Insulator-to-half metal transition and enhancement of structural distortions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Lu}_2 \text {NiIrO}_6$$\end{document}Lu2NiIrO6 double perovskite oxide via hole-doping

Using density functional theory calculations, we found that recently high-pressure synthesized double perovskite oxide \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Lu}_2 \text {NiIrO}_6$$\end{document}Lu2NiIrO6 exhibits ferrimagnetic (FiM) Mott-insulating state having an energy band gap of 0.20 eV which confirms the experimental observations (Feng et al. in Inorg Chem 58:397–404, 2019). Strong antiferromagnetic superexchange interactions between high-energy half-filled \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Ni}^{+2}$$\end{document}Ni+2-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e_g^2\uparrow$$\end{document}eg2↑ and low-energy partially filled \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Ir}^{+4}\,t_{2g}^3\uparrow t_{2g}^2\downarrow$$\end{document}Ir+4t2g3↑t2g2↓ orbitals, results in a FiM spin ordering. Besides, the effect of 3d transition metal (TM = Cr, Mn, and Fe) doping with 50% concentration at Ni sites on its electronic and magnetic properties is explored. It is established that smaller size cation-doping at the B site enhances the structural distortion, which further gives strength to the FiM ordering temperature. Interestingly, our results revealed that all TM-doped structures exhibit an electronic transition from Mott-insulating to a half-metallic state with effective integral spin moments. The admixture of Ir 5d orbitals in the spin-majority channel are mainly responsible for conductivity, while the spin minority channel remains an insulator. Surprisingly, a substantial reduction and enhancement of spin moment are found on non-equivalent Ir and oxygen ions, respectively. This leads the Ir ion in a mixed-valence state of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+4$$\end{document}+4 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+5$$\end{document}+5 in all doped systems having configurations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5d^5$$\end{document}5d5 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{2g}^3\uparrow t_{2g}^2\downarrow$$\end{document}t2g3↑t2g2↓) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5d^4$$\end{document}5d4 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{2g}^2\uparrow t_{2g}^2\downarrow$$\end{document}t2g2↑t2g2↓), respectively. Hence, the present work proposes that doping engineering with suitable impurity elements could be an effective way to tailor the physical properties of the materials for their technological potential utilization in advanced spin devices.

Insulator-to-half metal transition and enhancement of structural distortions in Lu  . Strong antiferromagnetic superexchange interactions between high-energy half-filled Ni +2 -e 2 g ↑ and low-energy partially filled Ir +4 t 3 2g ↑ t 2 2g ↓ orbitals, results in a FiM spin ordering. Besides, the effect of 3d transition metal (TM = Cr, Mn, and Fe) doping with 50% concentration at Ni sites on its electronic and magnetic properties is explored. It is established that smaller size cation-doping at the B site enhances the structural distortion, which further gives strength to the FiM ordering temperature. Interestingly, our results revealed that all TM-doped structures exhibit an electronic transition from Mott-insulating to a half-metallic state with effective integral spin moments. The admixture of Ir 5d orbitals in the spin-majority channel are mainly responsible for conductivity, while the spin minority channel remains an insulator. Surprisingly, a substantial reduction and enhancement of spin moment are found on non-equivalent Ir and oxygen ions, respectively. This leads the Ir ion in a mixed-valence state of +4 and +5 in all doped systems having configurations of 5d 5 ( t 3 2g ↑ t 2 2g ↓ ) and 5d 4 ( t 2 2g ↑ t 2 2g ↓ ), respectively. Hence, the present work proposes that doping engineering with suitable impurity elements could be an effective way to tailor the physical properties of the materials for their technological potential utilization in advanced spin devices.
