Download Hi-Res ImageDownload to MS-PowerPointCite This:Inorg. Chem. 2017, 56, 22, 13732-13740

Investigation into Structural Phase Transitions in Layered Titanium-Oxypnictides by a Computational Phonon Analysis

Kousuke Nakano^*^⊥
,
Kenta Hongo^†^‡^§
, and
Ryo Maezono^*^⊥

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† Research Center for Advanced Computing Infrastructure, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan

‡ PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan

§ Center for Materials Research by Information Integration, Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science, Tsukuba 305-0047, Japan

⊥ School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan

*E-mail: [email protected]

Cite this: Inorg. Chem. 2017, 56, 22, 13732–13740

Publication Date (Web):November 2, 2017

https://doi.org/10.1021/acs.inorgchem.7b01709

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Abstract

Synopsis

Introduction

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Recently discovered layered titanium-oxypnictides, ATi₂Pn₂O [A = Na₂, Ba, (SrF)₂, and (SmO)₂; Pn = As, Sb, and Bi], (1-13) comprise a new superconducting family, and this superconducting mechanism has attracted intensive attentions because the crystal and electronic structures are similar to those of exotic superconductors such as cuprates (14) or iron arsenides. (15) The superconducting mechanism has been expected to be electron–phonon driven, (16-19) and the accompanying singularities in resistivity and susceptibility at low temperature are regarded as being due to conventional charge density wave (CDW). (17, 19-21) Though our latest phonon evaluation using GGA-PBE without assuming any magnetic orderings revealed that the singularities could be explained within the conventional CDW for Pn = As, (22) it is still unknown if this is the case for Pn = Sb and Bi. (16, 22) Interestingly, recent works are pointing out the possibility of exotic mechanism of the structural transition for these compounds: For BaTi₂Pn₂O (Pn = As and Sb), Frandsen et al. reported the breaking of the 4-fold symmetry at low temperature without any superstructure peaks by neutron and electron diffractions (23) and suggested the possibility of intra-unit-cell nematic CDW, which is observed in cuprates and iron arsenides superconductors, (24-26) to account for the breaking. A theoretical suggestion was made that such an exotic CDW could be realized by the orbital ordering mediated by spin fluctuations. (27) Thus, the mechanism of structural transition in layered titanium-oxypnictides is still under debate.

Davies et al. (28) have just synthesized large single crystals of Na₂Ti₂Pn₂O (Pn = As and Sb; Figure 1) in order to achieve reliable diffaction measurements and observed clear superstructure peaks of 2 × 2 × 2 and 2 × 2 × 1 for Pn = As and Sb, respectively. They did not detect any indication of spin orderings, so they concluded that the structural transition could be attributed to the conventional phonon-assisted CDW. From the theoretical side, examining whether or not the observed superstructures are explained by ab initio phonon calculations can provide a critical clue to the mechanism of structural transition. In the present study, we performed phonon calculations for Na₂Ti₂Pn₂O (Pn = As and Sb) using the GGA-PBE functional and compared the superstructures predicted by the calculations with the experimentally observed ones. The result shows that the phonon calculation can explain the observed C2/m (monoclinic No.12) structure for Pn = As, indicating that the present phonon calculation works well for this system. For Pn = Sb, however, we obtained a Cmce (orthorhombic No. 64) polymorph, being inconsistent with the observed one [Cmcm (orthorhombic No. 63)]. On the basis of these results combined with preceding studies (16, 22, 29-32) and further quantitative analysis, we propose a new possibility that a heavier Pn causes stronger electron correlations and induces the discrepancy.

Figure 1. Crystal structure of Na₂Ti₂Pn₂O (Pn = As and Sb). The space group is I4/*mmm*.

Results

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Figure 2 shows band structures of undistorted Na₂Ti₂Pn₂O (Pn = As and Sb). The results are consistent with the previous calculations, (32, 33) meaning that there is no artifact due to the choice of cutoff, k-meshes, smearing parameters, and pseudo potentials. Figure 3a shows the phonon dispersions for Pn = As, giving imaginary frequencies appearing around N = (2π/a)·(1/2, 0, a/2c) and Σ′ = (2π/a)·(1/2, 0, 0), where a and c are conventional lattice constants for the undistorted structure. The compatible modes with the experimental observation (28) where the twice larger periodicity along c-axis is realized are N = (2π/a)·(1/2, 0, a/2c) and N′ = (2π/a)·(0, 1/2, a/2c). We note that the previous phonon calculation (34) could not reproduce this doubled periodicity. We therefore took these for further lattice relaxations from the original I4/mmm structure along the mode displacements to get the C2/m (monoclinic, No. 12) superstructure (Figures 4a and 5a), being consistent with the experiments. (28) The results of geometry optimizations for the undistorted (I4/mmm) and distorted (C2/m) structures are shown in Tables 1 and 2. The resultant optimized geometry of the C2/m superstructure gives fairly good agreement with the experiments (28) within deviations at most 2.5%. (35) Although we could not confirm whether or not the negative modes disappear in the C2/m superstructure even at high-symmetry points because of intractable computational costs for the enlarged unit cell, it should be confirmed in the future.

Figure 2. Electronic band structures for undistorted Na₂Ti₂Pn₂O structure ((a) Pn = As, (b) Pn = Sb). The Fermi energy is set to 0 eV.

Figure 3. Phonon dispersions and phonon DOS for undistorted (I4/*mmm*) Na₂Ti₂Pn₂O (Pn = (a) As, (b) Sb). The red cross marks in (b) represent the frequencies with spin–orbit coupling.

Figure 4. In-plane superstructures obtained by our calculations for Pn = (a) As and (b) Sb, and (c) the observed in-plane superstructure for Pn = Sb. (28) Pn is located above and below the Ti₂O plane. Solid lines represent the original unit cells for I4/*mmm*. Thin dash lines represent the unit cells for 2 × 2 superstructures. Solid dash lines represent redefined unit cells for distorted superstructures. The conventional lattice vectors of the superstructure for (a) Pn = As (C2/m) are redefined as , , and , those for (b) Pn = Sb (*Cmce*) are redefined as , , and , and those for (c) Pn = Sb (*Cmcm*) are redefined as , , and , where , , and are conventional lattice vectors of the undistorted structures.

Figure 5. 3D superstructures obtained from our calculations for Pn = (a) As (C2/m) and (b) Sb (*Cmce*).

Table 1. Results of Geometry Optimization for Undistorted Na₂Ti₂Pn₂O Structure (Pn = As and Sb)^a

label	x	y	z	wyckoff
Pn = As (I4/mmm)
Na	0.50000	0.50000	0.18146	4e
Ti	0.50000	0.00000	0.00000	4c
As	0.00000	0.00000	0.11752	4e
O	0.50000	0.50000	0.00000	2b
Pn = Sb (I4/mmm)
Na	0.50000	0.50000	0.18369	4e
Ti	0.50000	0.00000	0.00000	4c
Sb	0.00000	0.00000	0.12015	4e
O	0.50000	0.50000	0.00000	2b

The relaxed conventional lattice parameters are a = 4.07 Å, c = 15.44 Å (a = 4.14 Å, c = 16.98 Å) for Pn = As (Sb), giving good agreement with the experiments. (2, 54) The height of Sb toward Ti₂O plane obtained from the present calculation is 2.04 Å, which is consistent with the experimental value at room temperature (2.01 Å). (54) For Pn = As, the height of As toward Ti₂O plane has not been determined in experiments, but the obtained value (1.81 Å) is quite consistent with the experimental results of BaTi₂As₂O (1.77 Å) (4) and (SrF)₂Ti₂As₂O (1.81 Å). (3)

Table 2. Results of Geometry Optimization for Na₂Ti₂Pn₂O Superstructures (Pn = As and Sb) Obtained by Phonon Calculations^a

label	x	y	z	wyckoff
Pn = As (C2/m)
Na	0.90907	0.00000	0.63699	4i
Na	0.40943	0.00000	0.63694	4i
Na	0.15932	0.24981	0.63725	8j
Ti	0.13031	0.11979	0.00000	8j
Ti	0.88019	0.36969	0.00000	8j
As	0.80877	0.00000	0.23625	4i
As	0.30933	0.00000	0.23625	4i
As	0.05905	0.24969	0.23623	8j
O	0.00000	0.00000	0.00000	2a
O	0.25000	0.25000	0.00000	4e
O	0.00000	0.50000	0.00000	2b
Pn = Sb (Cmce)
Na	0.18411	0.00000	0.00000	8d
Ti	0.00000	0.23266	0.26812	8f
Sb	0.37883	0.00000	0.00000	8d
O	0.00000	0.00000	0.00000	4a

The conventional lattice parameters after relaxation are a′=11.51 Å, b′ = 11.51 Å, c′ = 8.23 Å, and β = 110.46° (a′ = 17.04 Å, b′ = 5.84 Å, and c′ = 5.83 Å) for Pn = As (Sb).

For Pn = Sb, we obtained phonon dispersions as shown in Figure 3b. Imaginary frequencies appear widely around X = (2π/a)·(1/2, 1/2, 0) and P = (2π/a)·(1/2, 1/2, a/2c). The experiment (28) reported that the twice larger super periodicity is realized only in ab-plane, not along c-axis. Therefore, the X mode is likely to realize the instability toward the superstructure. By optimizing the geometry along the mode displacement, we obtained a Cmce (orthorhombic, No. 64, Figures 4b and 5b), being inconsistent with the observed Cmcm (orthorhombic, No. 63, Figure 4c) in the experiment. (28) To confirm the present conclusion further, we examined the stability by seeing if the imaginary frequencies disappear at the relaxed structure, as shown in Figure 6. In addition to the stability check, we compared enthalpies between our Cmce and the observed Cmcm. The optimized geometry with Cmce is found to be more stable by 1.1 (0.7) mRy per formula unit than that with Cmcm when using Marzari–Vanderbilt (Gaussian) smearing. These results indicate that the experimentally observed Cmcm is unfavorable at 0 K at the GGA level of DFT. It is, however, expected that GGA+U could reverse the order as discussed later. A comparison of Helmholtz free energies (E – TS) under quasiharmonic approximation (36) is necessary to discuss the stability more precisely, where the entropic term is calculated from phonon DOS. (36) It was, however, intractable because the large unit cell and the low symmetry of the Cmcm polymorph requires much more computational time to calculate its entropic term (TS). The results of geometry optimizations for the undistorted (I4/mmm) and distorted (Cmce) structures, and those for the experimentally observed superstructure (Cmcm) are shown in Tables 1–3.

Figure 6. Phonon dispersions for Na₂Ti₂Sb₂O superstructure (*Cmce*).

Table 3. Results of Geometry Optimization for Experimentally Observed Na₂Ti₂Sb₂O Superstructure^a

label	x	y	z	wyckoff
Pn = Sb (Cmcm)
Na	0.00000	0.37498	0.93293	8f
Na	0.00000	0.12503	0.43294	8f
Na	0.74999	0.12500	0.93275	16h
Ti	0.37417	0.00083	0.25000	8g
Ti	0.62584	0.24918	0.25000	8g
Ti	0.87581	–0.00085	0.25000	8g
Ti	0.12418	0.25082	0.25000	8g
Sb	0.00000	0.37533	0.12909	8f
Sb	0.00000	0.12532	0.62908	8f
Sb	0.75033	0.12499	0.12907	16h
O	0.00000	0.62500	0.25000	4c
O	0.00000	0.12500	0.25000	4c
O	0.75000	0.37500	0.25000	8g

The conventional lattice parameters after relaxation are a′ = 11.74 Å, b′ = 11.74 Å, and c′ = 16.83 Å.

Discussion

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The present results confront the sharp contrast between Pn = As and Sb in terms of whether or not the present phonon calculations can reproduce the experimental structural phase transitions. Since it is clearly reported (28) that the measured XRD results cannot be identified by the

× 1 superstructure (Figure 4b), the discrepancy would be intrinsic so that it should be accounted for by the effects that are not taken into account in the present calculations. A spin–orbit effect is likely to be the origin of the discrepancy because Sb is heavier than As. To confirm, we again performed phonon calculations with fully relativistic pseudopotentials at high symmetry positions (Figure 3b). Although the frequencies slightly change because of the spin–orbit effect, the X point that induces the Cmce superstructure still shows the largest imaginary frequency. This result indicates that the spin–orbit effect is not the origin of the discrepancy.

