Exploring the structural , electronic and magnetic properties of cation ordered 3d-5d double perovskite Bi$_2$FeReO$_6$ and Bi$_2$FeIrO$_6$ thin-films from first-principles

TL;DR

This study uses first-principles calculations to explore how strain and electronic correlations influence the magnetic and electronic properties of Bi-based 3d-5d double perovskite thin films, revealing potential for spintronics and photovoltaic applications.

Contribution

It provides the first detailed theoretical analysis of strain and correlation effects on Bi$_2$FeReO$_6$ and Bi$_2$FeIrO$_6$ thin films, highlighting their magnetic phase transitions and electronic structure.

Findings

Bi$_2$FeReO$_6$ transitions from anti-ferromagnetic insulator to ferrimagnetic semi-metal under strain.

Bi$_2$FeIrO$_6$ exhibits a correlation-driven transition from ferromagnetic insulator to ferrimagnetic half-metal.

Bi$_2$FeIrO$_6$ shows spatial separation of conduction and valence states, beneficial for photovoltaic applications.

Abstract

We report a first-principles study of Bi-based 3$d$-5$d$ ordered double perovskite oxides (A$_2$BB$^\prime$O$_6$) with a 3$d$ atom (Fe) at the B-site and 5$d$ atoms (Re,Ir) at the B$^\prime$-site while keeping highly polarizable ions (Bi$^{3+}$) at the A-site. We find that, under coherent heteroepitaxy, Bi$_2$FeReO$_6$} exhibits a strain-driven anti-ferromagnetic insulator to ferrimagnetic semi-metal transition, while Bi$_2$FeIrO$_6$ shows correlation driven ferromagnetic insulator to ferrimagnetic half-metal transition with calculated magnetic moments of 5 $\mu_B$/f.u. and 3 $\mu_B$/f.u., respectively. These properties along with the low band gaps in the insulating phases make the compounds appealing for spintronics applications. Furthermore, in Bi$_2$FeIrO$_6$, the conduction and valence states are localized on different transition metal sublattices implying more efficient electron-hole separation upon photoexcitation, a desirable feature for photovoltaic applications.

Tables

Table 1. Table 1: Structural information for both C-AFM and G-AFM magnetic ordering at -2.7% strain.

Type	$a$ (Å)	$b$ (Å)	$c$ (Å)	$\alpha {(}^{\circ })$	$\beta {(}^{\circ })$	$\gamma {(}^{\circ })$
C-AFM	5.364	5.364	8.652	90.00	90.28	90.00
G-AFM	5.364	5.364	9.094	90.00	84.75	90.00

Equations

$$\boxed{ϵ=(\bar{a}-{\bar{a}}_{ref})/{\bar{a}}_{ref}}$$

$$\boxed{\mathbf{t}=\frac{{\mathbf{r}}_{\mathbf{A}}+{\mathbf{r}}_{\mathbf{O}}}{\sqrt{2}\times (\frac{{\mathbf{r}}_{\mathbf{B}}}{2}+\frac{{\mathbf{r}}_{{\mathbf{B}}^{\prime }}}{2}+{\mathbf{r}}_{\mathbf{O}})}}$$

Full text

I Introduction

Transition metal (TM) double-perovskites (DP) (A2BB′O6) have gained enormous attention recently due to their fascinating properties in the areas of magnetism, ferroelectrics, spintronics and multiferroics Vopson (2015) and long served as a platform for device applications. Particularly, multiferroic materials are quite promising due to their multipurpose technological implications Spaldin and Fiebig (2005); Catalan and Scott (2009). These materials are characterized by coexistence of ferroic orders such as ferroelectricity, ferromagnetism and/or ferroelasticity along with a coupling of at least two of these orders which can, in turn, lead to magnetoelectric, magnetoelastic effects, etc. A prominent example of DP multiferroic is \ceBi2FeCrO6 (BFCO), which was designed from the AFM parent multiferroic compound \ceBiFeO3 (BFO) by replacing half the Fe ions by Cr with an aim to increase the magnetic moment through ferrimagnetic interaction of $\it{B}$ and $\it{B^{\prime}}$ sites while retaining ferroelectricity and magneto-electric coupling intact Baettig and Spaldin (2005). Due to AFM ordering, the parent compound BFO shows $\sim$ 0 magnetic moment, however, BFCO was predicted to show a magnetic moment of 2 $\mu_{B}$ per formula unit (f.u.) in its bulk form with a G-type AFM ordering.

