Iron is more preferable than cobalt in permanent magnet applications considering its low price plus that Fe has a larger magnetic moment than Co. Thus by extending our work on the binary Co-N, the ternary Fe-Co-N system has been investigated as rare-earth free magnets [1, 2]. We found substituting a fraction of Co with Fe helps to stabilize the newly proposed structures and at the same time further improve the magnetic properties.
The crystal structures are directly taken from those for ConN (n = 3–8) obtained in the AGA searches and all possible Fe substitutions are enumerated for each parent structure. It should be noted that the structures of iron nitrides and cobalt nitrides are rather similar due to the similarities between Fe and Co, although the ground-state structure for the same compositions can be different. In fact, we found that all the reported structures for Fe3N, Fe4N and Fe8N in the literature exist in our structure pools of Co–N.
In the following table, the calculated magnetic moment per transition metal (TM) and MAE values are listed. The crystal structures of the listed configurations can be found by clicking the name of each composition.
[1] X Zhao, L Ke, CZ Wang, and KM Ho, Metastable cobalt nitride structures with high magnetic anisotropy for rare-earth free magnets. Physical Chemistry Chemical Physics 18 (46), 31680-31690 (2016).
[2] X Zhao, CZ Wang, Y. X. Yao, and KM Ho, Large magnetic anisotropy predicted for rare-earth free Fe16-xCxN2 alloys. Physical Review B 94 (22), 224424 (2016).
| (Fe, Co)3N [txt] | |||
|
Fe1Co5N2.1 |
-7.47035 |
C 1 2 1 |
M(TM)=0.805412 μB/atom MAE = -0.29 MJ/m3 |
|
Fe1Co5N2.4 |
-7.44195 |
A m m 2 |
M(TM)=1.08878 μB/atom MAE = 0.73 MJ/m3 |
|
Fe1Co5N2.5 |
-7.44107 |
C 2/m 2/m 2/m |
M(TM)=1.08579 μB/atom MAE = 1.51 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe2Co4N2.1 |
-7.64346 |
C 2 2 21 |
M(TM)=0.998925 μB/atom Triaxial anisotropy |
|
Fe2Co4N2.2 |
-7.64267 |
C 1 c 1 |
M(TM)=0.922825 μB/atom MAE = -1.13 MJ/m3 |
|
Fe2Co4N2.9 |
-7.6183 |
A m m 2 |
M(TM)=1.12756 μB/atom MAE = 1.68 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe3Co3N2.1 |
-7.81671 |
P 1 |
M(TM)=1.05669 μB/atom MAE = -0.89 MJ/m3 |
|
Fe3Co3N2.4 |
-7.80089 |
A m m 2 |
M(TM)=1.16098 μB/atom MAE = 1.54 MJ/m3 |
|
Fe3Co3N2.6 |
-7.79979 |
A m m 2 |
M(TM)=1.36449 μB/atom MAE = 2.50 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe4Co2N2.1 |
-7.98879 |
C 1 2 1 |
M(TM)=1.29211 μB/atom MAE = -1.54 MJ/m3 |
|
Fe4Co2N2.5 |
-7.97085 |
C 2/m 2/c 21/m |
M(TM)=1.49513 μB/atom MAE = 2.22 MJ/m3 |
|
Fe4Co2N2.10 |
-7.96279 |
A m m 2 |
M(TM)=1.42332 μB/atom MAE = 1.64 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe5Co1N2.1 |
-8.15858 |
C 1 2 1 |
M(TM)=1.43039 μB/atom Triaxial anisotropy |
|
Fe5Co1N2.4 |
-8.12622 |
A m m 2 |