Recently, double perovskite oxides (DPO) having a chemical formula ABB ′ O 6 (A = alkaline earth or rare earth metal atoms and BB ′ = 3d and 4/5d transition metals such as B = Fe, Cr, Mn, Co, and Ni; B ′ = Mo , Re, Os, Ir, and W) have been attracting a lot of attention due to their unusual physical properties such as large magnetoresistance at or above room temperature 1-6 , high-temperature ferromagnetism(FM)/ferrimagnetism(FiM) 7-10 , half-metallicity 6,[11][12][13][14] , FM/FiM Mott-insulator [15][16][17][18] , multiferroicity 19 , exchange bias 20 , and magneto-dielectricity 21 . Particularly, a half-metallic (HM) state in Sr 2 FeMoO 6 1,7,22 and Sr 2 FeReO 6 2,23,24 (i.e., one spin channel exhibits a conducting nature while the other is insulator or semiconductor) having Curie temperature ( T C ) of 400-415 K is found, which displayed novel applications for spintronics perspective 25,26 . In most of the experiments, it is analyzed that HM is FM such as La 1−x Sr x MnO 3 27 and few are HM FiMs or highly spin-polarized like Sr 2 CrReO 6 having a T C of 635 K 8,9,28,29 . The highest T C of 725 K is observed in Sr 2 CrOsO 6 with the magnetic moment of 1.92 to 2.04 µ B 12,15,16 . Very recently, Feng et al. 18 , synthesized disordered monoclinic Lu 2 NiIrO 6 (LNIO) DPO under high-pressure (6 GPa) and high-temperature (1300 °C), where authors observed a FiM Mott-insulating state having a highest T C of 207 K among the disordered DPOs. A FiM Mott-insulating ground state in the LNIO was also verified by first-principle calculations, where a strong superexchange AFM coupling between Ni and Ir ions is energetically favorable 30 . A small and large energy band gaps ( E g ) of 0.20 and 2.25 eV exist in the spin-majority and spin-minority channels, respectively. Hence, due to a small energy gap and high T C among the Ir-based DPOs, LNIO could be an essential material in the designing of hard magnetic memory devices by tailoring its properties. The above mention properties of the DPOs have been stimulated the researchers to synthesize or predict new materials with improved electronic and magnetic properties.
As it is experimentally and theoretically established that DPOs are considered beneficial candidates for electron and hole-doping at A or B site, aiming to obtain optimized physical properties that were not present in their undoped form [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] . For example, in a widely studied Sr 2 FeMoO 6 DPO, electron doping which is obtained by partial replacement of Sr +2 with La +3 /Nd +3 results in the enhancement of T C [31][32][33][34] . Interestingly, the electrical . The Lu, Ni, Ir, O1, O2, and O3 ions occupy the Wyckoff positions 4e(0.9755,0.07858,0.2507), 2c(0.5,0,0.5), 2b(0.5,0,0), 4e(0.1372,0.4484,0.2521), 4e(0.6820,0.3061,0.0592), and 4e(0.1786,0.1880,0.9396), respectively. Our prior DFT calculations 30 and Feng et al. experiment 18 exhibit that Mott-insulating FiM state is more energetically stable than that of FM and AFMs structures in pristine LNIO, because AFM superexchange coupling between Ni and Ir are strongly favorable at the diagonals. Moreover, it is found that the next magnetic state close to the FiM ground state is FM 30 , therefore, we considered the FM and different FiM structure for further doping engineering in the present study. The schematic representation of crystal structures of Lu 2 Ni 0.5 TM 0.5 IrO 6 in an FM, FiM-I, FiM-II, FiM-III, and FiM-IV spin orderings are shown in Fig. 1a-e, respectively. In an FM spin ordering, Ni, TM, and Ir ions spins are parallel (Fig. 1a), while they are anti-parallel within both in-plane and out-ofplane directions in FiM-I state (Fig. 1b). In the case of FiM-II structure, Ni, TM, and one Ir ion spins are parallel to each other (i.e., ferromagnetically coupled) and the second Ir ion is anti-parallel to all of them as shown in Fig. 1c. For FiM-III spin ordering, TM and both Ir ions spins are anti-align than that of Ni (Fig. 1d), while both Ir and Ni ions spins are aligned with each other than that of TM in FiM-IV structure (Fig. 1e). Here, it is very important to note that only ordered TM-doped structures are considered likewise undoped one. However, a disordered between Ni and TM ions may exist due to a small difference in their size or charge which highly demands its experimental verification.