In practice, multiferroics can be prepared as high quality epitaxial thin films on oxide substrates. The epitaxial strain (ES), which can be introduced by varying lattice mismatch between the thin-film and substrate, has the tendency to control the material properties and to stabilize other metastable magnetic structures Meng et al. (2018); Lu and Rondinelli (2016); Lee and Rabe (2010); Chen and Millis (2016); Gan et al. (1998). The potential of multiferroic materials towards photovoltaic (PV) and photocatalytic (PC) application is currently being explored. The narrow band gap, which arises due to electron-electron interaction governing the magnetic ordering, makes multiferroics special candidates for PV application over the general perovskite materials Grinberg et al. (2013). Among multiferroics, BFO was considered to show appreciable PV effect due to the presence of a direct band gap, a fact latter corroborated by Chui et al. Choi et al. (2009). However, the power conversion efficiency (PCE) of BFO based thin film devices is still very low for practical application. Lowering the band gap of these oxides without affecting their FE properties is a promising conceptual route to obtain solar energy conversion devices with higher PCE. Recently, it was shown that the epitaxial multiferroic ordered BFCO thin-films possess a power conversion efficiency of 6.5% under the illumination of red light laser Nechache et al. (2011) and 8.1% under AM1.5G illumination Nechache et al. (2015). In both the works, it was pointed out that the Fe and Cr cation order and the narrow band gap play a crucial role in the PV performance of BFCO thin films. Kim et al. Kim et al. (2018) recently attributed the excellent performance of BFCO to the spatial separation of the photoexcited electron and hole states onto the Fe and Cr sites, respectively, with the extent of separation increasing with the disorder at the $B$-site.

Recently, we have shown that epitaxially grown (001) BFCO thin-films are unstable to anti-site defects and prefer a C-type AFM (C-AFM) ordered ground state Rout et al. (2016), both features leading to loss of magnetization Khare et al. (2013); et al. (2014, 2015). The anti-site defects (disordering) occur basically due to the similarity of charge and ionic radii of Fe3+ and Cr3+ ions. We have also recently shown that by manipulating both ES and aliovalent A-site doping in BFCO thin films Rout and Srinivasan (2018), one can not only mitigate the issues like cation disorder and low magnetism but also significantly reduce the band gap, a desirable feature for PV applications. An alternative approach to suppress B-site disorder and encode functionality in Bi-based DPs is to form 3$d$-5$d$ oxides Ležaić and Spaldin (2011a). Doping with 5$d$ TM ions can not only improve magnetisation but also prevent the formation of antisite defects like BFCO thin-films due to their larger sizes compared to the 3$d$ ions. Apart from this, the mixture of 3$d$-5$d$ ions would likely improve the transition temperature as seen in case of Ca, Sr-based systems, due to the induced magnetic moment at the nonmagnetic sites Feng et al. (2014); Krockenberger et al. (2007).

In this work, we investigate the strain-dependent magnetic and electronic properties of two new double-perovskite 3$d$-5$d$ systems: \ceBi2FeReO6 (BFRO) and \ceBi2FeIrO6 (BFIO) from first-principles DFT simulations. BFO was chosen as a starting point for the doping with 5$d$ ions given its robust ferroelectric nature. We chose Fe atom as the 3$d$ ion in the B-site as it usually occurs in high-spin 3+ oxidation state, which could lead to large magnetic moment in DPs, stronger magnetic interactions and hence larger transition temperatures.

Our calculations predict an anti-polar $P2_{1}/n$-like structure for both compounds if grown on cubic substrates. We find that a C-type AFM ordering is favored for BFRO, while BFIO becomes a ferromagnetic insulator through out the ES region.

