On the energy scale involved in the metal to insulator transition of quadruple perovskite EuCu3Fe4O12: infrared spectroscopy and ab-initio calculations

Optical measurements were carried out by infrared spectroscopy on AA′3B4O12 A-site ordered quadruple perovskite EuCu3Fe4O12 (microscopic sample) as function of temperature. At 240 K (=TMI), EuCu3Fe4O12 undergoes a very abrupt metal to insulator transition, a paramagnetic to antiferromagnetic transition and an isostructural transformation with an abrupt large volume expansion. Above TMI, optical conductivity reveals a bad metal behavior and below TMI, an insulating phase with an optical gap of 125 meV is observed. As temperature is decreased, a large and abrupt spectral weight transfer toward an energy scale larger than 1 eV is detected. Concurrently, electronic structure calculations for both high and low temperature phases were compared to the optical conductivity results giving a precise pattern of the transition. Density of states and computed optical conductivity analysis identified Cu3dxy, Fe3d and O2p orbitals as principal actors of the spectral weight transfer. The present work constitutes a first step to shed light on EuCu3Fe4O12 electronic properties with optical measurements and ab-initio calculations.

semiconductor transition around 255 K 10 . On the other hand, large size rare earth ions family (Ln = La, Pr, Nd, Pm, Sm, Eu, Gd and Tb) undergoes the following intermetallic charge transfer 3Cu 2+ + 4Fe 3.75+ → 3Cu 3+ + 4Fe 3 + leading to a paramagnetic-metal to an AFM-insulator phase transition between 240 K and 350 K 9 . These properties result from the transition between the high valence state of Cu 3+ at the square-coordinated A sites and the Fe 3.75+ at the octahedron-coordinated B sites. The charge transfer occurs under high pressure conditions for many  Scientific RepoRts | 6:28624 | DOI: 10.1038/srep28624 materials 11 but in LnCFO it is triggered by a slight change of temperature promising potential room temperature applications. For instance, the temperature transition is T MI = 310 K in SmCFO. La x Ln 1−x Cu 3 Fe 4 O 12 substituted systems could allow a modulation of the MIT temperature and LaCu 3 Fe 4(1−x) Mn 4(x) O 12 doped compounds is an example of a controlled NTE 12 . LnCFO with smaller Ln ions are subjected to volume change at temperatures that provide a good opportunity to control simultaneously both physical properties and thermal expansion and allow the development of thermal sensors 13,14 . This paves the way for many potential technological applications with composite and single-phase compounds 15 . EuCu 3 Fe 4 O 12 (ECFO) is very representative of large size LnCFO and its optical properties have never been measured yet. It exhibits the earlier cited intermetallic charge transfer between Cu and Fe at 240 K traduced by a MIT, a paramagnetic to antiferromagnetic transition and an isostructural volume change 8,13,16,17 . On cooling, all the metal-oxygen bonds lengths change significantly. The Cu-O bonds shrink simultaneously with the charge transfer between Cu 3dxy and Fe 3d via O 2p orbitals and the Fe-O bonds expand. Although many theoretical and computational studies have been recently devoted to describe the electronic structure and the mechanism of the MIT in LnCFO 9,16,[18][19][20] , experimental investigations of the electronic properties across the MIT are still missing.
In this paper, we report on low-energy electrodynamics of ECFO investigated by infrared spectroscopy. We found that ECFO undergoes an abrupt metal to insulator transition (MIT) at 240 K associated with a change of optical properties over an energy scale larger than 1 eV. The comparison with DFT calculations shows that, despite the large amount of energy involved in the MIT, ECFO is a moderately correlated system. Furthermore, both Fe 3d and Cu 3d bands are strongly modified at the transition, in relation with the charge transfer and the magnetic transition.

