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Whether FeTe is superconductor: Insights from first-principles calculations
Physica C 492 (2013) 152–157
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Whether FeTe is superconductor: Insights from first-principles calculations Jian Li, GuiQin Huang ⇑, XingFeng Zhu Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China
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Article history: Received 26 May 2013 Received in revised form 9 June 2013 Accepted 19 June 2013 Available online 28 June 2013 Keywords: A. Iron-based superconductor B. Lattice dynamics C. Electron–phonon interaction D. First-principles
a b s t r a c t We present a first-principles pseudopotential study on the electronic structure, phonon structure and the electron–phonon interaction of stoichiometric FeTe in both the nonmagnetic and double stripe antiferromagnetic phases. Our electronic structure calculations show that the nesting effect of Fermi surface is not present in stoichiometric FeTe after considering the magnetic interaction. Comparing the phonon behavior in the double stripe antiferromagnetic phase with that in the nonmagnetic phase, we find that the spin–lattice interaction can lead to the phonon softening and increase electron–phonon coupling constant k by about 33%, which is similar to other iron-based superconductors in the single stripe antiferromagnetic phase. We suggest that the phonon softening may have no clear contact with the specific magnetic order in the ground state. Finally, we make some discussion about whether FeTe can be superconductor combining our first-principles calculations. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The discovery of the LaFeAs(O,F) superconductor with Tc 26 K [1] has received tremendous attention. Not long after this discovery was made, the superconductivity was found in many iron pnictides [2–6]. The parent compounds of the iron pnictides-based superconductors display ubiquitous magnetic and structural phase transitions, for which the ground state is in a single stripe antiferromagnetic (SS-AFM) phase [7,8] below a tetragonal–orthorhombic structural transition temperature. The superconducting mechanism in Fe-based compounds is still under debate. It is generally believed that the superconductivity in Fe-based compounds is associated with antiferromagnetic fluctuations. However, many studies have shown that the role of phonons in the Cooper pairing cannot be entirely discarded. Many first-principles calculations [9–13] have shown that the spin–lattice interaction results in phonon softening and may lead to a large increase in the electron–phonon (EP) coupling. The observation of a large Fe isotope effect [14] implied that the EP interaction should play an important role in the superconducting mechanism. Besides iron pnictides family, the research of iron-based superconductors has been extended to iron chalcogenides family. The superconducting transition temperature Tc for iron chalcogenides has increased from an initial 8 K [15] to 15 K [16–18] with a suitable amount of Te substitution, and to 37 K [19] under high pressure. Iron chalcogenides do not have charge reservoir layers, ⇑ Corresponding author. Tel.: +86 025 85891951 8406. E-mail address: [email protected] (G. Huang). 0921-4534/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2013.06.010
while consist of only stacked layers of Fe-X (X = S, Se and Te) along the c-axis. Due to the simple structure and composition, which is the simplest among Fe-based superconductors, Fe chalcogenide superconductors are good candidates for applications. For iron chalcogenides Fe1+yTexSe1x, the experiments [20,21] showed that it is stable for values of x between 0 and 1. The minimum value of y is approximately 0.06 when x = 1, but for smaller values of x (increasing Se content), the value of y approaches 0. The extra Fe(y) is considered to reside in the interstitial sites. Neutronscattering studies on static magnetic orders and spin excitations in the system Fe1+ySexTe1x with different Fe compositions suggest that excess Fe appears to be important for stabilizing the magnetic order that competes with superconductivity [22]. Liu et al. [23] found that the excess Fe at interstitial sites of the (Te and Se) layers not only suppresses superconductivity but also results in a weakly localized electronic state. Among many iron chalcogenides, FeTe has shown properties quite different from some of the other iron chalcogenides and iron pnictides. FeTe is not superconducting except in the special case of the tensile-stressed FeTe thin film [24]. Neutron powder diffraction analysis confirmed that Fe1+yTe undergo a tetragonal to monoclinic phase transition at 67 K [25,26]. While other iron chalcogenides and iron pnictides undergo a tetragonal to orthorhombic phase transition at low temperature [7,8,27]. Furthermore, FeTe compound [22,25,28–30] has double stripe antiferromagnetic (DSAFM) order with (0.5, 0) ordering vector, while other iron-based superconducting materials exhibit SS-AFM order with the (0.5, 0.5) ordering vector. The calculations by Shi et al. [31] showed that the double stripe order changes to the single stripe order for
