First-principles study of superconducting in LiFeAs: FM, AFM, and NM states via DFT and DFT+U techniques Open Access

Iron-based superconductors are a class of high-temperature superconducting materials characterized by layers of iron and pnictogen/chalcogen.¹ In 2006, the discovery of superconductivity in LaOFeP with a transition temperature (Tc) of approximately 6 K marked the emergence of iron-based superconductors (IBSCs).² This was followed by a groundbreaking development in 2008 when superconductivity was observed in fluorine-doped LaOFeAs [La(O, F)FeAs] with a significantly higher Tc of 26 K,³ capturing widespread interest in the scientific community.⁴ Since their discovery, IBSCs have been the focus of extensive research due to their unconventional pairing mechanisms, high upper critical fields, and promising applications in energy and quantum technologies.⁵ Their superconducting properties arise from unique electron pairing mechanisms, strong electronic correlations, and the intricate interplay between magnetism and superconductivity.⁶ Among IBSCs, the 1111-type compounds, such as LaFeAsO and SmFeAsO, played a pivotal role in the initial breakthroughs.^7,8 Researchers have strategically enhanced their superconducting performance by doping these materials with fluorine or introducing oxygen deficiencies, significantly improving their transition temperatures and overall superconducting properties.⁹ In rare-earth-based 1111-type superconductors, the transition temperature (Tc) can exceed 55 K, making them some of the highest-Tc IBSCs.^10,11 The 122-type family, including BaFe₂As₂ and SrFe₂As₂, exhibits superconductivity upon chemical doping or applied pressure, with Tc reaching up to 38 K.^12,13 In contrast, the 11-type compounds, such as FeSe and FeTe, possess simple two-dimensional FeCh (Ch=Se, Te) layer structures.¹⁴ FeSe, in particular, has a superconducting transition temperature of approximately 8 K under ambient conditions, but Tc can be significantly enhanced to 37 K through pressure or intercalation.¹⁵ Another important subclass, the 245-type superconductors, consists of compounds with the chemical formula A₂Fe₄Se₅, where A represents an alkali metal such as potassium (K), rubidium (Rb), or cesium (Cs). These materials exhibit superconductivity with Tc values around 32 K.¹⁶ Our study focuses on the unique 111-type superconductor LiFeAs, which comprises alternating layers of FeAs and alkali metals (Li, Na).¹⁷ Notably, LiFeAs exhibits superconductivity at ∼18 K without the need for chemical doping or external pressure, making it an ideal system for investigating intrinsic superconducting mechanisms.^18,19 This distinctive property has garnered significant interest, particularly in exploring its superconducting gap structure and the role of antiferromagnetic (AFM) spin fluctuations, which are believed to be crucial in the superconducting pairing mechanism.^20,21 The intrinsic superconductivity of LiFeAs, along with the absence of long-range magnetic order in its normal state,²² makes it a key system for exploring the intricate relationship between superconductivity and magnetism in IBScs.²³ Early studies have identified AFM spin fluctuations in LiFeAs, suggesting their essential role in mediating electron pairing and driving superconductivity.²⁴ The study of superconductivity in the ferromagnetic, antiferromagnetic, and non-magnetic phases of LiFeAs further highlights the intricate relationship between magnetism and electron pairing mechanisms in IBSCs.²⁵ In particular, AFM correlations are believed to enhance superconductivity by facilitating spin-mediated electron pairing,²⁶ making the AFM phase especially relevant for understanding the underlying pairing interactions in LiFeAs.²⁷ Both experimental and theoretical studies indicate that AFM spin fluctuations create a favorable environment for the emergence of superconductivity.²⁸ A widely accepted theory proposes that magnetism and superconductivity in IBSCs originate from the same fundamental interactions, with spin fluctuations serving as a key driving force for Cooper pair formation.²⁹ This perspective underscores the importance of LiFeAs as a model system for elucidating the unconventional pairing mechanisms in iron-based superconductors. In the non-magnetic and antiferromagnetic phases, the fluctuations enhance superconductivity by providing a pairing mechanism, while in the ferromagnetic phase, magnetism can suppress the superconducting state by breaking electron pairs.³⁰ Another theoretical approach to understanding LiFeAs involves the study of multi-band superconductivity, where multiple electron bands contribute uniquely to the superconducting state.³¹ The interplay between different magnetic phases and the band structure is crucial for determining the superconducting gap symmetry and the overall behavior of the material under various magnetic orders.³² A related study on Ag₂FeSiS₄, Li₂FeSnS₄, and Li₂FeGeS₄ revealed that density functional theory (DFT) tends to underestimate the bandgap and magnetic moments due to delocalization errors in Fe-d states. However, the DFT+U correction significantly improves the accuracy of electronic and magnetic property predictions by incorporating strong electron correlation effects.³³ In our study, we systematically investigate the structural, electronic, and magnetic properties of LiFeAs in ferromagnetic (FM), antiferromagnetic (AFM), and non-magnetic (NM) configurations using both DFT and DFT+U methods. This comparative analysis allows us to assess the impact of electron correlations on the superconducting and magnetic properties of LiFeAs, providing deeper insights into its unconventional superconductivity and the role of magnetism in its electronic behavior.

