Metal-to-Insulating Transition in the Perovskite System YSr2Cu2FeO8−δ (0 < δ < 1) Modeled by DFT Methods Marianela Gómez-Toledo, Sara A. López-Paz, Susana García-Martín, and M. Elena Arroyo-de Dompablo* Cite This: https://doi.org/10.1021/acs.inorgchem.2c03475 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information ABSTRACT: Progress in the design of functional perovskite oxides relies on advances in density functional theory (DFT) methods to efficiently and effectively model complex systems composed of several transition-metal ions. This work reports the application of DFT methods to investigate the electronic structure of the YSr2Cu2FeO8−δ (0 < δ < 1) family in which the insulating, metal, or superconducting behaviors and even anion conductivity can be tuned by modifying the oxygen content. In particular, we assess the performance of the generalized gradient approximation (GGA), its Hubbard-U correction (GGA + U), and the strongly constrained and appropriately normed (SCAN) to model the metallic (idealized YSr2Cu2FeO8) and insulating (idealized YSr2Cu2FeO7) phases of the system. The analysis of the DFT results is supported by DC resistivity measurements that denote the metal character of the synthesized YSr2Cu2FeO7.86 and the semiconducting character of YSr2Cu2FeO7.08 prepared under reducing conditions. In addition, the band gap of YSr2Cu2FeO7.08, in the range of 0.73−1.2 eV, has been extracted from diffuse reflectance spectroscopy (DRS). While the three methodologies (GGA, GGA + U, SCAN) permit the reproduction of the crystal structures of the synthetized oxides (determined here in the case of YSr2Cu2FeO7.08 by neutron powder diffraction (NPD)), the SCAN emerges as the only one capable to predict the basic electronic and magnetic properties across the YSr2Cu2FeO8−δ (0 < δ < 1) series. The picture that emerges for the metal (δ = 0) to insulating (δ = 1) transition is the one in which oxygen vacancies contribute electrons to the filling of the Cu/Fe-3dx2−y2 states of the conduction band. These results validate the SCAN functional for future DFT investigations of complex functional oxides that combine several transition metals. 1. INTRODUCTION Perovskite-type oxides (ABO3 and related materials) exhibit a broad range of functional properties that derive in multiple and relevant applications.1 To better understand the properties and optimize the applications of these oxides, a profound knowledge of their crystal and electronic-structure relation- ships is compulsory. Nowadays, electronic-structure calcula- tions based on density functional theory (DFT) are extensively applied to successfully predict and design materials with particular properties. Since the development of DFT by Holenberg, Kohn, and Sham,2,3 a great deal of improvement on exchange-correlation (XC) functionals has been reported, such as the widely used generalized gradient approximation (GGA) developed in the late 1980s.4,5 The GGA functionals have offered some acceptable results in the modeling of perovskite oxides based on d0 transition metals (TM).6−9 However, the overestimation of electron delocalization and metallic character is a known failure of DFT methods for systems with localized and strongly interacting d-electrons and f-electrons.10−13 In the 1990s, the DFT + U method introduced an explicit treatment of electron correlation with a Hubbard-like model for a subset of states in the system.10,14 Vast literature demonstrates the suitability of the DFT + U approach to investigate TM oxides with strong Coulomb correlations. More recently, the strongly constrained and appropriately normed (SCAN) meta-GGA functional15 has shown good performance to model the basic physical properties and phenomena associated to correlated oxides.16,17 For instance, investigations on perovskite-related oxides using meta-GGA functionals (and particularly SCAN) have accu- rately described the transition from the insulating to the metallic character of La2CuO4 by substitution of La by Sr in the superconducting system;18 the layered ordering stabiliza- Received: September 30, 2022 Articlepubs.acs.org/IC © XXXX The Authors. Published by American Chemical Society A https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX D ow nl oa de d vi a U N IV C O M PL U T E N SE D E M A D R ID o n Fe br ua ry 1 6, 2 02 3 at 0 9: 43 :5 1 (U T C ). Se e ht tp s: //p ub s. ac s. or g/ sh ar in gg ui de lin es f or o pt io ns o n ho w to le gi tim at el y sh ar e pu bl is he d ar tic le s. https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Marianela+Go%CC%81mez-Toledo"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sara+A.+Lo%CC%81pez-Paz"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Susana+Garci%CC%81a-Marti%CC%81n"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="M.+Elena+Arroyo-de+Dompablo"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="M.+Elena+Arroyo-de+Dompablo"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.inorgchem.2c03475&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?goto=articleMetrics&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?goto=recommendations&?ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?goto=supporting-info&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=abs1&ref=pdf pubs.acs.org/IC?ref=pdf https://pubs.acs.org?ref=pdf https://pubs.acs.org?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://pubs.acs.org/IC?ref=pdf https://pubs.acs.org/IC?ref=pdf https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ https://acsopenscience.org/open-access/licensing-options/ tion of the Bi2MFeO6 perovskites (M = Al, Ga, In) induced by the Fe−magnetic interactions;19 the effect of the hole and electron doping in the electronic structure of Sm1−xMxNiO3 (M = Ca, Ce);20 and have predicted the structural cubic- symmetry breaking, band-gap existence, and magnetic behavior in ABO3 perovskites with B = 3d-TM.21 Despite the substantial progress in the computational investigation of perovskites, the scenario complicates when different TM ions occupy the B positions, even if this occurs in an ordered manner. Hence, assessing the performance of DFT methodologies and, specifically, of the recently developed SCAN functional at a basic property-level prediction�crystal, electronic, and magnetic structures�is a prerequisite to further investigating the particular properties of complex perovskite oxides. In the present work, we focus on the YSr2Cu2FeO8−δ (0 < δ < 1) family derived from the so-called “YBaCuO” superconducting cuprates.22,23 Figure 1a,b displays the graphic representation of the crystal structure of the idealized stoichiometric endmembers YSr2Cu2FeO8 and YSr2Cu2FeO7 (δ = 0 and 1, respectively). The structures consist of an alternation of FeO2−δ/SrO/CuO2/Y/CuO2/SrO layers along the c-axis or a-axis (space group (S.G.) P4/mmm and S.G. Ima2 settings, respectively). The idealized YSr2Cu2FeO8, with [FeO6] octahedral units in the Fe layers, presents a tetragonal (S.G. P4/mmm) crystal structure with ap × ap × 3ap unit cell dimensions (ap refers to the lattice parameter of the cubic perovskite structure).24 Lowering the oxygen content (δ > 0) creates vacancies in the O3 positions of the FeO2−δ layer (Figure 1) so that in the YSr2Cu2FeO8−δ family, the Fe atoms may adopt octahedral, tetrahedral, and/or square pyramid coordination.23−27 In combination with the Y and Sr ordering, there is layered ordering of the coordination polyhedra (octahedra O, square pyramid SP, and tetrahedra T) around the Fe and Cu atoms in the manner O/SP/SP/O in the idealized YSr2Cu2FeO8 and like T/SP/SP/T in the idealized YSr2Cu2FeO7. In addition, in the idealized YSr2Cu2FeO7, the different orientation of the tetrahedral coordination polyhedra of the Fe atoms leads to a sixfold superstructure (6ap × √2ap × √2ap within the Ima2 space group).23,28 YSr2Cu2FeO8−δ (0 < δ < 1) compounds show a non- stoichiometric anion sublattice resulting from the interplay between different oxidation states of Fe and Cu atoms.22,23,29 Oxides of the system, with different oxygen content and properties, have already been reported. The highly oxidized term YSr2Cu2FeO7.85 obtained experimentally in ozone flow, with Fe in the unusual 4+ formal oxidation state and mixed Cu3+ and Cu2+ valences, is a metallic oxide with a superconducting transition at Tc = 70 K.24 The compound presents magnetic ordering arising from the ferromagnetic (FR) interactions below TN = 110 K between Fe4+ cations with parallel in-plane spins in the FeO2−δ layers coupled with a soft character of the antiferromagnetic (AFM) interactions between layers.24 The low oxygen content terms YSr2Cu2FeO7.08, 27 YSr2Cu2FeO7.11, 28 and YSr2Cu2FeO7.04, 26 prepared under reducing conditions, are insulators with mainly Fe3+ and Cu2+. In between those extremes, air-synthesized YSr2Cu2FeO7.56, mixed valence Fe3+/Fe4+ and Cu2+/Cu3+ oxide, exhibits an interesting electrochemical behavior associated with catalytic activity in the oxygen reduction Figure 1. Crystal structure representations of (a) idealized stoichiometric oxide YSr2Cu2FeO8 (ap × ap × 3ap unit cell, S.G. P4/mmm) and (b) idealized stoichiometric oxide YSr2Cu2FeO7 (6ap × √2ap × √2ap unit cell, S.G. Ima2). Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX B https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig1&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig1&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig1&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig1&ref=pdf pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as reaction (ORR), being a potential air electrode for solid oxide fuel cells (SOFCs).26,27 Modeling the evolution of the electronic structure of YSr2Cu2FeO8−δ from the metallic phase (δ ∼ 0) to the insulating one (δ ∼ 1), which is to say, the metal-to-insulating transition as a function of the oxygen content, constitutes a challenge for DFT methods, apart from the relevance of tuning the electronic properties of these materials to manage particular applications. Indeed, few computational works deal with the two facts that are found in YSr2Cu2FeO8−δ oxides: first, the combination of two transition-metal ions in the B positions of the crystal structure, and second, the occurrence of oxygen nonstoichiometry. Both aspects highly condition the electronic properties of the materials. We here report DFT calculations for the idealized stoichiometric compounds YSr2Cu2FeO8 and YSr2Cu2FeO7 as representatives of the experimentally obtained YSr2Cu2FeO7.85 and YSr2Cu2FeO7.08. The calculations have been performed within the GGA-Perdew, Burke, and Ernzerhof (PBE) functional (hereafter denoted as simply GGA), its Hubbard correction PBE + U (denoted as GGA + U), and the meta-GGA-SCAN functional (denoted as SCAN). We demonstrate that the three methodologies fairly reproduce the crystal structures. However, the prediction of the electrical and magnetic properties depends on the functional used for the calculation. While the metallic behavior and magnetic features of the YSr2Cu2FeO8 phase are well described with the GGA and SCAN functionals, the SCAN and GGA + U offer the best approaches to investigate the YSr2Cu2FeO7 com- pound. We also support the electronic-structure calculations with resistivity experiments that confirm the metal-to- insulating transition in the YSr2Cu2FeO8−δ (0 < δ < 1) system. In addition, the optical band gap of YSr2Cu2FeO7.08 has been determined from diffuse reflectance spectroscopy (DRS). 2. METHODOLOGY 2.1. Experimental Section. Our previous works cover the synthesis and structural characterization of several YSr2Cu2FeO8−δ oxides.24,27,30 In this work, polycrystalline YSr2Cu2FeO8−δ (δ = 0.15 and 0.92) compounds have been prepared by the conventional ceramic method in air. The intimate mixtures of Fe2O3 (Aldrich 99.99%), CuO (Aldrich 99.9999%), previously decarbonated Y2O3 (Aldrich 99.9%), and previously dehydrated SrCO3 (Aldrich 99.9%) in the stoichiometric relations were subjected to an initial treatment at 1173 K for 12 h in air. The resulting powders were ground in an agate mortar, pelletized, and subjected to several treatments at 1253 K in air, for 72 h, with intermediate grindings. The air-prepared sample was heated at 1023 K for 24 h in N2 flow to obtain YSr2Cu2FeO7.08 oxide and the N2 prepared compound was oxidized in ozone at 473 K to obtain YSr2Cu2FeO7.85. The crystal structure of the YSr2Cu2FeO7.08 compound at room temperature (RT) was determined by neutron powder diffraction (NPD) using the high-resolution D2B instrument at the ILL (Grenoble, France) with a wavelength of λ = 1.594 Å. Rietveld refinements were performed following the Fullprof software.31 DC electrical resistivity measurements of sintered pellets of YSr2Cu2FeO7.85 and YSr2Cu2FeO7.08 have been performed in the temperature region 5 < T < 300 K using a Quantum Design PPMS device. Four-probe electrical contacts were made using conductive mixed silver paste and gold wires. The resistivity was measured in sweep mode with a heating rate of 2 K/min. DRS measurements have been carried out to determine the optical band gap in YSr2Cu2FeO7.08. The experiments have been performed in a Cary 5G spectrophotometer with an external integrating sphere. The measurement range was 300− 3300 nm and the data interval was 1 nm. As stated by Kubelka and Munk,32 diffuse reflectance spectra can be transformed into absorption spectra through the Kubelka−Munk function (F(R∞), eq 1) F R K S R R ( ) (1 ) 2 2 = = (1) where R∞ is the absolute reflectance of an infinitely thick specimen and K and S are the absorption and scattering coefficients, respectively. F(R∞) is proportional to the extinction coefficient (α), which can be expressed by eq 2, according to the Tauc method33 h A h E( ) ( )1/ g= (2) where h is the Plank constant, ν is the photon frequency, Eg is the band-gap energy, and A is a constant. The γ factor considers the nature of the electronic transition, being equal to 1/2 for allowed direct and 2 for allowed indirect transition. Replacing α with F(R∞) results in the following expression (eq 3) F R h A h E( )( ) ( )1/ g= (3) The band gap can thus be extracted from diffuse reflectance spectra transformed according to eq 3. Linear fitting of the Tauc plot followed by extrapolating to the x-axis intersection gives the band-gap value. 2.2. Computational Section. Calculations for the idealized stoichiometric endmembers of the YSr2Cu2FeO8−δ family, YSr2Cu2FeO8 and YSr2Cu2FeO7, have been performed using the ab initio total-energy and molecular dynamics program Vienna ab initio simulation package (VASP) developed at the Universitaẗ Wien.34,35 The interaction of core electrons with the nuclei is described by the projector augmented wave (PAW) method36 with 2s22p4 of O, 3s23p63d74s1 of Fe, 3p63d104p1 of Cu, 4s24p65s2 of Sr, and 4s24p64d15s2 of Y treated as valence electrons. For the GGA approximation, we selected the exchange and correlation functional form developed by Perdew, Burke, and Ernzerhof (PBE).37 On the other hand, for the meta-GGA approx- imation, the strongly constrained and appropriately normed (SCAN)15 functional was used. In all cases, the energy cut off for the plane wave basis set was kept fixed at a constant value of 600 eV throughout the calculations. The integration in the Brillouin zone is done on appropriate sets of k-points determined by the Monkhorst−Pack scheme. The k-point meshes were set at 2 × 8 × 8 for YSr2Cu2FeO7 and 10 × 10 × 4 for YSr2Cu2FeO8, using a Gaussian smearing parameter of 0.05 eV. For the density of states (DOS) calculations, the tetrahedron method with Blöchl corrections38 was used. Self- consistency was achieved with a tolerance in total energy of 1 × 10−4 eV for geometry optimization and 1 × 10−6 eV for DOS calculations. A local Hubbard-U (GGA + U) was added to Fe and Cu atoms following the simplified rotationally invariant framework developed by Dudarev et al.39 Typically, U is formulated as Ueff Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX C pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as = U − J, where U is the onsite Coulomb term and J the exchange term. In this work, this effective parameter is simply referred to as U. The J value was fixed to 1 eV. An effective U value of 4 eV was used for the d orbitals of Cu and Fe, that were found appropriate in previous GGA + U investiga- tions.13,40−42 The local magnetic moments are taken from the difference between the projected electron density of up and down spins onto 1 Å radius sphere. Bader charge analysis43 was performed on the charge density files44 using the pymatgen package.45 In the present work, we have performed calculations using the idealized stoichiometric compositions YSr2Cu2FeO7 and YSr2Cu2FeO8 and perfect Cu/Fe ordering within the crystal structures. The crystallographic model of YSr2Cu2FeO8 oxide has been constructed taking the initial positions from YSr2Cu2FeO7.86 (ICSD file 11514),24 considering a ferromag- netic 2 × 2 × 1 superstructure of the tetragonal ap × ap × 3ap unit cell shown in Figure 1a (that is, Y4Sr8Cu8Fe4O32 composition). For YSr2Cu2FeO7 oxide, the 6ap × √2ap × √2ap (S.G. Ima2) unit cell has been used for the calculations (Y4Sr8Cu8Fe4O28), corresponding to an ideal arrangement of the tetrahedral chains (Figure 1b). The initial cell parameters and atomic positions of YSr2Cu2FeO7 were taken from the ICSD record of isostructural YSr2Cu2GaO7. 