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FeTe1-xSex when x > 0.18. The pattern of two magnetic orders is shown in Fig. 1. For DS-AFM magnetic structure (Fig. 1(a)), it consists of two spin sublattices. Within each sublattice, the spins have a ferromagnetic alignment along y-axis and antiferromagnetic alignment along x-axis. The single stripe order shown in Fig. 1(b) 1 0 direction, and antiferrohas a ferromagnetic alignment along ½1 magnetic alignment along [1 1 0] direction. For iron chalcogenides, we have done a first-principles study on the phonon structure and the EP interaction for superconducting FeTe0.5Se0.5 compound [13]. The calculations showed that the softening of phonon originated from spin–phonon coupling may lead to a large increase in EP coupling. FeTe has same crystal structure as FeSe in the room temperature, but it is not superconducting and has different magnetic ground state as discussed above. In order to better understand the superconductivity in Fe-based superconductors and why FeTe does not show superconductivity, further study about FeTe compound is desired. There have been substantial works on the electronic structure for this material [30,32,33]. Recently, researchers turn their attention to the phonon properties of FeTe. Several groups [34–36] have reported phonon Raman-scattering measurements as well as the results with first-principles calculations for FeTe. However, their calculations were limited to the phonons at the zone-center. Here, in this paper, we study the electronic structure, phonon structure and EP interaction for FeTe in both nonmagnetic (NM) and DS-AFM phases. Comparing the calculated results in the DS-AFM phase with those in the NM phase, it is found that the spin–phonon coupling can also lead to the phonon softening and increase EP coupling strength, which is similar to superconducting FeTe0.5Se0.5 compound and other iron-pnictides superconductors in the SS-AFM phase. The possible appearance of superconductivity in stoichiometric FeTe is discussed. 2. Computational method The calculations have been performed in a plane-wave pseudopotential representation through the PWSCF program of the Quantum-ESPRESSO distribution [37]. The ultrasoft pseudopotentials are used to model the electron–ion interactions, and the generalized gradient approximation (GGA) of Perdew–Burke– Ernzerhof [38] for exchange–correlation potential is adopted. We employ a cutoff of 45Ry and 450Ry for wave function and charge densities, respectively. For the NM and DS-AFM phases, the a a c unit cell and 2a b c supercell are used, respectively. For the a a c unit cell, the Brillouin zone integrations of the electronic structure calculations are performed with (8, 8, 6) grid by using the first-order Hermite–Gaussian smearing
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technique. Within the framework of the linear response theory, the dynamical matrixes and the electron–phonon interaction coefficients are calculated for (4, 4, 3) grid of special q points in the irreducible Brillouin zone. The dense (16, 16, 12) grid is used in the Brillouin zone integrations in order to produce the accurate EP interaction matrix. For the calculations of DS-AFM phase with 2a b c supercell, k points equivalent to those in the calculations for the NM phase have been used. 3. Results and discussion 3.1. Ground configuration The experimental measurements [20,21] show that Fe1+yTe contain excess Fe with a narrow range of variation in y which are partially occupied interstitial sites. However, the effect of the excess Fe is not considered in our first-principles calculations. The lattice parameters obtained experimentally [26] are: a = 3.8219 Å, c = 6.2851 Å for tetragonal NM phase and a = 3.8312 Å, b = 3.7830 Å, c = 6.2643 Å, b = 89.17° for monoclinic DS-AFM phase, respectively. In our calculations, the experimental lattice parameters are employed for both the NM and DS-AFM phases. The internal coordinates are then relaxed. The obtained internal coordinates (ZTe) are 0.2546 and 0.2821 for NM phase and DS-AFM phase, respectively. The latter is very close to the experimental value (ZTe = 0.2800) [26], which implies the presence of long-range magnetic order in FeTe compound. The optimized Chalcogen height above Fe layers for FeTe is bigger than that for FeTe0.5Se0.5 in our previous calculations [13]. In other words, substitution of Se at the Te site decreases the average value of Chalcogen height, which is consistent with the calculations by Moon et al. [29] and Kumar et al. [33]. The height of anion atoms above Fe layers is of crucial importance for Fe-based superconductors. Many authors have discussed the dependence of superconductivity in terms of height of anion atoms [29,33,39,40]. Next, we compare the total energy for the NM phase, DS-AFM phase and SS-AFM phase, and determine which one is the ground state of FeTe. When the energy of the NM phase is set to zero, we find that the energies of the DS-AFM phase and SS-AFM phase are 746.3 meV/f.u. and 669.7 meV/f.u., respectively. Our calculations by GGA find that the ground state of FeTe is in the DSAFM phase, which is in agreement with the experiments [22,25]. The calculations by Kumar et al. [33] and Ding et al. [41] also suggested that the magnetic ground state in FeTe is strongly dependent on exchange–correlation potential employed. Local density approximation (LDA) yields a SS-AFM state while GGA favors a
Fig. 1. Schematic in-plane AFM spin arrangements in (a) a double stripe structure and (b) a single stripe structure.