The calculations were performed using DFT and DFT+U as implemented in the Quantum ESPRESSO package.³⁴ The Projector Augmented-Wave (PAW) pseudopotentials were employed with the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA). The studied system, LiFeAs, crystallizes in the tetragonal structure with space group P4/mm (No. 129).³⁵ The structural optimization was carried out until all atomic forces converged to negligible values, ensuring a stable geometry. Once the equilibrium structure was obtained, band structure calculations were performed. The kinetic energy cutoff was set to ∼816 eV, and the charge density cutoff was fixed at 6530 eV. The Brillouin zone was sampled using an 8 × 8 × 6 Monkhorst–Pack k-point mesh for electronic structure calculations. A denser k-point grid of 24 × 24 × 18 was used for phonon dispersion calculations. The Methfessel–Paxton smearing method with a smearing width of 0.02 was employed to improve convergence. The calculated lattice constant obtained using DFT is 3.651 Å, while the DFT+U method yields 3.768 Å. The latter shows excellent agreement with the experimental and theoretical reported values of 3.771 and 3.769 Å,^36,37 respectively, highlighting the significance of electron correlation corrections in accurately capturing the structural properties of LiFeAs. The slight variations in lattice parameters are attributed to electron correlation effects, which are accounted for using the Hubbard U parameter. The visualization of the crystal structure was performed using XcrysDen, and the electronic band structure was plotted along high-symmetry directions in the Brillouin zone: Γ–X–M–Γ–Z–R–A–Z.³⁸ The electronic configurations of the constituent elements in LiFeAs are Li: 1s²2s¹, Fe: [Ar]3d⁶4s², and As:[Ar]3d¹⁰4s²4p³. The iron 3d orbitals play a crucial role in determining the on-site Coulomb interaction, necessitating the inclusion of the Hubbard U correction. In theoretical and computational studies, the Hubbard U parameter for iron (Fe) has been calculated to range from ∼2.25 to 6.0 eV, depending on the specific material and computational approach used.³⁹ The computed Hubbard parameter U for Fe in this study was ∼5.0 eV with the linear response method, which aligns with previous reports.^40,41 In addition, research on transition metal oxides utilized machine learning algorithms to determine optimal U parameters, demonstrating the effectiveness of Bayesian optimization in selecting appropriate u values tailored to the specific iron-containing material and the properties under investigation.⁴² The exchange–correlation functional in the DFT+U calculations employed the PBE-sol (Perdew–Burke–Ernzerhof), which is a well-established generalized gradient approximation (GGA) functional. PBE is widely used for materials with localized d-electrons, such as iron pnictides, and is known to provide a good balance between computational efficiency and accuracy for the structural and electronic properties of the system.⁴³ 

The optimized crystal structure of LiFeAs (Fig. 1) belongs to the tetragonal system, characterized by alternating layers of Li, Fe, and As. The FeAs layers play a crucial role in determining the superconducting and magnetic properties, while Li atoms serve as spacers, influencing the interlayer coupling.⁴⁴ In Fig. 1(a), the standard DFT approach, which often underestimates electron correlations, yields the following calculated bond lengths and bond angles: Fe–Fe: 2.6713 Å, As–Fe: 2.2865 Å, Li–Fe: 2.6875 Å, Fe–Fe–As: 124.783°, and Li–Fe–As: 64.345° values exhibit good agreement with previously studied values.⁴⁵ However, the DFT+U approximation, as shown in Fig. 1(b), overcorrects electronic interactions, leading to slightly different structural parameters. The bond lengths and bond angles obtained using DFT+U are Fe–Fe: 2.8708 Å, As–Fe: 2.8804 Å, Li–Fe: 2.9492 Å, Fe–Fe–As: 126.207°, and Li–Fe–As: 67.307°. The observed variations between DFT and DFT+U results highlight the impact of electron correlation corrections on structural properties,⁴⁶ emphasizing the importance of selecting an appropriate computational approach for accurately describing LiFeAs.