46 Although the magnetic structure of YSr2Cu2FeO8−δ phases with high δ values (δ ∼ 1) has not yet been experimentally determined, magnetic interactions associated to Fe3+ and Cu2+ cations are expected, and, as explained below, different magnetic structures have been considered. 3. RESULTS AND DISCUSSION 3.1. Experimental Section. The crystal structure and superconducting behavior of the compound with the highest oxygen content, YSr2Cu2FeO7.86, has previously been re- ported.24 In this work, the crystal structure of YSr2Cu2FeO7.08 is refined by NPD. Table 1 lists the results of the Rietveld refinement of the NPD pattern of YSr2Cu2FeO7.08 (Figure 2). The refined occupation factors of 8i and 8h crystallographic positions reveal certain disorder (antisite location) of the Fe and Cu atoms. Note that consistently with the oxygen content (δ = 0.92 in YSr2Cu2FeO8−δ), there is an occupation of 0.574 for O3 in 8i positions. In the idealized term δ = 1 (YSr2Cu2FeO7) where only tetrahedral-Fe is present, the fractional occupancy of O3 is of 0.5. Importantly, the results indicate that corrugation of the [FeO4] tetrahedral units and their relative orientation along the stacking direction originate an additional superstructure with a diagonal orthorhombic unit cell of dimensions √2ap × 6ap × √2ap in the Imma space group (note the change of S.G. setting as described in Table 2). Therefore, the refined crystal structure of YSr2Cu2FeO7.08 is in close agreement with the one reported by Mochiku et al. (ICSD file 151653) for the YSr2Cu2FeO7.11 compound.28 The crystallographic model with the Imma space group accounts for the presence of two types of tetrahedral chains in the Fe layers, which are left- and right-hand rotated. In this sense, the crystal structure of YSr2Cu2FeO7.08 can be considered as a disordered version of the model crystal structure of the stoichiometric YSr2Cu2GaO7 determined by Roth et al. (ICSD file 71263, used for the DFT calculations)46 in which the presence of a single chain orientation is well captured within the Ima2 space group, as it is represented in Figure 1b. The variation of the resistivity with the temperature of YSr2Cu2FeO7.86 shows the expected superconducting/metallic transition at Tc = 70 K (Figure 3a).24 Above the Tc, the increase of the electrical resistance with temperature reflects the metallic character (inset in Figure 3a). On the contrary, YSr2Cu2FeO7.08 oxide presents a semiconducting/insulating transition near 200 K (Figure 3b). The logarithmic plot of resistance (inset in Figure 3b) shows an activated behavior in the 200−300 K temperature range, with an activation energy (Ea) of 0.147(4) eV. The optical band gap of the YSr2Cu2FeO7.08 phase has been extracted from DRS measurements. The Tauc plot and Kubelka−Munk analysis offer an approximate estimation of optical band gap.32,33,47 However, if the nature of the electronic transition is not well known (as in the present case), the γ parameter (eq 2) value becomes an important source of uncertainty. For YSr2Cu2FeO7.08, considering a direct allowed electronic transition, from the Tauc plot we derive a band-gap value of 1.2 eV, while a band gap of 0.73 eV results if an indirect electronic transition is considered (Figure 3c). Methods such as photoluminescence (PL)48 and X-ray photoelectron spectroscopy (XPS)49 that offer an accurate band-gap determination are out of the scope of this paper. Given the above, this work considers the interval 1.2−0.73 eV Table 1. Atomic Positions and Cell Parameters Obtained from the Rietveld Refinement of the NPD Data for YSr2Cu2FeO7.08 a atom site x y z Biso (Å) occ. Y 4a 0 0 0 0.20(4) 1 Sr 8h 0 0.34911(7) 0.0067(8) 0.68(4) 1 Fe1/Cu1 8i 0.0440(8) 0.25 0.5584(5) 1.0(7) 0.426(7)/0.074(7) Cu2/Fe2 8h 0 0.42610(8) 0.5000(5) 0.28(3) 0.85(1)/0.15(1) O1 8h 0 0.3257(1) 0.4739(7) 1.30(5) 1 O2a 8g 0.25 0.0630(1) 0.25 0.39(2) 1 O2b 8g 0.25 −0.0649(1) 0.25 0.39(2) 1 O3 8i 0.390(1) 0.25 0.616(1) 2.1(1) 0.574(3) aS.G. Imma (no. 74); a = 5.4053(1) Å, b = 22.9136(5) Å, c = 5.4577(1) Å, V = 675.98(2) Å3, δ = 0.92; Rp = 3.62%; Rwp = 4.66%; χ2 = 4.22. Figure 2. Rietveld refinement of the room temperature (RT) NPD pattern of YSr2Cu2FeO7.08. Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX D https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig2&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig2&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig2&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig2&ref=pdf pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as to compare the band gap of YSr2Cu2FeO7.08 with the DFT- calculated band gap. 3.2. DFT Investigation of YSr2Cu2FeO8−δ. 3.2.1. Metallic YSr2Cu2FeO8 Phase. Regardless of the constraints in comparing the experimental data of YSr2Cu2FeO7.85 (δ = 0.15) and the idealized model YSr2Cu2FeO8 (δ = 0), all of the utilized DFT methodologies reproduce the experimental lattice parameters and bond distances (Table 2), with small deviations ranging from a maximum of 4% (GGA + U) to a minimum of 0.2% (SCAN). The compression of the Fe octahedra (d Fe−O1/d Fe−O3 < 1) and the elongation of the Cu-square pyramid (d Cu−O1/d Cu−O2 > 1) along the c-axis are also well captured. There are, however, some subtle differences in the predicting capabilities of the four DFT methodologies. Both the GGA and GGA + U methods tend to produce larger lattice parameters, bonding distances (see for instance Fe−O1), and cell volume than the SCAN functional. For the YSr2Cu2FeO8−δ family, both a and c lattice parameters decrease with increasing oxygen content,23 and hence the idealized stoichiometric compound YSr2Cu2FeO8 should have a lower volume than the synthesized YSr2Cu2FeO7.85. In this respect, the SCAN functional offers superior performance in predicting such volume reduction. The calculated magnetic moments and effective Bader charges (Table 3) differ among the different methodologies due to the distinct description of the transition-metal−oxygen bonding. The effective charge of all ions increases from the GGA to the GGA + U, as expected, due to the decreasing covalency of the Fe−O and Cu−O chemical bonds when correlation effects are taken into account. The poor electron localization in the GGA and SCAN approximations yields low magnetic moments on the transition-metal ions (0−0.2 and 2.7−3.0 μB per Cu and Fe atom, respectively). Treating the correlation effects results in higher electron localization and larger calculated magnetic moments for Cu atoms (0.5 μB) and Fe atoms (3.4 μB). Neutron diffraction results and Mössbauer spectra of YSr2Cu2FeO7.85 yielded a magnetic moment μ0 (Fe) = 1.7−2 μB per Fe atom that the authors attributed to Fe4+ ion in low-spin configuration (t2g 4eg0).24 No magnetic moment was detected for Cu3+/2+ ions. In this regard, although quantitative comparison of magnetic moments with experiments is complicated due to the observed Cu/Fe antisite mixing24,50 and differences in the oxygen content, the GGA, and SCAN methodologies offer a more appropriate description than the GGA + U. The three DFT approximations predict the metallic behavior of the YSr2Cu2FeO8 oxide (see calculated DOS in Figure 4). Compared to the GGA method, the introduction of the U term produces a downshift of the occupied Cu/Fe-3d states. The U parameter keeps the 3d orbitals of Fe ions atomic-like, diminishing their hybridization with the 2p orbitals of the oxygen ions (less covalent Fe−O bonding). Although the Fe down-spin states are partially occupied under all approxima- tions, the occupancy is the lowest for the GGA + U methodology, therefore resulting in the larger magnetic moment of 3.4 μB per Fe atom, which is close to that expected for a high-spin Fe4+ configuration (t2g 3eg1), and deviates from the experimental observations. 