In BFRO thin-films, we show that at higher compressive strain, there is a C to G-AFM (1$\mu_{B}$/f.u.) transition accompanied by monoclinic to monoclinic structural transition due to octahedral reorientation. However, in BFIO thin-films, we find a correlation driven metal-to-insulator transition under ES. We find that the 3$d$ and 5$d$ cations adopt high spin 2+ and 4+ oxidation state (denoted below as (2+,4+)), respectively, in case of BFRO thin films. In BFIO, however, there is a competition between (2+,4+) and (3+,3+) states affected by onsite correlation at the low-spin Ir sites. We predict that correlation effects along with the stability of the 3+ oxidation state on the high-spin Fe sites will lead to the stabilisation of the (3+,3+) state in BFIO, with a magnetic moment of 5$\mu_{B}$/f.u., under all ES. Furthermore, BFRO is predicted to be an AFM insulator under ES, whereas the Ir-based DP is a ferromagnetic insulator. Ferromagnetic insulators (FM-I) are rare and very promising for their spintronics and PV applicability Meng et al. (2018); Wang et al. (2015). So far, most of the synthesized 3$d$-5$d$ DP materials are half-metallic in nature. However, \ceBi2FeIrO6 is a promising material as it exhibits both ferromagnetism and insulating properties simultaneously. Considering the presence of 5$d$ elements, we included SOC in our calculation but found that SOC does not have a significant effect on the magnetic properties while it has a small impact on the electronic properties, particularly resulting in a slight band gap reduction. We show that the correlation effect on 5$d$ site plays a very crucial in opening the band gap and magnetic phase transition, which was completely ignored in the previous study Ležaić and Spaldin (2011b). Presence of very narrow band gap $\sim$1.1 eV in both the compounds (considering correlation effect on both 3$d$-5$d$ ions) makes them suitable candidates for PV applications.

II Method of Calculation

Our calculations employed a spin-polarized GGA+$U$ Anisimov et al. (1997); Cococcioni and de Gironcoli (2005); Himmetoglu et al. (2011) approach using the revised version Perdew-Burke-Ernzerhof (PBE) Perdew et al. (1996, 1997) for solids, PBEsol Perdew et al. (2008) as exchange-correlation functional within the framework of the Quantum-ESPRESSO code Giannozzi et al (2006). Ionic cores were modeled by ultrasoft pseudopotentials keeping the 4$f$ electrons of 5$d$ transition metals and Bi atoms as part of the core. Plane-wave cut-off energy of 85 Ry was used for representing wavefunctions, and 700 Ry for the augmentation charge. The Hubbard $U$ parameter can be calculated ab initio using the linear response formalism  Cococcioni and de Gironcoli (2005); Himmetoglu et al. (2011). We found the $U$ values to be 6.4 eV (Fe) and 3.6 eV (Re) in BFRO system, whereas in BFIO case, the $U$ values were 6.38 (Fe) and 5.18 (Ir). We used a $10\times 10\times 8$ Monkhorst-Pack k-point mesh for Brillouin zone integration. For the density of states (DOS) calculations, a denser Monkhorst-Pack k-point grid of $16\times 16\times 16$ was employed. All the structures were relaxed until the Hellmann-Feynmann forces are less than 0.26 meV/Å.

For both the compounds, we have constructed 20-atom $\sqrt{2}\times\sqrt{2}\times 2$ tetragonal supercells (shown in Figure 1), starting from a simple cubic double-perovskite structure, to allow for appropriate magnetic ordering of ions along (111) direction. The structures were chosen to conform to $P2_{1}/n$ (antipolar) and $R$3 (polar) space groups, respectively, given their compatibility with cubic substrates Khare et al. (2013); et al. (2015). These essentially differ by the sense and relative magnitudes of oxygen octahedral rotations as indicated by the Glazer notations $a^{-}a^{-}c^{+}$ and $a^{-}a^{-}a^{-}$, respectively Glazer (1975, 1972). Using the substrate \ceSrTiO3 pseudo-cubic lattice parameter $a_{cub}=3.90$Å  Janotti et al. (2012) as a reference, we generated structures mimicking the epitaxially strained films by varying the in-plane lattice parameters over a range of realistic substrate strains corresponding to (001) epitaxial growth. The in-plane lattice parameters of supercell are set to $\bar{a}=\bar{b}=\sqrt{2}\times a_{cub}$ while the $c$ parameters have been relaxed for each in-plane strain. The ES can be defined as

[TABLE]

where $\bar{a}_{ref}$ is the unstrained lattice parameter. The selection of Re and Ir structures is based on the adapted tolerance factor $\bf t$ of the double-perovskites Corrêa et al. (2010). The tolerance factor for DPs A2BB′O6, can be written as:

[TABLE]

where rA, rB and r${}_{B}^{\prime}$ are the ionic radii of the respective ions and rO is the ionic radius of oxygen. It is known that, for double-perovskite family, if t $<$ 0.97 the compound becomes either monoclinic ($P2_{1}/n$) or orthorhombic Serrate et al. (2007). In case of \ceBi2FeReO6, the calculated average tolerance factor is 0.93 while for \ceBi2FeIrO6, it is 0.95. Hence, both structures are expected to take perovskite form.