In this study, all the band structures range between −2 and 2 eV for non-magnetic and magnetic plots. The electronic band structure of LiFeAs, computed using DFT [Fig. 2(a)] and DFT+U [Fig. 2(b)], influences electron correlation effects on its superconducting and electronic properties. Standard DFT calculations tend to underestimate electronic correlations, leading to more delocalized Fe 3d states and an overestimated metallic nature, which agrees with the report.⁴⁷ This results in multiple band crossings near the EF, which do not fully capture the intricate electronic interactions essential for superconductivity. In contrast, the DFT+U approximation accounts for strong electron correlations, leading to increased localization of Fe 3d orbitals and significant modifications in the band structure. In addition, the DFT+U method provides a more refined description of the electronic structure, offering insights into the delicate balance between magnetism and superconductivity in LiFeAs. In the DFT approximation [Fig. 3(a], the PDOS shows that the Fe 3d states dominate near the EF, contributing significantly to the metallic nature of LiFeAs. The As 4p states are mainly located at lower energies, with noticeable hybridization between Fe 3d and As 4p orbitals. The density of states at the Fermi level, N(EF), is 3.928 states/eV in the DFT calculation, indicating a high electronic density that supports superconducting behavior. However, DFT alone tends to overdelocalize Fe 3d states, underestimating electron correlation effects, which are essential in Fe-based superconductors. When incorporating DFT+U Fig. 3(b), the on-site Coulomb interaction U modifies the electronic structure by localizing the Fe 3d states,⁴⁸ shifting their weight away from the Fermi level and reducing their direct contribution to conduction. This results in a lower N(EF) value of 3.031 states/eV, indicating a decrease in the electronic density at the Fermi level compared to standard DFT. The narrowing of the Fe 3d bandwidth enhances correlation effects and slightly modifies the hybridization between Fe 3d and As 4p orbitals. The DFT+U correction is often necessary for a more accurate representation of correlated d-electron materials, aligning better with experimental findings.⁴⁹ In the FM configuration, Fe atoms align their magnetic moments parallel, leading to significant spin splitting. The spin-up (I) bands [Fig. 4(a)] exhibit metallic behavior, with Fe-d states dominating near the EF.⁵⁰ Hole- and electron-like pockets at the Γ and M points indicate a strong itinerant character, which is essential for superconductivity.⁵¹ Conversely, the spin-down (II) bands [Fig. 4(b)] show a reduced density of states near EF, highlighting spin asymmetry due to exchange interactions. The presence of such strong spin polarization suggests that FM ordering influences charge carrier distribution and modifies the pairing interactions that govern superconductivity.⁵² In contrast, the AFM phase [Figs. 4(c) and 4(d)] exhibits a more symmetric electronic structure due to the antiparallel alignment of Fe magnetic moments. Unlike the FM phase, spin-up and spin-down bands are nearly identical, reflecting spin compensation in the AFM states. Notably, some bandgaps emerge along specific k-paths, indicating partial localization of electronic states. This suppression of spin splitting suggests a more balanced distribution of charge carriers, with AFM fluctuations playing a key role in the superconducting pairing mechanism. The FM phase enhances spin-polarized transport properties, making it relevant for spintronic applications,⁵³ whereas the AFM phase exhibits electronic structures more conducive to superconducting interactions. The spin-polarized band structure of LiFeAs calculation was performed using DFT+U approximation and plotted with the energy range of −2 to 2 eV for both spin-up and spin-down systems shown in Fig. 5. In the FM phase, the up-spin [Fig. 5(a)] and down-spin [Fig. 5(b)] bands show enhanced exchange splitting compared to DFT approximation Figs. 4(a) and 4(b) calculations. The up-spin bands exhibit a more localized character with flatter dispersion, indicating stronger Coulomb interactions.