Journal of Physics and Chemistry of Solids

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Journal of Physics and Chemistry of Solids 145 (2020) 109541

Available online 11 May 2020

Tuning tetrahedral structure and electronic properties of FeSe films through strain engineering

Xin Wang

^a

, Hua Li

^a

, Yanyan Huang

^a

, Zhengchao Dong

^a^,^b^,^*

, Chonggui Zhong

^a^,^c^,^**

, Junming Liu

^b

aSchool of Sciences, Nantong University, Nantong, 226019, China

bLaboratory of Solid State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

cSchool of Physical Science and Technology, Soochow University, Suzhou, 215006, China

A R T I C L E I N F O Keywords:

Strain Magnetism Electronic structures Superconductivity

A B S T R A C T

We demonstrate that the magnetic, tetrahedral structure, and electronic properties of FeSe films are closely related to the in-plane biaxial strain. Our calculations show that the magnetic ground state of FeSe films maintain their striped antiferromagnetic order even under biaxial compressive or tensile strain. Upon increasing the compressive strain, the structure of the FeSe4 tetrahedron is distorted along the c-axis and deviates greatly from the ideal tetrahedron structure due to the variation in the bond angle and bond length. These variations lead to the increased hybridization of the Fe-3d and Se-4p states, greater nesting between the electron and hole bands, and more electronic states near the Fermi level. The applied compressive strain can suppress the antiferromagnetism of the system and results in an enhancement of the superconductivity of FeSe films. Conversely, the band structure and electronic properties of the system under tensile strain show opposite changes and tend to suppress the superconductivity of FeSe films. These results indicate that tuning the strain may be an effective way to control the superconducting properties of FeSe films.

1. Introduction

Since the discovery of superconducting LaFeAsO1 xFx materials, various iron-based superconductors (IBS) have been extensively studied.

A remarkable feature of IBS is that their superconductivity (SC) originates from the suppression of the antiferromagnetic state and the structural phase transition of the parent material, which can be controlled by doping or applying external pressure [1,2].

Among the IBS that have been reported to date, the FeSe “11” family has been reported to have the simplest crystal structure and composition [3]. However, differing from other known IBS, this family only contains a coplanar tetrahedral unit stacked along the c-axis without any charge reservoir layer, and high pressure can result in a significant improve- ment in the SC by increasing the short-range spin fluctuations or inducing structure transitions in the FeSe system [4–7]. For example, the superconducting transition temperature (Tc) of bulk FeSe can be pro- moted from 8.5 to 37 K under a pressure of 1.48 GPa [7]. When the applied external pressure reaches a certain threshold, the system will

undergo a phase transition from a tetragonal to orthorhombic structure, leading to a further increase in the Tc [5].

Likewise, the Tc of FeSe also strongly depends on chemical doping.

Investigations have shown that although bulk FeSe exhibits SC at 8 K, the Tc will increase to 12 K when smaller S atoms are doped within its structure [8], while partially replacing Se with Te in this thin film can increase the Tc to 23 K [9]. Moreover, recent studies have also shown that the electron and hole bands at the Fermi surface decrease toward band inversion for FeTe₁ _xSe_xmonolayer grown on SrTiO₃, increasing the Tc up to 65 K [10].

Taking all these findings into account, it can be said that the variation in the FeSe₄tetrahedron caused by different dopants and pressure may affect the SC of the system by tuning the structures of the electronic and energy band. Interestingly, high-resolution neutron powder diffraction studies have also shown that the distorted FeSe4 tetrahedron tends to enhance the Tc of bulk FeSe indicating that the electronic band structure with a distorted tetrahedron plays an important role in increasing the SC [11,12]. Since the doping and high pressure can

* Corresponding author. School of Sciences, Nantong University, Nantong, 226019, China.

** Corresponding author. School of Sciences, Nantong University, Nantong, 226019, China.

E-mail addresses: [email protected] (Z. Dong), [email protected] (C. Zhong).

Contents lists available at ScienceDirect

Journal of Physics and Chemistry of Solids

journal homepage: http://www.elsevier.com/locate/jpcs

https://doi.org/10.1016/j.jpcs.2020.109541

Received 18 October 2019; Received in revised form 2 May 2020; Accepted 4 May 2020

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improve the SC by tuning the structure of the FeSe4 tetrahedron, applied strain should also be able to promote the SC in a similar manner.

In this work, we have explored the effect of strain on the magnetism, tetrahedral structure, and electronic properties of FeSe using first- principles calculations and investigated the relevance between the strain-induced variation in the FeSe4 tetrahedron and electronic structure. We have shown that although different compressive or tensile strains are applied, the magnetic ground state retains a striped antiferromagnetic (SAFM) order. The electronic density of states (DOS) near the Fermi energy (EF) increases due to the enlargement of hole pockets at the Fermi surface and the antiferromagnetism of the FeSe films is weakened under compressive strain, indicating it may tend to improve the SC. However, a completely opposite effect was produced under tensile strain, which tended to annihilate the SC of FeSe films.