Structural stability and magnetic ground state. To estimate the relative structural stability of TMdoped LNIO systems, formation energy ( E f ) in each case is calculated as: where E doped and E undoped refers to the total energy of TM-doped and undoped LNIO DPO, respectively. µ TM and µ Ni are the chemical potentials of the TM and Ni atoms, which are the total energies of the most stable low-temperature phases of the bulk TM and Ni ( E TM and E Ni ), respectively. The calculated values of E f for Cr-, Mn-, and Fe-doped LNIO materials are − 0.52, − 1.21, and − 1.65 eV, respectively (also listed in Table 1). The "−" values of E f for all TM-doped systems indicate that they are thermodynamically stable and can be easily  Fig. 2a-c for Cr-, Mn, and Fe-doped LNIO structures, respectively. The phonon dispersions show a set of 60 phonon branches owing to the presence of 20 atoms per primitive cell. The higher frequency manifold is mainly attributed to vibrations of oxygen atoms which are dispersive and well separated in the higher energy regime as compared to the atomic species 49 . The absence of the imaginary frequencies in all TM-doped systems, which provides real evidence of the structures dynamic stability. The lower manifold from 0 to + 6 THz consists of the acoustic modes (24 phonon branches for each case) but it can also be noticed that some of the modes have strongly mixed character, which may lead the systems to metallicity.   Table 1. Calculated formation energy ( E f ) in eV, magnetic energy differences: FiM ordering temperature ( T C1 ) in K, and energy band gap ( E g ) in eV for Lu 2 Ni 0.5 TM 0.5 IrO 6 (TM = Cr, Mn, and Fe) double perovskite oxides. The "−" and " + " signs in E f and E show that doped crystal structure and FiM spin ordering are energetically stable, respectively. Moreover, " HM" in the E g column represents the half-metallic nature of the system along with total spin moments per unit cell ( m tot. /u.c.) as well as per formula unit ( m tot. /f.u.) and partial spin moments on Ni ( m Ni ), TM ( m TM ), Ir ( m Ir ), and O ( m O ) ions.  www.nature.com/scientificreports/ Next, the energetically favorable magnetic ground state in undoped and doped TM-doped LNIO DPO is examined by comparing the total energies of FM with different FiM structures as The computed values of E 1 , E 2 , E 3 , and E 4 are listed in Table 1. The "−" and " + " signs of E means that FM and FiM spin ordering are more energetically stable, respectively. Our calculations show that FiM-I spin ordering in the undoped and all doped structures are energetically favorable (i.e., E 1 is the ground state in each case) than that of FM and remaining FiM structures. This means that Ni and TM ion spins want to remain parallel with each other at the diagonal site, but prevail anti-parallel with Ir in both in-plane and out-of-plane. From E 1 , the FiM ordering temperature T C1 in each doped case is computed as " 2/3·�E k B ", where k B is the Boltzmann constant. The calculated T C1 for undoped, Cr, Mn, and Fe-doped LNIO materials are 219, 369, 339, and 360 K (also listed in Table 1) corresponds to E 1 in each case, respectively. It is also important to note that our computed T C of 219 K in undoped LNIO material is very close to the experimentally observed value of 207 K 18 . Interestingly, present calculations predicted that T C enhanced when one of the Ni ions is replaced with TM having the highest T C1 = 292 K for Cr-doped material. This means that the structural distortion increases with the TM-doping as compared to the undoped one. As, FiM-I spin ordering is the energetically favorable magnetic ground state in the undoped and all TM-doped LNIO structures, therefore, for further investigations only FiM-I magnetic structure is taken into account in all cases.