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DS-AFM state. For the DS-AFM phase, the obtained magnetic moment per Fe atom by the GGA calculation in this paper is about 2.77lB, which is bigger than those calculated by Ma et al. [30] (2.50lB) and Gnezdilov et al. [36] (2.52lB) using the LDA. 3.2. Electronic structure The calculated electronic structures for FeTe compound are plotted in Fig. 2. The Fermi energy is set at zero. Fig. 2(a) and (b) are the calculated electronic band structure and electronic density of states (DOS) for FeTe in the NM phase. Fig. 2(c) and (d) are the corresponding plots for FeTe in the DS-AFM phase. For the NM phase, from Fig. 2(a) we can see that both the conduction bands and valence bands cross the Fermi level. The Fermi surface consists of electron-type sections at the zone corner and hole-type sections around the zone center. But after considering the magnetic interaction, the striking change of the band structure (see Fig. 2c) is that the hole pockets around C point sink below the Fermi level and then the possible nesting effect of Fermi surface (FS) is not present. Comparing Fig. 2(b) with Fig. 2(d), it is found that there is large difference in the DOS curves between the NM and DS-AFM phases. For the NM phase, the calculated DOS near the Fermi level are mainly from the contribution of Fe d states. While for the DS-AFM phase, the magnetic coupling leads to large hybridization between the Fe d states and the Te p states from about 2 eV to Fermi level. 3.3. Phonon structure We use the linear-response technique to study the lattice dynamics of FeTe in both NM and DS-AFM phases. For the tetragonal NM phase, its space group is P4/nmm. According to the group theory classification, there are four Raman-active modes [A1g(Te) + B1g(Fe) + 2Eg(Te, Fe)] and two infrared active modes [A2u(Te, Fe) + Eu(Te, Fe)] at the C point. A and B modes are polarized
along the direction of Z axis, while E modes are doubly degenerate and polarized in the plane. Our calculated frequencies of Ramanactive modes at C point for the tetragonal NM phase are listed in Table 1. The frequency of B1g mode from the vibration of Fe atom is 258.6 cm1, which is nearly the same as that (254.9 cm1) in FeTe0.5Se0.5 in our previous calculation [42]. The phonon Raman spectra also get similar conclusion between the Fe1.074Te compound and the superconducting FeTe0.6Se0.4 [35]. For the A1g mode from the vibration of Te, the frequency (162.4 cm1) is smaller than that (183.5 cm1) for FeTe0.5Se0.5 [42] due to larger mass of Te atom. For the monoclinic DS-AFM phase, its space symmetry group is P21/m. At the C point, there are 12 Raman-active modes [Ag + Bg] and 12 infrared active modes [Au + Bu]. From the higher tetragonal symmetry to lower monoclinic symmetry, the doubly degenerate Eg mode splits into Ag and Bg modes. Our calculated frequencies of Raman-active modes at C point for the monoclinic phase are also listed in Table 1, together with the results in previous calculation [36]. After considering the magnetic interaction, the softening of phonon modes is obvious. Our results are consistent very well with those in Ref. [36] except for Ag mode which corresponds to the beating of two Te atoms against each other along the Z direction. The frequency of this mode (148.0 cm1) in our calculation is smaller than that (164.5 cm1) in Ref. [36]. This difference may stem from different Chalcogen height. The optimized tellurium height (ZTe = 0.276) by the LDA in Ref. [36] is smaller than our optimized value (ZTe = 0.2821) by GGA, which leads to a stronger force constant and then increases the frequency. Several experimental data by Raman-scattering measurements are also listed in Table 1 for comparison. Our computations for the DSAFM phase are in much better agreement with experiments than those obtained for the NM phase. In Fig. 3, we show the calculated phonon dispersion curves of FeTe along high symmetry directions in the Brillouin zone. Fig. 3(a) and (b) are calculated for the NM phase and DS-AFM
Fig. 2. The electronic structure for FeTe, the Fermi energy is set at zero. (a) For the electronic band structure in the NM phase, (b) for the electronic DOS in the NM phase, (c) for the electronic band structure in the DS-AFM phase, and (d) for the electronic DOS in the DS-AFM phase.
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Table 1 The frequencies (cm1) of Raman-active modes for FeTe from theory calculations and experimental measurements. NM
Double stripe AFM
FeTe Eg A1g B1g Eg
78.7 162.4 258.6 272.9
Bg Ag Ag Ag Bg Ag
Experiment
FeTe
Ref. [36]
Ref. [34]
Ref. [35]
Ref. [36]
79.2 90.0 148.0 211.4 216.1 244.7
76.8 86.8 164.5 206.5 214.8 243.6
159.1 196.3
158 202
155.2 201.4
Fig. 4. The total and partial phonon DOS for FeTe. (a) For the NM phase and (b) for the DS-AFM phase.
indicate that the spin–lattice interaction results in the phonon softening. Furthermore, an evident frequency gap in the range of 164.5 cm1 < x < 196.0 cm1 exists in the NM phase of FeTe, which disappears in the DS-AFM phase due to the significant phonon softening in the middle-frequency and high-frequency region.