2. Computational methods

First-principles calculations based on density functional theory (DFT) were performed using the Vienna ab initio simulation package (VASP) [13], in which the projector augmented wave method was used.

The electronic exchange and correlation functions were considered by the generalized gradient approximation using the Perdew-Burke-Ernzerhof (PBE) method [14]. Herein, we considered that

the FeSe films are relatively thicker rather than just a few atomic layers and the periodic structure is also along the out-of-plane direction, as found in the FeSe bulk material. Then, in view of the lattice periodic expansion at the different magnetic structures, we adopted a ffiffiffi

p2 a� ffiffiffi

p2

b�2c supercell to calculate the FeSe band structure and electronic properties, as shown in Fig. 1(a). To ensure convergence, the cut-off energy for the plane waves was set at 500 eV and all the atoms were allowed to relax until the energy difference was <10 ⁶eV Γ centered 11�11�7k points mesh was used for the first Brillouin zone for all the magnetic states calculations, including non-magnetic (NM), ferromag- netic (FM), SAFM, and checkerboard antiferromagnetic (CAFM) order (Fig. 2).

In-plane biaxial lattice strain in the films can be achieved by con- trolling the lattice mismatch within the substrate. Herein, we assumed that the FeSe film grows epitaxially on different tetragonal substrates and the two in-plane lattice constants were kept equal (a_FeSe¼b_FeSe) to match the strain observed experimentally induced by the substrate.

Then, for every given lattice constant (aFeSe), the out-of-plane lattice constant (c_FeSe) and the position of the internal atoms were optimized during the calculation of the different magnetic structures. Subse- quently, we computed the band structure and electronic properties of FeSe based on the fully optimized structure.

3. Results and discussion

3.1. Magnetic ground state under strain

We first optimized the lattice parameters of unstrained non-magnetic FeSe film. The obtained lattice parameters were a ¼b ¼3.686 Å, which are very close to those of monolayer FeSe [15]. To explore the effect of strain on the magnetic and electronic properties of FeSe films, we applied 1–6% compressive and tensile strains to all four magnetic states.

The energy variation of the super cell for the four magnetic states under compressive and tensile strain is presented in Fig. 3. It is clear that the energy of the SAFM order remains the lowest at all the applied strains studied, indicating that neither tensile nor compressive strain can cause any magnetic phase transition in this system and its ground state was always SAFM order. This is consistent with the magnetic ground state determined in previously reported inelastic neutron-scattering studies [16] and further proves the reliability of our calculations.

Furthermore, upon increasing the compressive strain, the energy difference between SAFM and CAFM becomes smaller and the competition becomes stronger in the FeSe films. These variations tend to annihilate its spin density wave [17] and favor the generation of a superconducting state in the system.

Fig. 1. Crystal structure of FeSe: (a) ffiffiffi p2

� ffiffiffi

p2

� ffiffiffi

p2

supercell and (b) FeSe4

tetrahedron. The purple and green balls represent the Fe and Se atoms, respectively.

Fig. 2.Spin order of the Fe ion in FeSe: (a) FM order, (b) SAFM order, and (c) CAFM order. The arrows represent the direction of the atomic spins.

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3.2. Variation in the FeSe4 tetrahedron structure and superconductivity Since the Tc in IBS is very sensitive to the distortion in the FeSe4

tetrahedron in the superconducting layer [11,12], we investigated the strain-induced variation in the FeSe4 tetrahedron structures and

thickness (L) (Fig. 1(b)).

In terms of the symmetry of the FeSe film structure, the distance between the Fe atom at the center and the four Se near it is always identical in the FeSe4 tetrahedron, and thereby we have only showed one of the Fe-Se bond lengths in Fig. 4. While for the bond length and bond angle of Se-Se and Se-Fe-Se, we chose the plane of the Fe atom in the center of the FeSe4 tetrahedron as a reference. Because all of the Se- Se bond lengths above (and below) this plane are equivalent, and the same is true for the Se-Fe-Se bond angles above (and below) this plane, as well as the bond lengths and bond angles of those across the plane, we chose the Se1-Se2, Se1-Se3 bond and the Se1-Fe-Se2 and Se1-Fe-Se3 bond angles as representative parameters to investigate the distortions in the FeSe4 tetrahedron (see Fig. 1(b)).