III Results and Discussions

III.1 Strain-dependence ground-state structure of \ceBi2FeReO6

We first investigated the effect of ES on the ground-state structure of BFRO compound. We considered three types of AFM (A, C, G-type) and the FM orders for the calculations Rout et al. (2016). We have considered the two lowest energy phases $P2_{1}/n$ and $R$3 phase, which were also previously found to be stable for similar systems under various strains  Ležaić and Spaldin (2011b). The ES is introduced in thin-film by constraining the two in-plane lattice vectors to be equal in length and enforce the angle between them to be 90∘.

We first obtained the optimized geometries in the $P2_{1}/n$ and $R$3 phases for different magnetic orderings at all the considered ES. The minimum energy structure at each strain was obtained by allowing the length and angle of out-of-plane lattice parameter to relax simultaneously along with the ionic positions. Figure 2 depicts the energy (relative to the global minimum structure, i.e. $P2_{1}/n$ at 2% strain) of the lowest lying states as a function of ES. From Figure 2, it is clear that the ferroelectric phase ($R$3) is not favorable under the considered epitaxial strains.

We find that C-AFM of $P2_{1}/n$ phase is the most stable structure over the broad range of strain leading to zero total magnetic moment due to exact cancellation of the spin magnetic moment. Most interestingly, a magnetic ordering transition (from C-AFM to G-AFM) is seen at -2.7%, which suggests that a net magnetic moment can also be achieved in \ceBi2FeReO6 thin-films through compressive strain. We ascribe the magnetic phase transition to the oxygen octahedra reorientation induced monoclinic to monoclinic structural transition. The structures of both C and G-AFM BFRO are shown in Figure 3 and the corresponding structural information for both the magnetic ordered structure at -2.7% strain are provided in Table 1.

The monoclinic angle (angle between $a$ and $c$ lattice parameters) changes from being obtuse in the C-AFM to be acute in the G-AFM structure. This transformation results from a sudden oxygen octahedra reorientation at -2.7% strain (see Figure 3). So, beyond -2.7% strain, magnetic ground-state for BFRO can be achieved with a magnetic moment of 1$\mu_{B}$/f.u.. The polar $R$3 phase, however, remains higher in energy in this strain region. One unusual finding in case of BFRO thin-film is the oxygen octahedral distortion around the Fe atom. It was observed that the Fe atom undergoes a Jahn-Teller-like distortion, leading to three different types of Fe-O bond length whereas the Re atom remains undisturbed. The three unequal bonds at reference (0% strain) are axial Fe-Oax long bond (2.28 Å), equatorial Fe-Oeq medium bond (2.14 Å) and apical Fe-Oap short bond (2.05 Å). This octahedral distortion pattern is also seen in other strain regions.

III.2 Electronic and magnetic properties of \ceBi2FeReO6

In this section, we analyze the electronic structure of \ceBi2FeReO6 thin-films in the antipolar $P2_{1}/n$ structure. We also briefly discuss about the magnetic properties of the corresponding structure.

We find that the BFRO structure prefers to adopt C-AFM ordering, where the spins on Fe (3$d$) and Re (5$d$) transition metal ions anti-aligned in the plane of epitaxy (in-plane) but align parallelly perpendicular to this plane (out-of-plane). However, the structure undergoes a magnetic phase transition beyond -2.7% strain leading to a G-AFM ordered phase where the spins are anti-aligned both in-plane and out-of-plane. The total density of states (DOS) and the contributions to it from the $d$ and $p$ states of Fe (Re) and O, respectively, for both the spin channels, calculated within GGA+$U$ (only on Fe) at reference strain (0%) are shown in Figure 4.

