Introduction

Motivated by recent susceptibility measurements of D. Kurzydlowski et al.1, which indicates that KAgF3 compound exhibits strong antiferromagnetic (AFM) coupling reminiscent of that found in copper(II) oxides2,3, we carried out investigation on electronic properties of fluoride and half–fluoride KAgF3–related superlattices (SLs). For a long time, the discovery of high–temperature superconductivity in under doped cuprates4 initiated the quest for finding related transition–metal compounds with possible superconductivity. Ag2+ is isoelectronic to Cu2+ (d9 configuration). F− and O2− are also isoelectronic ions, closed–shell species. Moreover, both F− and O2− are weak–field ligands. Previous theoretical studies5,6,7 of Grochala and Hoffmann have also suggested that properly hole– or electron–doped AgII fluorides might be good superconductors, due to similarity in structure and properties between the AgII fluorides and the cuprate superconductors.

[CuO2]∞ plane with tetragonal tetra coordination of Cu (weak apical Cu–O bonds), is an essential structural element for superconductivity in cuprates. Analogous [AgF2]∞ plane with Ag centers in a tetragonal tetra coordination is still not known experimentally. However, benefit from recent development of heterostructure interface technology, superlattices containing AgIIF2 square lattices can be prepared by using appropriate synthetic techniques. Superlattice is consisted of alternating layers of different transition metal compounds8,9,10,11,12,13,14,15, even technically a single atomic layer can be inserted at interface12. Here, interface can be used to modulate electronic structure for manipulating physical properties and generating novel phases which are not present in the bulk constituents16,17,18,19,20. In our paper, our research focus on artificial superlattice materials design and their electronic properties, different from research on real bulk AgII fluorides materials5,6,7.

We investigate electronic structures, magnetic states, model hamiltonian parameters and effective Fermi surfaces (FSs) for purely–fluoride and half–fluoride superlattices KZnF3/KAgF3 and SrTiO3/KAgF3, as illustrated in the top panels of Fig. 1 and compare these with corresponding properties of the cuprate superconductors. These fluorides exhibit cupratelike band structures and strong AFM fluctuations. The energy bands around the Fermi level are sensitive to in–plane strain and the FS shapes present considerable similarity to those in cuprates. Model hamiltonian parameters are extracted and compared to La2CuO4 (LCO), HgBa2CuO4 (HBCO). Strong AFM coupling found in bulk KAgF3 is held in purely–fluoride KZnF3/KAgF3. While half–fluoride SrTiO3/KAgF3 is at the edge of superconducting transition, in which FM state becomes much high in energy and AFM state is just below nonmagnetic (NM) state by only 11.675 meV/Ag due to out–of–plane electronic reconstruction. Our finding suggests that fluoride and half–fluoride KAgF3–related SLs indeed have the potential to become 2D AFM precursors of a new AgII family of high-temperature superconductors.

Figure 1
figure 1

Schematic geometrical structures, GGA bandstructures and the effective the Fermi surfaces centered at Γ point in first Brillouin Zone from band for bulk HBCO, SrTiO3/KAgF3, KZnF3/KAgF3 without and with in–plane compression strain, bulk LCO from left to right.

The Fermi level εF is set at zero. Dark cyan and orange fatbands represent contribution of and orbitals respectively.

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Results

For the in–plane lattice constant a, we took that of KZnF3 (4.068 Å) for purely–fluoride KZnF3/KAgF3 SL and took that of STO (3.905 Å) for half–fluoride SrTiO3/KAgF3 SL. The lattice constant c and atomic z coordinates were fully relaxed. The structural difference between two kinds of SLs results from different polarization strength in neighboring atomic layers of AgF2 plane. Negatively charged F and positively charged K cation are displaced relative to each other in KF atomic layers and thereby polarize the cation and anion planes so as to affect apical Ag–F bond length. AgF2 layer acts as the mirror plane of whole unit cell.

A large cation–anion polarization occurs in KF plane of half–fluoride SrTiO3/KAgF3 and fluorin atoms move symmetrically against AgF2 plane by 0.163 Å. This polarization distortion produces a local ionic dipole moment and together with in–plane strain it leads to a large apical Ag–F distance . This apical Ag–F bond length is more close to those of cuprates than recent reported 3.405 Å for SrTiO3/CsAgF3 SL20, due to the smaller size of the K+ cation. However, in purely–fluoride KZnF3/KAgF3 SL, polarization distortion is weak and is just 0.004 Å toward AgF2 plane. As a result, apical Ag–F bond length is smaller than that in SrTiO3/KAgF3 by 0.298 Å.