3.2.2. Insulating YSr2Cu2FeO7 Phase. Figure 5a−c shows the magnetic structures considered to model the idealized YSr2Cu2FeO7 oxide. In the A-type structure, there are FM Cu/ Fe in-plane interactions, while the planes order antiferromag- netically along the a-axis (tetragonal c-axis in YSr2Cu2FeO8). InT ab le 2. C al cu la te d U ni tC el lP ar am et er s (Å ), U ni tC el lV ol um e (Å 3 ) ,V ol um e pe r A to m (Å 3 ) ,a nd Se le ct ed B on d Le ng th s (Å ) fo r YS r 2 C u 2 Fe O 7 an d YS r 2 C u 2 Fe O 8 Id ea liz ed O xi de sa YS r 2 Fe C u 2 O 8 ex pe rim en ta lY Sr 2F eC u 2 O 7. 85 G G A G G A + U SC AN YS r 2 Fe C u 2 O 7 ex pe rim en ta lb YS r 2 Fe C u 2 O 7. 08 C -A F G G A C -A F G G A + U C -A F SC AN a, b 3. 81 45 (3 ) 3. 82 52 3. 83 15 3. 78 61 a 22 .9 13 6( 5) b 23 .1 33 7 23 .1 42 4 22 .8 52 9 c 11 .3 27 (7 ) 11 .3 80 3 11 .5 45 7 11 .2 75 5 b 5. 45 77 (1 )b 5. 50 07 5. 50 69 5. 44 11 V 16 4. 81 (1 ) 16 6. 52 16 9. 50 16 1. 62 c 5. 40 53 (1 )b 5. 42 41 5. 42 65 5. 37 44 V pe r at om 11 .7 7 11 .8 9 12 .1 0 11 .5 4 V 67 5. 98 (2 ) 69 0. 13 69 1. 63 66 8. 22 d Fe − O 3 1. 90 72 (2 ) 1. 91 26 1. 91 57 1. 89 30 V pe r at om 13 .0 0 13 .2 7 13 .3 0 12 .8 5 d Fe − O 1 1. 84 3( 4) 1. 85 50 1. 88 13 1. 84 17 m ea n d Fe − O 1. 87 32 1. 87 54 1. 90 14 1. 87 32 d Fe − O 1/ d Fe − O 3 0. 96 63 0. 96 99 0. 98 20 0. 97 29 Fe − O 3− Fe 12 4. 6° 12 6. 0° 12 2. 9° 12 4. 5° d C u− O 2 1. 92 44 (4 ) 1. 93 55 1. 94 73 1. 91 47 d C u− O 2 1. 93 3( 2) /1 .9 34 (2 ) 1. 93 65 /1 .9 45 6 1. 94 13 /1 .9 50 7 1. 92 67 /1 .9 33 8 d C u− O 1 2. 11 7( 4) 2. 11 34 2. 11 97 2. 08 12 d C u− O 1 2. 30 2( 4) 2. 43 27 2. 38 83 2. 34 49 d C u− O 1/ d C u− O 2 1. 10 00 1. 09 19 1. 08 85 1. 08 70 d C u− O 1/ d C u− O 2 1. 19 06 1. 25 33 1. 22 73 1. 21 48 d C u− C u 3. 40 7( 4) 3. 44 35 3. 54 39 3. 42 97 d C u− C u 3. 38 4( 4) 3. 28 37 3. 35 06 3. 30 95 d C u− Fe 3. 96 0( 3) 3. 96 84 4. 00 09 3. 92 29 d C u− Fe 4. 05 6( 2) 4. 16 39 4. 13 37 4. 08 15 a T he ex pe rim en ta ld at a of YS r 2 C u 2 Fe O 7. 86 (I C SD � 11 51 4) an d YS r 2 C u 2 Fe O 7. 08 (t hi s w or k) ar e in cl ud ed fo r co m pa ris on .F or th e G G A + U m et ho d, a va lu e of U = 4 eV is us ed fo r bo th C u an d Fe . b La tti ce pa ra m et er s gi ve n in th e se tti ng fo r th e S. G .I m a2 .T he un it ce ll m et ric s co rr es po nd in g w ith th e S. G .I m m a (T ab le 1) is a (I m m a) < > c (I m a2 ); b (I m m a) < > a (I m a2 ); an d c (I m m a) < > b (I m a2 ). Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX E pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as the C-type, for each magnetic site, an in-plane AFM configuration between nearest-neighbor spins exits, while a FM configuration is set between the Fe and Cu planes. However, the sign reverses across the Y-layers due to the AFM direct exchange between Cu2+ cations at the face-confronted pyramids. Within each (CuO2−SrO−FeO−SrO−CuO2) block, a C-type magnetic ordering is thus defined since the Cu/Fe magnetic moments can be grouped as chains along the a-axis (tetragonal c-axis in YSr2Cu2FeO8). The G-type presents the same AFM in-plane magnetic ordering of the C-type, but with AFM interactions between the Cu and Fe planes. The four magnetic states tested to model YSr2Cu2FeO7 follow the energetic ordering: FM ∼ A-AFM ≫ G-AFM ∼ C- AFM (Table 4). The large stabilization of the G and C-AFM types (about 0.4 eV/fu respective to the FM configuration) denotes strong in-plane Cu/Fe AFM interactions. On the Figure 3. Normalized DC resistance for (a) YSr2Cu2FeO7.85 and (b) YSr2Cu2FeO7.08 oxides. The Arrhenius plot used for the determination of the activation energy (Ea) is also shown in panel (b) as an inset. Tauc plot for YSr2Cu2FeO7.08 oxide considering direct (c) and indirect (d) allowed electronic transitions. Table 3. Calculated Local Magnetic Moments μ (in μB per Atom) and Effective Bader Charges (Q) for Idealized YSr2Cu2FeO7 and YSr2Cu2FeO8 Oxides a YSr2Cu2FeO8 C-AFM YSr2Cu2FeO7 GGA GGA + U SCAN GGA GGA + U SCAN Q (Fe) 1.796 1.881 1.930 Q (Fe) 1.481 1.643 1.628 Q (Cu) 1.073 1.090 1.157 Q (Cu) 0.942 1.010 1.081 Q (O1) −1.158 −1.187 −1.228 Q (O1) −1.267 −1.324 −1.347 Q (O2) −1.187 −1.192 −1.232 Q (O2) −1.235 −1.260 −1.310 Q (O3) −1.125 −1.175 −1.175 Q (O3) −1.210 −1.297 −1.300 μ (Fe) 2.7 3.4 3.0 μ (Fe) 3.6 4.1 3.9 μ (Cu) 0.0 0.5 0.2 μ (Cu) 0.0 0.5 0.5 μ (O1) 0.1 0.0 0.1 μ (O1) 0.2 0.2 0.2 μ (O2) 0.0 0.1 0.0 μ (O2) 0.0 0.0 0.0 μ (O3) 0.2 0.1 0.1 μ (O3) 0.0 0.0 0.0 aWithin the GGA + U method, a value of U = 4 eV is used for both Cu and Fe. Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX F https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig3&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig3&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig3&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig3&ref=pdf pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as other hand, the small energy difference between G and C-AFM types, and between A-AFM and FM types, (5 meV/fu) suggests weak interplane magnetic interactions. The GGA, GGA + U, and SCAN methodologies predict the C-AFM to be the ground state, which has therefore been chosen to investigate the crystal and electronic structures of YSr2Cu2FeO7. Independently on the utilized functional, the optimization of the crystal structure of the idealized YSr2Cu2FeO7 oxide results in lattice parameters in reasonable agreement with the experimental values of YSr2Cu2FeO7.08 with errors below 2.1% (Table 2 and Figure S1). The GGA and GGA + U tend to overestimate the lattice parameters and TM−O distances, while the SCAN functional underestimates them. For the Fe environment, all of the approximations give a satisfactory description of the average bond distances (errors below 0.7%), and even of the corrugation of the [FeO] layers, the SCAN results being the closest to the experimental values. However, the Cu−O square pyramidal environment is more elongated than the one experimentally observed (d axial/d equatorial, d Cu−O1/d Cu−O2 in Table 2). Since the hybridization of the Cu-apical oxygen plays a significant role in the electronic structure of YBCO-related oxides,51 it is worth noting that the deviations in the Cu−O1 bond lengths are of 5.5% (GGA), 3.6% (GGA + U), and 1.7% (SCAN). According to the major deviation in the Cu−O1 bond distance, the GGA fails to reproduce the semiconducting behavior of YSr2Cu2FeO7.08 (calculated DOS in Figure 6a) in clear disagreement with the experimental observations (Figure 3b). While the GGA incorrectly predicts the metallic behavior for the ground state of idealized YSr2Cu2FeO7, a band gap of 0.85 eV opens in the GGA + U (U-Cu and U-Fe = 4 eV), and noteworthy, a near band gap of 0.63 eV is obtained using the SCAN functional (Figure 6). Compared to the YSr2Cu2FeO8 phase, in both SCAN and GGA + U, the effective charge of the TMs decreases (Table 3), and the TM−O distances increase (Table 2), in agreement with the lower formal oxidation states of Fe3+ and Cu2+ in YSr2Cu2FeO7. The effective charge on oxygen ions increases, approaching the oxide ion O2−. SCAN and GGA + U methods predict nearly the same calculated magnetic moments for TM ions: μ(Cu) = 0.5 μB per atom and μ(Fe) ∼ 4 μB per atom. The magnetic moment of the Cu ions is in good agreement with the experimental values reported in similar Cu2+ compounds.52,53 The magnetic moment on Fe ions suggests a high-spin Fe3+ configuration (e2t23, magnetic moment of the free ion μ0 = 5.0 μB). It is worth to note that magnetic moment values between 3 and 4 μB per atom have been experimentally observed in other complex Fe3+- tetrahedral oxides.54,55 On the other hand, the Fe−O and Cu−O covalencies bring an appreciable spin moment of ∼0.2 μB in the shared O1 site. As observed in the atom-projected density of states (Figure 6c), the U term shifts the TM-3d states to lower energies; yet, there is a good hybridization