Octahedral distortion. It is previously established that deviation of 3d-O-5d bond angles from the perfect geometry of the high cubic symmetry structure ( 180 • ) in a distorted DPOs lead to a strong AFM superexchange coupling between magnetic ions, which results in a FiM ordering 46,50-54 and large structural distortions enhance the FiM ordering temperature [55][56][57] . Therefore, we displayed the DFT relaxed three peculiar TM-O-Ir bond angles on TMO 6 and IrO 6 octahedron for undoped, Cr-doped, Mn-doped, and Fe-doped LNIO materials in Fig. 3a-d, respectively. The calculated Ni-O1-Ir/Ni-O2-Ir/Ni-O3-Ir bond angles of 136 • /142 • /140 • in undoped LNIO (see Fig. 3a) are in a good agreement with the experimentally observed values of 135.4 • /142.5 • /140.8 •18 . Surprisingly, our results show that the substitution of smaller TM cations into Ni-site produced a significant structural distortion which further affects the electronic and magnetic properties. As the Cr-doped LNIO system exhibits large structural distortions (i.e., smaller bond angles) than that of undoped and other doped systems, compare the bond angles magnitudes in Fig. 3b with that of Fig. 3a,c,d, respectively. This usually demands a higher energy difference between the different magnetic structures, which results in a higher T C as displayed in Table 1.

Electronic properties.
To explicitly display the TM-doping impact on the electronic properties of LNIO DPO, we first produced the spin-polarized total density of states (TDOS) for undoped LNIO material in Fig. 4a to provide a frame of reference. One can see that system exhibits an insulating behavior with an E g of 0.20/2.25 www.nature.com/scientificreports/ eV in the spin-majority/spin-minority channel, which is in good agreement with experimental 18 and previous theoretical work 30 . Next, we studied the TM-doping influence on the electronic structure of LNIO which exhibits substantial changes. For this, spin-polarized TDOS for Cr, Mn, and Fe-doped LNIO systems are plotted in Fig. 4b-d, respectively, where all the doped materials showing the HM behavior in which the spin-majority channel is conductor while the spin-minority channel is an insulator.
To elucidate the origin of the metallic electronic states in these doped systems, we plotted the spin-polarized partial density of states (PDOS) projected on the Ni/Cr 3d, Ir 5d, and O 2p orbitals in undoped LNIO (left column) and Cr-doped LNIO ( Lu 2 Ni 0.5 Cr 0.5 IrO 6 : right column) DPO in Fig. 5, for example. Our calculations clearly show that both 3d states of Ni ions stay away from the Fermi level ( E F ) in undoped LNIO material (see Fig. 5a), while Ir 5d states grow around E F in both valence and conductions bands (Fig. 5b) with small contributions from O 2p states (Fig. 5c). Furthermore, the PDOS analysis in undoped LNIO material indicates that Ni1 and Ni2 3d spin-polarized states are overlapped which means that both ions are showing equivalent contributions to the electronic structure. A similar trend of PDOS can also be seen for Ir and oxygen ions. In the case of Crdoped LNIO ( Lu 2 Ni 0.5 Cr 0.5 IrO 6 ) material, Ni/Cr 3d states lie very below and above the E F in the valence and conduction bands (Fig. 5a ′ ), respectively and not contributing to the metallicity as found in the case of undoped one. Interestingly, Ir2 5d states substantially shift from valence to conduction band by crossing E F in the spin majority channel and are primarily responsible for metallicity with a significant contribution from Ir1 5d states (see Fig. 5b ′ ). A small contribution of O 2p states to the metallicity in the spin majority channel is also evident as displayed in Fig. 5c ′ . In contrast, an insulating behavior is established in the spin-minority channel for each PDOS as found in the case of undoped one. Hence, with the metallic electronic state in the spin-majority channel and an insulating in the spin-minority channel, the Lu 2 Ni 0.5 Cr 0.5 IrO 6 material is predicted to be an HM.
Here it is very important to note that Ir1 PDOS tends towards degeneracy, which means that it is close to non spin-polarized state having an almost negligible magnetic moment (discuss below). A similar PDOS behavior is also found in the case of Mn-and Fe-doped systems ( Lu 2 Ni 0.5 Mn 0.5 IrO 6 and Lu 2 Ni 0.5 Fe 0.5 IrO 6 ) as shown in Figs. 1S and 2S of the Supporting Information (SI), respectively.