Fig. 3. The calculated phonon dispersion curves of FeTe in both NM phase and DSAFM phase. (a) For the NM phase and (b) for the DS-AFM phase.
phase, respectively. From the higher tetragonal symmetry to lower monoclinic symmetry, some degenerate phonon modes split and lead to rich structures in the dispersion curves. Comparing Fig. 3(b) with Fig. 3(a), we can find that after taking the magnetic interaction into account, some atomic vibration modes become soften, especially for the modes in the middle-frequency and high-frequency region. The similar phenomena of phonon softening have been observed in the SS-AFM phase for other iron-based superconductors such as in BaFe2As2, LiFeAs, FeSe and FeTe0.5Se0.5 [9–13]. So it seems that the phonon softening has no clear contact with the specific magnetic order in the ground state. The calculated total and partial phonon DOS for FeTe are shown in Fig. 4. Fig. 4(a) and (b) are calculated for the NM phase and DSAFM phase, respectively. For each phase, the vibrations of Fe atoms mainly occupy the high-frequency region, while the vibrations of Te atoms mainly occupy the low-frequency region due to their difference of mass. With respect to the NM phase, the phonon DOS curve of DS-AFM phase shifts obviously toward the side of low frequency. The calculated maximum frequency in the DS-AFM phase is smaller about 30 cm1 than that in the NM phase. These facts
3.4. Electron–phonon interaction The EP coupling constant k is directly obtained by evaluating R 1 2 xÞ 2 k ¼ 2 0 a Fð x dx, where the spectral function a F (x) can be determined by the linear-response theory. The calculated spectral function a2F (x) for FeTe in both NM and DS-AFM phases are plotted in Fig. 5. The curves of the spectral function and the curves of the phonon DOS have the same variation trend, indicating that all the vibration modes contribute to the EP interaction. For the NM phase, the calculated EP coupling constant k for FeTe is 0.30, which is larger than the value in superconductor FeSe (k = 0.17) [32] and FeTe0.5Se0.5 (k = 0.22) [13]. For the DS-AFM phase, the calculated EP coupling constants k is 0.40, increasing by about 33% with respect to the value in the NM phase. So our results clearly reveal that the spin-phonon coupling enhances the EP coupling strength for FeTe in the DS-AFM phase just as that for other iron-based superconductors [9–13] in the SS-AFM phase.
4. Discussion Finally, we make some discussion about whether FeTe can be superconductor combining experiments with our calculated results.
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investigated by the first-principles calculations. Our calculations by GGA find that the ground state of FeTe is in the DS-AFM phase, which is in agreement with the experiments. Our electronic structure calculations show that the nesting effect of electron and hole pockets at the FS is not present in stoichiometric FeTe after considering the magnetic interaction. Comparing the phonon behavior in the DS-AFM phase with that in the NM phase, we find that the spin–lattice interaction can lead to the phonon softening and increase EP coupling constant k by about 33%, which is similar to other iron-based superconductors in the SS-AFM phase. We suggest that the phonon softening may have no clear contact with the specific magnetic order in the ground state. Finally, we make some discussion about whether FeTe can be superconductor according to insights from experiments and our calculated results. Acknowledgments Fig. 5. The calculated spectral function for FeTe in both NM and DS-AFM phases.
(1) Insight from experiment. Experimental measurements [43,44] show that FeTe contains 7–25% of excess Fe in its crystal structure, and thus the physical properties of FeTe depend on the content of excess Fe. McQueen et al. [45] have also reported an extreme sensitivity of superconductivity in FeSe to stoichiometry, which suggested that Fe1.03Se does not show superconductivity whereas Fe1.01Se does. The recent experimental observation for Fe1+yTe0.8S0.2 [46], Fe1+yTe0.7Se0.3 [47] and Fe1+yTe0.6S0.4 [48] found that the superconductivity is achieved or enhanced by deintercalating the excess Fe. So we guess that there is a possibility of appearance of superconductivity in FeTe if excess Fe can be removed. (2) Insight from electronic structure. Our electronic structure calculations show that the nesting of electron and hole pockets at the FS is not present in hypothetical stoichiometric FeTe. Kumar et al. [33] also found that there is enhancement in conditions of FS nesting going from FeSe to FeTe0.5Se0.5, and then lost in going to FeTe. The importance of spin fluctuations due to the nesting feature of FS and the possibility of s±-wave pairing have been proposed in Refs. [49,50]. However, Kuroki et al. [50] also suggested d-wave state can be another candidate for the pairing symmetry in the absence of the nesting of electron and hole at the FS. If there is a possibility of appearance of superconductivity in stoichiometric FeTe, the pairing symmetry in FeTe may be different from that in FeTe0.5Se0.5. (3) Insight from electron–phonon interaction. Our calculations show that spin–phonon coupling enhances the EP coupling strength, and the obtained EP coupling constant k in stoichiometric FeTe is larger than that in stoichiometric FeSe and FeTe0.5Se0.5. If superconductivity in these materials is of purely EP mechanism, FeTe should have higher Tc than FeSe and FeTe0.5Se0.5. However, this is contrary to existing studies [9,11,12,32] which show EP mechanism alone cannot explain high Tc of iron-based superconductors. In order to better understand the mechanism of superconductivity in Fe-based superconductors, the further study for the stoichiometric FeTe is needed experimentally.