Results and Discussion
Optical measurements. Reflectivity spectra of ECFO, R(ω), are shown for different temperatures from room temperature to around the MIT temperature in Fig. 2. For 300 K, the reflectance exhibits a metallic response, slowly decreasing from 0.9 to 0.15 over the measured frequency range. However, no clear plasma edge is observed. Such a behavior is often found in correlated transition metal oxides [21][22][23][24][25] . As the temperature is decreased down to 250 K, the spectra do not show any qualitative change. By contrast, the reflectivity is rapidly reduced between 245 K and 235 K in both far infrared and mid infrared ranges. Below 230 K, spectra display an insulating behavior and several phonon modes are detected. Seven of the 12 infrared active modes predicted by group theory can be observed.
The optical conductivity σ(ω) deduced from reflectivity spectra by Variation Dielectric Function technique (VDF) [26][27][28] is shown in Fig. 3. In the metallic paramagnetic phase (T > 240 K), the optical conductivity is nearly flat and slightly decreases at low frequency to reach approximately 1 000 Ω −1 cm −1 at 100 cm −1 . It clearly deviates from usual Drude model since it exhibits a broad bump at 200 cm −1 . This could be due to either localization by disorder [29][30][31] , electronic correlations 32,33 or strong electron-lattice coupling (polarons) 29,34,35 . With decreasing temperature, the optical conductivity dramatically drops three order of magnitude at low frequency, and exhibits an insulating behavior, with an optical gap energy Δ ≈ 125 meV and a broad mid infrared band. Moreover, note that the optical conductivity is larger in the metallic phase than in the insulating phase up to 9 000 cm −1 . The optical gap energy is determined by a linear extrapolation at the inflection point of the onset of σ(ω) 36 (inset of Fig. 3). The electronic gaps extracted from optical conductivity spectra are reported in Fig. 4a. The very abrupt transition clearly deviates from a BCS-like behavior. Note that the gap value in the insulating phase (Δ ≈ 125 meV) is slightly smaller than previous DFT calculations of other LnCu 3 Fe 4 O 12 that predict Δ between 300 and 800 meV 16,18,20 . As shown in Fig. 4b, the temperature dependence of the normalized conductivity taken at 100 cm −1 (the lowest measured frequency), and the one obtained from transport measurements 37 are in very good agreement.  Note that we found a quite large discrepancy between the conductivity obtained by transport (of order of 1 Ω −1 cm −1 ) and the value of the 300 K optical conductivity at 100 cm −1 (1000 Ω −1 cm −1 ). However, since the sample is a very small polycristal, such a discrepancy can easily be due to the determination of geometrical parameters (cross section, distance between electrodes), grain boundaries and low density of the sample. In order to estimate the typical energy scale involved in the MIT mechanism, the optical conductivity spectral weight (SW) was calculated from the optical conductivity: c 0 c SW is related to the charge carrier density contributing to the optical properties up to a cutoff energy ω c . As shown in Fig. 5a, the spectral weight is not recovered up to 10 000 cm −1 implying that electronic properties of ECFO are modified over an unusually large spectral range at the MIT. In addition, the temperature dependence of the SW calculated (Fig. 5b) at ω c ≈ 1 000 cm −1 (i.e. order of the gap energy) clearly shows a step-like behavior.
Ab-initio calculations. In order to get a better insight of the electronic structure and to identify low energy optical excitations, DFT + U calculations were performed. The calculation has been carried out for both the insulating and the metallic phases by using ECFO crystallographic data for 100 K and 300 K. Low temperature phase (LT) was taken anti-ferromagnetic G-type on Fe lattice, as shown in Fig. 6a, in accordance with experimental x-ray diffraction data 38 .
In order to reproduce the order of magnitude of the experimental gap, we choose U = 1.5 eV. Such a value of U is not uncommon since it usually ranges between 2 eV and 7 eV in most transition metal compounds [39][40][41][42] . Note that for U < 1.5 eV, DFT + U predicts a metallic ground state in disagreement with experiments. In addition, values of U > 1.5 eV do not drastically affect the physics 16,18,20 . A more detailed investigation of U parameter has been performed by Isoyama et al. 18 on the LaCFO compound.