We suggest the possibility that the GGA-PBE functional does not properly reproduce the electron correlation effects for Pn = Sb, and this could be the reason for the present discrepancy. The conclusion was obtained by the following discussion: In iron arsenide superconductors, the strength of electron correlation is well-captured by a trend of h, a vertical distance between Fe layer and Pn/Ch (Pn = P and As; Ch = Se and Te). (30) Miyake et al. applied constrained random-phase approximation (cRPA) to iron arsenide superconductors and revealed that the covalency of Fe-Pn/Ch bonding estimated by DFT-LDA calculation and the resultant Wannier orbitals can be used for a measure of the magnitude of electron correlation in the family. (30) When h gets larger, the covalency gets weaker to make Fe 3d more localized, and the spin/orbital polarizations get enhanced as one of the electron correlation effects. This measure probably works well for layered titanium-oxypnictides because they have crystal and electronic structures similar to those of iron arsenides. (8, 15, 23, 30, 31) In order to apply the measure to the layered titanium-oxypnictides, we quantitatively analyzed the covalencies of Ti–Pn bonding in Na₂Ti₂Pn₂O (Pn = As and Sb). The ratio of partial density of states (pDOS) of each atom to total density of states (tDOS) can be used as a measure of covalency, (37, 38) which is one of the common methods to evaluate covalency within DFT framework. (37-41) In this method, it is necessary to calculate a center of mass (CM) of atomic orbital for each atom. The CM is calculated by the following equation: (38)

(1)where A is an element, ε is an energy, g^A(ε) is pDOS of A at ε, and CM^A is a center of mass of the element A. Note that the energy window [ε₂, ε₁] in the equation has to be chosen in such a way that it encompasses all relevant bands contributing to the bond. (38) The difference in CM can be used as a measure of covalency of the bond. (38) If the difference in the CM between X and Y (|CM^X – CM^Y|) is small, then the covalency of the bond is strong, and vice versa. Figure 7 shows the obtained pDOS and center of masses of Ti 3d, As 4p, and Sb 5p orbitals for Na₂Ti₂Pn₂O (Pn = As and Sb). The pDOS indicates the existence of two types of bonds: One is Ti–O bonding contributing to [− 8.0 to −4.9 (4.5) eV], another is Ti–Pn bonding contributing to [− 4.9 (4.5) to 0.0 eV (Fermi energy)] for Pn = As (Sb). Note that the result that Ti–Pn bonding is related to Fermi surface is consistent with the previous study by Singh. (31) The lack of overlap between Pn and O states indicates that no Pn–O bonding is formed in the compound (Figure 7). Figure 7 shows that Ti–O bonding does not change between As and Sb. On the other hand, there is a significant difference in pDOS between As and Sb, indicating that the nature of Ti–Pn bonding changes between them. To quantify the covalencies of Ti–Pn bonding, we calculated the center of masses according to eq 1. The results are shown in Figure 7 as solid lines. We adopted [ε₂, ε₁] = [− 4.9 eV, 0.0 eV] and [− 4.5 eV, 0.0 eV] for As and Sb, respectively. As a result, we obtained |CM^Ti3d – CM^Sb5p| = 0.77 eV and |CM^Ti3d – CM^As4p| = 0.68 eV. The smaller value of |CM^Ti3d – CM^As4p| indicates that Ti–As bonding is more covalent than Ti–Sb bonding. According to electronegativity, which is one of the simplest measures of covalency, Ti–Sb bonding seems more covalent than Ti–As one. Our results, however, show that the simple measure is invalid for the layered titanium-oxypnicitdes. In the compounds, the distance of Ti–Pn (the height of Pn toward Ti₂O plane) governs the covalency as well as electronegativity. This is the same trend as in iron arsenide superconductors. To confirm our conclusion, we also calculated electron density of Na₂Ti₂Pn₂O and visualize (0 2 0) plane including Ti–Pn bondings. Figure 8 shows that the electron density between Ti–Sb (Ti–As) bonding is 0.03–0.04 electron/bohr³ (0.04–0.05 electron/bohr³). The result indicates that Ti–As bonding is more covalent than Ti–Sb one again, which is consistent with the above pDOS analysis. Our analysis implies the correlation effect gets more enhanced for Sb than As in layered titanium-oxypnictides. The trend is again consistent with our previous study for BaTi₂Pn₂O (Pn = As, Sb, and Bi), where we showed that the phonon calculation using GGA-PBE could explain experiments only for Pn = As, but not for the other heavier Pn. (22) It might be a general tendency also applicable to the layered titanium-oxypnictides that the larger h enhances the electron correlation as the origin of the present discrepancy. Calculating the absolute values of electron correlation (e.g., effective Coulombic interaction, U) of the layered titanium-oxypnictides is an important future challenge.

Figure 7. Partial density of states and center of masses of Na₂Ti₂Pn₂O (a) Pn = As, (b) Pn = Sb.

Figure 8. Electron densities of Na₂Ti₂Pn₂O (a) Pn = As, (b) Pn = Sb along Ti–Pn bonds. The electron densities are plotted in the same range (0.03–0.07 electron/bohr³), and the aspects are consistent with each crystal structure.

Putting the discrepancy for Pn = Sb aside for a while, we can provide a plausible explanation for the origin of the lattice instability (Figure 3) from the above analysis: The lattice instability mainly derives from in-plane Ti displacements (Figure 4). To account for the interatomic forces to restore the lattice displacements, we can ignore (at least for the discussion of the instability) the contribution from Na because there are no bonds between Na and Ti (Figure 1). Starting with X mode for Pn = As and Sb, the imaginary frequency appears only for Pn = Sb. Figure 9a shows the change in potential energy accompanying the displacement of Ti atoms according to the phonon showing the imaginary (lowest) frequency at X point in Pn = Sb (As). The result shows that the original position is the most stable for Pn = As, but it is not for Pn = Sb. A double-well potential is realized for Pn = Sb. These phonons correspond to the Ti displacement toward Pn on the Ti₂O plane as shown in Figure 9b. One of possible restoring forces would come from the Coulombic attraction from the valence electrons between Ti and O atoms, but the force is almost orthogonal to the displacement and hence we can ignore it. (42) In contrast, Pn is located in the same direction of Ti displacement, being responsible for the restoring forces. The displacement heads for the intermediate point of Pn located above and below the Ti₂O plane (Figure 9c). Ti atom is surrounded by these Pn (Figure 9c), so forces in the z direction were canceled. However, the forces in the y direction could be responsible for the restoring forces (Figure 9c). To discuss the difference between As and Sb, we focus on the high electron density region surrounded by Ti and Pn atoms (Figure 8). When we focus on the Ti atom shown in Figure 9c, it approaches (recedes from) the left (right) high electron density region. The Ti atom feels the Coulombic repulsion from the left region, because another Ti atom on the opposite side simultaneously approaches the region (Figure 9b). They compress the high electron density region, resulting in the increase of the Coulomb energy. The magnitude of the high density region is 0.04 electron/bohr³ (0.03 electron/bohr³) for Pn = As (Sb). This implies that the Coulombic repulsion effect in Pn = As is larger than that in Pn = Sb. In contrast, the Ti atom feels Coulombic attraction from the right region. The effect of Coulombic attraction is again larger for Pn = As because of the higher electron density of the region. These are the reasons for the difference that the original position is the most stable for Pn = As, but it is not for Pn = Sb. For N mode, the imaginary frequency appears commonly for Pn = As and Sb. This is also accountable along the above Discussion section. In this mode, the Ti–Pn interaction has little effect on the restoring forces because Ti and Pn move in the same direction (Figure 4a). The magnitude of the Coulombic repulsion and attraction from the high electron density region are expected to be much smaller because Pn moves in the same direction of Ti. In this case, the possible restoring force would originate from the nearest oxygen; again, this is orthogonal to the displacement, giving too weak a contribution and leading to the instability. This is the reason why the imaginary frequencies appear at N mode for both Pn.

Figure 9. (a) Change in potential energy accompanying the displacement of Ti atoms according to the phonon showing the imaginary (lowest) frequency at X point in Pn = Sb (As). The horizontal axis corresponds to the magnitude of the displacement from the original positon. (b) Two-dimensional image of the displacement parttern of Ti atoms. (c) Three-dimensional image of the displacement parttern of the Ti atom enclosed in a red broken line in (b).

We return to the discussion of the discrepancy for Pn = Sb. If the discrepancy is attributed to the electron correlation as we suggest, then calculations using exchange-correlation functionals beyond GGA such as GGA+U and hybrid functionals are necessary to reproduce the experimentally observed superstructure of Pn = Sb within DFT framework. Though we could not perform further phonon calculations with GGA+U or hybrid functional due to the limitation of the implementation, we note that an interesting case has been reported for BaTi₂Sb₂O that only structural optimization with GGA+U could reproduce the observed transition from P4/mmm to Pmmm, otherwise without +U it cannot be explained. (43) GGA+U has also been applied to Na₂Ti₂Sb₂O (32) to examine possible magnetic orderings, identifying a bicollinear antiferromagnetic ordering is the most stable. The ordering is unfortunately not able to solely account for the observed superstructure, (28) but when combined with a phonon evaluation under the supposed ordering, it might give further instability toward the enlarged superstructure, which is possibly consistent with the observed symmetry. A model Hamiltonian can be used to explicitly take the electron correlation effect into consideration. In fact, plausible explanations for the observed intra-unit-cell nematic CDW transition, (23) which could not be explained by the present phonon calculations, have been proposed by using a model Hamiltonian. (27, 43) The ideas are based on spin fluctuations to form magnetic orderings at low temperature, triggering another structural instability over the conventional prediction. Such a mechanism is not able to be described within the present calculation, (16, 22) and could be a possible origin for the discrepancy. For the key issue (i.e. spin fluctuations), there are still a small number of experiments (NMR and μSR) giving the controversy about the existence of the fluctuations. (17-19, 28, 44) Inelastic magnetic neutron scattering can be expected to provide conclusive information about this.

Conclusions

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We applied ab initio phonon analysis to layered titanium-oxypnictides, Na₂Ti₂Pn₂O (Pn = As and Sb), and found a clear contrast between the cases with lighter/heavier pnictogen in comparison with experiments. The result completely explains the experimental structure at low temperature, C2/m for Pn = As, within the conventional charge density wave, while the calculation predicts that a Cmce polymorph is more stable than the experimentally observed superstructure (Cmcm) for Pn = Sb. To reveal the origin of discrepancy, we focus on the height of Pn toward Ti₂O plane in layered titanium-oxypnictides. This is because the strength of electron correlation is well-captured by a trend of h, a vertical distance between Fe layer and Pn or Ch in iron arsenide superconductors that have similar electronic structures to our layered titanium-oxypnictides. On the basis of quantitative analysis, we concluded that Ti–As bonding is more covalent than Ti–Sb one and the distance of Ti–Pn (the height of Pn toward Ti₂O plane) governs the covalency. The result indicates that the covalency of Ti–Pn bonding cannot be explained only by electronegativity in layered titanium-oxpnictides, which is the same trend as in iron arsenide superconductors. The result supports the similarity between iron arsenide and layered titanium-oxypnictide superconductors that has been proposed so far and probably stimulates further experimental and theoretical studies of layered titanium-oxypnictides. Our analysis could support the correlation effect gets more enhanced for Sb than for As in layered titanium-oxypnictides. Thus, we suggest the possibility that the GGA-PBE functional does not properly reproduce the electron correlation effects for Pn = Sb. This could cause the present discrepancy. If the discrepancy is attributed to the electron correlation as we suggest, then calculations using exchange-correlation functionals beyond GGA such as GGA+U and hybrid functionals are necessary to reproduce the experimentally observed superstructure of Pn = Sb. As shown in the present study, examining whether or not the observed superstructures are explained by ab initio phonon calculations can provide a clue to the mechanism of structural transition. The combination of diffraction studies and phonon calculations will be more important in the field of inorganic chemistry.

Computational Details

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All the calculations were done within DFT using the GGA-PBE exchange-correlation functional, (45) implemented in Quantum Espresso package. (46) We chose the PBE functional because it has been used for the layered titanium-oxypnictides so for and then no critical discrepancy has been reported, for example, compared to the ARPES measurement. (21) We adopted PAW (47) pseudopotentials in most calculations. The present PAW implementation takes into account the scalar relativistic effects. (48, 49) Only for spin–orbit case, we adopted Ultrasoft (US) pseudo potentials that take into account the fully relativistic effects. (48, 49) We restricted ourselves to spin unpolarized calculations. The valence electron configurations used for the US and PAW pseudopotentials are 2s²2p⁶3s¹ (Na), 3s²3p⁶3d²4s² (Ti), 4s²4p³ (As), 5s²5p³ (Sb), and 2s²2p⁴ (O). Lattice instabilities were detected by the negative (imaginary) phonon dispersions evaluated for undistorted and distorted structures. Taking each of the negative phonon modes, the structural relaxations along the mode were evaluated by the BFGS optimization scheme with the structural symmetries fixed to C2/m for Na₂Ti₂As₂O and Cmce for Na₂Ti₂Sb₂O. For phonon calculations, we used the linear response theory implemented in Quantum Espresso package. (50) Crystal structures and Fermi surfaces were depicted by using VESTA (51) and XCrySDen, (52) respectively.

To deal with all the compounds systematically, we checked the convergence of plane-wave cutoff energies (E_cut), k-meshes, q-meshes, and smearing parameters. The most strict condition among the compounds was taken to achieve the convergence within ±1.0 mRy per formula unit in the ground state energy, resulting in E_cut^(WF) = 90 Ry for wave function and E_cut^(ρ) = 800 Ry for charge density. For undistorted Na₂Ti₂As₂O and Na₂Ti₂Sb₂O, (6 × 6 × 6) k-meshes were used for the Brillouin zone integration. Phonon dispersions were calculated on (6 × 6 × 6) q-meshes. For Na₂Ti₂As₂O (C2/m) and Na₂Ti₂Sb₂O (Cmce), (4 × 4 × 4) k-meshes were used. For Na₂Ti₂Sb₂O, (4 × 4 × 4) q-meshes were used to calculate phonon dispersions. We also calculated a ground state energy of the experimentally observed superstructure for Na₂Ti₂Sb₂O (Cmcm) (28) with (6 × 6 × 3) k-meshes. The Marzari–Vanderbilt cold smearing scheme (53) with a broadening width of 0.01 Ry was applied to all the compounds. All the calculations were performed with primitive Brillouin zones.

The primitive Brillouin zone for undistorted Na₂Ti₂Pn₂O (I4/mmm) is shown in Figure 10a. The special k and q points are Γ = (2π/a)·(0, 0, 0), N = (2π/a)·(1/2, 0, a/2c), P = (2π/a)·(1/2, 1/2, a/2c), X = (2π/a)·(1/2, 1/2, 0), Σ′ = (2π/a)·(1/2, 0, 0), and Z = (2π/a)·(0, 0, a/c) in Cartesian axis, where a and c are conventional lattice constants for the undistorted structures. The primitive Brillouin zone for Na₂Ti₂Sb₂O superstructure (Cmce) is also shown in Figure 10b. The special k and q points are Γ = (2π/a′)·(0, 0, 0), X = (2π/a′)·(1, 0, 0), S = (2π/a′)·(1/2, a′/2b′, 0), Z = (2π/a′)·(0, 0, a′/2c′), A = (2π/a′)·(1, 0, a′/2c′), R = (2π/a′)·(1/2, a′/2b′, a′/2c′) in Cartesian axis, where a′, b′, and c′ are conventional lattice constants for the superstructure.

Figure 10. Primitive Brillouin zones (a) for undistorted Na₂Ti₂Pn₂O structure (I4/*mmm*) and (b) for Na₂Ti₂Sb₂O superstructure (*Cmce*).