M(TM)=1.48389 μB/atom MAE = 1.42 MJ/m3 |
|
Fe5Co1N2.5 |
-8.12154 |
C 2/m 2/m 2/m |
M(TM)=1.54524 μB/atom MAE = 1.10 MJ/m3 |
|
----------------- |
------------------ |
------------------------------ |
---------------------------------- |
| (Fe. Co)4N [txt] | |||
|
Fe1Co7N2.1 |
-7.37181 |
P 4/m 2/m 2/m |
M(TM)=1.3746 μB/atom MAE = -0.53 MJ/m3 |
|
Fe1Co7N2.3 |
-7.36769 |
I 4/m 2/m 2/m |
M(TM)=1.37355 μB/atom MAE = 1.06 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe2Co6N2.1 |
-7.53209 |
P 4/m -3 2/m |
M(TM)=1.49044 μB/atom MAE ~ 0 MJ/m3 |
|
Fe2Co6N2.3 |
-7.51883 |
I 4 m m |
M(TM)=1.47866 μB/atom MAE = 1.54 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe3Co5N2.1 |
-7.67426 |
P 2/m 2/m 2/m |
M(TM)=1.55768 μB/atom MAE ~ 0 MJ/m3 |
|
Fe3Co5N2.3 |
-7.66095 |
I 4/m 2/m 2/m |
M(TM)=1.56437 μB/atom MAE = 1.02 MJ/m3 |
|
Fe3Co5N2.9 |
-7.65149 |
I -4 m 2 |
M(TM)=1.51736 μB/atom MAE = 1.63 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe4Co4N2.1 |
-7.81151 |
P 4/m 2/m 2/m |
M(TM)=1.60031 μB/atom MAE = -0.46 MJ/m3 |
|
Fe4Co4N2.10 |
-7.79279 |
I m m 2 |
M(TM)=1.5812 μB/atom MAE = 0.92 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe5Co3N2.1 |
-7.93252 |
P 2/m 2/m 2/m |
M(TM)=1.64434 μB/atom MAE = -0.91 MJ/m3 |
|
Fe5Co3N2.7 |
-7.92117 |
I 4/m 2/m 2/m |
M(TM)=1.6677 μB/atom MAE = 2.40 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe6Co2N2.1 |
-8.05045 |
P m m 2 |
M(TM)=1.76074 μB/atom MAE = -0.75 MJ/m3 |
|
Fe6Co2N2.4 |
-8.0493 |
I 4 m m |
M(TM)=1.70771 μB/atom MAE = 1.06 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe7Co1N2.1 |
-8.17125 |
P 4/m 2/m 2/m |
M(TM)=1.86265 μB/atom MAE = 1.06 MJ/m3 |
|
Fe7Co1N2.3 |
-8.16825 |
I 4 m m |
M(TM)=1.83459 μB/atom MAE = 0.91 MJ/m3 |
|
----------------- |
------------------ |
------------------------------ |
---------------------------------- |
| (Fe, Co)5N [txt] | |||
|
Fe2Co8N2.1 |
-7.43359 |
A m m 2 |
M(TM)=1.41332 μB/atom MAE = 0.78 MJ/m3 |
|
Fe2Co8N2.9 |
-7.42683 |
A m m 2 |
M(TM)=1.38048 μB/atom MAE = 0.78 MJ/m3 |
|
Fe2Co8N2.10 |
-7.42641 |
I 4/m |
M(TM)=1.26867 μB/atom MAE = -1.86 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe4Co6N2.1 |
-7.66212 |
A m m 2 |
M(TM)=1.52287 μB/atom MAE = 1.44 MJ/m3 |
|
Fe4Co6N2.3 |
-7.66162 |
A m m 2 |
M(TM)=1.50444 μB/atom MAE = 1.40 MJ/m3 |
|
Fe4Co6N2.5 |
-7.65985 |
A m m 2 |
M(TM)=1.50918 μB/atom MAE = 1.55 MJ/m3 |
|
Fe4Co6N2.6 |
-7.6597 |
A m m 2 |
M(TM)=1.51738 μB/atom MAE = 1.24 MJ/m3 |
|
Fe4Co6N2.7 |
-7.65928 |
A m m 2 |
M(TM)=1.50873 μB/atom MAE = 1.50 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe6Co4N2.1 |
-7.87069 |
A m m 2 |
M(TM)=1.57219 μB/atom MAE = 0.68 MJ/m3 |
|
Fe6Co4N2.4 |
-7.86703 |
A m m 2 |
M(TM)=1.5922 μB/atom MAE = 1.44 MJ/m3 |
|
Fe6Co4N2.8 |
-7.86594 |
A m m 2 |
M(TM)=1.57123 μB/atom MAE = 1.15 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe8Co2N2.1 |