In the following, we investigated the strain-induced changes in the Se1-Fe-Se2 (and Se1-Fe-Se3) bond angle, Se-Fe (and Se-Se) bond length, and the thickness of the FeSe4 tetrahedron (Fig. 1(b)). It was observed that increasing the compression strain significantly increases the Se1-Fe- Se3 bond angle, the Se1-Fe-Se2 angle continued to decrease and the Fe–Se bond length is drastically reduced, and at the same time, the in- plane Se1-Se2 bonds also become shorter, while the interlayer Se1-Se3 bonds become longer when compared with the unstrained FeSe films, as shown in Fig. 4(a–c). However, we found no indication of FeSe4 tetrahedron tilting along the z-axis. These changes indicate that the FeSe4

tetrahedron becomes elongated under compressive strain and deviates from the regular tetrahedron structure. According to the results obtained in the pressure and doping experiments, these variations in the FeSe4

tetrahedron are helpful to increase the Tc of FeSe films [18–21].

The L of the FeSe4 tetrahedron was also influenced at different levels by strain, as shown in Fig. 4(b). It is found that the L of the FeSe Fig. 3. The energy per supercell of the four possible magnetic states of FeSe

under different in-plane biaxial strains. The negative and positive values denote compressive and tensile strains, respectively.

Fig. 4.The (a) Se1-Fe-Se2 and Se1-Fe-Se3 bond angles, (b) Se-Fe bond length and thickness (L) of the FeSe4 tetrahedron, (c) Se1-Se2 and Se1-Se2 bond lengths, and (d) magnetic moment of individual Fe ions in FeSe as a function of the strain (including compressive and tensile strains).

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superconductor increases drastically upon increasing the compressive strain, but only decreases weakly upon increasing the tensile strain.

When a compression strain of 5% was applied, the L increases by

>10%, while when a tensile strain of the same magnitude was applied to the FeSe film, the L decreases by only 1.5%. It has been reported that the L in the FeSe IBS is closely linked to the Tc, which increases with an increase in L [6,12]. Thus, it can be concluded that the extension and distortion of the FeSe₄tetrahedron was accompanied with enhanced SC [6,19,22,23]. That is, we have deduced that the application of compressive strain should be favorable toward improving the SC of FeSe films.

In contrast, upon increasing the biaxial tensile strain, the Se1-Fe-Se3 bond angle decreases, the Se1-Fe-Se2 angle becomes significantly larger than the ideal tetrahedral angle, and both the Fe-Se and Se1-Se2 bond lengths increase, while the Se1-Se3 bond length slowly decreases, as shown in Fig. 4. Unlike the FeSe4 tetrahedron under biaxial compressive strain, the FeSe4 tetrahedron under biaxial tensile strain deforms along the direction away from the c-axis, which makes the tetrahedron flatter when compared to the unstrained FeSe system.

In addition, we also found that the localized magnetic moment of Fe decreases gradually upon increasing the compression, as shown in Fig. 4

(d). The suppression of the AFM implies that the SC can be enhanced [4, 24]. From the variations in the bonds, the length of the Fe-Se bond decreases and the Fe-3d and Se-4p states hybridize more strongly due to compression strain, making it easier for the electrons to pair [25,26].

3.3. Band structure and electronic properties

The changes in the structural parameters of FeSe under strain also cause concomitant variations in its electronic properties. The band structures of FeSe in the absence of strain and under different biaxial strains are shown in Fig. 5. According to the energy band calculations, we also obtained diagrams of the hole-electron Fermi pockets of the SAFM order in the kz¼0 plane (Fig. 6).

In the unstrained state (Fig. 5(a)), we found that the top of the valence band was not completely occupied and three hole Fermi pockets appear at the Γ point. The three bands at the Γ point are dominated by the dyz, dxz, and dxy states of Fe. The hole bands exhibit strong scattering properties along the Γ-X and M-Γ directions, indicating that the FeSe superconductor is a strongly anisotropic two-dimensional layered system [27] and the strong magnetic exchange coupling only exists within the [FeSe] layer. Furthermore, corresponding to the calculated DOS Fig. 5. The band structures of the FeSe thin films under different strains: (a) no strain, (b) 2%, (c) 4%, and (d) 6% compressive strain; (e) þ2%, (f) þ4%, and (g) þ6% tensile strain.

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shown in Fig. 7, the occupied Fe 3d states near the Fermi energy reveal that the strong couplings originate from the Fe ions in the layer [16].

Thus, we can infer that the interaction between the layers is very weak and the SC in this system originates from direct Fe-Fe interactions in the same layer. Moreover, two large electron-Fermi pockets cross the Fermi level around the M and A points, which is in agreement with the experimental observations from angle-resolved photoemission spec- troscopy (ARPES) and other theoretical calculations for FeSe materials [28,29].