⁵⁴ The spin-down bands display a shift in energy levels, possibly leading to a reduced DOS at the EF. This enhanced spin polarization suggests that the inclusion of Hubbard U strengthens electron correlations, making the FM phase more distinct in terms of electronic transport and magnetization.⁵⁵ In the AFM phase, the spin-up Fig. 5(c) and spin-down Fig. 5(d) bands became symmetric. Compared to the FM case, the AFM bands show reduced metallicity, and in some cases, a small gap appears due to stronger electron localization. The Hubbard U correction further suppresses bandwidth and modifies band dispersions, which could influence superconductivity in LiFeAs. However, in DFT+U, the Fe-3d bands shift downward due to enhanced electron localization, leading to modified exchange splitting and reducing the DOS at the EF. The increased localization in DFT+U results in stronger magnetic exchange interactions, which can impact the material’s superconducting and spintronic applications. In the FM (I) configuration, the DFT approximation results, as shown in Fig. 6(a), reveal a high density of Fe-3d states near the Fermi level, with N(EF) = 0.7685 states/eV. This indicates a pronounced metallic character, accompanied by significant spin splitting between the spin-up and spin-down states. In contrast, for the AFM (II) configuration, the spin-resolved DOS in Fig. 6(b) exhibits near symmetry, with a substantially lower N(EF) of 0.1668 states/eV. This suggests a strong antiferromagnetic coupling, where opposing spin alignments effectively cancel the net magnetization.⁵⁶ However, in DFT+U, Figs. 6(c) and 6(d), the Fe-3d states shift to lower energies due to enhanced electron localization, reducing the N(EF) to 1.302 states/eV for FM and N(EF) to 0.3859 states/eV for AFM configurations, modifying spin polarization. This redistribution of states influences magnetic exchange interactions and the stability of ferromagnetism, potentially affecting superconducting properties.⁵⁷ In the DFT approximation, Figs. 7(a) and 7(b), results, the Fe-3d states are dominant near the Fermi level, and the up-spin and down-spin states are nearly symmetric with AFM order. The Fe-3d states dominate the electronic structure near the Fermi level, exhibiting a high density of states N(EF) and a pronounced peak around 13 states/eV. Meanwhile, the strong hybridization between Fe-3d and As-p orbitals persists, reinforcing the material’s metallic character and contributing to its electronic stability.⁵⁸ In the DFT+U approximation, Figs. 7(c) and 7(d), the Hubbard U correction introduces stronger Fe-3d electron localization, shifting the Fe-3d states to lower energies and reducing N(EF) around 6.5 states/eV. This shift weakens Fe–As hybridization, altering the exchange interactions and potentially affecting the magnetic stability and superconducting properties agreed upon in the report.⁵⁹ In addition, in Fig. 7(d), Fe-3d states exhibit stronger localization, shifting further below the Fermi level. Table I shows that the structural and magnetic properties of LiFeAs were analyzed using DFT and DFT+U approximations. The lattice parameters, unit volume, total energy, Fermi energy, and magnetic moments for NM, FM, and AFM phases were calculated. The DFT+U approximation increases lattice parameters, total energy, and unit cell volume while decreasing EF compared to the DFT approximation. This effect arises due to the enhanced treatment of electron correlations in localized d-orbitals, leading to stronger Coulomb interactions and reduced electron delocalization.⁶⁰ The increase in lattice parameters and volume suggests a weakening of bonding interactions, while the lower EF indicates a shift in electronic states, potentially affecting conductivity, magnetic properties, and superconducting behavior. In the FM configurations, the lattice parameter increases by 0.1125 Å, but the unit volume shrinks by 0.9232 a.u.³ compared to the NM state. Similarly, in the AFM phase, the lattice parameter increases by 0.1458 Å, and the volume expands by 12.7042 a.u.³ compared to the NM state. The total energy in DFT+U is higher, with the FM configuration about a 0.06% increase and the AFM configuration a 0.05% increase compared to the DFT result, indicating stronger electronic interactions. The Fermi energy decreased in DFT+U approximation by FM coupling 1.7253 eV and by AFM 1.659 eV, suggesting a shift in electronic structure due to correlation effects.