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Corresponding Authors
- Kousuke Nakano - School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan; http://orcid.org/0000-0001-7756-4355; Email: [email protected]
- Ryo Maezono - School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan; Email: [email protected]
Author
- Kenta Hongo - Research Center for Advanced Computing Infrastructure, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan; PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan; Center for Materials Research by Information Integration, Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science, Tsukuba 305-0047, Japan; http://orcid.org/0000-0002-2580-0907
Notes
The authors declare no competing financial interest.

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The computation in this work has been performed using the facilities of the Research Center for Advanced Computing Infrastructure (RCACI) at JAIST. R.M. and K.H. are also grateful to MEXT-FLAGSHIP2020 (hp170269, hp170220) for their computational resources. K.H. is grateful for financial support from a KAKENHI grant (JP17K17762), a Grant-in-Aid for Scientific Research on Innovative Areas “Mixed Anion” project (JP16H06439) from MEXT, PRESTO (JPMJPR16NA) and the Materials research by Information Integration Initiative (MI²I) project of the Support Program for Starting Up Innovation Hub from Japan Science and Technology Agency (JST). R.M. is grateful to MEXT-KAKENHI (26287063, 17H05478), a Grant-in-Aid for Scientific Research on Innovative Areas "Mixed Anion" project (JP16H06440), a grant from the Asahi glass Foundation, and US-AFOSR-AOARD for their financial supports.

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This article references 54 other publications.