of TM-3d to O-2p states (see band at −6 eV). In summary, for the insulating compound, SCAN offers very similar results to the GGA + U in terms of band-gap and magnetic moments, although there are clear differences in the shape and nature of the states at the Fermi level. To further analyze the appropriateness of the SCAN vs. the GGA + U method, in a Figure 4. Calculated total and atom-projected density of states for YSr2Cu2FeO8: (a) GGA functional, (b) SCAN functional, and (c) GGA + U method. The Fermi level is set as the zero of energy. Up-spin (or majority) and down-spin (or minority) contributions are shown in the upper and lower parts of the panels, respectively. Color code: total DOS in gray, Cu contribution in blue, Fe contribution in green, and O contribution in red. DOS units refer to the calculated cell. Figure 5. (a−c) Magnetic structures (C, G, A) used to simulate YSr2Cu2FeO7 (S.G. Ima2). Arrows indicate the spin orientation of the Fe and Cu atoms within the magnetic structure. Color code: Fe atoms in brown, Cu atoms in blue, Sr atoms in green, Y atoms in gray, and O atoms in red. Table 4. Calculated Total-Energy Differences for Magnetic Configurations (Figure 5a−c) in YSr2Cu2FeO7 (in eV/fu)a type GGA GGA + U SCAN A-AFM 0.020 0.020 −0.075 C-AFM −0.248 −0.424 −0.414 G-AFM −0.228 −0.375 −0.408 aThe FM ordering is set as the zero of energy. Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX G https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.2c03475/suppl_file/ic2c03475_si_001.pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig4&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig5&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig5&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig5&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig5&ref=pdf pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as first approximation, the calculated DOS could be qualitatively compared with experimental photoelectron spectroscopy (PES). It is however important to point out that such comparison neglects the excitation aspects, which can be taken into account by quasi-particle calculations in the GW approach.56 For the sake of completeness, the relation between the electronic properties and the magnetic structure of YSr2Cu2FeO7 is analyzed within the SCAN and GGA + U Figure 6. Calculated total and atom-projected density of states (DOS) for the ground-state C-magnetic structure of the idealized YSr2Cu2FeO7: (a) GGA functional, (b) SCAN functional, and (c) GGA + U method. The Fermi level is set as the zero of energy. Up-spin (or majority) and down- spin (or minority) contributions are shown. Color code: total black, Cu contribution in blue, Fe contribution in green, and O contribution in red. DOS units refer to the calculated cell. Figure 7. Orbital-projected density of states within the SCAN functional for (a) idealized YSr2Cu2FeO8 showing the Fe-3d, O3-2p and O1-2p and Cu-3d, O2-2p, and O1-2p orbitals, and (b) idealized YSr2Cu2FeO7 showing the Cu-3d, O2-2p and O1-2p and Fe-3d, O3-2p, and O1-2p orbital contribution. Color code: up-spin (or majority) in blue and down-spin (or minority) in black. (c) Crystallographic cell used for the orbital- projected DOS of YSr2Cu2FeO7 (in red) and its relation to the to the crystal setting in the Ima2 S.G. (in black). Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX H https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig6&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig7&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig7&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig7&ref=pdf https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?fig=fig7&ref=pdf pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as methods (Figure S2). Once more, both DFT approximations yield the same results in terms of the insulating/metallic behavior. The calculated DOS for the G magnetic structure, with in-plane Cu/Fe AFR interactions, corresponds to an insulating compound with the same band gap of the C- magnetic structure (0.63 eV in SCAN, 0.85 eV in GGA+ U). The FR and A magnetic structures, with in-plane Cu/Fe FR interactions, generate metallic properties. These results reveal that, for the idealized YSr2Cu2FeO7, the insulating character couples to the in-plane AFM Cu/Fe ordering. 3.2.3. On the Metal-to-Insulating Transition in the YSr2Cu2FeO8−δ (0 < δ < 1) Family. The above results highlight that the SCAN functional reproduces the metal and the insulating character of YSr2Cu2FeO8 and YSr2Cu2FeO7 compounds, respectively. The orbital-projected DOS (Figure 7) adds more insights into the comprehensive interpretation of the chemical bonding and the evolution of the electronic properties as a function of the δ value. Starting with the metallic YSr2Cu2FeO8, in the Fe octahedra, the hybridization of O3(2p)−Fe(3dx2−y2) and O1(2p)−Fe(3dz2) produces the lower energy band σ-O(p)−Fe(eg) and the upper energy band σ*-O(p)−Fe(eg). As observed in Figure 7a, the occupation of the bonding sigma band occurs in both spin channels, with the Fermi level crossing the 3dx2−y2 majority spin orbital. The Π O(2p)−Fe(3t2g) bands are fully occupied in the up-spin channel, but also show some occupancy in the down-spin channel. As deduced from the calculated magnetic moments, the 3d-Fe orbitals filling does not correspond to either LS-Fe4+ (t2g 4eg0) or HS-Fe4+ (t2g 3eg1), but to an itinerant character where every 3d orbital contributes to the magnetic moment, in agreement with the metallic properties of the oxide. For the Cu-3d states, the crystal field splitting of the Cu−O square pyramidal environment lifts the degeneracy of the Cu-eg orbitals to the lower-lying 3dz2 and higher-lying 3dx2−y2 orbitals. The strong hybridization O2(2p)−Cu(3dx2−y2) produces a wide band that is partially filled in both spin channels, yielding a low net spin of 0.3 μB. The Fermi level lies in the band constructed mainly from the Cu-3dx2−y2 and O2-2p orbitals and in a minor extent in the band constructed from Fe-3dx2−y2 and O3-2p orbitals. Therefore, these bands have the largest implication in the electronic properties of the YSr2Cu2FeO8−δ family. Upon vacancies incorporation in YSr2Cu2FeO8 (Figure 7a) to form YSr2Cu2FeO7 (Figure 7b), according to the Fermi- level displacement, electron filling occurs in the Cu-3dx2−y2 derived band. Since in YSr2Cu2FeO7 the Cu ions have the nominal valence of 2+, and hence a nominal d9 state, there are fully occupied t2g orbitals and dz2 orbitals, while the dx2−y2 orbital remains half-filled yielding a low net spin of 0.5 μB. The energy gap opens between the occupied and the unoccupied Cu-3dx2−y2 orbitals. On the other hand, the analysis of the Fe-3d states upon electron doping of YSr2Cu2FeO8 is more complicated, since the coordination around the Fe atoms changes from octahedral in YSr2Cu2FeO8 to tetrahedral in YSr2Cu2FeO7. According to crystal field theory, in the tetrahedral field, the Fe-3d orbitals split into two manifolds, a lower one with two levels and an upper one with three levels (these would be of e and t2 character respectively, if the local symmetry were perfectly tetrahedral). This is not observed in Figure 7b due to the orientation of the Fe tetrahedra relative to the crystallographic cell axes utilized for the orbital-projected DOS (Figure 7c). Nevertheless, for all of the Fe-3d states, the up-spin channel is fully occupied and the down-spin channel is almost empty, the energy separation between up and down- spin channels being rather large. This electron density localization leads to the aforementioned high-spin Fe3+ configuration. In summary, the results of the SCAN methodology indicate that in the YSr2Cu2FeO8−δ family, the lowering of the oxygen content drives the metal-to-insulating transition by electron doping. A reduction in the oxygen content (higher δ value) results in a decrease in the nominal valence of Cu/Fe ions, and hence in the filling of the Cu/Fe-3dx2−y2 states. This picture is fully consistent with the well-documented importance of filling control in the electronic structure of high Tc cuprates, a typical example being the insulating to metal transition in La2−xSrxCuO4 induced by hole doping (x = 0 metallic).18,57 Remarkably, the SCAN functional