5. Conclusions The electronic structure, lattice dynamics and EP interaction for stoichiometric FeTe in both NM and DS-AFM phases have been
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Whether FeTe is superconductor: Insights from first-principles calculations Jian Li, GuiQin Huang ⇑, XingFeng Zhu Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China
a r t i c l e
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Article history: Received 26 May 2013 Received in revised form 9 June 2013 Accepted 19 June 2013 Available online 28 June 2013 Keywords: A. Iron-based superconductor B. Lattice dynamics C. Electron–phonon interaction D. First-principles
a b s t r a c t We present a first-principles pseudopotential study on the electronic structure, phonon structure and the electron–phonon interaction of stoichiometric FeTe in both the nonmagnetic and double stripe antiferromagnetic phases. Our electronic structure calculations show that the nesting effect of Fermi surface is not present in stoichiometric FeTe after considering the magnetic interaction. Comparing the phonon behavior in the double stripe antiferromagnetic phase with that in the nonmagnetic phase, we find that the spin–lattice interaction can lead to the phonon softening and increase electron–phonon coupling constant k by about 33%, which is similar to other iron-based superconductors in the single stripe antiferromagnetic phase. We suggest that the phonon softening may have no clear contact with the specific magnetic order in the ground state. Finally, we make some discussion about whether FeTe can be superconductor combining our first-principles calculations. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The discovery of the LaFeAs(O,F) superconductor with Tc 26 K [1] has received tremendous attention. Not long after this discovery was made, the superconductivity was found in many iron pnictides [2–6]. The parent compounds of the iron pnictides-based superconductors display ubiquitous magnetic and structural phase transitions, for which the ground state is in a single stripe antiferromagnetic (SS-AFM) phase [7,8] below a tetragonal–orthorhombic structural transition temperature. The superconducting mechanism in Fe-based compounds is still under debate. It is generally believed that the superconductivity in Fe-based compounds is associated with antiferromagnetic fluctuations. However, many studies have shown that the role of phonons in the Cooper pairing cannot be entirely discarded. Many first-principles calculations [9–13] have shown that the spin–lattice interaction results in phonon softening and may lead to a large increase in the electron–phonon (EP) coupling. The observation of a large Fe isotope effect [14] implied that the EP interaction should play an important role in the superconducting mechanism. Besides iron pnictides family, the research of iron-based superconductors has been extended to iron chalcogenides family. The superconducting transition temperature Tc for iron chalcogenides has increased from an initial 8 K [15] to 15 K [16–18] with a suitable amount of Te substitution, and to 37 K [19] under high pressure. Iron chalcogenides do not have charge reservoir layers, ⇑ Corresponding author. Tel.: +86 025 85891951 8406. E-mail address: [email protected] (G. Huang). 0921-4534/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2013.06.010
while consist of only stacked layers of Fe-X (X = S, Se and Te) along the c-axis. Due to the simple structure and composition, which is the simplest among Fe-based superconductors, Fe chalcogenide superconductors are good candidates for applications. For iron chalcogenides Fe1+yTexSe1x, the experiments [20,21] showed that it is stable for values of x between 0 and 1. The minimum value of y is approximately 0.06 when x = 1, but for smaller values of x (increasing Se content), the value of y approaches 0. The extra Fe(y) is considered to reside in the interstitial sites. Neutronscattering studies on static magnetic orders and spin excitations in the system Fe1+ySexTe1x with different Fe compositions suggest that excess Fe appears to be important for stabilizing the magnetic order that competes with superconductivity [22]. Liu et al. [23] found that the excess Fe at interstitial sites of the (Te and Se) layers not only suppresses superconductivity but also results in a weakly localized electronic state. Among many iron chalcogenides, FeTe has shown properties quite different from some of the other iron chalcogenides and iron pnictides. FeTe is not superconducting except in the special case of the tensile-stressed FeTe thin film [24]. Neutron powder diffraction analysis confirmed that Fe1+yTe undergo a tetragonal to monoclinic phase transition at 67 K [25,26]. While other iron chalcogenides and iron pnictides undergo a tetragonal to orthorhombic phase transition at low temperature [7,8,27]. Furthermore, FeTe compound [22,25,28–30] has double stripe antiferromagnetic (DSAFM) order with (0.5, 0) ordering vector, while other iron-based superconducting materials exhibit SS-AFM order with the (0.5, 0.5) ordering vector. The calculations by Shi et al. [31] showed that the double stripe order changes to the single stripe order for