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A layered pnictide-oxide BaTi2As2O have been prepd. and characterized. It shares similar characteristics with Na2Ti2Sb2O. The crystal has a layered structure with a tetragonal P4/nmm group (a = 4.047(3), c = 7.275(4) Å). The resistivity shows an anomaly at 200 K, which should be ascribed to an SDW or structural transition. The SDW or structural transition is confirmed by magnetic susceptibility and heat capacity measurements. These properties are very similar to those obsd. in parent compds. of high-Tc iron-based pnictide superconductors where the supercond. shows up when the anomaly due to the SDW or structural transition is suppressed. Li+ doping significantly suppresses the anomaly, but no supercond. emerges.
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Superconductivity in BaTi2Sb2O with a d1 square lattice
Yajima, Takeshi; Nakano, Kousuke; Takeiri, Fumitaka; Ono, Toshio; Hosokoshi, Yuko; Matsushita, Yoshitaka; Hester, James; Kobayashi, Yoji; Kageyama, Hiroshi
Journal of the Physical Society of Japan (2012), 81 (10), 103706/1-103706/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
We prepd. a new two-dimensional oxyantimonide, BaTi2Sb2O, which shows a superconducting transition at 1.2 K, representing the first supercond. in a system with Ti3+ (d1) in a square lattice. The TiO2Sb4 mixed anionic coordination stabilizes a unique half-filled Ti dxy orbital configuration in Ti2O plane, which is analogous to Cu2+ (d9) in the high-Tc superconductors. A charge d. wave (CDW)- or spin d. wave (SDW)-like anomaly appears at 50 K, which is significantly reduced compared with 200 K for the isostructural and non-superconducting BaTi2As2O.
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Yajima, T.; Nakano, K.; Takeiri, F.; Hester, J.; Yamamoto, T.; Kobayashi, Y.; Tsuji, N.; Kim, J.; Fujiwara, A.; Kageyama, H. Synthesis and Physical Properties of the New Oxybismuthides BaTi₂Bi₂O and (SrF)₂Ti₂Bi₂O with a d¹ Square Net J. Phys. Soc. Jpn. 2013, 82, 013703 DOI: 10.7566/JPSJ.82.013703
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Synthesis and physical properties of the new oxybismuthides BaTi2Bi2O and (SrF)2Ti2Bi2O with a d1 square net
Yajima, Takeshi; Nakano, Kousuke; Takeiri, Fumitaka; Hester, James; Yamamoto, Takafumi; Kobayashi, Yoji; Tsuji, Naruki; Kim, Jungeun; Fujiwara, Akihiko; Kageyama, Hiroshi
Journal of the Physical Society of Japan (2013), 82 (1), 013703/1-013703/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
We have recently reported the d1 square-lattice compd. BaTi2Sb2O, which shows supercond. at Tc = 1.2 K coexisting with a charge- or spin-d. wave (CDW/SDW) state. Here, we successfully prepd. two new oxybismuthides, BaTi2Bi2O and (SrF)2Ti2Bi2O, as the first Pn = Bi compds. in the ATi2Pn2O family. The CDW/SDW state disappeared for both compds., presumably owing to the considerable interaction between the Ti-3d and Bi-6s orbitals. The complete suppression of the CDW/SDW instability resulted in an enhanced Tc of 4.6 K for BaTi2Bi2O. However, (SrF)2Ti2Bi2O exhibits no supercond., suggesting the importance of the interlayer interaction for supercond.
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Yajima, T.; Nakano, K.; Takeiri, F.; Nozaki, Y.; Kobayashi, Y.; Kageyama, H. Two Superconducting Phases in the Isovalent Solid Solutions BaTi₂Pn₂O (Pn = As, Sb, and Bi) J. Phys. Soc. Jpn. 2013, 82, 033705 DOI: 10.7566/JPSJ.82.033705
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Two superconducting phases in the isovalent solid solutions BaTi2Pn2O (Pn = As, Sb, and Bi)
Yajima, Takeshi; Nakano, Kousuke; Takeiri, Fumitaka; Nozaki, Yasumasa; Kobayashi, Yoji; Kageyama, Hiroshi
Journal of the Physical Society of Japan (2013), 82 (3), 033705/1-033705/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
We have recently reported two superconductors with the d1 square lattice, BaTi2Sb2O (Tc = 1.2 K) and BaTi2Bi2O (Tc = 4.6 K). In order to find a clue behind the supercond. of these materials, we synthesized isovalent solid solns. of BaTi2(As1-xSbx)2O and BaTi2(Sb1-yBiy)2O. Despite Vegard's law behavior in cell consts., a two-dome structure in Tc was obsd. with two distinct superconducting phases ("0.9 ≤ x; y ≤ 0.3" and "0.6 ≤ y ≤ 1") sepd. by a metallic phase. This result implies a multiband nature at the Fermi surface in BaTi2Pn2O.
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Zhai, H.-F.; Jiao, W.-H.; Sun, Y.-L.; Bao, J.-K.; Jiang, H.; Yang, X.-J.; Tang, Z.-T.; Tao, Q.; Xu, X.-F.; Li, Y.-K.; Cao, C.; Dai, J.-H.; Xu, Z.-A.; Cao, G.-H. Superconductivity, charge- or spin-density wave, and metal-nonmetal transition in BaTi₂(Sb_1-xBi_x)₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 100502 DOI: 10.1103/PhysRevB.87.100502
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Nakano, K.; Yajima, T.; Takeiri, F.; Green, M. A.; Hester, J.; Kobayashi, Y.; Kageyama, H. T_c Enhancement by Aliovalent Anionic Substitution in Superconducting BaTi₂(Sb_1–xSn_x)₂O J. Phys. Soc. Jpn. 2013, 82, 074707 DOI: 10.7566/JPSJ.82.074707
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Tc enhancement by aliovalent anionic substitution in superconducting BaTi2(Sb1-xSnx)2O
Nakano, Kousuke; Yajima, Takeshi; Takeiri, Fumitaka; Green, Mark A.; Hester, James; Kobayashi, Yoji; Kageyama, Hiroshi
Journal of the Physical Society of Japan (2013), 82 (7), 074707/1-074707/5CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
BaTi2Sb2O is a Tc = 1.2 K superconductor with a d1 square lattice, and isovalent Bi substitution for Sb can increase its Tc to 4.6 K (BaTi2Bi2O), accompanied by the complete suppression of charge d. wave (CDW) or spin d. wave (SDW) transition. In the present study, we demonstrate that aliovalent Sn substitution (hole doping) also increases Tc up to 2.5 K for BaTi2(Sb0.7Sn0.3)2O, while suppressing CDW/SDW transition only slightly. The overall electronic phase diagram of BaTi2(Sb,Sn)2O is qual. similar to that of cation-substituted (hole-doped) (Ba,Na)Ti2Sb2O, but quant. differences such as in Tc are obsd., which is discussed in terms of Ti-Pn hybridization and chem. disorder.
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Pachmayr, U.; Johrendt, D. Superconductivity in Ba_1-xK_xTi₂Sb₂O (0 ≤ x ≤ 1) controlled by the layer charge Solid State Sci. 2014, 28, 31 DOI: 10.1016/j.solidstatesciences.2013.12.005
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Pachmayr, Ursula; Johrendt, Dirk
Solid State Sciences (2014), 28 (), 31-34CODEN: SSSCFJ; ISSN:1293-2558. (Elsevier Masson SAS)
The solid soln. of antimonide-oxides Ba1-xKxTi2Sb2O (0 ≤ x ≤ 1) has been synthesized by solid-state reactions and characterized by X-ray powder diffraction (CeCr2Si2C-type structure; P4/mmm, Z = 1). The crystal structure consists of Ti2Sb2O-layers that are stacked with layers of barium atoms along the c-axis. BaTi2Sb2O is a known superconductor with a crit. temp. (Tc) of 1.2 K. Substitution of barium through potassium raises Tc up to 6.1 K at 12% potassium, while no supercond. emerges with concns. higher than 20%. Anomalies in elec. transport and magnetic susceptibility indicate charge d. wave (CDW) instabilities. The CDW transition temps. (Ta) decrease from 50 K in the parent compd. to 28 K at 10% potassium substitution. No CDW transition was detected at higher concns., and no evidence for a redn. of the lattice symmetry below Ta was found. The lattice parameters vary linearly while the unit cell vol. increases with higher potassium concns. The phase diagrams Tc(x) and Ta(x) of Ba1-xKxTi2Sb2O are remarkably similar to the known series Ba1-xNaxTi2Sb2O (0 ≤ x ≤ 0.33) in spite of the reverse vol. effect. From this we conclude that the charge and not the vol. dets. the phase diagrams of these superconducting antimonide-oxides.
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von Rohr, Fabian; Nesper, Reinhard; Schilling, Andreas
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We report on the synthesis and the phys. properties of Ba1-xRbxTi2Sb2O (x ≤ 0.4) by x-ray diffraction, superconducting quantum interference device magnetometry, resistivity, and specific-heat measurements. Upon hole doping by substituting Ba with Rb, we find supercond. with a max. Tc = 5.4 K. Simultaneously, the charge-d.-wave transition temp. is strongly reduced from TCDW ≈ 55 K in the parent compd. BaTi2Sb2O and seems to be suppressed for x ≥ 0.2. The bulk character of the superconducting state for the optimally doped sample (x = 0.2) is confirmed by the occurrence of a well developed discontinuity in the sp. heat at Tc, with ΔC/Tc ≈ 22 mJ/mol K2, as well as a large Meissner-shielding fraction of ≈40%. The isotropically averaged lower and upper crit. fields of the optimally doped sample (x = 0.2) are estd. to μ0Hc,1(0) ≈ 3.8 mT and μ0Hc,2(0) ≈ 2.3 T, resp., indicating that these compds. are strongly type-II superconductors.
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Kitagawa, S.; Ishida, K.; Nakano, K.; Yajima, T.; Kageyama, H. s-wave superconductivity in superconducting BaTi₂Sb₂O revealed by ^121/123Sb-NMR/nuclear quadrupole resonance measurements Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 060510 DOI: 10.1103/PhysRevB.87.060510
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s-wave superconductivity in superconducting BaTi2Sb2O revealed by 121/123Sb-NMR/nuclear quadrupole resonance measurements
Kitagawa, S.; Ishida, K.; Nakano, K.; Yajima, T.; Kageyama, H.
Physical Review B: Condensed Matter and Materials Physics (2013), 87 (6), 060510/1-060510/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We report the 121/123Sb-NMR/NQR (NQR) measurements on the superconductor BaTi2Sb2O with a two-dimensional Ti2O square-net layer formed with Ti3+ (3d1). NQR measurements revealed that the in-plane four-fold symmetry is broken at the Sb site below TA ∼ 40 K, without an internal field appearing at the Sb site. These exclude a spin-d. wave (SDW)/ charge d. wave (CDW) ordering with incommensurate correlations, but can be understood with the commensurate CDW ordering at TA. The spin-lattice relaxation rate 1/T1, measured at the four-fold symmetry breaking site, decreases below superconducting (SC) transition temp. Tc, indicative of the microscopic coexistence of supercond. and the CDW/SDW phase below TA. Furthermore, 1/T1 of 121Sb-NQR shows a coherence peak just below Tc and decreases exponentially at low temps. These results are in sharp contrast with those in cuprate and iron-based superconductors, and strongly suggest that its SC symmetry is classified to an ordinary s-wave state.
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Nozaki, Y.; Nakano, K.; Yajima, T.; Kageyama, H.; Frandsen, B.; Liu, L.; Cheung, S.; Goko, T.; Uemura, Y. J.; Munsie, T. S. J.; Medina, T.; Luke, G. M.; Munevar, J.; Nishio-Hamane, D.; Brown, C. M. Muon spin relaxation and electron/neutron diffraction studies of BaTi₂(As_1-xSb_x)₂O: Absence of static magnetism and superlattice reflections Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 214506 DOI: 10.1103/PhysRevB.88.214506
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Gooch, M.; Doan, P.; Tang, Z.; Lorenz, B.; Guloy, A. M.; Chu, P. C. W. Weak coupling BCS-like superconductivity in the pnictide oxide Ba_1-xNa_xTi₂Sb₂O (x = 0 and 0.15) Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 064510 DOI: 10.1103/PhysRevB.88.064510
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Tan, S. Y.; Jiang, J.; Ye, Z. R.; Niu, X. H.; Song, Y.; Zhang, C. L.; Dai, P. C.; Xie, B. P.; Lai, X. C.; Feng, D. L. Photoemission study of the electronic structure and charge density waves of Na₂Ti₂Sb₂O Sci. Rep. 2015, 5, 9515 DOI: 10.1038/srep09515
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Photoemission study of the electronic structure and charge density waves of Na2Ti2Sb2O
Tan, S. Y.; Jiang, J.; Ye, Z. R.; Niu, X. H.; Song, Y.; Zhang, C. L.; Dai, P. C.; Xie, B. P.; Lai, X. C.; Feng, D. L.
Scientific Reports (2015), 5 (), 9515CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
The electronic structure of Na2Ti2Sb2O single crystal is studied by photon energy and polarization dependent angle-resolved photoemission spectroscopy (ARPES). The obtained band structure and Fermi surface agree well with the band structure calcn. of Na2Ti2Sb2O in the non-magnetic state, which indicates that there is no magnetic order in Na2Ti2Sb2O and the electronic correlation is weak. Polarization dependent ARPES results suggest the multi-band and multi-orbital nature of Na2Ti2Sb2O. Photon energy dependent ARPES results suggest that the electronic structure of Na2Ti2Sb2O is rather two-dimensional. Moreover, we find a d. wave energy gap forms below the transition temp. and reaches 65 meV at 7 K, indicating that Na2Ti2Sb2O is likely a weakly correlated CDW material in the strong electron-phonon interaction regime.
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Nakano, K.; Hongo, K.; Maezono, R. Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors Sci. Rep. 2016, 6, 29661 DOI: 10.1038/srep29661
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Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors
Nakano, Kousuke; Hongo, Kenta; Maezono, Ryo
Scientific Reports (2016), 6 (), 29661CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
There has been a puzzle between expts. and theor. predictions on the charge ordering of layered titanium-oxypnictides superconductors. Unconventional mechanisms to explain this discrepancy have been argued so far, even affecting the understanding of supercond. on the compd. We provide a new theor. prediction, by which the discrepancy itself is resolved without any complicated unconventional explanation. Phonon dispersions and changes of nesting vectors in Fermi surfaces are clarified to lead to the variety of superlattice structures even for the common crystal structures when without CDW, including orthorhombic 2 × 2 × 1 one for BaTi2As2O, which has not yet been explained successfully so far, being different from tetragonal √2 × √2 × 1 for BaTi2Sb2O and BaTi2Bi2O. The electronic structure anal. can naturally explain exptl. observations about CDW including most latest ones without any cramped unconventional mechanisms.
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Frandsen, B. A.; Bozin, E. S.; Hu, H.; Zhu, Y.; Nozaki, Y.; Kageyama, H.; Uemura, Y. J.; Yin, W.-G.; Billinge, S. J. L. Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors Nat. Commun. 2014, 5, 5761 DOI: 10.1038/ncomms6761
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Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors
Frandsen, Benjamin A.; Bozin, Emil S.; Hu, Hefei; Zhu, Yimei; Nozaki, Yasumasa; Kageyama, Hiroshi; Uemura, Yasutomo J.; Yin, Wei-Guo; Billinge, Simon J. L.
Nature Communications (2014), 5 (), 5761CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
Understanding the role played by broken-symmetry states such as charge, spin and orbital orders in the mechanism of emergent properties, such as high-temp. supercond., is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theor., but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here, we show that the recently discovered BaTi2Sb2O superconductor and its parent compd. BaTi2As2O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell nematic charge order with d-wave symmetry, pointing to the ubiquity of the phenomenon. These findings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide high-temp. superconducting materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to supercond.
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Lawler, M. J.; Fujita, K.; Lee, J.; Schmidt, A. R.; Kohsaka, Y.; Kim, C. K.; Eisaki, H.; Uchida, S.; Davis, J. C.; Sethna, J. P.; Kim, E.-A. Intra-unit-cell electronic nematicity of the high-T_c copper-oxide pseudogap states Nature 2010, 466, 347 DOI: 10.1038/nature09169
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Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
Lawler, M. J.; Fujita, K.; Lee, Jhinhwan; Schmidt, A. R.; Kohsaka, Y.; Kim, Chung Koo; Eisaki, H.; Uchida, S.; Davis, J. C.; Sethna, J. P.; Kim, Eun-Ah
Nature (London, United Kingdom) (2010), 466 (7304), 347-351CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
In the high-transition-temp. (high-Tc) superconductors the pseudogap phase becomes predominant when the d. of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any assocd. order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the detn. of a quant. order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO2 unit cell. We analyze spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi2Sr2CaCu2O8+δ and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90°-rotational symmetry within every CuO2 unit cell.
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Kasahara, S.; Shi, H.; Hashimoto, K.; Tonegawa, S.; Mizukami, Y.; Shibauchi, T.; Sugimoto, K.; Fukuda, T.; Terashima, T.; Nevidomskyy, A. H.; Matsuda, Y. Electronic nematicity above the structural and superconducting transition in BaFe₂(As_1-xP_x)₂ Nature 2012, 486, 382 DOI: 10.1038/nature11178
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Electronic nematicity above the structural and superconducting transition in BaFe2(As1-xPx)2
Kasahara, S.; Shi, H. J.; Hashimoto, K.; Tonegawa, S.; Mizukami, Y.; Shibauchi, T.; Sugimoto, K.; Fukuda, T.; Terashima, T.; Nevidomskyy, Andriy H.; Matsuda, Y.
Nature (London, United Kingdom) (2012), 486 (7403), 382-385CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