In BFRO, Re prefers 4+ oxidation state (high spin) and Fe prefers to stay in high spin 2+ oxidation state. The thick black line represents the total DOS for both the spin channels (spin up and down). The up and down channels contribute equally to the DOS indicating an AFM ground state. The orange solid line represents the local density of states (LDOS) for Fe (3$d$) orbits and the solid blue lines LDOS for 5$d$ (Re) states. The LDOS which arise from oxygen $p$ orbitals, denoted by magenta color, contribute predominantly to the total density of states (see Figure 4). The structure is insulating, with a small gap of 0.4 eV in the GGA+$U$ calculations. However, this gap is significantly enhanced up to 1.2 eV after incorporating onsite Coulomb repulsion $U=$3.6 eV on Re-sites as shown in Figure 4. This suggests that the correlation effects arising from Re atoms would be important in this system. The band near the Fermi energy arises predominantly from Re 5$d$ ($t_{2g}$) states with strong oxygen 2$p$ orbital hybridization. The bands just above the Fermi level have a predominantly Re 5$d$ ($e_{g}$) character in both spin channels. The Fe $t_{2g}$ bands lie between -8.5 to -5 eV for both the spin channels while the $e_{g}$ bands extend from -5 to about -1.8 eV below the Fermi energy. There are two in-plane and one out-of-plane Fe-O-Re angles measuring 141∘, 149∘ and 148∘, respectively. The two in-plane angles are different due to oxygen octahedral distortion around the Fe atom.

With these angular orientations, the magnetic moments on Fe and Re are coupled through antiferromagnetic superexchange mechanism Goodenough (1955); Kanamori (1959); Wollan (1960) along the in-plane direction and coupled ferromagnetically along out-of-plane.

Similarly, the DOS for G-AFM at -2.7% strain is also shown in Figure 5. Here, the correlation effect on both Fe and Re-sites are taken into account for the DOS calculations. Unlike the C-AFM phase, in this case, neither the total DOS nor the LDOS are identical in both the spin channels. The difference in the DOS indicates the ferrimagnetic (FiM) nature of the compound. The $t_{2g}$ bands of Fe are sharply localized within -8.5 to -6.0 eV energy window, while the $t_{2g}$ states of Re-sites are localized in the minority spin channel immediately below the Fermi energy. Interestingly, the valence and conduction band edges correspond to different spin channels and there is no gap in between. Hence, there is an insulator (C-AFM) to semi-metal (G-AFM) transition at -2.7% strain. The half-metallic (or semi-metallic) state (see Figure 5) results despite using $U$ on both the TM sites, making it less likely to be an artifact of the DFT method employed. This is indeed one of our important findings in this compound under ES.

III.3 Strain-dependence ground-state structure of \ceBi2FeIrO6

In this section, we have studied the influence of ES on \ceBi2FeIrO6 thin-films. The ionic positions and the corresponding $c$-axis at each strain are optimized by using GGA+$U$ (used $U$ only on Fe) approach in $P2_{1}/n$ symmetry. We also studied the effect of $U$ on Ir (5$d$) sites as it plays a very crucial role in predicting the electronic properties as seen in the previous section. The optimized energies are plotted against the ES as shown in Figure 6 which shows the lowest energy magnetic states with large magnetic moments due to the existence of different oxidation numbers in the TM ions. As can be seen in Figure 6, the G-AFM emerged as the lowest energy state throughout the epitaxial strain. The FiM ground-state (solid black pointed circle line) possesses a 2+ (Fe) and 4+ (Ir) oxidation state which contributes to a net magnetic moment of 3 $\mu_{B}$/f.u., while the solid square pointed line represents the higher energy ferromagnetic structure with 3+ (Fe) and 3+ (Ir) oxidation states. In both the cases, the Fe-site assumes a high-spin configuration while Ir prefers low-spin.