When compared with the band structure of unstrained FeSe, the hole bands gradually shift upward along the Γ-Z line upon increasing the biaxial compressive strain, as shown in Fig. 5(b–d). In particular, when the FeSe film was subjected to 6% compressive strain, the sizes of the small hole pockets are significantly increased near the Γ and Z points, and the openings of the electron pockets at the M points become slightly enlarged near the Fermi level when compared with those of unstrained FeSe. These variations result in a greater overlap and nesting between the electron and hole pockets in the compressed FeSe films, as shown in Fig. 6(b–d). The enlarged electron and hole Fermi pockets promote electron scattering at the Fermi surface and may enhance the SC in the FeSe system [30].

On the other hand, it has been demonstrated that the superconducting properties of the FeSe crystal can be improved using biaxial

compressive strain. For example, the Tc of FeSe can be increased 30–40%

with underlying scotch tape used as an in-situ strain generator [31] and ARPES experiments also showed that the Tc of the FeSe system can be enhanced by 40% under compressive strain [32]. Similarly, high-resolution synchrotron powder X-ray diffraction (XRD) and other measurements under high pressure indicate that compressive strain can lead to a significant increase in the Tc of FeSe films [33,34]. Moreover, it is known that the larger hole bands and enhanced DOS near the EF of FeTexSe1 x can strongly promote its SC and lead to a higher Tc [1,10, 27].

Under biaxial tensile strain, the most prominent change is the downward shift of the hole bands near the Fermi level. According to Fig. 5(e and f), one hole pocket near the Γ point sinks below the Fermi level, resulting in the disappearance of a hole pocket at the center of the Brillouin zone. Finally, only a small hole pocket was observed when the tensile strain was increased to 6%, as shown in Fig. 6(g). In addition, only one electronic pocket gradually deepens at the M point, as shown in Fig. 5(e–g). Thus, the electronic DOS near the Fermi level decreases. As shown in the experimental data, no SC was observed in the FeSe films subjected to tensile strain until the temperature decreased to 5 K [35].

These results further support the deduction that compressive strain is favorable for achieving SC in FeSe upon increasing the electronic-hole Fermi pocket nesting, while tensile strain has an opposite effect.

Fig. 6.Diagrams showing the hole and electron Fermi pockets of the FeSe films under (a) no strain, (b) 2%, (c) 4%, and (d) 6% compressive strain; (e) þ2%, (f) þ4%, and (g) þ6% tensile strain.

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The calculated DOS obtained for FeSe films under different biaxial strains are shown in Fig. 7. Regardless of whether the system is under strain or not, there is always a dominant contribution from Fe-3d states at the Fermi surface. Moreover, there is a strong hybridization between the Fe-3d and Se-4p electrons near E_F, which implies that the exchange interaction is not only due to the direct d-d coupling of the nearest Fe atoms, but can be motivated by the p-d orbital hybridization of Fe and Se atoms [25]. In addition, other experiments have suggested that the increase in Tc and the enhancement in the superconductivity originate from the compressed lattice, which further proves the reliability of our conclusions [36–38].

When compared with the unstrained or tensile-strained FeSe films, the electronic DOS near the EF becomes greater under compressive strain, reaching a maximum when the FeSe film is subjected to 6%

compressive strain (Fig. 7). This indicates that FeSe becomes more metallic under biaxial compressive strain. Moreover, because the Fe-3d electrons that yield large magnetic moments become delocalized, the

DOS increases and the local magnetic moment reduces, which increases the tendency of the system to exhibit SC [4,39]. These results are also consistent with previous discussions, which have shown that the Te-doped tetragonal FeSe enhances the SC upon increasing the DOS near the E_F[1].

4. Conclusion

We have studied the effect of strain on FeSe using first-principles calculations based on DFT. Our results reveal that the FeSe4 tetrahedron is distorted under biaxial compressive strain. The larger thickness of the FeSe4 tetrahedron leads to the stronger hybridization of the Fe-3d and Se-4p states, as well as a greater overlap between the electron and hole bands. We also found that as the compressive strain increases, the localized magnetic moments of the Fe ions is reduced and the hole pockets expand near the Fermi surface, leading to the enhancement in the electronic DOS near the EF. These trends indicate that compressive strain can suppress the antiferromagnetism and tends to promote the superconductivity of FeSe film by facilitating the spin fluctuations in the system. In particular, the effects of biaxial tensile strain are opposite; it tends to suppress the superconducting phase.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

CRediT authorship contribution statement

Xin Wang: Writing - original draft. Hua Li: Investigation. Yanyan Huang: Methodology, Formal analysis. Zhengchao Dong: Conceptu- alization, Project administration. Chonggui Zhong: Writing - review &

editing. Junming Liu: Supervision.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11604163 and No.11604164), the Natural Science Foundation of the Jiangsu Province of China (Grant No. BK2012655), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX18_2412), and the Modern Education Tech- nology Center of NTU.

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