ECFO Total Density of State (TDOS) and site Projected DOS (PDOS) are displayed in Fig. 7a,b. As expected, the TDOS of the AFM phase shows an insulating state with a gap of 250 meV that is in reasonable agreement with Δ exp ≈ 125 meV. TDOS is constituted of a wide band of energy from − 7 eV to − 0.2 eV and three bands above the Fermi level,  f , up to 3.75 eV. The PDOS (Fig. 7a) allows to identify a narrow spin polarized Fe 3d orbital occupancy at 1.8 eV and a strong hybridization of Cu 3d and O 2p states around 0.2 eV. Note that the Fe 3d spin state is in good agreement with neutron diffraction data 38 ; the calculated Fe magnetic moment (integrated inside the Fe muffin-tin sphere) M Fe calc = 3.97 μ B is very close to the experimental one M Fe exp = 4.03 μ B . The calculated Cu magnetic moment is zero in accordance with neutron diffraction data 38 . It is worth noting that PDOS of Fe 3d orbitals are all the same whereas Cu 3dxy differs from other Cu 3d . More precisely, beyond  f , Cu DOS is essentially composed of Cu 3dxy orbitals state as seen in Fig. 7a and noticed by Hongping et al. in the study of LaCFO 16 . So Cu 3dxy orbitals hold a central role in the valence transition.
In order to describe the ECFO paramagnetic high temperature phase (HT), we used a ferrimagnetic structure FiM (as drawn in Fig. 6b) since paramagnetic structure is difficult to set up in DFT calculations. Several studies 17,20 used a FiM order insofar as the physics of the metallic phase of LnCFO is quite well captured. TDOS and PDOS of the HT phase are displayed in Fig. 7b. The expected metallic state is well reproduced since  f is occupied by a wide valence band from − 7 eV to 4.2 eV. The PDOS shows that Cu 3d , Fe 3d and O 2p orbitals are hybridized around the Fermi level to constitute a wide spread band driving the metallic state. Also for this phase, Cu 3dxy is the only orbital that differs from other Cu 3d orbitals by crossing  f . This supports the fact that Cu 3dxy is involved in the low frequency (< 600 cm −1 ) behavior of the HT optical conductivity (Fig. 3). Moreover, Cu ions now wear a non zero magnetic moment M Cu calc = + 0.32 μ B that is coupled antiparallel to the iron one of M Fe calc = − 3.60 μ B . The observed calculated changes between LT and HT phases illustrate the charge transfer between Cu 3dxy site orbital and Fe 3d one via O 2p orbital hybridization. In addition, the modifications of DOS over an energy scale larger than 1.5 eV (the lowest value of U that reproduces the gap) show that the energy scale involved in the charge transfer is larger than 1.5 eV. This is roughly consistent with our spectral weight study (Fig. 5) which indicates that the mechanisms involved in the MIT occur beyond 1 eV.
For the purpose of the comparison with the experiment, we have calculated the optical conductivity by Random Phase Approximation (RPA) using our DFT electronic structure calculations. Although RPA does not take into account many body effects, it is expected to roughly capture the physics. LT and HT calculated optical conductivities (σ RPA ) are presented in Fig. 8. It is worth noting that σ RPA of the LT phase exhibits an electronic gap of 250 meV (2 000 cm −1 ). This is the same order, or even larger than our experimental gap of 125 meV and previous LnCFO DFT studies 16,18,20 . The first bump at 6 000 cm −1 on the low temperature σ RPA (blue curve) is assigned to the LT optical conductivity excitation detected at 5 000 cm −1 (Fig. 3). Two more excitations are predicted at 10 500 cm −1 and 25 000 cm −1 . For the HT phase (metallic) σ RPA presents a clear Drude-like peak below 2 000 cm −1 that differs from the low frequency behavior detected by spectroscopy for the HT phase (Fig. 3). Such a difference is not very surprising since DFT calculations do not incorporate temperature effects, strong electronic correlations or localization by disorder as discussed above. Nevertheless, the shape and the relative level of the calculated conductivities, are compatible with a spectral weight displacement over a large energy scale since HT conductivity is higher than the LT conductivity from 0 cm −1 (0 eV) to 26 000 cm −1 (3.2 eV). The behavior of σ beyond this range is necessarily in favor of the spectral weight recovering since the charge carrier density is conserved.

