Cation and Spin Interactions in Cadmium Ferrite: A Quantum Mechanical Study
Abstract
1. Introduction
2. Result and Discussion
2.1. Energy, Geometric Structure, Charge and Spin Distribution, and Electronic Structure
2.2. Lattice Dynamics
2.3. Spectroscopic Characterization
3. Materials and Methods
4. Conclusions
Funding
Institutional Review Board Statement
Conflicts of Interest
References
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Functionals | (X = 0) | (X = 0.5) | (X = 1) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
FM | FRI | AFM | FM | FRI | AFM | FM | FRI | AFM | ||
B3LYP | E | −16,591.3505 | −16,591.3506 | −16,591.3508 | −16,591.3068 | −16,591.3192 | −16,591.3150 | −16,591.2923 | −16,591.3055 | −16,591.3173 |
ER | (0.008) | (0.005) | (0.000) | (1.197) | (0.859) | (0.974) | (1.591) | (1.232) | (0.911) | |
HSE06 | E | −16,590.0006 | −16,590.0008 | −16,590.0009 | −16,589.95282 | −16,589.9644 | −16,589.9602 | −16,589.9379 | −16,589.9502 | −16,589.9613 |
ER | (0.008) | (0.003) | (0.000) | (1.308) | (0.993) | (1.107) | (1.714) | (1.379) | (1.077) | |
PBE0 | E | −16,590.0070 | −16,590.0071 | −16,590.0072 | −16,589.9591 | −16,589.9702 | −16,589.9660 | −16,589.9438 | −16,589.9558 | −16,589.9665 |
ER | (0.005) | (0.003) | (0.000) | (1.308) | (1.006) | (1.121) | (1.725) | (1.398) | (1.107) |
Energy | X = 0 | X = 0.5 | X = 1 | |||
---|---|---|---|---|---|---|
FM | AFM | FM | AFM | FM | AFM | |
EL | −451,473.6017 | −451,473.6077 | −451,472.4116 | −451,472.6339 | −451,472.0165 | −451,472.6978 |
(0.006) | (0.000) | (1.196) | (0.973) | (1.591) | (0.909) | |
E0 | 0.848033 | 0.837199 | 0.838940 | 0.832946 | 0.829726 | 0.835760 |
ET | 0.419251 | 0.424238 | 0.424223 | 0.4273647 | 0.424812 | 0.423246 |
S (meV/(cell.K)) | 2.413010 | 2.451891 | 2.474677 | 2.5096526 | 2.458753 | 2.469079 |
PV | 0.000108 | 0.000108 | 0.000109 | 0.0001084 | 0.000108 | 0.000106 |
TS | 0.719439 | 0.7310314 | 0.737824 | 0.7482529 | 0.733077 | 0.736156 |
ET + PV-TS | −0.300078 | −0.3066847 | −0.313492 | −0.3207797 | −0.308156 | −0.312802 |
EL + E0 + ET + PV-TS | −451,473.0537 | −451,473.0772 | −451,471.8861 | −451,472.1217 | −451,471.4950 | −451,472.1748 |
(0.023) | (0.000) | (1.191) | (0.955) | (1.582) | (0.902) |
Functionals | CdFO | Fe (Oh) μB | Fe (Td) μB | Cd (Oh) μB | Cd (Td) μB | O μB | ||
---|---|---|---|---|---|---|---|---|
B3LYP | X = 0 | FM | 4.317 (4) | 0.063 (2) | 0.326 (8) | |||
FRI | 4.309 (3) | _ | _ | 0.032 (2) | 0.313 (2) | |||
−4.295 | 0.113 (6) | |||||||
