High-throughput computational discovery of In2Mn2O7 as a high Curie temperature ferromagnetic semiconductor for spintronics

Materials combining strong ferromagnetism and good semiconducting properties are highly desirable for spintronic applications (e.g., in spin-filtering devices). In this work, we conduct a search for concentrated ferromagnetic semiconductors through high-throughput computational screening. Our screening reveals the limited availability of semiconductors combining ferromagnetism and a low effective mass. We identify the manganese pyrochlore oxide In2Mn2O7 as especially promising for spin transport as it combines low electron effective mass (0.29 m0), a large exchange splitting of the conduction band (1.1 eV), stability in air, and a Curie temperature (about 130 K) among the highest of concentrated ferromagnetic semiconductors. We rationalise the high performance of In2Mn2O7 by the unique combination of a pyrochlore lattice favouring ferromagnetism with an adequate alignment of O–2p, Mn–3d, and In–5s forming a dispersive conduction band while enhancing the Curie temperature.


INTRODUCTION
Materials combining semiconductivity and magnetism open up possibilities for novel electronic devices that utilise electron spin in addition to charge degrees of freedom. 1,2 Ferromagnetic semiconductors (FMSs) are in particular valued for their potential in spintronics for spin-polarised transport. Compared to ferromagnetic metals, FMSs are more suited for injecting spin-polarised electrons into non-magnetic semiconductors. [3][4][5][6][7][8] A closely related and technologically important phenomenon is spin filtering, which can be realised through the use of FMSs as the tunneling barrier for generating highly spin-polarised current. [9][10][11][12][13][14] FMSs used in spintronics are primarily based on magnetic impurities embedded into conventional non-magnetic semiconductors. 15 The robustness of carrier-induced ferromagnetism is extremely sensitive to the growth conditions and processing methods, and the origin of room-temperature ferromagnetism of such diluted magnetic semiconductors remains a subject of debate. 2,16 In contrast, concentrated magnetic semiconductors exhibit long-range magnetism without resorting to extrinsic doping. A few concentrated FMSs have been reported, including Cr halides CrBr 3 17,18 and CrI 3 , [19][20][21][22][23] Cr spinel selenides, 6 Mn pyrochlore oxides, 24 and perovskites such as BiMnO 3 , 25 CuSeO 3 , 26 and YTiO 3 . 27 Among the most studied FMSs for spintronics are the Eu chalcogenides EuX (X = O,S,Se). [10][11][12]14,28 While providing very good performances in spin-filter devices, the EuX exhibit very low Curie temperature (e.g., T C = 69 K for EuO 29 ), which is characteristic for most FMSs known to date.
In addition, the electronic structure of FMSs needs to be tailored in the context of spin transport. For a barrierless electrical spin injection depicted in Fig. 1a, the efficiency is determined by the exchange splitting of the conduction band while a low effective electron mass is appreciated for achieving high carrier mobility.
Analogously, the exchange splitting is critical for spin filtering as it gives rise to spin-dependent potential barriers for the tunneling current (cf. Fig. 1b), resulting in spin-polarised current in favour of the spin with a lower potential barrier. 13,30,31 As such, EuO is in particular attractive for spin injection 32 and filtering 12 because of its large exchange splitting of the conduction band (0.6 eV) and highly dispersive conduction band. 33 Nevertheless, its poor air stability 34-37 along with the low T C present major obstacles for practical applications.
Combining strong ferromagnetism and attractive semiconducting properties in one material is therefore desirable but remains an open problem. Here, we set out to identify systematically concentrated FMSs through a large-scale computational screening of known compounds. We report on the materials identified and especially their semiconducting properties, their Curie-Weiss temperatures, and their stabilities. In particular, we identify the Mn pyrochlore oxide In 2 Mn 2 O 7 as a very promising material. We discuss its potential use for spin transport and the inherent structural and chemical reasons for its high performances.