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FeTe1-xSex when x > 0.18. The pattern of two magnetic orders is shown in Fig. 1. For DS-AFM magnetic structure (Fig. 1(a)), it consists of two spin sublattices. Within each sublattice, the spins have a ferromagnetic alignment along y-axis and antiferromagnetic alignment along x-axis. The single stripe order shown in Fig. 1(b) 1 0 direction, and antiferrohas a ferromagnetic alignment along ½1 magnetic alignment along [1 1 0] direction. For iron chalcogenides, we have done a first-principles study on the phonon structure and the EP interaction for superconducting FeTe0.5Se0.5 compound [13]. The calculations showed that the softening of phonon originated from spin–phonon coupling may lead to a large increase in EP coupling. FeTe has same crystal structure as FeSe in the room temperature, but it is not superconducting and has different magnetic ground state as discussed above. In order to better understand the superconductivity in Fe-based superconductors and why FeTe does not show superconductivity, further study about FeTe compound is desired. There have been substantial works on the electronic structure for this material [30,32,33]. Recently, researchers turn their attention to the phonon properties of FeTe. Several groups [34–36] have reported phonon Raman-scattering measurements as well as the results with first-principles calculations for FeTe. However, their calculations were limited to the phonons at the zone-center. Here, in this paper, we study the electronic structure, phonon structure and EP interaction for FeTe in both nonmagnetic (NM) and DS-AFM phases. Comparing the calculated results in the DS-AFM phase with those in the NM phase, it is found that the spin–phonon coupling can also lead to the phonon softening and increase EP coupling strength, which is similar to superconducting FeTe0.5Se0.5 compound and other iron-pnictides superconductors in the SS-AFM phase. The possible appearance of superconductivity in stoichiometric FeTe is discussed. 2. Computational method The calculations have been performed in a plane-wave pseudopotential representation through the PWSCF program of the Quantum-ESPRESSO distribution [37]. The ultrasoft pseudopotentials are used to model the electron–ion interactions, and the generalized gradient approximation (GGA) of Perdew–Burke– Ernzerhof [38] for exchange–correlation potential is adopted. We employ a cutoff of 45Ry and 450Ry for wave function and charge densities, respectively. For the NM and DS-AFM phases, the a a c unit cell and 2a b c supercell are used, respectively. For the a a c unit cell, the Brillouin zone integrations of the electronic structure calculations are performed with (8, 8, 6) grid by using the first-order Hermite–Gaussian smearing
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technique. Within the framework of the linear response theory, the dynamical matrixes and the electron–phonon interaction coefficients are calculated for (4, 4, 3) grid of special q points in the irreducible Brillouin zone. The dense (16, 16, 12) grid is used in the Brillouin zone integrations in order to produce the accurate EP interaction matrix. For the calculations of DS-AFM phase with 2a b c supercell, k points equivalent to those in the calculations for the NM phase have been used. 3. Results and discussion 3.1. Ground configuration The experimental measurements [20,21] show that Fe1+yTe contain excess Fe with a narrow range of variation in y which are partially occupied interstitial sites. However, the effect of the excess Fe is not considered in our first-principles calculations. The lattice parameters obtained experimentally [26] are: a = 3.8219 Å, c = 6.2851 Å for tetragonal NM phase and a = 3.8312 Å, b = 3.7830 Å, c = 6.2643 Å, b = 89.17° for monoclinic DS-AFM phase, respectively. In our calculations, the experimental lattice parameters are employed for both the NM and DS-AFM phases. The internal coordinates are then relaxed. The obtained internal coordinates (ZTe) are 0.2546 and 0.2821 for NM phase and DS-AFM phase, respectively. The latter is very close to the experimental value (ZTe = 0.2800) [26], which implies the presence of long-range magnetic order in FeTe compound. The optimized Chalcogen height above Fe layers for FeTe is bigger than that for FeTe0.5Se0.5 in our previous calculations [13]. In other words, substitution of Se at the Te site decreases the average value of Chalcogen height, which is consistent with the calculations by Moon et al. [29] and Kumar et al. [33]. The height of anion atoms above Fe layers is of crucial importance for Fe-based superconductors. Many authors have discussed the dependence of superconductivity in terms of height of anion atoms [29,33,39,40]. Next, we compare the total energy for the NM phase, DS-AFM phase and SS-AFM phase, and determine which one is the ground state of FeTe. When the energy of the NM phase is set to zero, we find that the energies of the DS-AFM phase and SS-AFM phase are 746.3 meV/f.u. and 669.7 meV/f.u., respectively. Our calculations by GGA find that the ground state of FeTe is in the DSAFM phase, which is in agreement with the experiments [22,25]. The calculations by Kumar et al. [33] and Ding et al. [41] also suggested that the magnetic ground state in FeTe is strongly dependent on exchange–correlation potential employed. Local density approximation (LDA) yields a SS-AFM state while GGA favors a
Fig. 1. Schematic in-plane AFM spin arrangements in (a) a double stripe structure and (b) a single stripe structure.
