 | 0 |
Fe(1) | 2a | 0, 0, 0 | 3.73 | 4.17 |
Fe(2) | 2b | 0, 0, 1/4 | 3.54 | 4.05 |
Fe(3) | 4f1 | 1/3, 2/3, 0.0272 | 3.43 | 4.05 |
Fe(4) | 4f2 | 1/3, 2/3, 0.1909 | 3.17 | 4.10 |
Fe(5) | 12k | 0.169, 0.338, 0.891 | 3.71 | 4.18 |
Total | – | – | 38.5 | 40.0 |
Table 2 Magnetic moments (μB) of Fe atoms and total magnetic moments for SrFe12O19 unit cell from GGA and GGA+U
Atom | Wyckoff site | Coordinates of atoms | Magnetic moment (GGA) | Magnetic moment (GGA+U) |
---|---|---|---|---|
Sr | 2d | 1/3, 2/3, 3/4 | 0 | 0 |
Fe(1) | 2a | 0, 0, 0 | 3.73 | 4.17 |
Fe(2) | 2b | 0, 0, 1/4 | 3.54 | 4.05 |
Fe(3) | 4f1 | 1/3, 2/3, 0.0272 | 3.43 | 4.05 |
Fe(4) | 4f2 | 1/3, 2/3, 0.1909 | 3.17 | 4.10 |
Fe(5) | 12k | 0.169, 0.338, 0.891 | 3.71 | 4.18 |
Total | – | – | 38.5 | 40.0 |
Fig. 2 Electronic band structure (a) and total density of states and atomic projected density (c) of states of SrFe12O19 from GGA, and electronic band structure (b), total density of states and atomic projected density (d) of states of SrFe12O19 from GGA+U
Substituted site | Esub/eV | mtot/mB | Dmtot |
---|---|---|---|
2a | -2.24 | 39.0 | -1.00 |
12k | -2.50 | 39.0 | -1.00 |
4f1 | -1.86 | 39.0 | -1.00 |
4f2 | -2.03 | 41.0 | 1.00 |
2b | -0.34 | 49.0 | 9.00 |
Table 3 Substitution energies of single Mn substituted strontium ferrite with Mn substituted Fe in five different sites, the total magnetic moments of substituted SrFe12-xMnxO19 and their changes relative to the pristine SrFe12O19
Substituted site | Esub/eV | mtot/mB | Dmtot |
---|---|---|---|
2a | -2.24 | 39.0 | -1.00 |
12k | -2.50 | 39.0 | -1.00 |
4f1 | -1.86 | 39.0 | -1.00 |
4f2 | -2.03 | 41.0 | 1.00 |
2b | -0.34 | 49.0 | 9.00 |
Configurations | Esub/eV | mtot/μB | Dmtot |
---|---|---|---|
[2a, 2a] | -2.88 | 38.0 | -2.00 |
[2a, 12k].1 | -4.02 | 38.0 | -2.00 |
[2a, 12k].2 | -3.98 | 38.0 | -2.00 |
[12k, 12k].1 | -3.90 | 38.0 | -2.00 |
[12k, 12k].2 | -3.90 | 38.0 | -2.00 |
[12k, 12k].3 | -3.97 | 38.0 | -2.00 |
[12k, 12k].4 | -3.90 | 38.0 | -2.00 |
[12k, 12k].5 | -3.95 | 38.0 | -2.00 |
[12k, 12k].6 | -3.99 | 38.0 | -2.00 |
[12k, 12k].7 | -4.00 | 38.0 | -2.00 |
Table 4 Substitution energies Esub, total magnetic moments mtot and their changes Dmtot relative to that of the pristine SrFe12O19 for different configurations of SrFe12-xMnxO19(x=1.0) with two Mn atoms substituted
Configurations | Esub/eV | mtot/μB | Dmtot |
---|---|---|---|
[2a, 2a] | -2.88 | 38.0 | -2.00 |
[2a, 12k].1 | -4.02 | 38.0 | -2.00 |
[2a, 12k].2 | -3.98 | 38.0 | -2.00 |
[12k, 12k].1 | -3.90 | 38.0 | -2.00 |
[12k, 12k].2 | -3.90 | 38.0 | -2.00 |
[12k, 12k].3 | -3.97 | 38.0 | -2.00 |
[12k, 12k].4 | -3.90 | 38.0 | -2.00 |
[12k, 12k].5 | -3.95 | 38.0 | -2.00 |
[12k, 12k].6 | -3.99 | 38.0 | -2.00 |
[12k, 12k].7 | -4.00 | 38.0 | -2.00 |
Site | SFO | [12k] | [2a] | [2a, 12k].1 | ||||
---|---|---|---|---|---|---|---|---|
Atoms | M | Atoms | M | Atoms | M | Atoms | M | |