Electronic nematicity, a unidirectional self-organized state that breaks the rotational symmetry of the underlying lattice, was obsd. in the Fe pnictide and Cu oxide high-temp. superconductors. Whether nematicity plays an equally important role in these two systems is highly controversial. In Fe pnictides, the nematicity has usually been assocd. with the tetragonal-to-orthorhombic structural transition at temp. Ts. Although recent expts. have provided hints of nematicity, they were performed either in the low-temp. orthorhombic phase or in the tetragonal phase under uniaxial strain, both of which break the 90° rotational C4 symmetry. Therefore, the question remains open whether the nematicity can exist above Ts without an external driving force. Here we report magnetic torque measurements of the isovalent-doping system BaFe2(As1-xPx)2, showing that the nematicity develops well above Ts and, moreover, persists to the non-magnetic superconducting regime, resulting in a phase diagram similar to the pseudogap phase diagram of the Cu oxides. By combining these results with synchrotron x-ray measurements, we identify two distinct temps.-one at T*, signifying a true nematic transition, and the other at Ts (<T*), which we show not to be a true phase transition, but rather what we refer to as a meta-nematic transition', in analogy to the well-known meta-magnetic transition in the theory of magnetism.
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Fujita, K.; Hamidian, M. H.; Edkins, S. D.; Kim, C. K.; Kohsaka, Y.; Azuma, M.; Takano, M.; Takagi, H.; Eisaki, H.; Uchida, S.-i.; Allais, A.; Lawler, M. J.; Kim, E.-A.; Sachdev, S.; Davis, J. C. S. Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates Proc. Natl. Acad. Sci. U. S. A. 2014, 111, E3026 DOI: 10.1073/pnas.1406297111
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Nakaoka, H.; Yamakawa, Y.; Kontani, H. Theoretical prediction of nematic orbital-ordered state in the Ti oxypnictide superconductor BaTi₂(As, Sb)₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 245122 DOI: 10.1103/PhysRevB.93.245122
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Davies, N. R.; Johnson, R. D.; Princep, A. J.; Gannon, L. A.; Ma, J.-Z.; Qian, T.; Richard, P.; Li, H.; Shi, M.; Nowell, H. Coupled commensurate charge density wave and lattice distortion in Na₂Ti₂Pn₂O (Pn = As, Sb) determined by X-ray diffraction and angle-resolved photoemission spectroscopy Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 104515 DOI: 10.1103/PhysRevB.94.104515
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Kuroki, K.; Usui, H.; Onari, S.; Arita, R.; Aoki, H. Pnictogen height as a possible switch between high-T_c nodeless and low-T_c nodal pairings in the iron-based superconductors Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 224511 DOI: 10.1103/PhysRevB.79.224511
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Miyake, T.; Nakamura, K.; Arita, R.; Imada, M. Comparison of ab initio low-energy models for LaFePO, LaFeAsO, BaFe₂As₂, LiFeAs, FeSe, and FeTe: electron correlation and covalency J. Phys. Soc. Jpn. 2010, 79, 044705 DOI: 10.1143/JPSJ.79.044705
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Comparison of ab initio low-energy models for LaFePO, LaFeAsO, BaFe2As2, LiFeAs, FeSe, and FeTe: electron correlation and covalency
Miyake, Takashi; Nakamura, Kazuma; Arita, Ryotaro; Imada, Masatoshi
Journal of the Physical Society of Japan (2010), 79 (4), 044705/1-044705/20CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
Effective low-energy Hamiltonians for several different families of iron-based superconductors are compared after deriving them from the downfolding scheme based on first-principles calcns. Systematic dependences of the derived model parameters on the families are elucidated, many of which are understood from the systematic variation of the covalency between Fe-3d and pnictogen-/chalcogen-p orbitals. First, LaFePO, LaFeAsO (1111), BaFe2As2 (122), LiFeAs (111), FeSe, and FeTe (11) have overall similar band structures near the Fermi level, where the total widths of 10-fold Fe-3d bands are mostly around 4.5 eV. However, the derived effective models of the 10-fold Fe-3d bands (d model) for FeSe and FeTe have substantially larger effective onsite Coulomb interactions U ∼ 4.2 and 3.4 eV, resp., after the screening by electrons on other bands and after averaging over orbitals, as compared to ∼2.5 eV for LaFeAsO. The difference is similar in the effective models contg. p orbitals of As, Se or Te (dp or dpp model), where U ranges from ∼4 eV for the 1111 family to ∼7 eV for the 11 family. The exchange interaction J has a similar tendency. The family dependence of models indicates a wide variation ranging from weak correlation regime (LaFePO) to substantially strong correlation regime (FeSe). The origin of the larger effective interaction in the 11 family is ascribed to smaller spread of the Wannier orbitals generating larger bare interaction, and to fewer screening channels by the other bands. This variation is primarily derived from the distance h between the pnictogen/chalcogen position and the Fe layer: The longer h for the 11 family generates more ionic character of the bonding between iron and anion atoms, while the shorter h for the 1111 family leads to more covalent-bonding character, the larger spread of the Wannier orbitals, and more efficient screening by the anion p orbitals. The screened interaction of the d model is strongly orbital dependent, which is also understood from the Wannier spread. The dp and dpp models show much weaker orbital dependence. The larger h also explains why the 10-fold 3d bands for the 11 family are more entangled with the smearing of the "pseudogap" structure above the Fermi level seen in the 1111 family. While the family-dependent semimetallic splitting of the bands primarily consists of dyz/dzx and dx2-y2 orbitals, the size of the pseudogap structure is controlled by the hybridization between these orbitals and dxy/d3z2-r2: A large hybridization in the 1111 family generates a large "band-insulating"-like pseudogap (hybridization gap), whereas a large h in the 11 family weakens them, resulting in a "half-filled" like bands of orbitals. This may enhance strong correlation effects in analogy with Mott physics and causes the orbital selective crossover in the three orbitals. On the other hand, the geometrical frustration t'/t, inferred from the ratio of the next-nearest transfer r' to the nearest one t of the d model is relatively larger for the 1111 family than the 11 one. The models comprehensively derived here may serve as a firm starting basis of understanding both common and diverse properties of the iron-based superconductors including magnetism and supercond.
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Singh, D. J. Electronic structure, disconnected Fermi surfaces and antiferromagnetism in the layered pnictide superconductor Na_xBa_1-xTi₂Sb₂O New J. Phys. 2012, 14, 123003 DOI: 10.1088/1367-2630/14/12/123003
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Yan, X.-W.; Lu, Z.-Y. Layered pnictide-oxide Na₂Ti₂Pn₂O (Pn = As, Sb): a candidate for spin density waves J. Phys.: Condens. Matter 2013, 25, 365501 DOI: 10.1088/0953-8984/25/36/365501
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Layered pnictide-oxide Na2Ti2Pn2O (Pn = As, Sb). A candidate for spin density waves
Yan, Xun-Wang; Lu, Zhong-Yi
Journal of Physics: Condensed Matter (2013), 25 (36), 365501, 9 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
From 1st-principles calcns., we have studied the electronic and magnetic structures of compd. Na2Ti2Pn2O (Pn = As or Sb), whose crystal structure is a bridge between or a combination of those of high-Tc superconducting cuprates and Fe pnictides. We find that in the ground state Na2Ti2As2O is a novel blocked checkerboard antiferromagnetic semiconductor with a small band gap of about 0.15 eV. In contrast, Na2Ti2Sb2O is a bi-collinear antiferromagnetic semimetal, with a small moment of about 0.5 μB around each Ti atom. We show that there is a strong Fermi surface nesting in Na2Ti2Pn2O, and we verify that the blocked checkerboard and bi-collinear antiferromagnetic states both are the spin d. waves induced by the Fermi surface nesting. A tetramer structural distortion is found in company with the formation of a blocked checkerboard antiferromagnetic order, in good agreement with the exptl. obsd. commensurate structural distortion but with space group symmetry retained after the anomaly happens.
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Suetin, D.; Ivanovskii, A. Structural, electronic properties, and chemical bonding in quaternary layered titanium pnictide-oxides Na₂Ti₂Pn₂O and BaTi₂Pn₂O (Pn = As, Sb) from FLAPW-GGA calculations J. Alloys Compd. 2013, 564, 117 DOI: 10.1016/j.jallcom.2013.02.155
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Structural, electronic properties, and chemical bonding in quaternary layered titanium pnictide-oxides Na2Ti2Pn2O and BaTi2Pn2O (Pn = As, Sb) from FLAPW-GGA calculations
Suetin, D. V.; Ivanovskii, A. L.
Journal of Alloys and Compounds (2013), 564 (), 117-124CODEN: JALCEU; ISSN:0925-8388. (Elsevier B.V.)
By the 1st-principles FLAPW-GGA calcns., we have investigated the main trends in structural, electronic properties, and chem. bonding for a series of quaternary Ti pnictide-oxides: Na2Ti2As2O, Na2Ti2Sb2O, BaTi2As2O, and BaTi2Sb2O, which attracted now much attention as parent phases for a novel group of layered Fe-free superconducting materials. Our results cover the optimized lattice parameters and at. positions, electronic bands, Fermi surface topol., total and partial d. of electronic states. Besides, Bader anal. and the charge d. maps are used to discuss the chem. bonding for the examd. materials. We find that the at. substitutions lead to anisotropic deformation of the crystal structure; this effect is related to strong anisotropy of interat. bonds, which are of a mixed (covalent-ionic-metallic) type - in blocks [Ti2Pn2O], whereas the bonding between blocks [Ti2Pn2O] and at. sheets of Na, Ba ions is of an ionic type. The actual effective at. charges differ from the formal ionic charges due to covalency in blocks [Ti2Pn2O]. The near-Fermi electronic bands, which are responsible for metallic-like behavior of these materials and will be involved in the formation of superconducting state, arise mainly from the Ti 3dxy, dx2-y2, and dz2 states of the blocks [Ti2Pn2O], which define also the anisotropic character of conduction happening mainly in these blocks. The differences in the topol. of the multi-sheet Fermi surfaces of these materials are discussed.
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Chen, D.; Zhang, T.-T.; Song, Z.-D.; Li, H.; Zhang, W.-L.; Qian, T.; Luo, J.-L.; Shi, Y.-G.; Fang, Z.; Richard, P.; Ding, H. New phase transition in Na₂Ti₂As₂O revealed by Raman scattering Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 140501 DOI: 10.1103/PhysRevB.93.140501
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Note that we need to take special care when comparing our calculated geometry with an experimental one due to Davis et al. (28) We found that the atomic positions listed in their Table 1 are incompatible with their superstructure vectors, , , and , described in their main text: (28) (1) If the description in the main text is assumed to be correct, then Na and Sb positions in the superstructure are respectively located unlikely far from their undistorted positions. (2) O is not located at (0.0, 0.0) in their Figure 6a, being inconsistent with their Table 1. Accordingly, we speculate that they again define the superstructure vectors compatible with the atomic positions in their Table 1, which differs from that in their main text. We also found y = 0.0 for As3 in their Table 1 must be a typo and correctly y = 0.25 because As3 should occupy 8j Wyckoff site and its undistorted position is y = 0.5. Assuming our speculation is correct, our optimized geometry parameters agree well with their experimental values.
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Van De Walle, A.; Ceder, G. The effect of lattice vibrations on substitutional alloy thermodynamics Rev. Mod. Phys. 2002, 74, 11 DOI: 10.1103/RevModPhys.74.11
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The effect of lattice vibrations on substitutional alloy thermodynamics
Van De Walle, A.; Ceder, G.
Reviews of Modern Physics (2002), 74 (1), 11-45CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
A review. A long-standing limitation of first-principles calcns. of substitutional alloy phase diagrams is the difficulty in accounting for lattice vibrations. A survey of the theor. and exptl. literature seeking to quantify the effect of lattice vibrations on phase stability indicates that they can be significant. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2 kB/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693 kB/atom). This article presents the basic formalism underlying ab initio phase diagram calcns., along with the generalization required to account for lattice vibrations. The authors review the various techniques allowing the theor. calcn. and the exptl. detn. of phonon dispersion curves and related thermodn. quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and vol. change arguments. Vibrational entropy change can be attributed to the changes in chem. bond stiffness assocd. with the changes in bond length that take place during a phase transformation. This so-called "bond stiffness vs. bond length" interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.
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Whangbo, M.-H.; Koo, H.-J.; Villesuzanne, A.; Pouchard, M. Effect of Metal-Oxygen Covalent Bonding on the Competition between Jahn-Teller Distortion and Charge Disproportionation in the Perovskites of High-Spin d⁴ Metal Ions LaMnO₃ and CaFeO₃ Inorg. Chem. 2002, 41, 1920 DOI: 10.1021/ic0110427
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Cammarata, A.; Rondinelli, J. M. Covalent dependence of octahedral rotations in orthorhombic perovskite oxides J. Chem. Phys. 2014, 141, 114704 DOI: 10.1063/1.4895967
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Covalent dependence of octahedral rotations in orthorhombic perovskite oxides
Cammarata, Antonio; Rondinelli, James M.
Journal of Chemical Physics (2014), 141 (11), 114704/1-114704/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The compositional dependence of metal-O BO6 octahedral distortions, including bond elongations and rotations, is frequently discussed in the ABO3 perovskite literature; structural distortions alleviate internal stresses driven by under- or over-coordinated bond environments. Here the authors identify the dependence of octahedral rotations from changes in metal-O bond covalency in orthorhombic perovskites. Using d. functional theory the authors formulate a covalency metric, which captures both the real and k-space interactions between the magnitude and sense, i.e., in-phase or out-of-phase, octahedral rotations, to explore the link between the ionic-covalent Fe-O bond and the interoctahedral Fe-O-Fe bond angles in Pbnm ferrates. The authors' survey finds that the covalency of the metal-O bond is correlated with the rotation amplitude: the more covalent the Fe-O bond, the less distorted is the structure and the more important the long-range inter-octahedral (Fe-O-Fe bond angle) interactions were found. Finally, to indirectly tune the B-O bond covalency by A-cation induced BO6 rotations independent of ionic size, facilitating design of targeted bonding interactions in complex perovskites. (c) 2014 American Institute of Physics.
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Hughbanks, T.; Hoffmann, R. Chains of trans-edge-sharing molybdenum octahedra: metal-metal bonding in extended systems J. Am. Chem. Soc. 1983, 105, 3528 DOI: 10.1021/ja00349a027
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Chains of trans-edge-sharing molybdenum octahedra: metal-metal bonding in extended systems
Hughbanks, Timothy; Hoffmann, Roald
Journal of the American Chemical Society (1983), 105 (11), 3528-37CODEN: JACSAT; ISSN:0002-7863.
A detailed anal. of bonding in systems with chains of condensed Mo octahedra is given. A 1-dimensional model proves to be applicable over the range of molybdates yet synthesized. The electronic coupling between chains is discussed. Distortions in newly synthesized quaternary systems are seen to result from increased electron count on the Mo chains. The band theoretic explanation of these distortions parallels the treatment of 2nd-order Jahn-Teller distortions.
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Dronskowski, R.; Bloechl, P. E. Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations J. Phys. Chem. 1993, 97, 8617 DOI: 10.1021/j100135a014
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Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations
Dronskowski, Richard; Bloechl, Peter E.
Journal of Physical Chemistry (1993), 97 (33), 8617-24CODEN: JPCHAX; ISSN:0022-3654.
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Grechnev, A.; Ahuja, R.; Eriksson, O. Balanced crystal orbital overlap population—a tool for analysing chemical bonds in solids J. Phys.: Condens. Matter 2003, 15, 7751 DOI: 10.1088/0953-8984/15/45/014
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Balanced crystal orbital overlap population-a tool for analysing chemical bonds in solids