Conclusion
Based on reflectivity measurements and first principle calculations, we reported the first infrared spectroscopy study of the A-site ordered quadruple perovskite EuCu 3 Fe 4 O 12 highlighting the opening of a 125 meV gap below 240 K with an abrupt metal to insulator transition. The charge transfer involves an energy scale larger than U = 1.5 eV that reflects the presence of electronic correlations in the material. The DFT + U study has been managed with a surprising small value of U (1.5 eV). We identified the mechanism responsible for the MIT as being the redistribution of density of states from Fe 3d orbitals to Cu 3dxy with the hybridization to O 2p orbitals. The next step will consist in driving the MIT by physical pressure for others LnCFO in order to disentangle the role of magnetism in the transition.

Methods
ECFO polycrystalline samples were synthesized under high pressure in a high pressure cell (15 GPa) and high temperature (1000 K) 37 . This technique severely restricts the volume of the sample to approximately millimeter size. The sample after synthesis has low density and is crumbly. Thus, a clean flat surface of 120 μm diameter was polished up to optical grade 0.25 μm. SXRD and Fe Mossbauer spectroscopy confirmed the composition of the samples and the valence state of both high and low temperature phases being EuCu +2 3 Fe +3,75 4 O 12 and EuCu 3+ 3 Fe 3+ 4 O 12 with a lattice constant of 7.33641(8) Å for 300 K and 7.37306(8) Å for 100 K. Near normal incidence reflectivity spectra were measured between 100 cm −1 and 30 000 cm −1 , from 150 K to 300 K. Low temperature measurements on such a small sample were obtained by using a homemade high-vacuum microscope including a x15 Schwarzchild objective connected to a BRUKER IFS 66v/S Fourier-transform spectrometer. After the initial measurement, the sample was coated with a 150 nm aluminium film and remeasured in the previous temperature range. These additional data were used as reference to calculate the reflectivity in order to take into account light scattering on the surface of the sample and possible misalignement induced by heating. Note that, due to the small size of the sample, diffraction limit is reached around 100 cm −1 . Above 10 000 cm −1 , light scattering due to surface roughness prevents to obtain a good signal to noise ratio. Thus, although both the shape and level of the reflectivity were reasonable according to infrared measurements and high energy  Fig. 7(a)). reflectivity obtained from x-ray atomic scattering functions as proposed by D. B. Tanner 43 , no clear conclusion can be drawn on the temperature dependence above 10 000 cm −1 . As a consequence, temperature dependent infrared data have been merged with the room temperature UV data. Optical conductivity spectra were obtained consistently by Variation Dielectric Function analysis (VDF) and Kramers-Kronig (KK) analysis. In order to proceed the KK analysis, reflectivity spectra were extrapolated at low frequency with Hagens-Rubens formula in the metallic phase and a constant value in the insulating phase, and by using high frequency extrapolation based on x-ray atomic scattering functions technique 43 . Spin-polarized first-principles DFT calculations have been carried out using the full-potential augmented plane-wave method with local orbitals (FP-APW + lo) as implemented in the ELK code. The generalized gradient approximation (GGA) using Perdew-Burke-Ernzerhof (PBE) parametrization was employed for the exchange-correlation energy potential. The Brillouin zone sampling was done using an uniformly spaced k-grid of 6 × 6 × 6. To avoid complexity, 4f states of europium atoms are considered as core states 44 , since they are not expected to be involved in low energy electronic properties. The structural parameters were taken from experimental X-ray crystallographic data at 100 K and 300 K, to describe low temperature (LT) and high temperature (HT) phases respectively. The broadening used to compare with the data is 0.25 eV 45 . In order to take into account the strong correlations for both Fe and Cu 3d electrons, DFT + U method was used to add the on-site Hubbard U eff = U− J term. Hereinabove, the term U eff is denoted just as U for simplicity. The dielectric function was computed in the Random Phase Approximation (RPA).