An evolution of Ag-eg states with structural chemical modification can be clearly observed in band structures of Fig. 1. Local ionic dipole moment perturbs electrostatic potential and changes band positions around the Fermi level. Spin–polarized GGA calculations give nonmagnetic ground state for both superlattices. Figure 1 shows energy bands of SrTiO3/KAgF3 and KZnF3/KAgF3 SLs in a 12 eV region around the Fermi level εF ≡ 0 and along the symmetry–lines . The energy bands of bulk LCO and HBCO are also plotted in Fig. 1 for comparison. For SLs, electronic properties around εF are still mainly controlled by Ag-eg bands, which are above the filled O/F-2p and Ag-t2g bands and below the empty Ti-3d/Zn-4s bands. We plot (dark cyan) and (orange) fatbands around εF to disclose their orbital contribution. For KZnF3/KAgF3 SL, antibonding band is just below the Fermi level at X point and resembles that of LCO. But Ag–eg antibonding band’s width is smaller than that of LCO and HBCO. Since electronic properties are subject to electron– and orbital–lattice couplings in perovskite–like materials, similar calculation is made for KZnF3/KAgF3 SL with an additional in–plane lattice constants of 3.905 Å. Energy bands are found to be sensitive to in–plane strain and this 4% compression strain increases band width close to that of LCO. However, in SrTiO3/KAgF3 case, the antibonding band between and F-p states disappears due to the weak mixing of Ag-3d and F-p states in z direction. eg bands from −3 to 2 eV appear more like that of HBCO with a larger apical Cu-O distance of 2.784 Å. Most importantly, atomic polarization results in oxygen 2p band edge of TiO2 plane upshift eventually above the Fermi level and charge transfer with band, as occurs in SrTiO3/CsAgF3 SL20. The FSs centered at Γ point for LCO, HBCO and KAgF3-related SLs are shown in the third row of Fig. 1. Compared to LCO (transition temperature Tc = 40 K), the FS of HBCO (Tc = 90 K) has the typical shape of high-Tc cuprates superconductor with constant–energy surface obviously bulging toward Γ point. The FS shape of KZnF3/KAgF3 without strain is at the edge of electron pocket and far away from that of HBCO or LCO. But the FS under 4% compression strain looks more like that of LCO. However, for STO/KAgF3 with polarized electron–doping in AgF2 plane, effective FS from band presents the considerable similarity to that of HBCO.

Next, we discuss the stability of magnetic states in superlattices under GGA + Ud scheme. AFM band structures indicate that KZnF3/KAgF3 SL presents a AFM insulating ground state with a energy gap of 0.445 eV. A 4% compression strain decreases energy gap to 0.232 eV. For SrTiO3/KAgF3, an AFM metallic ground state is obtained, which is aroused by charge transfer between O-px, py orbitals in TiO2 plane and covalent hybrid orbitals of and F-px, py in AgF2 plane. In Table 1, we summarize in–plane and apical bond lengths and , energy difference EFM − EAFM and magnetic moment on Ag/Cu atom in AFM state. The calculated nearest neighboring magnetic exchange coupling constant J (~(EFM − EAFM)/Cu) for LCO and HBCO is in qualitative agreement with the value derived from two–magnon scattering experiments [Jexpt = 128 meV]21. Generally, strong AFM coupling is held in heterostructure configuration with a confined 2D [AgF2]∞ plane. The obtained J value (~(EFM − EAFM)/Ag) in undoping purely–fluoride KZnF3/KAgF3 SLs is close to that found in bulk KAgF3 (~100 meV)1, but smaller than related cuprates (see Table 1) due to less localized in 4d-orbitals of Ag. And in–plane compression strain increases EFM − EAFM from 90.305 meV/Ag to 101.605 meV/Ag, similar to the trend for cuprates (e.g. from 127.8025 meV/Cu for HBCO to 177.465 meV/Cu for LCO in Table 1). Our finding suggests that fluoride KAgF3 related SLs indeed have the potential to become precursors of a new family of high-temperature superconductors which could benefit from enhancement of the critical superconducting temperature due to strong magnetic fluctuations22. In half–fluoride SrTiO3/KAgF3 SL, FM state becomes much high in energy and unavailable. AFM state is just below NM state by only 11.675 meV/Ag due to out–of–plane electronic reconstruction.

Table 1 The in–plane and apical bond length and in Å, energy differences EFM − EAFM in meV/Ag(Cu) and Ag/Cu atom's magnetic moment of AFM state in μ B/Ag(Cu), for LCO, HBCO, KZnF3/KAgF3 without and with strain, SrTiO3/KAgF3.
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Based on the aboved GGA simulations, we extract model hamiltonian parameters by MLWFs downfolding technique. Fourier transformation of the orthonormalized MLWE Hamiltonian H(k), yields on–site energies and hopping integrals

in a Wannier representation, where is orthonormal MLWF Wannier function in cell R associated with band m and is MLWF Wannier function in home cell associated with band n.