RESULTS
We consider a material to be a good FMS candidate if it offers a high ferromagnetic transition temperature and good semiconducting properties. Because electrons have much longer spin lifetimes than holes, 2 we focus on spin transport based on electrons as illustrated in Fig. 1, and hence look for FMSs with a large exchange splitting of the conduction band and a low electron effective mass. Starting from the materials project (MP) database comprising over 40,000 density-functional theory (DFT) calculations using the semilocal Perdew-Burke-Ernzerhof (PBE) functional 38 and the Hubbard U correction (PBE + U) 39 (for transition-metal oxides), we first screen the materials based on their thermodynamic stability (energy above convex hull at 0 K lower than 50 meV per atom) and electronic band gap (>100 meV). This step leads to about 15,300 semiconductors, out of which 3100 compounds show a finite magnetic moment (>0.5 μ B ) in the ground state (when the computation is initialised in a ferromagnetic state). Among these magnetic materials, only about 1000 compounds exhibit an electron effective mass (m Ã e ) smaller than 1.5 m 0 . In comparison, typical semiconductors (e.g. GaAs, Si, and ZnO) present m Ã e ranging from 0.05 to 0.5 m 0 . 40 Figure 2a shows the distribution of m Ã e for materials exhibiting a finite magnetisation compared to non-magnetic materials. It is clear that low m Ã e is more easily achieved in non-magnetic compounds. The need for magnetism often implies partially filled d bands. When the conduction-band character is dominated by these orbitals, their localised nature leads to a high effective mass. 41 Figure 2b confirms that low m Ã e materials are mainly of s character. The poor effective mass and strong ferromagnetism are, for instance, present in CrBr 3 and certain manganites such as LaMnO 3 , where a predominant 3d character in the lowest conduction band leads to a high m Ã e of over 10 m 0 . At variance, the low m Ã e of EuO (0.4 m 0 ) is remarkable in that the ferromagnetism arises from an indirect exchange between the localised Eu-4f electrons in the valence and the delocalised 5d/6s electrons in the conduction band. 33,42 The presence of a non-zero total magnetisation in the 0 K DFT computation with an initial ferromagnetic ordering does not imply that the ground state is necessarily ferromagnetic and that this ferromagnetic configuration is sustained at high temperature. We thereby estimate the magnetic ordering of the~1000 compounds by comparing the total energies of the ferromagnetic ground state to the antiferromagnetic (AFM) or ferrimagnetic (FiM) one. The difference serves as an indicator of whether the compound in question is dominated by ferromagnetic exchange interactions. To determine the magnetic ground state, we use supercells that contain at least four atoms for each distinct magnetic species. An exhaustive search of the lowest-energy AFM (or FiM) configuration is carried out by enumerating all possible configurations in which half of the magnetic sites are initialised with a positive magnetic moment whereas the other half with a negative magnetic moment. The absolute value of the initial magnetic moment follows the calculated magnetic moment in the FM configuration. We consider only the collinear magnetic configurations as noncollinear calculations would be computationally prohibitive at this stage of screening. We find that less than 30 compounds favour an FM ground state by over 10 meV per formula unit compared to the AFM or FiM configurations (see Table S1 of Supplementary Information), manifesting already the difficulty of finding semiconductors with robust ferromagnetism.
Our computational screening thus far relies on the PBE( + U) calculations. While instrumental in determining the energetic stability among various magnetic orderings, PBE and PBE + U with U values calibrated for formation enthalpies do not warrant a faithful description of the underlying electronic structure. For a higher accuracy and a better treatment, particularly of localised d and f electrons, hybrid functionals such as the Heyd-Scuseria-Ernzerhof (HSE) functional 43,44 should be used. 45 We have thus performed HSE calculations on the candidates exhibiting the most favourable ferromagnetic ordering (The HSE calculations exclude the pyrochlore oxides containing the lanthanide elements with partially filled f electrons due to convergence issues. Nevertheless, these materials are expected to exhibit more exotic magnetic properties than the simple ferromagnetic ordering 24 ). We report in Table 1 the electron effective mass as well as the Curie-Weiss temperature θ CW obtained from HSE calculations. The latter is defined from the paramagnetic response at high temperature, and is estimated with the random-phase approximation 46 as described in Supplementary Information. When known, we also report on their experimental Curie temperature T C . The difference between θ CW and T C indicates the degree of geometrical frustration in a magnetic system. 24 Notably, the FMSs listed in Table 1 can be classified into five categories: Eu chalcogenides, Cr spinel   Figure 3 shows the HSE band structure for a representative compound in each category. Our screening recovers the well-known FMSs in the context of spintronics such as EuO, CdCr 2 Se 4 , and BiMnO 3 . Less traditionally associated to spintronics are the Mn pyrochlores (e.g., In 2 Mn 2 O 7 ).