Note that the energy vs strain (Figure 6) was obtained by using the GGA+$U$ approach, where the on-site Coulomb repulsion only included for Fe-site. However, keeping the necessity of $U$ values on 5$d$-sites in mind Ou and Wu (2014), when we added $U$ (5.18 eV) on Ir sites, we observed a sudden change in the ground state. Moreover, adding $U$ on Ir sites the FiM (${2+}$, ${4+}$) state no longer remains as the lowest energy state. Instead, the ferromagnetic (${3+}$, ${3+}$) state get stabilized under strain (see Figure 6). The FiM (${2+}$, ${4+}$) state denoted by solid black line is shifted up in energy while the energy of the (${3+}$, ${3+}$) state, represented by the solid red line, is brought down significantly as compared to Figure 6. The ferromagnetic ground-state leads to a total magnetic moment of 5 $\mu_{B}$/f.u., which comes predominantly from the Fe sites, while the Ir ion undergoes a low spin $d^{6}$ configuration. In the Bi-based 3$d$-5$d$ compounds, this is a first observation of a 3+ (3$d$), 3+ (5$d$) states. In this compound, the magnetic moments of Fe atoms are aligned ferromagnetically and the induced moments on Ir sites are almost zero due to the low spin configuration as a result of which the total system becomes ferromagnetic.

The high $U$ value calculated for Ir is contrary to the usual expectation of lowered correlations in the more diffuse 5$d$ levels. Hence, we tested the robustness of the ($3+$,$3+$) state by scanning the $U$ (Ir) keeping the $U$ (Fe) fixed at 6.38 eV. The results are summarized in Figure 7.

We observed that, even at a lower $U$ value of 1.0 eV, the system already undergoes a transition from ferrimagnetic (Fe2+, Ir4+) to ferromagnetic (Fe3+, Ir3+) state. The energy of ferromagnetic states lowers further as we increase $U$ (Ir) towards our calculated value ($U$ = 5.18 eV). This result indicates that, correlation effects at Ir play an important role in BFIO making the FiM to FM transition a correlation driven one. We have also scanned the $U$ values for Fe-sites by fixing the $U$ values of Ir-sites to zero. interestingly the same phase transition was observed at $U$ = 5.8 eV, below which the system prefers to stay in the FM state while above it, the FiM state gets stabilized.

III.4 Electronic and magnetic properties of \ceBi2FeIrO6

In this section, we analyze the magnetic and electronic properties of DP \ceBi2FeIrO6 thin-films in detail. The DOS of both the possible (FM and FiM) phases are studied and are shown in Figure 8 and Figure 10, respectively. As is evidenced from Figure 8, the states close to Fermi level (EF) are dominated by Ir $d$-states strongly hybridized with O $p$-states. The dominating part of O $p$-states separated from Fe and Ir $d$-states are located below Fermi level within the range from -7.8 eV to -2.4 eV.

In the majority spin channel, the Fe $t_{2g}$, as well as $e_{g}$ states, remain filled while in Ir-sites the $t_{2g}$ states are completely filled and the $e_{g}$ states remain empty. In the minority spin channel, the Fe $t_{2g}$ and $e_{g}$ states remain completely empty while in Ir-sites the $t_{2g}$ states remain filled and the $e_{g}$ states stay completely empty, thus give rise to an insulating character in both the spin channels. This rare FM insulating nature of BFIO makes it very special.

Figure. 10 depicts the DOS of FiM metallic phase when the on-site Coulomb repulsion is switched off on 5$d$ (Ir)-sites. The metallic character of this state comes from the Ir majority spin channel due to the presence of a hole in $t_{2g}$ states (see also Figure 9). However, in the minority spin channel, all the $t_{2g}$ states of Ir are occupied. It is noticed that the $t_{2g}$ states of Fe and Ir co-exist around the Fermi level with a finite hybridization between them. In this state, Ir ion is in formal oxidation state 4+ and Fe takes high spin 2+ state, at U = 6.38 (Fe), 0 (Ir) (see Figure 7).

Due to these electronic configurations of outer valence shells and nearly 149∘ Fe-O-Ir angle, the magnetic moments of Fe and Ir interacts through an antiferromagnetic superexchange mechanism satisfying the Goodenough-Kanamori (GK) rules Goodenough (1955); Kanamori (1959); Wollan (1960). Therefore, the system ends up with a FiM configuration with a total magnetic moment of 1 $\mu_{B}$/f.u. Like the FM insulating state, the metallic AFM states are also very special due to their rare existence.

As we know, 5$d$ transition metals have an intrinsically strong spin-orbit coupling (SOC). Particularly, iridates are known to display SOC effect Zhao et al. (2008); Zeb and Kee (2012); Nie et al. (2015); Kim et al. (2014); Haskel et al. (2012); Ou and Wu (2014) in perovskites and DPs. Motivated by this, we extended our calculation to consider the SOC effect on top of GGA as well as GGA+$U$ functionals. We observed that adding SOC to GGA, lowered the band gap, while the insulating behavior was recovered by adding $U$. However, there is no major change in the magnetic properties of the system. Once again the system preferred to stay in the Fe3+, Ir3+ oxidation state even with SOC. The low spin 3+ oxidation state of Ir ($d^{6}$) ion, weakens the role of SOC in BFIO.