For a more deep understanding of the origin of metallic electronic states near E F , we produced the orbital-resolved PDOS on Ni/Cr/Ir 3d/3d/5d orbitals in undoped LNIO (left column) and Cr-doped LNIO E-E F (eV) www.nature.com/scientificreports/ ( Lu 2 Ni 0.5 Cr 0.5 IrO 6 : right column) systems in Fig. 3S of the SI. It is very well established that the crystal field splits the d orbitals into low energy triply t 2g ( d xy , d xz , and d yz ) and high energy doubly e g ( d x 2 −y 2 and d 3z 2 −r 2 ) states. Moreover, the tetrahedron distortion from perfect order reduces the O h symmetry to D 4h and finally lifts the orbital degeneracy. Hence, the t 2g further splits into singlet d xy , d xz , and d yz non-degenerate states. Similarly, the e g is also divided into singlet d x 2 −y 2 and d 3z 2 −r 2 non-degenerate states. From Fig. 3S(a) and 3S(b) of the SI, one can see that Ni1 and Ni2 3d orbitals lie away from the E F in undoped case, respectively. However, the admixture of Ir1 and Ir2 5d orbitals are dominant in both valence and conduction bands, see Fig. 3S(c,d), respectively. It is also very clear that a band gap exists between Ir 5d orbitals in undoped LNIO structure, which also confirms the Mott-insulating state of the system. Similarly, Ni and Cr 3d orbitals are almost showing the negligible contributions around E F in Cr-doped LNIO system as display in the Fig. 3S(a ′ ) and 3S(b ′ ) of the SI. Interestingly, the admixture of Ir1 (Fig. 3S(c ′ )) and Ir2 (Fig. 3S(d ′ )) 5d orbitals in the spin-majority channel are crossing the E F from the valence to conduction bands and are responsible for metallicity. However, the spin minority channels are exhibiting the insulating behavior, which results in the HM state of the system in Cr-doped LNIO system. For direct observation of the metallic electronic states in doped systems, we plotted the spin-polarized band structures along with the high symmetry directions of the monoclinic Brillouin zone for Lu 2 Ni 0.5 Cr 0.5 IrO 6 material within both GGA + U (left column) and GGA + U + SOC (right column) methods in Fig. 6, for instance. One can see that in the spin-majority channel, bands grow at the E F and exhibits metallic behavior as displayed in Fig. 6a within GGA + U scheme. On the other hand, the spin-minority channel shows an insulating nature having an energy gap of 2.32 eV. Hence, the spin majority bands are partially occupied, therefore, an HM state is formed which also confirms the calculated TDOS in Fig. 4b. Contrarily, a considerable downshift in the spin-majority and spin-minority bands are evident with the inclusion of SOC as compared to GGA + U method, compare the Fig. 6c,d with Fig. 6a,b, respectively. However, still a few spin-majority bands are crossing the E F from valence to conduction channel for GGA + U + SOC calculations (see Fig. 6c), while spin-minority channel remains insulator (see Fig. 6d). Hence one can conclude that despite the down shift of the bands within the GGA + U + SOC method, the HM state of the doped system remains the same as found in the case of GGA + U (without SOC) scheme.
To understand the physical mechanism behind the metallic behavior in these doped materials, we analyze the electronic configurations of ions in each case. In undoped LNIO, Ni is in + 2 state with a 3d 8 configuration which indicates that t 2g and e g states are fully and partially occupied, respectively. This means that three electrons lie in the spin-majority and three in the spin-minority channels of t 2g states (i.e., t 3 2g ↑ and t 3 2g ↓ ). The remaining two electrons partially filled the e g states of the spin-majority channel as e 2 g ↑ e 0 g ↓ . Thus, t 2g states completely remain in the valence band, while two up-filled and two down(dn)-empty states of e g reside in the valence and conduction bands, respectively. Similarly, Ir is in a +4 state having a configuration of 5d 5 in which t 2g and e g states are partially and empty, respectively. Five electrons of Ir ion are distributed as: three and two electrons lie in the spin-majority and spin-minority channels of t 2g states ( t 3 2g ↑ t 2 2g ↓ ), respectively. Hence, five (i.e., three up and two dn) states of Ir t 2g reside in the valence band and remaining shifts in the conduction region. On the other hand, all the Ir e g states remain in the conduction band. The schematic representation of electronic configurations for Ni +2 3d 8 and Ir +4 5d 5 orbitals are shown in Fig. 7a,b, respectively.