Understanding the lattice dynamics of LiFeAs is essential for unraveling the nature of its unconventional superconductivity.⁶⁹ The phonon spectrum provides critical insights into the interactions between lattice vibrations and electronic states, influencing superconducting behavior. Notably, the weak electron–phonon coupling observed in LiFeAs suggests that conventional phonon-mediated pairing alone is insufficient to explain its superconducting properties. Instead, alternative mechanisms, such as spin fluctuations or strong electronic correlations, will likely play a dominant role in the pairing interaction. The interplay between lattice vibrations and electronic degrees of freedom could still contribute indirectly to superconductivity by modifying the electronic structure or enhancing certain interactions.⁷⁰ Calculations were performed to evaluate the geometrical stability of LiFeAs in the DFT approximation. The absence of imaginary phonon frequencies at all k-points confirms that the structures are dynamically stable, with no indications of structural instability. This result ensures the robustness of the geometries studied in subsequent analyses.

Phonon dispersion Fig. 8(a) of LiFeAs reveals distinct features corresponding to acoustic and optical phonon modes. The acoustic phonons, including Transverse Acoustic (TA) and Longitudinal Acoustic (LA) branches, are found at lower energies and exhibit linear dispersion near the Γ-point, indicative of lattice vibrations. Acoustic phonons generally exhibit lower frequencies and are associated with lattice vibrations that propagate through the crystal. On the other hand, the optical phonons, which occur at higher frequencies, are divided into Longitudinal Optical (LO) and Transverse Optical (TO) branches.⁷¹ The LO–TO splitting can result from long-range Coulomb interactions, which are weakly ionic in LiFeAs. The dispersion of optical phonons is more pronounced due to the different atomic masses and force constants of the constituent elements.⁷² Phonon density of states Fig. 8(b) DOS provides insights into the distribution of phonon states available at different frequencies. A pronounced peak in the phonon DOS at certain frequencies indicates regions of strong coupling between phonons and electrons. In the LiFeAs system, the absence of imaginary frequencies in the phonon dispersion suggests dynamical stability, and the nature of the phonon modes could potentially enhance superconductivity by facilitating electron pairing.

In this study, we investigated the structural, electronic, and magnetic properties of LiFeAs in FM, AFM, and NM states using DFT and DFT+U techniques. The calculated lattice parameters of 3.651 Å (DFT) and 3.768 Å (DFT+U) indicate that the DFT+U approximation provides a significantly improved agreement with the experimental value of 3.771 Å. This suggests that the inclusion of the Hubbard U correction more accurately captures electron correlations, leading to a better representation of the material’s structural properties. The electronic band structures and DOS of LiFeAs show a metallic nature, with significant contributions from Fe d and As p states near the Fermi level. The bond lengths and angles increased with the inclusion of Hubbard parameter U, reflecting enhanced electron correlation effects. Electronic structure analysis reveals that DFT predicts a more delocalized band structure, whereas DFT+U induces stronger localization. The Fe-3d states shift to lower energies in DFT+U, reducing the density of states at the Fermi level, N(EF), to 1.302 states/eV in the FM phase and 0.3859 states/eV in the AFM phase. This reduction in N(EF) influences spin polarization and electronic interactions. In addition, DFT+U results in an increase in total energy, lattice parameter, and unit cell volume while decreasing the Fermi energy compared to standard DFT, impacting magnetic ordering and stability. The magnetic phase transition analysis indicates a significant shift from AFM coupling in DFT [with Tc^(MFA) = 38.7 K] to FM coupling in DFT+U [Tc^(MFA) = 464.2 K], demonstrating the profound effect of electron localization on magnetic interactions. The DFT+U approach provides a more accurate prediction of magnetic moments (3.13 μ_B per Fe atom), aligning closer to experimental observations (3.42 μ_B). This showcases the method’s strength in capturing magnetic properties. The non-magnetic configuration is most favorable for superconductivity, which is essential for Cooper pairing. In contrast, FM and AFM states suppress superconductivity due to spin polarization and band-splitting effects.

Future studies should explore the impact of dynamic electron correlations and spin–orbit coupling on superconductivity in LiFeAs under transition metal doping. In addition, pressure-dependent studies may provide deeper insight into the interplay between structural and superconducting properties, enhancing the understanding of Fe-based superconductors for practical applications.

We gratefully acknowledge Adama Science and Technology University (ASTU) and a travel grant from ASES-MANET(2023).

The authors have no conflicts to disclose.

Manza Zityab Kasiab: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – original draft (equal); Writing – review & editing (equal). Kumneger Tadele: Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Mesfin Asfaw Afrassa: Conceptualization (equal); Investigation (equal); Methodology (equal); Software (equal); Supervision (equal); Writing – review & editing (equal). Omololu Akin-Ojo: Investigation (equal); Methodology (equal); Software (equal); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.