To compare the performances of these different compounds, we plot in Fig. 4 m Ã e vs θ CW obtained from HSE calculations. We further indicate the stability of the materials against oxidation by showing the maximum oxygen chemical potential reachable while keeping the material thermodynamically stable. This provides a measure of air sensitivity: the higher oxygen chemical potential, the greater stability. The highest θ CW is clearly obtained among the double perovskites LaBMnO 6 (B = Ni, Co). In particular, La 2 NiMnO 6 shows near room-temperature ferromagnetism arising from the strong ferromagnetic superexchange interactions between the Mn 4+ and Ni 2+ . 47 However, the large m Ã e of over 1.1 m 0 could be a limiting factor for high mobility applications. Following La 2 NiMnO 6 , the sulfide and selenide spinels ACr 2 X 4 (A = Hg, Cd, Zn, and Mg; X = S, Se) show θ CW up to 200 K. The prevalence of Cr 3+ can be related to the high magnetic moment of its d 3 configuration. The strongest ferromagnetism is observed in CdCr 2 Se 4 in accordance with experiment. 48 MgCr 2 Se 4 , which has been overlooked as a ferromagnetic spinel in literature, shows comparable ferromagnetism as CdCr 2 Se 4 according to our computational screening. In any case, all these spinel chalcogenides show poor stability in air due to their sulfide or selenide chemistry. The air stability is also an issue for Eu chalcogenides. In fact, EuO is known for the difficulty in growing high-quality thin films since Eu 2+ is easily oxidised to Eu 3+ . [34][35][36][37] The remaining oxides are the pyrochlores and BiMnO 3 . Among the pyrochlores, In 2 Mn 2 O 7 is especially noteworthy as it shows the highest θ CW and the lowest m Ã e . While showing similar electronic and magnetic properties as BiMnO 3 , In 2 Mn 2 O 7 exhibits a higher air stability thanks to their high stability of the oxidation states of its cations: In 3+ and Mn 4+ . In comparison with EuO, it offers an even lower m Ã e (0.29 m 0 ), better air stability, and a significantly higher θ CW (155 K vs 76 K).
The calculated exchange splitting of the conduction band shown in Table 1 for the candidates confirms the good performance in spin filtering with EuO 12 and BiMnO 3 . 25 Table 1 implies that In 2 Mn 2 O 7 should also present an excellent spin-filter effect. But as uncertainty remains in the exchange splitting with the HSE calculations and little is known from experiment, we resort to the self-consistent quasiparticle GW calculations (QSGW) with vertex corrections 49 to calculate the electronic structure of In 2 Mn 2 O 7 . The QSGW method does not depend on any adjustable parameter and starting point, and it has been shown to provide a reasonable description of the electronic structure for correlated transition-metal oxides. 50 As shown in the QSGW band structure in Fig. 5a, the exchange splitting further opens up to 1.1 eV, in support of using In 2 Mn 2 O 7 for efficient spin filtering.

DISCUSSION
Our large-scale computational screening shows that the viable routes toward ferromagnetism in semiconducting materials involve either the partially filled Eu-4f electrons or the partially filled 3d electrons of transition metals such as Cr, Mn, and to some extent, V. Indeed, the identified FMSs are mostly Cr spinels and Mn pyrochlores. They are commonly characterised by the high-spin S = 3/2 state in the 3d 3 configuration, which in the (pseudo)cubic crystal field results in an occupied t 2g and an unoccupied e g manifold of states. For Cr spinels, the strength of ferromagnetism reduces from selenides to sulfides, and eventually inverts to antiferromagnetism for oxides as the ferromagnetic t 2g -e g exchange interaction is outweighed by the AFM t 2g -t 2g interaction. 51 While the same competing mechanism is also at play for the pyrochlores, the larger lattice constant stabilises the ferromagnetic configuration for a series of Mn and V pyrochlore oxides. The double perovskites, on the other hand, offer significantly higher T C than the simple perovskite counterparts such as BiMnO 3 and LaMnO 3 . The anomalously strong ferromagnetism of La 2 NiMnO 6 stems from the fully occupied e g state of Ni 2+ , which is unique to this type of material. In comparison, the e g state is either partially occupied for the Mn 3+ in BiMnO 3 , or simply empty for the Mn 4+ and Cr 3+ in the case of pyrochlores and spinels.
Our results confirm the challenge in combining adequate air stability, effective mass, and Curie temperature. In 2 Mn 2 O 7 offers an exceptional compromise between these three metrics. Among the ferromagnetic pyrochlore materials, In 2 Mn 2 O 7 shows a very low m Ã e of 0.29 m 0 , which is among the lowest for all identified FMSs. Such a low effective mass is the result of the prominent In-5s character of the conduction band minimum (CBM) in the minority spin channel, as clearly shown by the element-resolved band structure in Fig. 5a. In contrast, most pyrochlore oxides, such as Y 2 Mn 2 O 7 , exhibit much less dispersive CBM in both spin channels (cf. Fig. 5b) as the Y-5s states do not mix in the lower conduction band. In-5s states are known to lead to dispersive conduction band in binary and ternary oxides: 41 one of the highest electron mobility oxide being doped In 2 O 3 .