For Lu 2 Ni 0.5 Cr 0.5 IrO 6 doped material, Cr is in + 3 state with a 3d 3 configuration and produces a deficiency of five electrons when substituted at Ni +2 3d 8 sites. Hence, the hole was created due to a lack of electrons, therefore, E F shifts towards lower energies, and few bands crossing the E F from the valence to the conduction band. This results in a metallic state in the spin-majority channel, while a large band gap still exists in the spin-minority channel which leads the system into an HM state (see Fig. 4b). Similarly, Mn lies in + 3 state having 3d 4 configurations and the system lacks four electrons when it is replaced with Ni +2 3d 8 ions. Hence, e g states in the spinmajority channel will become fully unoccupied and E F shifts towards lower energies. Thus, few bands near E F in the spin-majority channel crossing the E F which result in a metallicity. On the other hand, the spin-minority channel remains insulator, which leads the system into an HM state (see Fig. 4c). Finally, Fe is also in + 3 state with a configuration of 3d 5 which produces a deficiency of three electrons when it replaced with Ni +2 3d 8 ion, which drags the system into HM state (see Fig. 4d) as discussed above. www.nature.com/scientificreports/ Magnetism. Next, we examined the calculated total/atom-resolved partial spin magnetic moments in undoped and TM-doped LNIO systems. As allocated in Table 1 18 . This overestimation is because antisite disorder is not taken into the account in the calculations. As it is theoretically found that when antisite disorder was considered in LNIO system 18 , the m tot. was 0.78 µ B /f.u. which is impending to the experimentally observed value of 0.52 µ B /f.u. at a very low temperature of 5 K. This shows that Ni and Ir ions remain in + 2 and +4 states having electronic configurations of t 3 2g ↑ t 3 2g ↓ e 2 g ↑ e 0 g ↓ and t 3 2g ↑ t 2 2g ↓ e 0 g ↑ e 0 g ↓ with spin states of S = 1 and S = 1/2 , respectively. Moreover, the computed partial spin magnetic moments on Ni and Ir ions are 1.66 and − 0.54 µ B , respectively which means that the Ni ion mainly contributing to m tot. . The "−" sign in the Ir moment indicates that its spin is anti-align to that of the Ni. This confirms the strong AFM superexchange coupling between Ni +2 and Ir +4 ions via oxygen ( Ni +2 -O −2 -Ir +4 ) which results in a FiM ordering.
In the case of doped materials, Ni moment magnitude almost remains the same ( ∼ 1.66 µ B ) as found in the case of undoped one (Table 1), which means that it remains in a +2 state. However, a strong reduction in the Ir1 spin magnetic moment is found as compared to the undoped one along with a small decrease in the Ir2 moment is also predicted. respectively. This shows that Ir ion lies in a mixed-valence state of +4 and +4/ + 5 with the configurations of 5d 5 ( t 3 2g ↑ t 2 2g ↓ ) and 5d 5 /5d 4 ( t 3 2g ↑ t 2 2g ↓ /t 2 2g ↑ t 2 2g ↓ ) in undoped and all doped structures, respectively. The schematic representation of Ir in +5 state having a configuration of 5d 4 ( t 2 2g ↑ t 2 2g ↓ ) with S = 0 is shown in Fig. 7c. The individual spin magnetic moments on Cr, Mn, and Fe ions are 2.66, 3.80, and 4.11 µ B , respectively. Besides the spin moments on the TM and Ir ion sites, the oxygen ions at non-equivalent sites are also spin-polarized (see Table 1) and a sizable spin moment of ∼ −0.40 µ B arises on the O2 atom in each doped case (see Table 1). Because, a strong hybridization between TM/Ir and oxygen atoms, results in a partial charge transfer from TM (i.e., Cr, Mn, and Fe) and Ir ions to oxygen.