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A new tool for analyzing theor. the chem. bonding in solids is proposed. A balanced crystal orbital overlap population (BCOOP) is an energy resolved quantity which is pos. for bonding states and neg. for antibonding states, hence enabling a distinction between bonding and antibonding contributions to the chem. bond. Unlike the conventional crystal orbital overlap population (COOP), BCOOP handles correctly the situation of crystal orbitals being nearly linear dependent, which is often the case in the solid state. Also, BCOOP is much less basis set dependent than COOP. A BCOOP implementation within the full-potential linear muffin tin orbital method is presented and illustrated for Si, TiC and Ru. Thus, BCOOP is compared to the COOP and crystal orbital Hamilton population (COHP) for systems with chem. bonds ranging from metallic to covalent character.
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The angle of O–Ti–Pn becomes 87° even at the most stable point for Pn = Sb. The corresponding displacement is 0.125 Å (Figure 9a). In this case, the restoring force between Ti and the nearest O contributing to the direction of the displacement is negligible because cos(87°) is only 0.05.
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43
Zhang, G.; Glasbrenner, J. K.; Flint, R.; Mazin, I. I.; Fernandes, R. M. Double-stage nematic bond ordering above double stripe magnetism: Application to BaTi₂Sb₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 95, 174402 DOI: 10.1103/PhysRevB.95.174402
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Herein we investigated the electronic properties of layered transition-metal oxides Na2Ti2Sb2O by 23Na NMR (NMR) measurement. The resistivity, susceptibility and sp. heat measurements show a phase transition at approx. 114 K (TA). No splitting or broadening in the central line of 23Na NMR spectra is obsd. below and above the transition temp. indicating no internal field being detected. The spin-lattice relaxation rate divided by T (1/T1T) shows a sharp drop at about 110 K which suggests a gap opening behavior. Below the phase transition temp. zone, 1/T1T shows Fermi liq. behavior but with much smaller value indicating the loss of large part of electronic d. of states (DOS) because of the gap. No signature of the enhancement of spin fluctuations or magnetic order is found with the decreasing temp. These results suggest a commensurate charge-d.-wave (CDW) phase transition occurring.
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Ozawa, T. C.; Pantoja, R.; Axtell, E. A.; Kauzlarich, S. M.; Greedan, J. E.; Bieringer, M.; Richardson, J. W. Powder Neutron Diffraction Studies of Na₂Ti₂Sb₂O and Its Structure Property Relationships J. Solid State Chem. 2000, 153, 275– 281 DOI: 10.1006/jssc.2000.8758
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Powder neutron diffraction studies of Na2Ti2Sb2O and its structure-property relationships
Ozawa, Tadashi C.; Pantoja, Rigo; Axtell, Enos A., III; Kauzlarich, Susan M.; Greedan, John E.; Bieringer, Mario; Richardson, James W., Jr.
Journal of Solid State Chemistry (2000), 153 (2), 275-281CODEN: JSSCBI; ISSN:0022-4596. (Academic Press)
The structure of Na2Ti2Sb2O was studied by temp.-dependent powder neutron diffraction. Na2Ti2Sb2O crystallizes in I4/mmm symmetry. The structure of this phase can be viewed as an anti-K2NiF4 type where Ti3+ ion is located between two O atoms forming a square-planar lattice. Powder neutron diffraction studies of Na2Ti2Sb2O indicate that this compd. has a structural distortion in the [Ti2Sb2O]2- layer at T ≈ 120 K. This transition corresponds well to the previously reported anomalous transition temp. of the magnetic susceptibility and electronic resistivity. Several models to explain the data are presented and discussed. (c) 2000 Academic Press.
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Figure 1
Figure 1. Crystal structure of Na₂Ti₂Pn₂O (Pn = As and Sb). The space group is I4/mmm.
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Figure 2
Figure 2. Electronic band structures for undistorted Na₂Ti₂Pn₂O structure ((a) Pn = As, (b) Pn = Sb). The Fermi energy is set to 0 eV.
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Figure 3
Figure 3. Phonon dispersions and phonon DOS for undistorted (I4/mmm) Na₂Ti₂Pn₂O (Pn = (a) As, (b) Sb). The red cross marks in (b) represent the frequencies with spin–orbit coupling.
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Figure 4
Figure 4. In-plane superstructures obtained by our calculations for Pn = (a) As and (b) Sb, and (c) the observed in-plane superstructure for Pn = Sb. (28) Pn is located above and below the Ti₂O plane. Solid lines represent the original unit cells for I4/mmm. Thin dash lines represent the unit cells for 2 × 2 superstructures. Solid dash lines represent redefined unit cells for distorted superstructures. The conventional lattice vectors of the superstructure for (a) Pn = As (C2/m) are redefined as , , and , those for (b) Pn = Sb (Cmce) are redefined as , , and , and those for (c) Pn = Sb (Cmcm) are redefined as , , and , where , , and are conventional lattice vectors of the undistorted structures.
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Figure 5
Figure 5. 3D superstructures obtained from our calculations for Pn = (a) As (C2/m) and (b) Sb (Cmce).
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Figure 6
Figure 6. Phonon dispersions for Na₂Ti₂Sb₂O superstructure (Cmce).
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Figure 7
Figure 7. Partial density of states and center of masses of Na₂Ti₂Pn₂O (a) Pn = As, (b) Pn = Sb.
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Figure 8
Figure 8. Electron densities of Na₂Ti₂Pn₂O (a) Pn = As, (b) Pn = Sb along Ti–Pn bonds. The electron densities are plotted in the same range (0.03–0.07 electron/bohr³), and the aspects are consistent with each crystal structure.
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Figure 9
Figure 9. (a) Change in potential energy accompanying the displacement of Ti atoms according to the phonon showing the imaginary (lowest) frequency at X point in Pn = Sb (As). The horizontal axis corresponds to the magnitude of the displacement from the original positon. (b) Two-dimensional image of the displacement parttern of Ti atoms. (c) Three-dimensional image of the displacement parttern of the Ti atom enclosed in a red broken line in (b).
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Figure 10
Figure 10. Primitive Brillouin zones (a) for undistorted Na₂Ti₂Pn₂O structure (I4/mmm) and (b) for Na₂Ti₂Sb₂O superstructure (Cmce).
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References
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This article references 54 other publications.
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  Yajima, T.; Nakano, K.; Takeiri, F.; Ono, T.; Hosokoshi, Y.; Matsushita, Y.; Hester, J.; Kobayashi, Y.; Kageyama, H. Superconductivity in BaTi₂Sb₂O with a d¹ Square Lattice J. Phys. Soc. Jpn. 2012, 81, 103706 DOI: 10.1143/JPSJ.81.103706
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  6
  Superconductivity in BaTi2Sb2O with a d1 square lattice
  Yajima, Takeshi; Nakano, Kousuke; Takeiri, Fumitaka; Ono, Toshio; Hosokoshi, Yuko; Matsushita, Yoshitaka; Hester, James; Kobayashi, Yoji; Kageyama, Hiroshi
  Journal of the Physical Society of Japan (2012), 81 (10), 103706/1-103706/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
  We prepd. a new two-dimensional oxyantimonide, BaTi2Sb2O, which shows a superconducting transition at 1.2 K, representing the first supercond. in a system with Ti3+ (d1) in a square lattice. The TiO2Sb4 mixed anionic coordination stabilizes a unique half-filled Ti dxy orbital configuration in Ti2O plane, which is analogous to Cu2+ (d9) in the high-Tc superconductors. A charge d. wave (CDW)- or spin d. wave (SDW)-like anomaly appears at 50 K, which is significantly reduced compared with 200 K for the isostructural and non-superconducting BaTi2As2O.
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7. 7
  Yajima, T.; Nakano, K.; Takeiri, F.; Hester, J.; Yamamoto, T.; Kobayashi, Y.; Tsuji, N.; Kim, J.; Fujiwara, A.; Kageyama, H. Synthesis and Physical Properties of the New Oxybismuthides BaTi₂Bi₂O and (SrF)₂Ti₂Bi₂O with a d¹ Square Net J. Phys. Soc. Jpn. 2013, 82, 013703 DOI: 10.7566/JPSJ.82.013703
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  7
  Synthesis and physical properties of the new oxybismuthides BaTi2Bi2O and (SrF)2Ti2Bi2O with a d1 square net
  Yajima, Takeshi; Nakano, Kousuke; Takeiri, Fumitaka; Hester, James; Yamamoto, Takafumi; Kobayashi, Yoji; Tsuji, Naruki; Kim, Jungeun; Fujiwara, Akihiko; Kageyama, Hiroshi
  Journal of the Physical Society of Japan (2013), 82 (1), 013703/1-013703/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
  We have recently reported the d1 square-lattice compd. BaTi2Sb2O, which shows supercond. at Tc = 1.2 K coexisting with a charge- or spin-d. wave (CDW/SDW) state. Here, we successfully prepd. two new oxybismuthides, BaTi2Bi2O and (SrF)2Ti2Bi2O, as the first Pn = Bi compds. in the ATi2Pn2O family. The CDW/SDW state disappeared for both compds., presumably owing to the considerable interaction between the Ti-3d and Bi-6s orbitals. The complete suppression of the CDW/SDW instability resulted in an enhanced Tc of 4.6 K for BaTi2Bi2O. However, (SrF)2Ti2Bi2O exhibits no supercond., suggesting the importance of the interlayer interaction for supercond.
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8. 8
  Yajima, T.; Nakano, K.; Takeiri, F.; Nozaki, Y.; Kobayashi, Y.; Kageyama, H. Two Superconducting Phases in the Isovalent Solid Solutions BaTi₂Pn₂O (Pn = As, Sb, and Bi) J. Phys. Soc. Jpn. 2013, 82, 033705 DOI: 10.7566/JPSJ.82.033705
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  8
  Two superconducting phases in the isovalent solid solutions BaTi2Pn2O (Pn = As, Sb, and Bi)
  Yajima, Takeshi; Nakano, Kousuke; Takeiri, Fumitaka; Nozaki, Yasumasa; Kobayashi, Yoji; Kageyama, Hiroshi
  Journal of the Physical Society of Japan (2013), 82 (3), 033705/1-033705/4CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
  We have recently reported two superconductors with the d1 square lattice, BaTi2Sb2O (Tc = 1.2 K) and BaTi2Bi2O (Tc = 4.6 K). In order to find a clue behind the supercond. of these materials, we synthesized isovalent solid solns. of BaTi2(As1-xSbx)2O and BaTi2(Sb1-yBiy)2O. Despite Vegard's law behavior in cell consts., a two-dome structure in Tc was obsd. with two distinct superconducting phases ("0.9 ≤ x; y ≤ 0.3" and "0.6 ≤ y ≤ 1") sepd. by a metallic phase. This result implies a multiband nature at the Fermi surface in BaTi2Pn2O.
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9. 9
  Zhai, H.-F.; Jiao, W.-H.; Sun, Y.-L.; Bao, J.-K.; Jiang, H.; Yang, X.-J.; Tang, Z.-T.; Tao, Q.; Xu, X.-F.; Li, Y.-K.; Cao, C.; Dai, J.-H.; Xu, Z.-A.; Cao, G.-H. Superconductivity, charge- or spin-density wave, and metal-nonmetal transition in BaTi₂(Sb_1-xBi_x)₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 100502 DOI: 10.1103/PhysRevB.87.100502
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10. 10
  Nakano, K.; Yajima, T.; Takeiri, F.; Green, M. A.; Hester, J.; Kobayashi, Y.; Kageyama, H. T_c Enhancement by Aliovalent Anionic Substitution in Superconducting BaTi₂(Sb_1–xSn_x)₂O J. Phys. Soc. Jpn. 2013, 82, 074707 DOI: 10.7566/JPSJ.82.074707
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  10
  Tc enhancement by aliovalent anionic substitution in superconducting BaTi2(Sb1-xSnx)2O
  Nakano, Kousuke; Yajima, Takeshi; Takeiri, Fumitaka; Green, Mark A.; Hester, James; Kobayashi, Yoji; Kageyama, Hiroshi
  Journal of the Physical Society of Japan (2013), 82 (7), 074707/1-074707/5CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
  BaTi2Sb2O is a Tc = 1.2 K superconductor with a d1 square lattice, and isovalent Bi substitution for Sb can increase its Tc to 4.6 K (BaTi2Bi2O), accompanied by the complete suppression of charge d. wave (CDW) or spin d. wave (SDW) transition. In the present study, we demonstrate that aliovalent Sn substitution (hole doping) also increases Tc up to 2.5 K for BaTi2(Sb0.7Sn0.3)2O, while suppressing CDW/SDW transition only slightly. The overall electronic phase diagram of BaTi2(Sb,Sn)2O is qual. similar to that of cation-substituted (hole-doped) (Ba,Na)Ti2Sb2O, but quant. differences such as in Tc are obsd., which is discussed in terms of Ti-Pn hybridization and chem. disorder.
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11. 11
  Pachmayr, U.; Johrendt, D. Superconductivity in Ba_1-xK_xTi₂Sb₂O (0 ≤ x ≤ 1) controlled by the layer charge Solid State Sci. 2014, 28, 31 DOI: 10.1016/j.solidstatesciences.2013.12.005
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  11
  Superconductivity in Ba1-xKxTi2Sb2O (0 ≤ x ≤ 1) controlled by the layer charge
  Pachmayr, Ursula; Johrendt, Dirk
  Solid State Sciences (2014), 28 (), 31-34CODEN: SSSCFJ; ISSN:1293-2558. (Elsevier Masson SAS)
  The solid soln. of antimonide-oxides Ba1-xKxTi2Sb2O (0 ≤ x ≤ 1) has been synthesized by solid-state reactions and characterized by X-ray powder diffraction (CeCr2Si2C-type structure; P4/mmm, Z = 1). The crystal structure consists of Ti2Sb2O-layers that are stacked with layers of barium atoms along the c-axis. BaTi2Sb2O is a known superconductor with a crit. temp. (Tc) of 1.2 K. Substitution of barium through potassium raises Tc up to 6.1 K at 12% potassium, while no supercond. emerges with concns. higher than 20%. Anomalies in elec. transport and magnetic susceptibility indicate charge d. wave (CDW) instabilities. The CDW transition temps. (Ta) decrease from 50 K in the parent compd. to 28 K at 10% potassium substitution. No CDW transition was detected at higher concns., and no evidence for a redn. of the lattice symmetry below Ta was found. The lattice parameters vary linearly while the unit cell vol. increases with higher potassium concns. The phase diagrams Tc(x) and Ta(x) of Ba1-xKxTi2Sb2O are remarkably similar to the known series Ba1-xNaxTi2Sb2O (0 ≤ x ≤ 0.33) in spite of the reverse vol. effect. From this we conclude that the charge and not the vol. dets. the phase diagrams of these superconducting antimonide-oxides.
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12. 12
  von Rohr, F.; Nesper, R.; Schilling, A. Superconductivity in rubidium-substituted Ba_1-xRb_xTi₂Sb₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 094505 DOI: 10.1103/PhysRevB.89.094505
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  12
  Superconductivity in rubidium-substituted Ba1-xRbxTi2Sb2O
  von Rohr, Fabian; Nesper, Reinhard; Schilling, Andreas
  Physical Review B: Condensed Matter and Materials Physics (2014), 89 (9), 094505/1-094505/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We report on the synthesis and the phys. properties of Ba1-xRbxTi2Sb2O (x ≤ 0.4) by x-ray diffraction, superconducting quantum interference device magnetometry, resistivity, and specific-heat measurements. Upon hole doping by substituting Ba with Rb, we find supercond. with a max. Tc = 5.4 K. Simultaneously, the charge-d.-wave transition temp. is strongly reduced from TCDW ≈ 55 K in the parent compd. BaTi2Sb2O and seems to be suppressed for x ≥ 0.2. The bulk character of the superconducting state for the optimally doped sample (x = 0.2) is confirmed by the occurrence of a well developed discontinuity in the sp. heat at Tc, with ΔC/Tc ≈ 22 mJ/mol K2, as well as a large Meissner-shielding fraction of ≈40%. The isotropically averaged lower and upper crit. fields of the optimally doped sample (x = 0.2) are estd. to μ0Hc,1(0) ≈ 3.8 mT and μ0Hc,2(0) ≈ 2.3 T, resp., indicating that these compds. are strongly type-II superconductors.
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13. 13
  Ji, Q.; Ma, Y.; Hu, K.; Gao, B.; Mu, G.; Li, W.; Hu, T.; Zhang, G.; Zhao, Q.; Zhang, H.; Huang, F.; Xie, X. Synthesis, Structural, and Transport Properties of Cr-Doped BaTi₂As₂O Inorg. Chem. 2014, 53, 13089 DOI: 10.1021/ic502192h
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14. 14
  Bednorz, J.; Müller, K. Possible high T_c superconductivity in the Ba-La-Cu-O system Z. Phys. B: Condens. Matter 1986, 64, 189 DOI: 10.1007/BF01303701
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  14
  Possible high Tc superconductivity in the barium-lanthanum-copper-oxygen system
  Bednorz, J. G.; Mueller, K. A.
  Zeitschrift fuer Physik B: Condensed Matter (1986), 64 (2), 189-93CODEN: ZPCMDN; ISSN:0722-3277.
  Metallic, O-deficient compds. in the Ba-La-Cu-O system, with compn. BaxLa5-xCu5O5(3-y) were prepd. in polycryst. form. Samples with x = 1 and 0.75, y >0, annealed below 900° under reducing conditions, consist of 3 phases, one of them a perovskite-like mixed valent Cu compd. Upon cooling, the samples show a linear decrease in resistivity, then an approx. logarithmic increase, interpreted as a beginning of localization. Finally, an abrupt decrease by up to 3 orders of magnitude occurs, reminiscent of the onset of percolative supercond. The highest onset temp. was obsd. in the 30 K range. It is markedly reduced by high current densities. Thus, it results partially from the percolative nature, but possibly also from 2-dimensional superconducting fluctuations of double perovskite layers of one of the phases present.
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15. 15