-8.06984 |
A m m 2 |
M(TM)=1.84668 μB/atom MAE = 1.50 MJ/m3 |
|
Fe8Co2N2.4 |
-8.06584 |
P 1 m 1 |
M(TM)=1.83223 μB/atom MAE = 1.31 MJ/m3 |
|
Fe8Co2N2.7 |
-8.06509 |
A m m 2 |
M(TM)=1.83768 μB/atom MAE = 1.42 MJ/m3 |
|
----------------- |
------------------ |
------------------------------ |
---------------------------------- |
| (Fe, Co)6N [txt] | |||
|
Fe2Co10N2.1 |
-7.37294 |
P 4 m m |
M(TM)=1.46446 μB/atom MAE = -0.15 MJ/m3 |
|
Fe2Co10N2.3 |
-7.36611 |
P 4/m 2/m 2/m |
M(TM)=1.44994 μB/atom MAE = 0.33 MJ/m3 |
|
Fe2Co10N2.4 |
-7.36389 |
P 4 m m |
M(TM)=1.44686 μB/atom MAE = -0.61 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe4Co8N2.1 |
-7.57664 |
P 4/m 2/m 2/m |
M(TM)=1.54049 μB/atom MAE = -0.45 MJ/m3 |
|
Fe4Co8N2.2 |
-7.57227 |
P m m 2 |
M(TM)=1.53926 μB/atom MAE = 0.81 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe6Co6N2.1 |
-7.75241 |
P 2/m 2/m 2/m |
M(TM)=1.57732 μB/atom MAE = 0.58 MJ/m3 |
|
Fe6Co6N2.3 |
-7.75065 |
P m m 2 |
M(TM)=1.58234 μB/atom MAE = 0.76 MJ/m3 |
|
Fe6Co6N2.14 |
-7.74481 |
P 4/m 2/m 2/m |
M(TM)=1.71769 μB/atom MAE = 1.54 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe8Co4N2.1 |
-7.92399 |
P 4 m m |
M(TM)=1.83061 μB/atom MAE = 1.81 MJ/m3 |
|
Fe8Co4N2.2 |
-7.92234 |
P 4/m 2/m 2/m |
M(TM)=1.88924 μB/atom MAE = 2.10 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe10Co2N2.1 |
-8.09796 |
P 4/m 2/m 2/m |
M(TM)=2.00246 μB/atom MAE = 0.88 MJ/m3 |
|
Fe10Co2N2.2 |
-8.09264 |
P 4/m 2/m 2/m |
M(TM)=1.98885 μB/atom MAE = 2.04 MJ/m3 |
|
Fe10Co2N2.10 |
-8.08798 |
P 4 m m |
M(TM)=1.91023 μB/atom MAE = 1.96 MJ/m3 |
|
----------------- |
------------------ |
------------------------------ |
---------------------------------- |
| (Fe, Co)7N [txt] | |||
|
Fe2Co12N2.1 |
-7.32508 |
A m m 2 |
M(TM)=1.47764 μB/atom MAE = -0.30 MJ/m3 |
|
Fe2Co12N2.2 |
-7.32469 |
C 2/m 2/m 2/m |
M(TM)=1.45682 μB/atom MAE = -1.13 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe4Co10N2.1 |
-7.50081 |
C 2/m 2/m 2/m |
M(TM)=1.5763 μB/atom MAE ~ 0 MJ/m3 |
|
Fe4Co10N2.9 |
-7.49141 |
A m m 2 |
M(TM)=1.56204 μB/atom MAE = 1.06 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe6Co8N2.1 |
-7.65329 |
A m m 2 |
M(TM)=1.58929 μB/atom Triaxial anisotropy |
|
Fe6Co8N2.4 |
-7.65219 |
A m m 2 |
M(TM)=1.63734 μB/atom MAE = 1.46 MJ/m3 |
|
Fe6Co8N2.6 |
-7.65212 |
A m m 2 |
M(TM)=1.60556 μB/atom MAE = 1.55 MJ/m3 |
|
Fe6Co8N2.10 |
-7.65159 |
A m m 2 |
M(TM)=1.67101 μB/atom MAE = 2.11 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe8Co6N2.1 |
-7.81238 |
A m m 2 |
M(TM)=1.8163 μB/atom MAE = 1.42 MJ/m3 |
|
Fe8Co6N2.3 |
-7.81121 |
P 1 m 1 |
M(TM)=1.78204 μB/atom MAE = 1.42 MJ/m3 |
|
Fe8Co6N2.5 |
-7.81056 |
A m m 2 |
M(TM)=1.80908 μB/atom MAE = 1.41 MJ/m3 |
|
Fe8Co6N2.10 |
-7.80861 |
A m m 2 |