AFM | 4.301 (2) | _ | _ | 0.000 (2) | −0.102 (4) | |||
−4.301 (2) | −0.102 (4) | |||||||
X = 0.5 | 4.304 (3) | 4.275 | 0.039 | 0.074 | 0.357 | 0.368 | ||
FM | 0.341(3) | 0.318(3) | ||||||
4.278(3) | −4.214 | −0.008 | 0.074 | 0.111 | 0.364 | |||
FRI | −0.028 (3) | 0.308 (3) | ||||||
AFM | 4.274 (2) −4.287 | −4.234 | −0.019 | 0.023 | −0.041 | 0.120 | ||
−0.164 (2) | −0.010 (2) | |||||||
−0.055 | 0.291 | |||||||
X = 1 | FM | 4.341 (2) | 4.261 (2) | 0.045 (2) | ̶ | 0.350 (4) | 0.326 (4) | |
FRI | 4.304 (2) | −4.194 | −0.002 (2) | _ | 0.054 (2) | 0.341 (2) | ||
4.256 | −0.042 (2) | 0.315 (2) | ||||||
AFM | 4.270 (2) | −4.195 (2) | −0.053 (2) | ̶ | 0.047(4) | −0.057(4) | ||
HSE06 | X = 0 | FM | 4.372 (4) | ̶ | ̶ | 0.064 (2) | 0.298 (8) | |
FRI | 4.365 (3) | _ | _ | 0.033 (2) | 0.287 (2) | |||
−4.354 | 0.104 (6) | |||||||
AFM | 4.359 (2) | _ | _ | 0.000 (2) | −0.093 (4) | |||
−4.360 (2) | 0.094 (4) | |||||||
X = 0.5 | FM | 4.361 (3) | 4.337 | 0.035 | 0.075 | 0.324 | 0.334 | |
0.314 (3) | 0.290 (3) | |||||||
FRI | 4.337 (3) | −4.279 | −0.009 | 0.075 | 0.099 | 0.333 | ||
−0.025 (3) | 0.282 (3) | |||||||
AFM | 4.334 (2)−4.347 | −4.298 | −0.018 | 0.024 | −0.038 | 0.110 | ||
−0.154 (2) | −0.006 (2) | |||||||
−0.045 | 0.267 | |||||||
X = 1 | FM | 4.400 (2) | 4.318 (2) | 0.043 (2) | - | 0.319 (4) | ||
0.319 (4) | ||||||||
FRI | 4.366 (2) | −4.257 | −0.005 (2) | - | 0.051 (2) | 0.312 (2) | ||
4.312 | −0.044 (2) | 0.292 (2) | ||||||
AFM | 4.334 (2) | −4.257 (2) | −0.055 (2) | - | 0.044 (4) | |||
−0.055 (4) | ||||||||
PBE0 | X = 0 | FM | 4.380 (4) | ̶ | ̶ | 0.064 (2) | 0.294 (6) | |
FRI | 4.374 (3) | _ | _ | 0.033 (2) | 0.283 (2) | |||
−4.364 | 0.102 (6) | |||||||
AFM | 4.369 (2) | _ | _ | −0.000 (2) | −0.093 (4) | |||
−4.369 (2) | 0.093 (4) | |||||||
X = 0.5 | FM | 4.369 (3) | 4.346 | 0.035 | 0.075 | 0.319 | 0.331 | |
0.310 (3) | 0.286 (3) | |||||||
FRI | 4.346 (3) | −4.289 | 0.075 | −0.010 | 0.097 | 0.329 | ||
−0.026 (3) | 0.279 (3) | |||||||
AFM | 4.344 (2)−4.356 | −4.308 | −0.018 | 0.024 | −0.038 | 0.109 | ||
−0.153 (2) | −0.007 (2) | |||||||
−0.046 | 0.266 | |||||||
X = 1 | FM | 4.409 (2) | 4.327 (2) | 0.043 (2) | - | 0.315 (4) | ||
0.296 (4) | ||||||||
FRI | 4.376 (2) | −4.268 | −0.005 (2) | - | 0.050 (2) | 0.308 (2) | ||
4.321 | −0.045 (2) | 0.288 (2) | ||||||
AFM | 4.346 (2) | −4.268 (2) | −0.055 (2) | - | 0.043 (4) | |||
−0.055 (4) |
Primitive Formula | Inversion Degree | Spin Arrangement | Band Gap | |||||
---|---|---|---|---|---|---|---|---|
B3LYP | HSE06 | PBE0 | ||||||