  Kamihara, Y.; Watanabe, T.; Hirano, M.; Hosono, H. Iron-Based Layered Superconductor La[O_1-xF_x]FeAs (x = 0.05–0.12) with T_c = 26 K J. Am. Chem. Soc. 2008, 130, 3296 DOI: 10.1021/ja800073m
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  15
  Iron-Based Layered Superconductor La[O1-xFx]FeAs (x = 0.05-0.12) with Tc = 26 K
  Kamihara, Yoichi; Watanabe, Takumi; Hirano, Masahiro; Hosono, Hideo
  Journal of the American Chemical Society (2008), 130 (11), 3296-3297CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The authors report that a layered iron-based compd. LaOFeAs undergoes superconducting transition under doping with F- ions at the O2- site. The transition temp. (Tc) exhibits a trapezoid shape dependence on the F- content, with the highest Tc of ∼26 K at ∼11 atom %.
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16. 16
  Subedi, A. Electron-phonon superconductivity and charge density wave instability in the layered titanium-based pnictide BaTi₂Sb₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 054506 DOI: 10.1103/PhysRevB.87.054506
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17. 17
  von Rohr, F.; Schilling, A.; Nesper, R.; Baines, C.; Bendele, M. Conventional superconductivity and charge-density-wave ordering in Ba_1-xNa_xTi₂Sb₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 140501 DOI: 10.1103/PhysRevB.88.140501
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18. 18
  Kitagawa, S.; Ishida, K.; Nakano, K.; Yajima, T.; Kageyama, H. s-wave superconductivity in superconducting BaTi₂Sb₂O revealed by ^121/123Sb-NMR/nuclear quadrupole resonance measurements Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 060510 DOI: 10.1103/PhysRevB.87.060510
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  18
  s-wave superconductivity in superconducting BaTi2Sb2O revealed by 121/123Sb-NMR/nuclear quadrupole resonance measurements
  Kitagawa, S.; Ishida, K.; Nakano, K.; Yajima, T.; Kageyama, H.
  Physical Review B: Condensed Matter and Materials Physics (2013), 87 (6), 060510/1-060510/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We report the 121/123Sb-NMR/NQR (NQR) measurements on the superconductor BaTi2Sb2O with a two-dimensional Ti2O square-net layer formed with Ti3+ (3d1). NQR measurements revealed that the in-plane four-fold symmetry is broken at the Sb site below TA ∼ 40 K, without an internal field appearing at the Sb site. These exclude a spin-d. wave (SDW)/ charge d. wave (CDW) ordering with incommensurate correlations, but can be understood with the commensurate CDW ordering at TA. The spin-lattice relaxation rate 1/T1, measured at the four-fold symmetry breaking site, decreases below superconducting (SC) transition temp. Tc, indicative of the microscopic coexistence of supercond. and the CDW/SDW phase below TA. Furthermore, 1/T1 of 121Sb-NQR shows a coherence peak just below Tc and decreases exponentially at low temps. These results are in sharp contrast with those in cuprate and iron-based superconductors, and strongly suggest that its SC symmetry is classified to an ordinary s-wave state.
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19. 19
  Nozaki, Y.; Nakano, K.; Yajima, T.; Kageyama, H.; Frandsen, B.; Liu, L.; Cheung, S.; Goko, T.; Uemura, Y. J.; Munsie, T. S. J.; Medina, T.; Luke, G. M.; Munevar, J.; Nishio-Hamane, D.; Brown, C. M. Muon spin relaxation and electron/neutron diffraction studies of BaTi₂(As_1-xSb_x)₂O: Absence of static magnetism and superlattice reflections Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 214506 DOI: 10.1103/PhysRevB.88.214506
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20. 20
  Gooch, M.; Doan, P.; Tang, Z.; Lorenz, B.; Guloy, A. M.; Chu, P. C. W. Weak coupling BCS-like superconductivity in the pnictide oxide Ba_1-xNa_xTi₂Sb₂O (x = 0 and 0.15) Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 064510 DOI: 10.1103/PhysRevB.88.064510
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21. 21
  Tan, S. Y.; Jiang, J.; Ye, Z. R.; Niu, X. H.; Song, Y.; Zhang, C. L.; Dai, P. C.; Xie, B. P.; Lai, X. C.; Feng, D. L. Photoemission study of the electronic structure and charge density waves of Na₂Ti₂Sb₂O Sci. Rep. 2015, 5, 9515 DOI: 10.1038/srep09515
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  21
  Photoemission study of the electronic structure and charge density waves of Na2Ti2Sb2O
  Tan, S. Y.; Jiang, J.; Ye, Z. R.; Niu, X. H.; Song, Y.; Zhang, C. L.; Dai, P. C.; Xie, B. P.; Lai, X. C.; Feng, D. L.
  Scientific Reports (2015), 5 (), 9515CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
  The electronic structure of Na2Ti2Sb2O single crystal is studied by photon energy and polarization dependent angle-resolved photoemission spectroscopy (ARPES). The obtained band structure and Fermi surface agree well with the band structure calcn. of Na2Ti2Sb2O in the non-magnetic state, which indicates that there is no magnetic order in Na2Ti2Sb2O and the electronic correlation is weak. Polarization dependent ARPES results suggest the multi-band and multi-orbital nature of Na2Ti2Sb2O. Photon energy dependent ARPES results suggest that the electronic structure of Na2Ti2Sb2O is rather two-dimensional. Moreover, we find a d. wave energy gap forms below the transition temp. and reaches 65 meV at 7 K, indicating that Na2Ti2Sb2O is likely a weakly correlated CDW material in the strong electron-phonon interaction regime.
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22. 22
  Nakano, K.; Hongo, K.; Maezono, R. Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors Sci. Rep. 2016, 6, 29661 DOI: 10.1038/srep29661
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  22
  Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors
  Nakano, Kousuke; Hongo, Kenta; Maezono, Ryo
  Scientific Reports (2016), 6 (), 29661CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
  There has been a puzzle between expts. and theor. predictions on the charge ordering of layered titanium-oxypnictides superconductors. Unconventional mechanisms to explain this discrepancy have been argued so far, even affecting the understanding of supercond. on the compd. We provide a new theor. prediction, by which the discrepancy itself is resolved without any complicated unconventional explanation. Phonon dispersions and changes of nesting vectors in Fermi surfaces are clarified to lead to the variety of superlattice structures even for the common crystal structures when without CDW, including orthorhombic 2 × 2 × 1 one for BaTi2As2O, which has not yet been explained successfully so far, being different from tetragonal √2 × √2 × 1 for BaTi2Sb2O and BaTi2Bi2O. The electronic structure anal. can naturally explain exptl. observations about CDW including most latest ones without any cramped unconventional mechanisms.
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23. 23
  Frandsen, B. A.; Bozin, E. S.; Hu, H.; Zhu, Y.; Nozaki, Y.; Kageyama, H.; Uemura, Y. J.; Yin, W.-G.; Billinge, S. J. L. Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors Nat. Commun. 2014, 5, 5761 DOI: 10.1038/ncomms6761
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  23
  Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors
  Frandsen, Benjamin A.; Bozin, Emil S.; Hu, Hefei; Zhu, Yimei; Nozaki, Yasumasa; Kageyama, Hiroshi; Uemura, Yasutomo J.; Yin, Wei-Guo; Billinge, Simon J. L.
  Nature Communications (2014), 5 (), 5761CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
  Understanding the role played by broken-symmetry states such as charge, spin and orbital orders in the mechanism of emergent properties, such as high-temp. supercond., is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theor., but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here, we show that the recently discovered BaTi2Sb2O superconductor and its parent compd. BaTi2As2O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell nematic charge order with d-wave symmetry, pointing to the ubiquity of the phenomenon. These findings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide high-temp. superconducting materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to supercond.
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24. 24
  Lawler, M. J.; Fujita, K.; Lee, J.; Schmidt, A. R.; Kohsaka, Y.; Kim, C. K.; Eisaki, H.; Uchida, S.; Davis, J. C.; Sethna, J. P.; Kim, E.-A. Intra-unit-cell electronic nematicity of the high-T_c copper-oxide pseudogap states Nature 2010, 466, 347 DOI: 10.1038/nature09169
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  24
  Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
  Lawler, M. J.; Fujita, K.; Lee, Jhinhwan; Schmidt, A. R.; Kohsaka, Y.; Kim, Chung Koo; Eisaki, H.; Uchida, S.; Davis, J. C.; Sethna, J. P.; Kim, Eun-Ah
  Nature (London, United Kingdom) (2010), 466 (7304), 347-351CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  In the high-transition-temp. (high-Tc) superconductors the pseudogap phase becomes predominant when the d. of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any assocd. order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the detn. of a quant. order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO2 unit cell. We analyze spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi2Sr2CaCu2O8+δ and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90°-rotational symmetry within every CuO2 unit cell.
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25. 25
  Kasahara, S.; Shi, H.; Hashimoto, K.; Tonegawa, S.; Mizukami, Y.; Shibauchi, T.; Sugimoto, K.; Fukuda, T.; Terashima, T.; Nevidomskyy, A. H.; Matsuda, Y. Electronic nematicity above the structural and superconducting transition in BaFe₂(As_1-xP_x)₂ Nature 2012, 486, 382 DOI: 10.1038/nature11178
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  25
  Electronic nematicity above the structural and superconducting transition in BaFe2(As1-xPx)2
  Kasahara, S.; Shi, H. J.; Hashimoto, K.; Tonegawa, S.; Mizukami, Y.; Shibauchi, T.; Sugimoto, K.; Fukuda, T.; Terashima, T.; Nevidomskyy, Andriy H.; Matsuda, Y.
  Nature (London, United Kingdom) (2012), 486 (7403), 382-385CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  Electronic nematicity, a unidirectional self-organized state that breaks the rotational symmetry of the underlying lattice, was obsd. in the Fe pnictide and Cu oxide high-temp. superconductors. Whether nematicity plays an equally important role in these two systems is highly controversial. In Fe pnictides, the nematicity has usually been assocd. with the tetragonal-to-orthorhombic structural transition at temp. Ts. Although recent expts. have provided hints of nematicity, they were performed either in the low-temp. orthorhombic phase or in the tetragonal phase under uniaxial strain, both of which break the 90° rotational C4 symmetry. Therefore, the question remains open whether the nematicity can exist above Ts without an external driving force. Here we report magnetic torque measurements of the isovalent-doping system BaFe2(As1-xPx)2, showing that the nematicity develops well above Ts and, moreover, persists to the non-magnetic superconducting regime, resulting in a phase diagram similar to the pseudogap phase diagram of the Cu oxides. By combining these results with synchrotron x-ray measurements, we identify two distinct temps.-one at T*, signifying a true nematic transition, and the other at Ts (<T*), which we show not to be a true phase transition, but rather what we refer to as a meta-nematic transition', in analogy to the well-known meta-magnetic transition in the theory of magnetism.
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26. 26
  Fujita, K.; Hamidian, M. H.; Edkins, S. D.; Kim, C. K.; Kohsaka, Y.; Azuma, M.; Takano, M.; Takagi, H.; Eisaki, H.; Uchida, S.-i.; Allais, A.; Lawler, M. J.; Kim, E.-A.; Sachdev, S.; Davis, J. C. S. Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates Proc. Natl. Acad. Sci. U. S. A. 2014, 111, E3026 DOI: 10.1073/pnas.1406297111
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27. 27
  Nakaoka, H.; Yamakawa, Y.; Kontani, H. Theoretical prediction of nematic orbital-ordered state in the Ti oxypnictide superconductor BaTi₂(As, Sb)₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 245122 DOI: 10.1103/PhysRevB.93.245122
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28. 28
  Davies, N. R.; Johnson, R. D.; Princep, A. J.; Gannon, L. A.; Ma, J.-Z.; Qian, T.; Richard, P.; Li, H.; Shi, M.; Nowell, H. Coupled commensurate charge density wave and lattice distortion in Na₂Ti₂Pn₂O (Pn = As, Sb) determined by X-ray diffraction and angle-resolved photoemission spectroscopy Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 104515 DOI: 10.1103/PhysRevB.94.104515
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29. 29
  Kuroki, K.; Usui, H.; Onari, S.; Arita, R.; Aoki, H. Pnictogen height as a possible switch between high-T_c nodeless and low-T_c nodal pairings in the iron-based superconductors Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 224511 DOI: 10.1103/PhysRevB.79.224511
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30. 30
  Miyake, T.; Nakamura, K.; Arita, R.; Imada, M. Comparison of ab initio low-energy models for LaFePO, LaFeAsO, BaFe₂As₂, LiFeAs, FeSe, and FeTe: electron correlation and covalency J. Phys. Soc. Jpn. 2010, 79, 044705 DOI: 10.1143/JPSJ.79.044705
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  30
  Comparison of ab initio low-energy models for LaFePO, LaFeAsO, BaFe2As2, LiFeAs, FeSe, and FeTe: electron correlation and covalency
  Miyake, Takashi; Nakamura, Kazuma; Arita, Ryotaro; Imada, Masatoshi
  Journal of the Physical Society of Japan (2010), 79 (4), 044705/1-044705/20CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
  Effective low-energy Hamiltonians for several different families of iron-based superconductors are compared after deriving them from the downfolding scheme based on first-principles calcns. Systematic dependences of the derived model parameters on the families are elucidated, many of which are understood from the systematic variation of the covalency between Fe-3d and pnictogen-/chalcogen-p orbitals. First, LaFePO, LaFeAsO (1111), BaFe2As2 (122), LiFeAs (111), FeSe, and FeTe (11) have overall similar band structures near the Fermi level, where the total widths of 10-fold Fe-3d bands are mostly around 4.5 eV. However, the derived effective models of the 10-fold Fe-3d bands (d model) for FeSe and FeTe have substantially larger effective onsite Coulomb interactions U ∼ 4.2 and 3.4 eV, resp., after the screening by electrons on other bands and after averaging over orbitals, as compared to ∼2.5 eV for LaFeAsO. The difference is similar in the effective models contg. p orbitals of As, Se or Te (dp or dpp model), where U ranges from ∼4 eV for the 1111 family to ∼7 eV for the 11 family. The exchange interaction J has a similar tendency. The family dependence of models indicates a wide variation ranging from weak correlation regime (LaFePO) to substantially strong correlation regime (FeSe). The origin of the larger effective interaction in the 11 family is ascribed to smaller spread of the Wannier orbitals generating larger bare interaction, and to fewer screening channels by the other bands. This variation is primarily derived from the distance h between the pnictogen/chalcogen position and the Fe layer: The longer h for the 11 family generates more ionic character of the bonding between iron and anion atoms, while the shorter h for the 1111 family leads to more covalent-bonding character, the larger spread of the Wannier orbitals, and more efficient screening by the anion p orbitals. The screened interaction of the d model is strongly orbital dependent, which is also understood from the Wannier spread. The dp and dpp models show much weaker orbital dependence. The larger h also explains why the 10-fold 3d bands for the 11 family are more entangled with the smearing of the "pseudogap" structure above the Fermi level seen in the 1111 family. While the family-dependent semimetallic splitting of the bands primarily consists of dyz/dzx and dx2-y2 orbitals, the size of the pseudogap structure is controlled by the hybridization between these orbitals and dxy/d3z2-r2: A large hybridization in the 1111 family generates a large "band-insulating"-like pseudogap (hybridization gap), whereas a large h in the 11 family weakens them, resulting in a "half-filled" like bands of orbitals. This may enhance strong correlation effects in analogy with Mott physics and causes the orbital selective crossover in the three orbitals. On the other hand, the geometrical frustration t'/t, inferred from the ratio of the next-nearest transfer r' to the nearest one t of the d model is relatively larger for the 1111 family than the 11 one. The models comprehensively derived here may serve as a firm starting basis of understanding both common and diverse properties of the iron-based superconductors including magnetism and supercond.
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31. 31
  Singh, D. J. Electronic structure, disconnected Fermi surfaces and antiferromagnetism in the layered pnictide superconductor Na_xBa_1-xTi₂Sb₂O New J. Phys. 2012, 14, 123003 DOI: 10.1088/1367-2630/14/12/123003
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32. 32
  Yan, X.-W.; Lu, Z.-Y. Layered pnictide-oxide Na₂Ti₂Pn₂O (Pn = As, Sb): a candidate for spin density waves J. Phys.: Condens. Matter 2013, 25, 365501 DOI: 10.1088/0953-8984/25/36/365501
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  32