2d | 2Sr | -0.004 | 2Sr | -0.003 | 2Fe | -0.004 | 2Sr | -0.003 |
2a | 1Fe | 4.165 | 1Fe | 4.171 | 1Mn | 3.866 | 1Mn | 3.786 |
1Fe | 4.165 | 1Fe | 4.164 | 1Fe | 4.164 | 1Fe | 4.164 | |
2b | 2Fe | 8.108 | 2Fe | 8.135 | 2Fe | 8.132 | 2Fe | 8.137 |
4f1 | 4Fe | -16.180 | 4Fe | -16.181 | 4Fe | -16.172 | 4Fe | -16.188 |
4f2 | 4Fe | -16.414 | 4Fe | -16.435 | 4Fe | -16.414 | 4Fe | -16.445 |
12k | 1Fe | 4.181 | 1Mn | 3.798 | 1Fe | 4.179 | 1Mn | 3.800 |
11Fe | 45.983 | 11Fe | 45.958 | 11Fe | 45.955 | 11Fe | 45.950 | |
4e | 4O | 0.716 | 4O | 0.563 | 4O | 0.711 | 4O | 0.517 |
4f | 4O | 0.696 | 4O | 0.555 | 4O | 0.673 | 4O | 0.218 |
6h | 6O | 0.876 | 6O | 0.870 | 6O | 0.860 | 6O | 0.342 |
12k | `12O | 0.814 | 12O | 0.683 | 12O | 0.311 | 12O | 1.095 |
12k | 12O | 1.916 | 120 | 1.733 | 12O | 1.821 | 12O | 1.812 |
Sm | 39.02 | 38.07 | 38.08 | 37.09 | ||||
mtot | 40 | 39 | 39 | 38 |
Table 5 Atomic magnetic moments in four different configurations: pristine strontium ferrite SFO, the [12k] configuration that SFO with one 12k Fe atom replaced by Mn, the [2a] configuration that SFO with one 2a Fe atom replaced by Mn, and the [2a,12k].1 structure that the stable configuration of SFO with two Fe atoms replaced by Mn
Site | SFO | [12k] | [2a] | [2a, 12k].1 | ||||
---|---|---|---|---|---|---|---|---|
Atoms | M | Atoms | M | Atoms | M | Atoms | M | |
2d | 2Sr | -0.004 | 2Sr | -0.003 | 2Fe | -0.004 | 2Sr | -0.003 |
2a | 1Fe | 4.165 | 1Fe | 4.171 | 1Mn | 3.866 | 1Mn | 3.786 |
1Fe | 4.165 | 1Fe | 4.164 | 1Fe | 4.164 | 1Fe | 4.164 | |
2b | 2Fe | 8.108 | 2Fe | 8.135 | 2Fe | 8.132 | 2Fe | 8.137 |
4f1 | 4Fe | -16.180 | 4Fe | -16.181 | 4Fe | -16.172 | 4Fe | -16.188 |
4f2 | 4Fe | -16.414 | 4Fe | -16.435 | 4Fe | -16.414 | 4Fe | -16.445 |
12k | 1Fe | 4.181 | 1Mn | 3.798 | 1Fe | 4.179 | 1Mn | 3.800 |
11Fe | 45.983 | 11Fe | 45.958 | 11Fe | 45.955 | 11Fe | 45.950 | |
4e | 4O | 0.716 | 4O | 0.563 | 4O | 0.711 | 4O | 0.517 |
4f | 4O | 0.696 | 4O | 0.555 | 4O | 0.673 | 4O | 0.218 |
6h | 6O | 0.876 | 6O | 0.870 | 6O | 0.860 | 6O | 0.342 |
12k | `12O | 0.814 | 12O | 0.683 | 12O | 0.311 | 12O | 1.095 |
12k | 12O | 1.916 | 120 | 1.733 | 12O | 1.821 | 12O | 1.812 |
Sm | 39.02 | 38.07 | 38.08 | 37.09 | ||||
mtot | 40 | 39 | 39 | 38 |
x | a/nm | c/nm | Volume/nm3 |
---|---|---|---|
0 | 0.5940 | 2.319 | 0.7063 |
0.5 | 0.5940 | 2.319 | 0.7063 |
1.0 | 0.5950 | 2.320 | 0.7071 |
Table 6 Lattice constants and volumes of pristine and Mn-doped strontium ferrites
x | a/nm | c/nm | Volume/nm3 |
---|---|---|---|
0 | 0.5940 | 2.319 | 0.7063 |
0.5 | 0.5940 | 2.319 | 0.7063 |
1.0 | 0.5950 | 2.320 | 0.7071 |
Fig. 3 Electronic band structure (a), total and projected density of states (c) of single Mn substituted SrFe12O19 (x=0.5), and electronic band structure (b), total and projected density of states (d) of Mn substituted SrFe12O19 (x=1.0) based on the GGA+U approach
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