M(TM)=1.80602 μB/atom MAE = 1.80 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe10Co4N2.1 |
-7.9691 |
A m m 2 |
M(TM)=1.93671 μB/atom MAE = -0.71 MJ/m3 |
|
Fe10Co4N2.2 |
-7.96774 |
P 1 m 1 |
M(TM)=1.95198 μB/atom MAE = 1.17 MJ/m3 |
|
Fe10Co4N2.6 |
-7.96555 |
A m m 2 |
M(TM)=1.92304 μB/atom MAE = 1.43 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe12Co2N2.1 |
-8.12076 |
A m m 2 |
M(TM)=2.04543 μB/atom MAE ~ 0 MJ/m3 |
|
Fe12Co2N2.6 |
-8.11541 |
A m m 2 |
M(TM)=1.986 μB/atom MAE = 0.92 MJ/m3 |
|
Fe12Co2N2.8 |
-8.11407 |
A m m 2 |
M(TM)=1.99391 μB/atom MAE = 1.23 MJ/m3 |
|
----------------- |
------------------ |
------------------------------ |
---------------------------------- |
| (Fe, Co)8N [txt] | |||
|
Fe2Co14N2.1 |
-7.30164 |
P 4/n 21/m 2/m (origin choice 2) |
M(TM)=1.34539 μB/atom MAE = -0.1 MJ/m3 |
|
Fe2Co14N2.2 |
-7.30037 |
F -4 3 m |
M(TM)=1.34164 μB/atom MAE ~ 0 MJ/m3 |
|
Fe2Co14N2.4 |
-7.29311 |
C 2/m 2/m 2/m |
M(TM)=1.37694 μB/atom MAE = -0.4 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe4Co12N2.1 |
-7.47033 |
F 4/m -3 2/m |
M(TM)=1.41038 μB/atom MAE ~ 0 MJ/m3 |
|
Fe4Co12N2.4 |
-7.45078 |
P 4/m 2/m 2/m |
M(TM)=1.49883 μB/atom MAE = 1.04 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe6Co10N2.1 |
-7.5925 |
I 4 m m |
M(TM)=1.39069 μB/atom MAE ~ 0 MJ/m3 |
|
Fe6Co10N2.5 |
-7.58933 |
P 2/m 2/m 2/m |
M(TM)=1.57258 μB/atom MAE = 0.82 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe8Co8N2.1 |
-7.72733 |
P 4/m 2/m 2/m |
M(TM)=1.86521 μB/atom MAE = 1.65 MJ/m3 |
|
Fe8Co8N2.2 |
-7.72244 |
P 4/m 2/m 2/m |
M(TM)=1.87292 μB/atom MAE = 1.12 MJ/m3 |
|
Fe8Co8N2.3 |
-7.72217 |
P 4/m 2/m 2/m |
M(TM)=1.65429 μB/atom MAE = 1.13 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe10Co6N2.1 |
-7.86078 |
I -4 m 2 |
M(TM)=1.92279 μB/atom MAE = -0.29 MJ/m3 |
|
Fe10Co6N2.2 |
-7.86061 |
P 4 m m |
M(TM)=1.95124 μB/atom MAE = 1.63 MJ/m3 |
|
Fe10Co6N2.6 |
-7.85725 |
P 4/n 21/m 2/m (origin choice 2) |
M(TM)=1.88739 μB/atom MAE = 2.34 MJ/m3 |
|
Fe10Co6N2.10 |
-7.85549 |
P 4/m 2/m 2/m |
M(TM)=1.88216 μB/atom MAE = 2.23 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe12Co4N2.1 |
-7.99799 |
I 4/m 2/m 2/m |
M(TM)=1.9752 μB/atom MAE = 1.25 MJ/m3 |
|
Fe12Co4N2.2 |
-7.99733 |
P 4/m 2/m 2/m |
M(TM)=2.05642 μB/atom MAE ~ 0 MJ/m3 |
|
Fe12Co4N2.10 |
-7.99189 |
P 2/m 2/m 2/m |
M(TM)=1.96714 μB/atom MAE = 1.93 MJ/m3 |
|
Fe12Co4N2.12 |
-7.99158 |
P m m 2 |
M(TM)=1.96887 μB/atom MAE = 2.15 MJ/m3 |
|
Fe12Co4N2.15 |
-7.99123 |
I 4/m 2/m 2/m |
M(TM)=1.95832 μB/atom MAE = 3.17 MJ/m3 |
|
-- |
-- |
-- |
-- |
|
Fe14Co2N2.1 |
-8.13411 |
P 4/n 21/m 2/m (origin choice 2) |
M(TM)=2.04074 μB/atom MAE = 1.41 MJ/m3 |
|
Fe14Co2N2.3 |
-8.13233 |
I -4 m 2 |
M(TM)=2.07693 μB/atom MAE = 1.66 MJ/m3 |
|
Fe14Co2N2.8 |
-8.13022 |
I 4 m m |
M(TM)=2.05312 μB/atom MAE = 1.76 MJ/m3 |