The s character in the conduction band is also at the origin of the strong ferromagnetism present in In 2 Mn 2 O 7 , leading to the highest T C among all pyrochlore oxides. Apparently, the semiempirical Goodenough-Kanamori rules of superexchange 52,53 do not fully account for such strong ferromagnetism as all the pyrochlore oxides considered in Table 1 Table S2 and Fig. S2 of Supplementary Information). More intuitively, the enhanced ferromagnetism can be understood by the indirect-exchange mechanism 60 involving virtual electron hopping from the O-p to the In-s states in the conduction band. This leaves the O-p state effectively spin polarised and enhances the ferromagnetic superexchange through the O atom. For this mechanism to take effect, the atomic valence s state needs to be in a reasonable proximity to the O-p state, which is exactly the case of the group 13 elements such as In and Tl, although Tl 2 Mn 2 O 7 is a half-metal. 54,[60][61][62][63] While pyrochlore oxides comprising other group 13 elements (such as B, Al, and Ga) do not appear as a candidate because of their instability, they indeed exhibit a highly dispersive s-like CBM from the minority channel and a high θ CW comparable to In 2 Mn 2 O 7 (see Table S3 of Supplementary Information for the properties of these hypothetical pyrochlore oxides).
Finally, the FMSs need to be n-type to facilitate the transport of spin-polarised electrons. To this end, we assess several dopants in In 2 Mn 2 O 7 , among which Sn and Mo are found to incorporate on the In site while acting as shallow donors, analogous to that in In 2 O 3 . 64,65 The computational details of defect calculations are described in Supplementary Information, whereas the formation energies of the dopants in various charge states are given in Fig.  S1. We additionally find no evidence of favourable self-trapping of electrons as small polarons in this material and a general unfavourability of native compensating centers like cation vacancies, which suggests that In 2 Mn 2 O 7 can be effectively ntype doped.
In conclusion, we have carried out a large-scale computational screening in quest of concentrated FMSs. Among the very few identified materials, the pyrochlore oxide In 2 Mn 2 O 7 emerges as a particularly interesting candidate that exhibits robust ferromagnetism, good air stability, and a low electron effective mass, an uncommon combination that is of great promise for high mobility spin transport. While In 2 Mn 2 O 7 does not yet fulfill the requirement of room-temperature ferromagnetism, its Curie temperature could be potentially increased with epitaxial strain. [66][67][68] Indeed, as shown in Supplementary Information, we find that tensile stress due to the lattice mismatch to some semiconductor substrates (such as Si and GaAs) can effectively increase the Curie temperature of In 2 Mn 2 O 7 , but it needs to be practiced with caution as it has adverse effects on the effective mass (see Fig. S3). Other routes, such as doping, can also be explored to enhance the

First-principles calculations
Collinear spin-polarised semilocal DFT-PBE and hybrid functional HSE calculations are performed with the Vienna ab initio simulation package (VASP). 73,74 Electron-ion interactions are described by the projectoraugmented-wave (PAW) method. 75,76 We use the Pymatgen package 77 to generate VASP input files based on the structures retrieved from the MP database. Throughout the calculations, the kinetic energy cut-off is set to 520 eV, and a regular Γ-centered k-point mesh is used with a grid density of 1600 k points per atom. For transition-metal oxides, the PBE calculation is carried out with the Hubbard U correction (PBE + U), for which the U parameters take the values adopted by the MP following the approach described by Wang et al. 78 Quasiparticle self-consistent GW calculations are performed with the ABINIT code 79,80 using the PseudoDojo optimised norm-conserving pseudopotentials. 81,82 Vertex corrections in the dielectric screening are accounted for through the use of the bootstrap exchange-correlation kernel. 49,83 The dielectric function is evaluated through the contour deformation method 84 including unoccupied states up to 150 eV above the Fermi level in the summations. The dielectric matrix is represented by a plane-wave basis set with an energy cut-off of 160 eV. The self-consistent iteration of the wavefunctions is restricted to the lowest 2N v states where N v is the number of the valence bands.

Effective mass calculation
The reported effective mass is defined as the conductivity effective mass ðm Ã Þ À1 ¼ σðT; μÞ nðT; μÞe 2 τ ; where the electrical conductivity σ and the charge carrier concentration n are computed directly from the Boltztrap calculations 85 with T = 300 K and a chemical potential μ leading to n = 10 18 cm −3 . The relaxation time τ is assumed to be independent of T and μ following previous highthroughput works. 41,86 DATA AVAILABILITY All data generated or analysed during this study are included in this published article (and its Supplementary Information files).