As can be seen in Fig. 8, the conduction band is made up almost entirely by Fe states whereas valence band results from Ir-O hybridised states. In principle, this implies that the photoexcitation can lead to electron-hole separation in the sublattices which is a desirable feature for photovoltaic applications.

IV Summary

In summary, we have designed two Bi-based double-perovskites \ceBi2FeReO6 and \ceBi2FeIrO6 mimicking the thin-film geometry grown along [001] direction. These two structures were constructed by keeping the Fe atom fixed at B-site and substituting Re and Ir (5$d$) atoms in B′-sites of ordered DP A2BB′O6 structure. The calculated tolerance factors indicate that both the compounds will adopt perovskite (orthorhombic/monoclinic) crystal structure. The \ceBi2FeReO6 thin-film becomes stable adopting a monoclinic $P2_{1}/n$ phase under a wide range of ES. By incorporating various types of magnetic ordering we show that the thin-film \ceBi2FeReO6 prefers a C-AFM spin ordering in its ground-state with zero magnetic moments. However, at -2.7% strain the structure adopts G-AFM ordering through a monoclinic to monoclinic structural transition. The G-AFM phase of BFRO provides a magnetic moment of 1 $\mu_{B}$/f.u. which is comparable to the previously reported Bi-based 3$d$-5$d$ compounds Ležaić and Spaldin (2011b). Our DOS calculations indicate that the \ceBi2FeReO6 is an insulator with a band gap of around 1.2 eV in thin film form. We find the correlation effect on Re (5$d$)-site to be very important, as on-site Coulomb repulsion ($U$) widens the band gap significantly. In this compound, Fe takes a high spin 2+ oxidation state, whereas Re adopts its formal high spin 4+ state. One important finding of our calculations is that the oxygen octahedra around Fe atoms undergo a distortion leading to long-short Fe-O bonds in the octahedra, which is not observed in the BFIO thin-film.

In \ceBi2FeIrO6 the $P2_{1}/n$ symmetry structure emerged as the ground state. Both the transition metals (Fe, Ir) takes 3+ oxidation state, where Fe acquires high spin configuration and Ir prefers to stay in a low spin. This configuration of \ceBi2FeIrO6 leads to a huge ferromagnetic ground state with a magnetic moment of 5 $\mu_{B}$/f.u. throughout the considered ES. However, when the onsite Coulomb repulsion term on Ir-site is switched off, the system stabilizes in FiM ground state with a magnetic moment of 3 $\mu_{B}$/f.u. over the ES. The DOS calculations show that the FM state is an insulator while the FiM state is a half-metal. Our calculations show that even a small value of $U$ on Ir site could, in principle, switch the (${2+}$, ${4+}$) oxidation state to (${3+}$, ${3+}$) state. So, there is a correlation driven metal to insulator transition in BFIO thin-film under ES. Given that ferromagnetic insulators and antiferromagnetic metals are very rare, the ab initio designed BFIO could prove to be quite technologically significant.

Both the compounds can be used in spintronic applications due to their magnetic and half-metallic nature. Apart from this, their narrow band-gaps ($\sim$ 1.2 and 1.3, respectively) make them a suitable candidate for PV applications. Although these materials are not ferroelectric, an appropriate doping strategy can make them ferroelectric Rout and Srinivasan (2018); Zhao et al. (2014). Apart from PV applications, these materials can also be used for the photocatalytic activity, such as solar water splitting and water purification. Like the parent BFO compound, the narrow band gap nature of these 3$d$-5$d$ compounds could allow them to harvest parts of the visible light of the solar spectrum. We hope that our observations will initiate further experimental efforts to verify the interesting predictions made in this work.

Acknowledgements.

The authors would like to thank Dr. D. S. Rana at IISER Bhopal for helpful discussions. The authors gratefully acknowledge IISER Bhopal for computational resources and funding. PCR is thankful to Council of Scientific and Industrial Research, India, for the research fellowship.