offers a feasible interpretation of the metal-to-insulating transition in the YSr2Cu2FeO8−δ family, when looking at the idealized compounds with δ = 0 and 1. However, in addition to distinct oxygen contents (δ values), the synthesized compounds YSr2Cu2FeO7.86 (δ = 0.14) and YSr2Cu2FeO7.08 (δ = 0.92) show antisite disorder, with a Cu/Fe mixing close to 15% (see Table 1 and ref 24). As noted by different authors,22−24,58,59 the mutual substitution of Cu and Fe depends on the annealing history/oxygen content. The simulation of the random distribution of the antisite defects that occurs in the real materials requires the utilization of the special quasi-random structures (SQS) approach,60 which is out of the scope of this work. The antisite disorder could perturb the AFM in-plane ordering that, as discussed above, is critically linked to the insulating behavior of the investigated compounds with the lowest oxygen contents (δ ∼ 0). It is foreseeable that the concentration and location of both oxygen vacancies and antisite defects drastically influence the magnetic and electronic properties of the YSr2Cu2FeO8−δ family. This is in agreement with the observed dependence between the property and the synthetic history of the materials. 4. CONCLUSIONS The precise modeling of the ground-state properties in complex oxides that contain more than one type of TM ions remains challenging, especially with the irruption of correlated oxides as functional materials. In this work, we have examined the capabilities of different DFT methodologies (GGA, GGA + U, SCAN) to model the crystal structure and the electronic and magnetic properties of YSr2Cu2FeO8−δ compounds in which the oxygen content in the FeO2−δ layers drives the average oxidation states of both Fe and Cu cations, thereby determining the electrical properties. We have found that the SCAN and GGA methodologies are valid to simulate the metallic properties of the oxide with the highest oxygen content of the family (δ = 0, idealized-YSr2Cu2FeO8) and the itinerant character of its bonding electrons. Introducing the U term (GGA + U) results in excessive electron localization and large magnetic moments that deviate from the experimental observations, therefore discarding this methodology for property prediction in the metallic phases of the YSr2Cu2FeO8−δ system. Contrariwise, the insulating character of the compound with the lowest oxygen content (δ = 1, idealized-YSr2Cu2FeO7) is well captured when electron correlations are treated by the U parameter using the GGA + U approximation. Importantly, the results point out that the SCAN functional also offers a good platform to investigate these insulating compounds. These results render the SCAN Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX I https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.2c03475/suppl_file/ic2c03475_si_001.pdf pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as functional as the only one well suited, among the utilized methodologies, to investigate the basic electronic properties across the YSr2Cu2FeO8−δ series. It should be noted that, together with the lack of an adjustable U parameter, other benefits of the SCAN functional are the affordable computa- tional cost and the transferability of results among different works. Yet, a severe limiting factor for the DFT investigation of the YSr2Cu2FeO8−δ family resides in the need of complex crystallographic models to take into account the antisite Cu/Fe disorder and the fractional occupancies of the O3 site that occur in the synthesized materials. ■ ASSOCIATED CONTENT *sı Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475. Calculated lattice parameters and density of states for the A-AFM, G-AFM, and FM magnetic structures of YSr2Cu2FeO7 (PDF) ■ AUTHOR INFORMATION Corresponding Author M. Elena Arroyo-de Dompablo − Departamento de Química Inorgánica, Universidad Complutense de Madrid, 28040 Madrid, Spain; orcid.org/0000-0001-5249-3562; Email: e.arroyo@quim.ucm.es Authors Marianela Gómez-Toledo − Departamento de Química Inorgánica, Universidad Complutense de Madrid, 28040 Madrid, Spain; orcid.org/0000-0001-5594-4146 Sara A. López-Paz − Departamento de Química Inorgánica, Universidad Complutense de Madrid, 28040 Madrid, Spain; Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland Susana García-Martín − Departamento de Química Inorgánica, Universidad Complutense de Madrid, 28040 Madrid, Spain; orcid.org/0000-0003-0729-4892 Complete contact information is available at: https://pubs.acs.org/10.1021/acs.inorgchem.2c03475 Author Contributions M.G.-T. performed the DFT calculations including the data preparation/analysis, tables, and graphical representations. She performed the spectroscopy measurements, interpretation, and graphics, and she also contributed in writing the original draft of the manuscript. S.A.L.-P. conducted the experimental research comprising the synthesis and structural and electrical characterization of the materials. S.G.-M. led the experimental project administration. M.E.A.-d.D. directed the computational investigation, led the computational project administration, and wrote the draft of the manuscript. All authors contributed in the discussion and writing of the final version of the manuscript. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS The authors thank MCIN/AEI/10.13039/501100011033 and “NextGenerationEU”/PRTR for funding the Projects PID2019-106662RB-C44 and TED2021-130452B-C21. M.E.A.-d.D. and M.G.-T. acknowledge funding for computa- tional research and spectroscopy measurements from Uni- versidad Complutense de Madrid (FEI-EU-22-01-4129585). M.G.-T. thanks Comunidad de Madrid for contract (PEJ-2020- AI/IND-18065) of the program “Ayudas para la contratación de Ayudantes de Investigación y Técnicos de Laboratorio”. The authors acknowledge Dr. Clemens Ritter for the neutron diffraction measurements and the ILL for beam time allocation in the D2B instrument under the experiment code 5-23-705. Data are available from ILL at DOI: 10.5291/ILL-DATA.5-23- 705. The authors are grateful to R. González-Prieto for his assistance in the Reflectance Diffuse Spectroscopy measure- ments. ■ REFERENCES (1) Irvine, J.; Rupp, J. L. M.; Liu, G.; Xu, X.; Haile, S.; Qian, X.; Snyder, A.; Freer, R.; Ekren, D.; Skinner, S.; Celikbilek, O.; Chen, S.; Tao, S.; Shin, T. H.; O’Hayre, R.; Huang, J.; Duan, C.; Papac, M.; Li, S.; Celorrio, V.; Russell, A.; Hayden, B.; Nolan, H.; Huang, X.; Wang, G.; Metcalfe, I.; Neagu, D.; Martin, S. G. Roadmap on inorganic perovskites for energy applications. J. Phys.: Energy 2021, 3, No. 031502. (2) Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev. B: Condens. Matter Mater. Phys. 1964, 136, B864−B871. (3) Kohn, W.; Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140, A1133. (4) Perdew, J. P. Generalized gradient approximations for exchange and correlation - a look backward and forward. Phys. B 1991, 172, 1− 6. (5) Perdew, J. P.; Yue, W. Accurate and simple density functional for the electronic exchange energy - Generalized Gradient Approxima- tion. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 33, 8800−8802. (6) Piskunov, S.; Heifets, E.; Eglitis, R. I.; Borstel, G. Bulk properties and electronic structure of SrTiO3, BaTiO3, PbTiO3 perovskites: an ab initio HF/DFT study. Comput. Mater. Sci. 2004, 29, 165−178. (7) Eng, H. W.; Barnes, P. W.; Auer, B. M.; Woodward, P. M. Investigations of the electronic structure of d0 transition metal oxides belonging to the perovskite family. J. Solid State Chem. 2003, 175, 94− 109. (8) Oja, R.; Tyunina, M.; Yao, L.; Pinomaa, T.; Kocourek, T.; Dejneka, A.; Stupakov, O.; Jelinek, M.; Trepakov, V.; van Dijken, S.; Nieminen, R. M. d0 Ferromagnetic Interface between Nonmagnetic Perovskites. Phys. Rev. Lett. 2012, 109, No. 127207. (9) Bilc, D. I.; Orlando, R.; Shaltaf, R.; Rignanese, G. M.; Iniguez, J.; Ghosez, P. Hybrid exchange-correlation functional for accurate prediction of the electronic and structural properties of ferroelectric oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, No. 165107. (10) Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Band Theory and Mott Insulators - Hubbard-U Instead of Stoner-I. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 44, 943−954. (11) Zhou, F.; Marianetti, C. A.; Cococcioni, M.; Morgan, D.; Ceder, G. Phase separation in LixFePO4 induced by correlation effects. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, No. 201101. (12) Ganduglia-Pirovano, M. V.; Hofmann, A.; Sauer, J. Oxygen vacancies in transition metal and rare earth oxides: Current state of understanding and remaining challenges. Surf. Sci. Rep. 2007, 62, 219. (13) Wang, L.; Maxisch, T.; Ceder, G. Oxidation energies of transition metal oxides within the GGA+U framework. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, No. 195107. (14) Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. First- principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA+U method. J. Phys.: Condens. Matter 1997, 9, 767−808. Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX J https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?goto=supporting-info https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.2c03475/suppl_file/ic2c03475_si_001.pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="M.+Elena+Arroyo-de+Dompablo"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://orcid.org/0000-0001-5249-3562 mailto:e.arroyo@quim.ucm.es https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Marianela+Go%CC%81mez-Toledo"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://orcid.org/0000-0001-5594-4146 https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sara+A.+Lo%CC%81pez-Paz"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Susana+Garci%CC%81a-Marti%CC%81n"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf https://orcid.org/0000-0003-0729-4892 https://pubs.acs.org/doi/10.1021/acs.inorgchem.2c03475?ref=pdf https://doi.org/10.1088/2515-7655/abff18 https://doi.org/10.1088/2515-7655/abff18 https://doi.org/10.1103/PhysRev.136.B864 https://doi.org/10.1103/PhysRev.140.A1133 https://doi.org/10.1103/PhysRev.140.A1133 https://doi.org/10.1016/0921-4526(91)90409-8 https://doi.org/10.1016/0921-4526(91)90409-8 https://doi.org/10.1103/PhysRevB.33.8800 https://doi.org/10.1103/PhysRevB.33.8800 https://doi.org/10.1103/PhysRevB.33.8800 https://doi.org/10.1016/j.commatsci.2003.08.036 https://doi.org/10.1016/j.commatsci.2003.08.036 https://doi.org/10.1016/j.commatsci.2003.08.036 https://doi.org/10.1016/s0022-4596(03)00289-5 https://doi.org/10.1016/s0022-4596(03)00289-5 https://doi.org/10.1103/PhysRevLett.109.127207 https://doi.org/10.1103/PhysRevLett.109.127207 https://doi.org/10.1103/PhysRevB.77.165107 https://doi.org/10.1103/PhysRevB.77.165107 https://doi.org/10.1103/PhysRevB.77.165107 https://doi.org/10.1103/PhysRevB.44.943 https://doi.org/10.1103/PhysRevB.44.943 https://doi.org/10.1103/PhysRevB.69.201101 https://doi.org/10.1103/PhysRevB.69.201101 https://doi.org/10.1016/j.surfrep.2007.03.002 https://doi.org/10.1016/j.surfrep.2007.03.002 https://doi.org/10.1016/j.surfrep.2007.03.002 https://doi.org/10.1103/PhysRevB.73.195107 https://doi.org/10.1103/PhysRevB.73.195107 https://doi.org/10.1088/0953-8984/9/4/002 https://doi.org/10.1088/0953-8984/9/4/002 https://doi.org/10.1088/0953-8984/9/4/002 pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as (15) Sun, J.; Ruzsinszky, A.; Perdew, J. P. Strongly Constrained and Appropriately Normed Semilocal Density Functional. Phys. Rev. Lett. 2015, 115, No. 036402. (16) Hinuma, Y.; Hayashi, H.; Kumagai, Y.; Tanaka, I.; Oba, F. Comparison of approximations in density functional theory calculations: Energetics and structure of binary oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96, No. 094102. (17) Kitchaev, D. A.; Peng, H.; Liu, Y.; Sun, J.; Perdew, J. P.; Ceder, G. Energetics of MnO2 polymorphs in density functional theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, No. 045132. (18) Furness, J. W.; Zhang, Y.; Lane, C.; Buda, I. G.; Barbiellini, B.; Markiewicz, R. S.; Bansil, A.; Sun, J. An accurate first-principles treatment of doping-dependent electronic structure of high-temper- ature cuprate superconductors. Commun. Phys. 2018, 1, No. 11. (19) Kaczkowski, J.; Pugaczowa-Michalska, M.; Płowas-́Korus, I. Isovalent cation ordering in Bi-based double perovskites: A density functional analysis. J. Magn. Magn. Mater. 2022, 548, No. 168984. (20) Iglesias, L.; Bibes, M.; Varignon, J. First-principles study of electron and hole doping effects in perovskite nickelates. Phys. Rev. B: Condens. Matter Mater. Phys. 2021, 104, No. 035123. (21) Varignon, J.; Bibes, M.; Zunger, A. Mott gapping in 3d ABO3 perovskites without Mott-Hubbard interelectronic repulsion energy U. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, No. 035119. (22) Shimoyama, J.; Otzschi, K.; Hinouchi, T.; Kishio, K. Discovery of superconductivity in Fe-based cuprates. Phys. C 2000, 341−348, 563−564. (23) Mochiku, T.; Nakano, Y.; Hoshikawa, A.; Sato, S.; Oikawa, K.; Ishigaki, T.; Kamiyama, T.; Kadowaki, K.; Hirata, K. Superstructure in Sr2YCu2FeO6+δ. Phys. C 2004, 412−414, 115−119. (24) López-Paz, S. A.; Martinez de Irujo-Labalde, X.; Sanchez- Marcos, J.; Ritter, C.; Moran, E.; Alario-Franco, M. A. Soft Magnetic Switching in a FeSr2YCu2O7.85 Superconductor with Unusually High Iron Valence. Inorg. Chem. 2019, 58, 12809−12814. (25) Mochiku, T.; Hata, Y.; Yamaguchi, K.; Tsuchiya, Y.; Hoshikawa, A.; Iwase, K.; Sulistyanintyas, D.; Ishigaki, T.; Yasuoka, H.; Hirata, K. Annealing effect on structure and superconductivity in FeSr2YCu2O6+δ magnetic superconductor. Phys. Procedia 2012, 45, 73−76. (26) Sansom, J. E. H.; Kendrick, E.; Rudge-Pickard, H. A.; Islam, M. S.; Wright, A. J.; Slater, P. R. Synthesis and characterisation of the perovskite- related cuprate phases YSr2Cu2MO7+y (M = Co, Fe) for potential use as solid oxide fuel cell cathode materials. J. Mater. Chem. 2005, 15, 2321−2327. (27) López-Paz, S. A.; Marin-Gamero, R.; Martinez de Irujo- Labalde, X.; Sanchez-Marcos, J.; Perez-Coll, D.; Franco, M. A. A. Y.; Garcia-Martin, S. YBaCuO-type perovskites as potential air electrodes for SOFCs. The case of YSr2Cu2FeO7+δ. J. Mater. Chem. A 2021, 9, 8554−8560. (28) Mochiku, T.; Nakano, Y.; Oikawa, K.; Kamiyama, T.; Fujii, H.; Hata, Y.; Suzuki, I.; Kakeya, I.; Kadowaki, K.; Hirata, K. Atomic ordering in FeSr2LnCu2O6+δ system (Ln = Nd, Y and Er). Phys. C 2003, 400, 43−52. (29) Pissas, M.; Kallias, G.; Moraitakis, E.; Niarchos, D.; Simopoulos, A. Site occupancy of Fe in the oxygen-saturated YSr2Cu3‑xFexOy compound for x=0.25 up to 1. Phys. C 1994, 234, 127−136. (30) Lopez-Paz, S. A.; Sari, D. P.; Hillier, A. D.; Alario-Franco, M. A. Coexistence of magnetism and superconductivity in the iron containing FeSr2YCu2O7.57 cuprate as studied by μ-SR. AIP Adv. 2021, 11, No. 015011. (31) Rodriguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 1993, 192, 55−69. (32) Kubelka, P.; Munk, F. A. Contribution to the Optics of Pigments. Z. Technol. Phys. 1931, 12, 593−599. (33) Tauc, J.; Grigorovici, R.; Vancu, A. Optical Properties And Electronic Structure of Amorphous Germanium. Phys. Status Solidi B 1966, 15, 627−637. (34) Kresse, G.; Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. (35) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. (36) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. (37) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (38) Blöchl, P. E.; Jepsen, O.; Andersen, O. K. Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 16223−16233. (39) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Szotek, Z.; Temmerman, W. M.; Sutton, A. P. Electronic structure and elastic properties of strongly correlated metal oxides from first principles: LSDA+U, SIC-LSDA and EELS study of UO2 and NiO. Phys. Status Solidi A 1998, 166, 429−443. (40) Arroyo y de Dompablo, M. E.; Lee, Y.-L.; Morgan, D. First Principles Investigation of Oxygen Vacancies in Columbite MNb2O6 (NI = Mn, Fe, Co, Ni, Cu). Chem. Mater. 2010, 22, 906−913. (41) Ritzmann, A. M.; Dieterich, J. M.; Carter, E. A. Density functional theory plus U analysis of the electronic structure and defect chemistry of LSCF (La0.5Sr0.5Co0.25Fe0.75O3‑δ). Phys. Chem. Chem. Phys. 2016, 18, 12260−12269. (42) Jain, A.; Shyue Ping, O.; Hautier, G.; Chen, W.; Richards, W. D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; Persson, K. A. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Mater. 