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DS-AFM state. For the DS-AFM phase, the obtained magnetic moment per Fe atom by the GGA calculation in this paper is about 2.77lB, which is bigger than those calculated by Ma et al. [30] (2.50lB) and Gnezdilov et al. [36] (2.52lB) using the LDA. 3.2. Electronic structure The calculated electronic structures for FeTe compound are plotted in Fig. 2. The Fermi energy is set at zero. Fig. 2(a) and (b) are the calculated electronic band structure and electronic density of states (DOS) for FeTe in the NM phase. Fig. 2(c) and (d) are the corresponding plots for FeTe in the DS-AFM phase. For the NM phase, from Fig. 2(a) we can see that both the conduction bands and valence bands cross the Fermi level. The Fermi surface consists of electron-type sections at the zone corner and hole-type sections around the zone center. But after considering the magnetic interaction, the striking change of the band structure (see Fig. 2c) is that the hole pockets around C point sink below the Fermi level and then the possible nesting effect of Fermi surface (FS) is not present. Comparing Fig. 2(b) with Fig. 2(d), it is found that there is large difference in the DOS curves between the NM and DS-AFM phases. For the NM phase, the calculated DOS near the Fermi level are mainly from the contribution of Fe d states. While for the DS-AFM phase, the magnetic coupling leads to large hybridization between the Fe d states and the Te p states from about 2 eV to Fermi level. 3.3. Phonon structure We use the linear-response technique to study the lattice dynamics of FeTe in both NM and DS-AFM phases. For the tetragonal NM phase, its space group is P4/nmm. According to the group theory classification, there are four Raman-active modes [A1g(Te) + B1g(Fe) + 2Eg(Te, Fe)] and two infrared active modes [A2u(Te, Fe) + Eu(Te, Fe)] at the C point. A and B modes are polarized
along the direction of Z axis, while E modes are doubly degenerate and polarized in the plane. Our calculated frequencies of Ramanactive modes at C point for the tetragonal NM phase are listed in Table 1. The frequency of B1g mode from the vibration of Fe atom is 258.6 cm1, which is nearly the same as that (254.9 cm1) in FeTe0.5Se0.5 in our previous calculation [42]. The phonon Raman spectra also get similar conclusion between the Fe1.074Te compound and the superconducting FeTe0.6Se0.4 [35]. For the A1g mode from the vibration of Te, the frequency (162.4 cm1) is smaller than that (183.5 cm1) for FeTe0.5Se0.5 [42] due to larger mass of Te atom. For the monoclinic DS-AFM phase, its space symmetry group is P21/m. At the C point, there are 12 Raman-active modes [Ag + Bg] and 12 infrared active modes [Au + Bu]. From the higher tetragonal symmetry to lower monoclinic symmetry, the doubly degenerate Eg mode splits into Ag and Bg modes. Our calculated frequencies of Raman-active modes at C point for the monoclinic phase are also listed in Table 1, together with the results in previous calculation [36]. After considering the magnetic interaction, the softening of phonon modes is obvious. Our results are consistent very well with those in Ref. [36] except for Ag mode which corresponds to the beating of two Te atoms against each other along the Z direction. The frequency of this mode (148.0 cm1) in our calculation is smaller than that (164.5 cm1) in Ref. [36]. This difference may stem from different Chalcogen height. The optimized tellurium height (ZTe = 0.276) by the LDA in Ref. [36] is smaller than our optimized value (ZTe = 0.2821) by GGA, which leads to a stronger force constant and then increases the frequency. Several experimental data by Raman-scattering measurements are also listed in Table 1 for comparison. Our computations for the DSAFM phase are in much better agreement with experiments than those obtained for the NM phase. In Fig. 3, we show the calculated phonon dispersion curves of FeTe along high symmetry directions in the Brillouin zone. Fig. 3(a) and (b) are calculated for the NM phase and DS-AFM
Fig. 2. The electronic structure for FeTe, the Fermi energy is set at zero. (a) For the electronic band structure in the NM phase, (b) for the electronic DOS in the NM phase, (c) for the electronic band structure in the DS-AFM phase, and (d) for the electronic DOS in the DS-AFM phase.
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Table 1 The frequencies (cm1) of Raman-active modes for FeTe from theory calculations and experimental measurements. NM
Double stripe AFM
FeTe Eg A1g B1g Eg
78.7 162.4 258.6 272.9
Bg Ag Ag Ag Bg Ag
Experiment
FeTe
Ref. [36]
Ref. [34]
Ref. [35]
Ref. [36]
79.2 90.0 148.0 211.4 216.1 244.7
76.8 86.8 164.5 206.5 214.8 243.6
159.1 196.3
158 202
155.2 201.4
Fig. 4. The total and partial phonon DOS for FeTe. (a) For the NM phase and (b) for the DS-AFM phase.
indicate that the spin–lattice interaction results in the phonon softening. Furthermore, an evident frequency gap in the range of 164.5 cm1 < x < 196.0 cm1 exists in the NM phase of FeTe, which disappears in the DS-AFM phase due to the significant phonon softening in the middle-frequency and high-frequency region.