(Cd2)[Fe4]O8 | X = 0.0 | FM | 4.884 | 3.012 | 4.719 | 3.120 | 5.436 | 3.790 |
FRI | 3.430 | 2.916 | 3.542 | 3.043 | 4.311 | 3.763 | ||
AFM | 3.112 | 3.112 | 3.251 | 3.246 | 3.977 | 3.977 | ||
(CdFe)[CdFe3]O8 | X = 0.5 | FM | 4.951 | 3.018 | 4.740 | 2.950 | 5.455 | 3.633 |
FRI | 3.221 | 3.120 | 3.228 | 3.161 | 3.988 | 3.876 | ||
AFM | 3.111 | 3.145 | 3.144 | 3.260 | 3.870 | 4.001 | ||
(Fe2)[ Cd2Fe2]O8 | X = 1.0 | FM | 5.078 | 2.677 | 4.858 | 2.700 | 5.561 | 3.392 |
FRI | 3.430 | 2.916 | 3.750 | 2.922 | 4.502 | 3.643 | ||
AFM | 3.523 | 3.005 | 3.565 | 3.079 | 4.305 | 3.808 |
Vibrational Modes (cm−1) | Ref. [31] | Ref. [32] | Ref. [23] | Current Work (X = 0.0) | |
---|---|---|---|---|---|
FM | AFM | ||||
v1 | 549.61–553.47 | 553–578 | 548–549 | 536.36 | 527.47 |
v2 | 424.26–410.75 | 438–403 | 374–380 | 350.10 | 348.04 |
v3 | 279.02 | 285.00 Sh-305.12 | |||
v4 | 153.38 | 137.49 |
X= 0.0 | X =1.0 | ||
---|---|---|---|
FM | FM | AFM | |
T2g (1) | 138.26 | I | I |
199.10 | 199.57 | ||
206.96 | 209.02 | ||
227.00 | 230.68 | ||
262.98 | 255.89 | ||
302.33 | |||
I | 306.95 | ||
317.03 | |||
312.22 | |||
324.24 | 332.23 | ||
328.27 | |||
Eg (1) | 349.37 | I | 337.12 |
T2g (2) | 462.57 | 390.50 | 413.13 |
464.58 | |||
451.39 | 479.93 | ||
483.01 | I | ||
T2g (3) | 591.82 | 535.77 | 541.58 |
552.35 | 556.23 | ||
580.72 | 583.89 | ||
A1g | 686.15 | 697.72 | 685.11 |
Raman Symmetry Assignment | Ref. [36] | Ref. [23] | Ref. [24] | Ref. [25] | Current Work (X = 0) | |
---|---|---|---|---|---|---|
FM | AFM | |||||
T2g (1) | 138 | 137 | ||||
Eg | 325–329 | 314 | 349 | 347 | ||
T2g (2) | 438–445 | 331 | 463 | 452 | ||
T2g (3) | 446 | 472 | 592 | 588 | ||
A1g | 644 | 634–636 | 652 | 674 | 686 | 682 |
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Almutairi, T.S. Cation and Spin Interactions in Cadmium Ferrite: A Quantum Mechanical Study. Int. J. Mol. Sci. 2025, 26, 4912. https://doi.org/10.3390/ijms26104912
Almutairi TS. Cation and Spin Interactions in Cadmium Ferrite: A Quantum Mechanical Study. International Journal of Molecular Sciences. 2025; 26(10):4912. https://doi.org/10.3390/ijms26104912
Chicago/Turabian StyleAlmutairi, Tahani Saad. 2025. "Cation and Spin Interactions in Cadmium Ferrite: A Quantum Mechanical Study" International Journal of Molecular Sciences 26, no. 10: 4912. https://doi.org/10.3390/ijms26104912
APA StyleAlmutairi, T. S. (2025). Cation and Spin Interactions in Cadmium Ferrite: A Quantum Mechanical Study. International Journal of Molecular Sciences, 26(10), 4912. https://doi.org/10.3390/ijms26104912