2013, 1, No. 011002. (43) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (44) Henkelman, G.; Arnaldsson, A.; Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 2006, 36, 354−360. (45) Ong, S. P.; Richards, W. D.; Jain, A.; Hautier, G.; Kocher, M.; Cholia, S.; Gunter, D.; Chevrier, V. L.; Persson, K. A.; Ceder, G. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis. Comput. Mater. Sci. 2013, 68, 314−319. (46) Roth, G.; Adelmann, P.; Heger, G.; Knitter, R.; Wolf, T. The crystal-structure of RESr2GaCu2O7. J. Phys. I 1991, 1, 721−741. (47) Dolgonos, A.; Mason, T. O.; Poeppelmeier, K. R. Direct optical band gap measurement in polycrystalline semiconductors: A critical look at the Tauc method. J. Solid State Chem. 2016, 240, 43−48. (48) Wu, J.; Walukiewicz, W.; Yu, K. M.; Ager, J. W.; Haller, E. E.; Lu, H.; Schaff, W. J.; Saito, Y.; Nanishi, Y. Unusual properties of the fundamental band gap of InN. Appl. Phys. Lett. 2002, 80, 3967−3969. (49) Kobayashi, H.; Mori, T.; Namba, K.; Nakato, Y. New method for determination of energy distribution of surface states in the semiconductor band-gap: XPS measurements under biases. Solid State Commun. 1994, 92, 249−254. (50) Pissas, M.; Kallias, G.; Simopoulos, A.; Niarchos, D.; Sonntag, R. Neutron diffraction study of the deoxygenated YSr2Cu3‑xFexO6+y (x = 0.8 and 1) compound. Phys. B 1998, 253, 1−9. (51) Ohta, Y.; Tohyama, T.; Maekawa, S. Transition-temperature in copper-oxide superconductors correlated with energy-level of apical oxygen. Phys. C 1990, 166, 385−387. (52) Tranquada, J. M.; Moudden, A. H.; Goldman, A. I.; Zolliker, P.; Cox, D. E.; Shirane, G.; Sinha, S. K.; Vaknin, D.; Johnston, D. C.; Alvarez, M. S.; Jacobson, A. J.; Lewandowski, J. T.; Newsam, J. M. Antiferromagnetism in YBa2Cu3O6+x. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 38, 2477−2485. (53) Tranquada, J. M.; Cox, D. E.; Kunnmann, W.; Moudden, H.; Shirane, G.; Suenaga, M.; Zolliker, P.; Vaknin, D.; Sinha, S. K.; Alvarez, M. S.; Jacobson, A. J.; Johnston, D. C. Neutron-diffraction determination of antiferromagnetic structure of Cu ions in YBa2Cu3O6+x with x = 0.0 and 0.15. Phys. Rev. Lett. 1988, 60, 156− 159. Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX K https://doi.org/10.1103/PhysRevLett.115.036402 https://doi.org/10.1103/PhysRevLett.115.036402 https://doi.org/10.1103/PhysRevB.96.094102 https://doi.org/10.1103/PhysRevB.96.094102 https://doi.org/10.1103/PhysRevB.93.045132 https://doi.org/10.1038/s42005-018-0009-4 https://doi.org/10.1038/s42005-018-0009-4 https://doi.org/10.1038/s42005-018-0009-4 https://doi.org/10.1016/j.jmmm.2021.168984 https://doi.org/10.1016/j.jmmm.2021.168984 https://doi.org/10.1103/PhysRevB.104.035123 https://doi.org/10.1103/PhysRevB.104.035123 https://doi.org/10.1103/PhysRevB.100.035119 https://doi.org/10.1103/PhysRevB.100.035119 https://doi.org/10.1103/PhysRevB.100.035119 https://doi.org/10.1016/s0921-4534(00)00593-1 https://doi.org/10.1016/s0921-4534(00)00593-1 https://doi.org/10.1016/j.physc.2004.01.042 https://doi.org/10.1016/j.physc.2004.01.042 https://doi.org/10.1021/acs.inorgchem.9b01770?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/acs.inorgchem.9b01770?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/acs.inorgchem.9b01770?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1016/j.phpro.2013.04.055 https://doi.org/10.1016/j.phpro.2013.04.055 https://doi.org/10.1039/b502641e https://doi.org/10.1039/b502641e https://doi.org/10.1039/b502641e https://doi.org/10.1039/d1ta00111f https://doi.org/10.1039/d1ta00111f https://doi.org/10.1016/s0921-4534(03)01322-4 https://doi.org/10.1016/s0921-4534(03)01322-4 https://doi.org/10.1016/0921-4534(94)90064-7 https://doi.org/10.1016/0921-4534(94)90064-7 https://doi.org/10.1063/9.0000093 https://doi.org/10.1063/9.0000093 https://doi.org/10.1016/0921-4526(93)90108-I https://doi.org/10.1016/0921-4526(93)90108-I https://doi.org/10.1002/pssb.19660150224 https://doi.org/10.1002/pssb.19660150224 https://doi.org/10.1103/PhysRevB.54.11169 https://doi.org/10.1103/PhysRevB.54.11169 https://doi.org/10.1103/PhysRevB.59.1758 https://doi.org/10.1103/PhysRevB.59.1758 https://doi.org/10.1103/PhysRevB.50.17953 https://doi.org/10.1103/PhysRevLett.77.3865 https://doi.org/10.1103/PhysRevLett.77.3865 https://doi.org/10.1103/PhysRevB.49.16223 https://doi.org/10.1103/PhysRevB.49.16223 https://doi.org/10.1002/(SICI)1521-396X(199803)166:1<429::AID-PSSA429>3.0.CO;2-F https://doi.org/10.1002/(SICI)1521-396X(199803)166:1<429::AID-PSSA429>3.0.CO;2-F https://doi.org/10.1002/(SICI)1521-396X(199803)166:1<429::AID-PSSA429>3.0.CO;2-F https://doi.org/10.1021/cm901723j?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/cm901723j?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/cm901723j?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1039/c6cp01720g https://doi.org/10.1039/c6cp01720g https://doi.org/10.1039/c6cp01720g https://doi.org/10.1063/1.4812323 https://doi.org/10.1063/1.4812323 https://doi.org/10.1016/j.commatsci.2005.04.010 https://doi.org/10.1016/j.commatsci.2005.04.010 https://doi.org/10.1016/j.commatsci.2012.10.028 https://doi.org/10.1016/j.commatsci.2012.10.028 https://doi.org/10.1051/jp1:1991165 https://doi.org/10.1051/jp1:1991165 https://doi.org/10.1016/j.jssc.2016.05.010 https://doi.org/10.1016/j.jssc.2016.05.010 https://doi.org/10.1016/j.jssc.2016.05.010 https://doi.org/10.1063/1.1482786 https://doi.org/10.1063/1.1482786 https://doi.org/10.1016/0038-1098(94)90886-9 https://doi.org/10.1016/0038-1098(94)90886-9 https://doi.org/10.1016/0038-1098(94)90886-9 https://doi.org/10.1016/s0921-4526(98)00393-7 https://doi.org/10.1016/s0921-4526(98)00393-7 https://doi.org/10.1016/0921-4534(90)90419-f https://doi.org/10.1016/0921-4534(90)90419-f https://doi.org/10.1016/0921-4534(90)90419-f https://doi.org/10.1103/PhysRevB.38.2477 https://doi.org/10.1103/PhysRevLett.60.156 https://doi.org/10.1103/PhysRevLett.60.156 https://doi.org/10.1103/PhysRevLett.60.156 pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as (54) De Irujo-Labalde, X. M.; Amador, U.; Ritter, C.; Goto, M.; Patino, M. A.; Shimakawa, Y.; Garcia-Martin, S. 3D to 2D Magnetic Ordering of Fe3+ Oxides Induced by Their Layered Perovskite Structure. Inorg. Chem. 2021, 60, 8027−8034. (55) Martínez de Irujo-Labalde, X.; Goto, M.; Urones-Garrote, E.; Amador, U.; Ritter, C.; Patino, M. E. A.; Koedtruad, A.; Tan, Z.; Shimakawa, Y.; Garcia-Martin, S. Multiferroism induced by spontaneous structural ordering in antiferromagnetic iron perovskites. Chem. Mater. 2019, 31, 5993−6000. (56) Jiang, H.; Gomez-Abal, R. I.; Rinke, P.; Scheffler, M. First- principles modeling of localized d states with the GW @ LDA + U approach. Phys. Rev. B 2010, 82, No. 045108. (57) Imada, M.; Fujimori, A.; Tokura, Y. Metal-insulator transitions. Rev. Mod. Phys. 1998, 70, 1039−1263. (58) Fujii, H.; Mihara, Y.; Mochiku, T.; Hata, Y.; Kadowaki, K. Order, disorder and superconductivity in FeSr2YCu2O6+δ. Phys. C 2004, 415, 85−93. (59) Hata, Y.; Mihara, Y.; Mochiku, T.; Suzuki, J.; Kakeya, I.; Kadowaki, K.; Kita, E.; Yasuoka, H. Redistribution of Fe ion and superconductivity of FeSr2YCu2O6+y system. Phys. C 2004, 417, 17− 24. (60) Zunger, A.; Wei, S. H.; Ferreira, L. G.; Bernard, J. E. Special quasirandom structures. Phys. Rev. Lett. 1990, 65, 353−356. Inorganic Chemistry pubs.acs.org/IC Article https://doi.org/10.1021/acs.inorgchem.2c03475 Inorg. Chem. XXXX, XXX, XXX−XXX L https://doi.org/10.1021/acs.inorgchem.1c00529?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/acs.inorgchem.1c00529?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/acs.inorgchem.1c00529?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/acs.chemmater.9b02716?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1021/acs.chemmater.9b02716?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as https://doi.org/10.1103/PhysRevB.82.045108 https://doi.org/10.1103/PhysRevB.82.045108 https://doi.org/10.1103/PhysRevB.82.045108 https://doi.org/10.1103/RevModPhys.70.1039 https://doi.org/10.1016/j.physc.2004.07.020 https://doi.org/10.1016/j.physc.2004.10.002 https://doi.org/10.1016/j.physc.2004.10.002 https://doi.org/10.1103/PhysRevLett.65.353 https://doi.org/10.1103/PhysRevLett.65.353 pubs.acs.org/IC?ref=pdf https://doi.org/10.1021/acs.inorgchem.2c03475?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as