Fig. 3. The calculated phonon dispersion curves of FeTe in both NM phase and DSAFM phase. (a) For the NM phase and (b) for the DS-AFM phase.
phase, respectively. From the higher tetragonal symmetry to lower monoclinic symmetry, some degenerate phonon modes split and lead to rich structures in the dispersion curves. Comparing Fig. 3(b) with Fig. 3(a), we can find that after taking the magnetic interaction into account, some atomic vibration modes become soften, especially for the modes in the middle-frequency and high-frequency region. The similar phenomena of phonon softening have been observed in the SS-AFM phase for other iron-based superconductors such as in BaFe2As2, LiFeAs, FeSe and FeTe0.5Se0.5 [9–13]. So it seems that the phonon softening has no clear contact with the specific magnetic order in the ground state. The calculated total and partial phonon DOS for FeTe are shown in Fig. 4. Fig. 4(a) and (b) are calculated for the NM phase and DSAFM phase, respectively. For each phase, the vibrations of Fe atoms mainly occupy the high-frequency region, while the vibrations of Te atoms mainly occupy the low-frequency region due to their difference of mass. With respect to the NM phase, the phonon DOS curve of DS-AFM phase shifts obviously toward the side of low frequency. The calculated maximum frequency in the DS-AFM phase is smaller about 30 cm1 than that in the NM phase. These facts
3.4. Electron–phonon interaction The EP coupling constant k is directly obtained by evaluating R 1 2 xÞ 2 k ¼ 2 0 a Fð x dx, where the spectral function a F (x) can be determined by the linear-response theory. The calculated spectral function a2F (x) for FeTe in both NM and DS-AFM phases are plotted in Fig. 5. The curves of the spectral function and the curves of the phonon DOS have the same variation trend, indicating that all the vibration modes contribute to the EP interaction. For the NM phase, the calculated EP coupling constant k for FeTe is 0.30, which is larger than the value in superconductor FeSe (k = 0.17) [32] and FeTe0.5Se0.5 (k = 0.22) [13]. For the DS-AFM phase, the calculated EP coupling constants k is 0.40, increasing by about 33% with respect to the value in the NM phase. So our results clearly reveal that the spin-phonon coupling enhances the EP coupling strength for FeTe in the DS-AFM phase just as that for other iron-based superconductors [9–13] in the SS-AFM phase.
4. Discussion Finally, we make some discussion about whether FeTe can be superconductor combining experiments with our calculated results.
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investigated by the first-principles calculations. Our calculations by GGA find that the ground state of FeTe is in the DS-AFM phase, which is in agreement with the experiments. Our electronic structure calculations show that the nesting effect of electron and hole pockets at the FS is not present in stoichiometric FeTe after considering the magnetic interaction. Comparing the phonon behavior in the DS-AFM phase with that in the NM phase, we find that the spin–lattice interaction can lead to the phonon softening and increase EP coupling constant k by about 33%, which is similar to other iron-based superconductors in the SS-AFM phase. We suggest that the phonon softening may have no clear contact with the specific magnetic order in the ground state. Finally, we make some discussion about whether FeTe can be superconductor according to insights from experiments and our calculated results. Acknowledgments Fig. 5. The calculated spectral function for FeTe in both NM and DS-AFM phases.
(1) Insight from experiment. Experimental measurements [43,44] show that FeTe contains 7–25% of excess Fe in its crystal structure, and thus the physical properties of FeTe depend on the content of excess Fe. McQueen et al. [45] have also reported an extreme sensitivity of superconductivity in FeSe to stoichiometry, which suggested that Fe1.03Se does not show superconductivity whereas Fe1.01Se does. The recent experimental observation for Fe1+yTe0.8S0.2 [46], Fe1+yTe0.7Se0.3 [47] and Fe1+yTe0.6S0.4 [48] found that the superconductivity is achieved or enhanced by deintercalating the excess Fe. So we guess that there is a possibility of appearance of superconductivity in FeTe if excess Fe can be removed. (2) Insight from electronic structure. Our electronic structure calculations show that the nesting of electron and hole pockets at the FS is not present in hypothetical stoichiometric FeTe. Kumar et al. [33] also found that there is enhancement in conditions of FS nesting going from FeSe to FeTe0.5Se0.5, and then lost in going to FeTe. The importance of spin fluctuations due to the nesting feature of FS and the possibility of s±-wave pairing have been proposed in Refs. [49,50]. However, Kuroki et al. [50] also suggested d-wave state can be another candidate for the pairing symmetry in the absence of the nesting of electron and hole at the FS. If there is a possibility of appearance of superconductivity in stoichiometric FeTe, the pairing symmetry in FeTe may be different from that in FeTe0.5Se0.5. (3) Insight from electron–phonon interaction. Our calculations show that spin–phonon coupling enhances the EP coupling strength, and the obtained EP coupling constant k in stoichiometric FeTe is larger than that in stoichiometric FeSe and FeTe0.5Se0.5. If superconductivity in these materials is of purely EP mechanism, FeTe should have higher Tc than FeSe and FeTe0.5Se0.5. However, this is contrary to existing studies [9,11,12,32] which show EP mechanism alone cannot explain high Tc of iron-based superconductors. In order to better understand the mechanism of superconductivity in Fe-based superconductors, the further study for the stoichiometric FeTe is needed experimentally.
5. Conclusions The electronic structure, lattice dynamics and EP interaction for stoichiometric FeTe in both NM and DS-AFM phases have been
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