To understand the charge transfer mechanism, we plotted the spin-magnetization density isosurface plots for undoped and Cr-doped ( Lu 2 Ni 0.5 Cr 0.5 IrO 6 ) materials in Fig. 8a,b, respectively. As one can see in the undoped case (Fig. 8a), Ni 3d and Ir 5d orbitals are primarily contributing to the spin density. It is a well-known fact that Ni is in + 2 state with a d 8 configuration in LNIO. Thus, the t 2g ( d xy , d yz , and d xz ) states are fully occupied by maintaining six electrons, while the remaining two unpaired electrons lie in the e g ( d x 2 −y 2 and d 3z 2 −r 2 ) states. Therefore, the e g orbital characteristics are visible in the isosurfaces of the Ni ions in both undoped and Cr-doped LNIO materials as displayed in Fig. 8a,b, respectively. Moreover, very small spin densities have also appeared on the oxygen atoms. Because of a small charge transfer on the oxygen ions due to superexchange coupling between Ni +2 and Ir +4 ions via oxygen ( Ni +2 -O −2 -Ir +4 ). Interestingly, substantial changes occur in the magnitude of spin densities when one of the Ni ions is replaced with Cr, see Fig. 8b. The most striking feature of the present calculations is that spin-density around Ir1 ion is almost disappeared, while a small decrease in Ir2 is evident which confirms the calculated spin magnetic moments on Ir ions in Cr-doped LNIO system in Table 1. Moreover, the spin density nature of Cr ion is due to the admixture of d xy , d yz , and d xz (i.e., t 2g ) orbitals character. Besides, a substantial amount of spin density arises on the oxygen ions in Cr-doped (Fig. 8b) system than that of undoped one (Fig. 8a), because extra charge transfer from Ni/Cr and Ir ions to oxygen due to strong hybridization between them.

Conclusion
Employing non-degenerate DFT calculations, the electronic and magnetic properties of undoped and transition metal (TM) = Cr, Mn, and Fe-doped Lu 2 NiIrO 6 double perovskite oxides are investigated, where TM ions having 50% concentration are substituted at Ni-site. We found that the undoped material is a ferrimagnetic (FiM) Mott-insulator, while all the doped structures exhibit half-metallic FiM behavior. The metallic electronic states in the spin majority channels mainly belong to the admixture of Ir 5d orbitals in each case. It is also established that Ir ion lies in a mixed-valence state of +4 and +5 in all doped systems with configurations of 5d 5 ( t 3 2g ↑ t 2 2g ↓ ) and 5d 4 ( t 2 2g ↑ t 2 2g ↓ ), respectively, which results in a strong reduction of magnetic moment on the Ir 5d 4 ion. Interestingly, our calculations revealed that structural distortion enhanced when one of the Ni ions is replaced with TM, and maximum deviation from the perfect cubic symmetry is obtained in the case of the Cr-doped www.nature.com/scientificreports/ Lu 2 NiIrO 6 material, which further optimize the FiM ordering temperature. Therefore, Lu 2 Ni 0.5 Cr 0.5 IrO 6 system exhibits a higher FiM ordering temperature of 292 K as compared to undoped and other doped systems. Hence, these doped materials show promise of their probable feasible applications in hard magnetic memory devices.

Computational methods
First-principles electronic structure calculations based on DFT were performed using a full-potential linearized augmented plane wave method as implemented in the WIEN2K code 58 . The exchange-correlation functional which is parameterized by generalized gradient approximation (GGA) 59 plus on-site Coulomb interaction (GGA+U) approach was employed with U = 3.85, 3.5, 4.0, 5.0, 5.1, and 2.8 eV for Lu 4f, Cr 3d, Mn 3d, Fe 3d, Ni 3d, and Ir 5d states, respectively 60 . In all cases, the spin non-degenerate version of the GGA is utilized for both with and without SOC calculations. For the wave function expansion inside the atomic spheres, a maximum value of l max = 12 is chosen and the plane-wave cutoff is set to R mt × K max = 7 with G max = 24 . A 7 × 7 × 9 k-space grid with 128 points within the irreducible wedge of the Brillouin zone is found to be well converged. Along with this, full relaxation of the atomic positions by minimizing the atomic forces up to 2 mRy/a.u. is taken into account in each case. Self-consistency is assumed for a total energy convergence of less than 10 −5 Ry. www.nature.com/scientificreports/