  Layered pnictide-oxide Na2Ti2Pn2O (Pn = As, Sb). A candidate for spin density waves
  Yan, Xun-Wang; Lu, Zhong-Yi
  Journal of Physics: Condensed Matter (2013), 25 (36), 365501, 9 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
  From 1st-principles calcns., we have studied the electronic and magnetic structures of compd. Na2Ti2Pn2O (Pn = As or Sb), whose crystal structure is a bridge between or a combination of those of high-Tc superconducting cuprates and Fe pnictides. We find that in the ground state Na2Ti2As2O is a novel blocked checkerboard antiferromagnetic semiconductor with a small band gap of about 0.15 eV. In contrast, Na2Ti2Sb2O is a bi-collinear antiferromagnetic semimetal, with a small moment of about 0.5 μB around each Ti atom. We show that there is a strong Fermi surface nesting in Na2Ti2Pn2O, and we verify that the blocked checkerboard and bi-collinear antiferromagnetic states both are the spin d. waves induced by the Fermi surface nesting. A tetramer structural distortion is found in company with the formation of a blocked checkerboard antiferromagnetic order, in good agreement with the exptl. obsd. commensurate structural distortion but with space group symmetry retained after the anomaly happens.
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33. 33
  Suetin, D.; Ivanovskii, A. Structural, electronic properties, and chemical bonding in quaternary layered titanium pnictide-oxides Na₂Ti₂Pn₂O and BaTi₂Pn₂O (Pn = As, Sb) from FLAPW-GGA calculations J. Alloys Compd. 2013, 564, 117 DOI: 10.1016/j.jallcom.2013.02.155
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  33
  Structural, electronic properties, and chemical bonding in quaternary layered titanium pnictide-oxides Na2Ti2Pn2O and BaTi2Pn2O (Pn = As, Sb) from FLAPW-GGA calculations
  Suetin, D. V.; Ivanovskii, A. L.
  Journal of Alloys and Compounds (2013), 564 (), 117-124CODEN: JALCEU; ISSN:0925-8388. (Elsevier B.V.)
  By the 1st-principles FLAPW-GGA calcns., we have investigated the main trends in structural, electronic properties, and chem. bonding for a series of quaternary Ti pnictide-oxides: Na2Ti2As2O, Na2Ti2Sb2O, BaTi2As2O, and BaTi2Sb2O, which attracted now much attention as parent phases for a novel group of layered Fe-free superconducting materials. Our results cover the optimized lattice parameters and at. positions, electronic bands, Fermi surface topol., total and partial d. of electronic states. Besides, Bader anal. and the charge d. maps are used to discuss the chem. bonding for the examd. materials. We find that the at. substitutions lead to anisotropic deformation of the crystal structure; this effect is related to strong anisotropy of interat. bonds, which are of a mixed (covalent-ionic-metallic) type - in blocks [Ti2Pn2O], whereas the bonding between blocks [Ti2Pn2O] and at. sheets of Na, Ba ions is of an ionic type. The actual effective at. charges differ from the formal ionic charges due to covalency in blocks [Ti2Pn2O]. The near-Fermi electronic bands, which are responsible for metallic-like behavior of these materials and will be involved in the formation of superconducting state, arise mainly from the Ti 3dxy, dx2-y2, and dz2 states of the blocks [Ti2Pn2O], which define also the anisotropic character of conduction happening mainly in these blocks. The differences in the topol. of the multi-sheet Fermi surfaces of these materials are discussed.
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34. 34
  Chen, D.; Zhang, T.-T.; Song, Z.-D.; Li, H.; Zhang, W.-L.; Qian, T.; Luo, J.-L.; Shi, Y.-G.; Fang, Z.; Richard, P.; Ding, H. New phase transition in Na₂Ti₂As₂O revealed by Raman scattering Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 140501 DOI: 10.1103/PhysRevB.93.140501
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35. 35
  Note that we need to take special care when comparing our calculated geometry with an experimental one due to Davis et al. (28) We found that the atomic positions listed in their Table 1 are incompatible with their superstructure vectors, , , and , described in their main text: (28) (1) If the description in the main text is assumed to be correct, then Na and Sb positions in the superstructure are respectively located unlikely far from their undistorted positions. (2) O is not located at (0.0, 0.0) in their Figure 6a, being inconsistent with their Table 1. Accordingly, we speculate that they again define the superstructure vectors compatible with the atomic positions in their Table 1, which differs from that in their main text. We also found y = 0.0 for As3 in their Table 1 must be a typo and correctly y = 0.25 because As3 should occupy 8j Wyckoff site and its undistorted position is y = 0.5. Assuming our speculation is correct, our optimized geometry parameters agree well with their experimental values.
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36. 36
  Van De Walle, A.; Ceder, G. The effect of lattice vibrations on substitutional alloy thermodynamics Rev. Mod. Phys. 2002, 74, 11 DOI: 10.1103/RevModPhys.74.11
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  36
  The effect of lattice vibrations on substitutional alloy thermodynamics
  Van De Walle, A.; Ceder, G.
  Reviews of Modern Physics (2002), 74 (1), 11-45CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
  A review. A long-standing limitation of first-principles calcns. of substitutional alloy phase diagrams is the difficulty in accounting for lattice vibrations. A survey of the theor. and exptl. literature seeking to quantify the effect of lattice vibrations on phase stability indicates that they can be significant. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2 kB/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693 kB/atom). This article presents the basic formalism underlying ab initio phase diagram calcns., along with the generalization required to account for lattice vibrations. The authors review the various techniques allowing the theor. calcn. and the exptl. detn. of phonon dispersion curves and related thermodn. quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and vol. change arguments. Vibrational entropy change can be attributed to the changes in chem. bond stiffness assocd. with the changes in bond length that take place during a phase transformation. This so-called "bond stiffness vs. bond length" interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.
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37. 37
  Whangbo, M.-H.; Koo, H.-J.; Villesuzanne, A.; Pouchard, M. Effect of Metal-Oxygen Covalent Bonding on the Competition between Jahn-Teller Distortion and Charge Disproportionation in the Perovskites of High-Spin d⁴ Metal Ions LaMnO₃ and CaFeO₃ Inorg. Chem. 2002, 41, 1920 DOI: 10.1021/ic0110427
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38. 38
  Cammarata, A.; Rondinelli, J. M. Covalent dependence of octahedral rotations in orthorhombic perovskite oxides J. Chem. Phys. 2014, 141, 114704 DOI: 10.1063/1.4895967
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  Covalent dependence of octahedral rotations in orthorhombic perovskite oxides
  Cammarata, Antonio; Rondinelli, James M.
  Journal of Chemical Physics (2014), 141 (11), 114704/1-114704/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The compositional dependence of metal-O BO6 octahedral distortions, including bond elongations and rotations, is frequently discussed in the ABO3 perovskite literature; structural distortions alleviate internal stresses driven by under- or over-coordinated bond environments. Here the authors identify the dependence of octahedral rotations from changes in metal-O bond covalency in orthorhombic perovskites. Using d. functional theory the authors formulate a covalency metric, which captures both the real and k-space interactions between the magnitude and sense, i.e., in-phase or out-of-phase, octahedral rotations, to explore the link between the ionic-covalent Fe-O bond and the interoctahedral Fe-O-Fe bond angles in Pbnm ferrates. The authors' survey finds that the covalency of the metal-O bond is correlated with the rotation amplitude: the more covalent the Fe-O bond, the less distorted is the structure and the more important the long-range inter-octahedral (Fe-O-Fe bond angle) interactions were found. Finally, to indirectly tune the B-O bond covalency by A-cation induced BO6 rotations independent of ionic size, facilitating design of targeted bonding interactions in complex perovskites. (c) 2014 American Institute of Physics.
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39. 39
  Hughbanks, T.; Hoffmann, R. Chains of trans-edge-sharing molybdenum octahedra: metal-metal bonding in extended systems J. Am. Chem. Soc. 1983, 105, 3528 DOI: 10.1021/ja00349a027
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  Chains of trans-edge-sharing molybdenum octahedra: metal-metal bonding in extended systems
  Hughbanks, Timothy; Hoffmann, Roald
  Journal of the American Chemical Society (1983), 105 (11), 3528-37CODEN: JACSAT; ISSN:0002-7863.
  A detailed anal. of bonding in systems with chains of condensed Mo octahedra is given. A 1-dimensional model proves to be applicable over the range of molybdates yet synthesized. The electronic coupling between chains is discussed. Distortions in newly synthesized quaternary systems are seen to result from increased electron count on the Mo chains. The band theoretic explanation of these distortions parallels the treatment of 2nd-order Jahn-Teller distortions.
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40. 40
  Dronskowski, R.; Bloechl, P. E. Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations J. Phys. Chem. 1993, 97, 8617 DOI: 10.1021/j100135a014
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  Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations
  Dronskowski, Richard; Bloechl, Peter E.
  Journal of Physical Chemistry (1993), 97 (33), 8617-24CODEN: JPCHAX; ISSN:0022-3654.
  After giving a concise overview of the current knowledge in the field of quantum mech. bonding indicators for mols. and solids, the authors show how to obtain energy-resolved visualization of chem. bonding in solids by d.-functional electronic structure calcns. From a band structure energy partitioning scheme, i.e., rewriting the band structure energy as a sum of orbital pair contributions, the authors derive what is to be defined as crystal orbital Hamilton populations (COHP). In particular, a COHP(ε) diagram indicates bonding, nonbonding, and antibonding energy regions within a specified energy range while an energy integral of a COHP gives access to the contribution of an atom or a chem. bond to the distribution of 1-particle energies. A further decompn. into specific AOs or symmetry-adapted linear combinations of AOs (hybrids) can easily be performed by using a projector technique involving unitary transformations. Because of its structural simplicity and the availability of reliable thermodn. data, the authors study the bonding within cryst. silicon (diamond phase) 1st. As a basis set, both bcc. screened and diamond screened at.-centered tight-binding linear muffin-tin orbitals (TB-LMTOs) are used throughout. The shape of COHP vs. energy diagrams and the significance of COHP subcontributions (s-s, sp3-sp3) are analyzed. Specifically, the difference between the COHPs energy integral (1-particle bond energy) and the exptl. bond energy is critically examd. While abs. values for the 1-particle bond energy show a high basis set dependence due to changing on-site (crystal field) COHP terms, the shape of off-site (bonding) COHP functions, elucidating the local bonding principle within an extended structure, remains nearly unaffected.
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41. 41
  Grechnev, A.; Ahuja, R.; Eriksson, O. Balanced crystal orbital overlap population—a tool for analysing chemical bonds in solids J. Phys.: Condens. Matter 2003, 15, 7751 DOI: 10.1088/0953-8984/15/45/014
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  Balanced crystal orbital overlap population-a tool for analysing chemical bonds in solids
  Grechnev, Alexei; Ahuja, Rajeev; Eriksson, Olle
  Journal of Physics: Condensed Matter (2003), 15 (45), 7751-7761CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
  A new tool for analyzing theor. the chem. bonding in solids is proposed. A balanced crystal orbital overlap population (BCOOP) is an energy resolved quantity which is pos. for bonding states and neg. for antibonding states, hence enabling a distinction between bonding and antibonding contributions to the chem. bond. Unlike the conventional crystal orbital overlap population (COOP), BCOOP handles correctly the situation of crystal orbitals being nearly linear dependent, which is often the case in the solid state. Also, BCOOP is much less basis set dependent than COOP. A BCOOP implementation within the full-potential linear muffin tin orbital method is presented and illustrated for Si, TiC and Ru. Thus, BCOOP is compared to the COOP and crystal orbital Hamilton population (COHP) for systems with chem. bonds ranging from metallic to covalent character.
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42. 42
  The angle of O–Ti–Pn becomes 87° even at the most stable point for Pn = Sb. The corresponding displacement is 0.125 Å (Figure 9a). In this case, the restoring force between Ti and the nearest O contributing to the direction of the displacement is negligible because cos(87°) is only 0.05.
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43. 43
  Zhang, G.; Glasbrenner, J. K.; Flint, R.; Mazin, I. I.; Fernandes, R. M. Double-stage nematic bond ordering above double stripe magnetism: Application to BaTi₂Sb₂O Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 95, 174402 DOI: 10.1103/PhysRevB.95.174402
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44. 44
  Fan, G.; Zhang, X.; Shi, Y.; Luo, J. Charge density wave transition in Na₂Ti₂Sb₂O probed by ²³Na NMR Sci. China: Phys., Mech. Astron. 2013, 56, 2399 DOI: 10.1007/s11433-013-5347-3
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  Charge density wave transition in Na2Ti2Sb2O probed by 23Na NMR
  Fan, Guo Zhi; Zhang, Xu; Shi, You Guo; Luo, Jian Lin
  Science China: Physics, Mechanics & Astronomy (2013), 56 (12), 2399-2403CODEN: SCPMCL; ISSN:1674-7348. (Springer)
  Herein we investigated the electronic properties of layered transition-metal oxides Na2Ti2Sb2O by 23Na NMR (NMR) measurement. The resistivity, susceptibility and sp. heat measurements show a phase transition at approx. 114 K (TA). No splitting or broadening in the central line of 23Na NMR spectra is obsd. below and above the transition temp. indicating no internal field being detected. The spin-lattice relaxation rate divided by T (1/T1T) shows a sharp drop at about 110 K which suggests a gap opening behavior. Below the phase transition temp. zone, 1/T1T shows Fermi liq. behavior but with much smaller value indicating the loss of large part of electronic d. of states (DOS) because of the gap. No signature of the enhancement of spin fluctuations or magnetic order is found with the decreasing temp. These results suggest a commensurate charge-d.-wave (CDW) phase transition occurring.
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45. 45
  Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865 DOI: 10.1103/PhysRevLett.77.3865
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  Generalized gradient approximation made simple
  Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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46. 46
  Giannozzi, P. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials J. Phys.: Condens. Matter 2009, 21, 395502 DOI: 10.1088/0953-8984/21/39/395502
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  QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
  Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
  Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
  QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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  Blöchl, P. E. Projector augmented-wave method Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953 DOI: 10.1103/PhysRevB.50.17953
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  Projector augmented-wave method
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  The structure of Na2Ti2Sb2O was studied by temp.-dependent powder neutron diffraction. Na2Ti2Sb2O crystallizes in I4/mmm symmetry. The structure of this phase can be viewed as an anti-K2NiF4 type where Ti3+ ion is located between two O atoms forming a square-planar lattice. Powder neutron diffraction studies of Na2Ti2Sb2O indicate that this compd. has a structural distortion in the [Ti2Sb2O]2- layer at T ≈ 120 K. This transition corresponds well to the previously reported anomalous transition temp. of the magnetic susceptibility and electronic resistivity. Several models to explain the data are presented and discussed. (c) 2000 Academic Press.
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Investigation into Structural Phase Transitions in Layered Titanium-Oxypnictides by a Computational Phonon Analysis

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Abstract

Synopsis

Introduction

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Discussion

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Author Information

Acknowledgment

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Abstract

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