We choose to downfold to a 6-band hamiltonian describing the in-plane , px, py orbitals and out–of–plane , two pz orbitals. In particular, four parameters capture the essential physics: the eg crystal field splitting energy , the in–plane charge–transfer energy , the direct in–plane Ag–F hopping tpd and the shortest–ranged in–plane F–F hoppings tpp. The extracted values are tabulated in Table 2 and corresponding interpolated band structure are shown in Fig. 2.

Table 2 Tight–binding parameters of the six–band p-d model, containing the in–plane , px, py orbitals and out–of–plane , pz orbitals for LCO, HBCO, KZnF3/KAgF3 without and with in–plane strain, SrTiO3/KAgF3.
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Figure 2
figure 2

Effective eg MLWF bands (red dash lines) for bulk HBCO, SrTiO3/KAgF3, KZnF3/KAgF3 without and with in–plane compression strain, bulk LCO superimposed to the GGA electronic bands (green solid lines).

The Fermi level εF is set at zero.

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The hopping integrals tpd and tpp of LCO and HBCO are in good agreement with the 3–band model results23,24 and the analysis of the photoelectron spectroscopy25. While the data of ΔCT are further corrected in our model by including three additional out–of–plane orbitals. Compared to cuprates, purely–fluoride KZnF3/KAgF3 has relatively larger , ΔCT and in–plane Ag–F hopping tpd and smaller hopping tpp. In–plane compression strain increase the values of the former three parameters , ΔCT and tpd, but has only a slight change on the hopping tpp. Under the same in–plane lattice constant 3.905 Å, half–fluoride SrTiO3/KAgF3 has obvious larger , ΔCT and slightly increased tpp, compared to purely–fluoride KZnF3/KAgF3. Across cuprate families, the charge transfer energy is an increasing linear function of Madelung potential difference for a hole between the copper and in–plane oxygen and correlate with the maximum superconducting transition temperature Tc,max26. The decreasing ΔCT correlates with a enhanced Tc,max. Here, half–fluoride SrTiO3/KAgF3 has a slight reduced ΔCT value 3.459 eV between the silver and in–plane fluorine, compared to the reported 3.504 eV for SrTiO3/CsAgF3 20, while purely–fluoride KZnF3/KAgF3 has a obvious smaller charge transfer gap, as shown in Table 2.

Discussion

In conclusion, we investigate cupratelike electronic structures and strong AFM fluctuations effect in the proposed KAgF3–related superlattices. Compared to bulk KAgF3, undoping purely–fluoride KZnF3/KAgF3 SL has a similar magnetic coupling constant. A 4% in–plane compression strain stabilizes AFM state further and makes the FS shape to deviate from the edge of electron pocket and to resemble that of LCO. In half–fluoride SrTiO3/KAgF3 SL, atomic polarization induces out–of–plane electronic reconstruction occurring between O-px, py orbitals in TiO2 plane and covalent hybrid orbitals of and F-px, py in AgF2 plane, which results in AFM state instability by a smaller energy difference ENM − EAFM of 11.675 meV/Ag. And FS shape of half–fluoride SL presents considerable similarity to that in HBCO. Therefore, fluoride and half–fluoride KAgF3–related superlattices indeed have the potential to become 2D AFM precursors of a new AgII family of high–temperature superconductors, which could benefit from enhancement of the critical superconducting temperature due to strong magnetic fluctuation and the relative small charge transfer gap in KZnF3/KAgF3.

Method

We carried out the numerical calculations using the Vienna ab initio Simulation Package (VASP)27,28,29,30 within the framework of the generalized gradient approximation (GGA) (Perdew-Burke-Ernzerhof exchange correlation functional)31 and recently developed maximally localized Wannier functions (MLWFs) downfolding technique32,33,34. The ion–electron interaction was modeled by the projector augmented wave (PAW) method35,36 with a uniform energy cutoff of 500 eV. Spacing between k points was 0.02 Å−1. The geometrcal structures of the SLs were optimized by employing the conjugate gradient technique and in the final geometry, no force on the atoms exceeded 0.01 eV/Å. For magnetic states calculations, we used Ud = 7.5 eV and Jd = 0.98 eV for Cu-3d state37 and a smaller Ud = 5 eV and Jd = 0.98 for Ag-4d state38.

Additional Information

How to cite this article: Yang, X. and Su, H. Electronic Properties of Fluoride and Half-fluoride Superlattices KZnF3/KAgF3 and SrTiO3/KAgF3. Sci. Rep. 5, 15849; doi: 10.1038/srep15849 (2015).