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

Abstract

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 CrBr₃^17,18 and CrI₃,^{19,20,21,22,23} Cr spinel selenides,⁶ Mn pyrochlore oxides,²⁴ and perovskites such as BiMnO₃,²⁵ CuSeO₃,²⁶ and YTiO₃.²⁷ 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 EuO²⁹), 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 injection³² and filtering¹² because of its large exchange splitting of the conduction band (0.6 eV) and highly dispersive conduction band.³³ Nevertheless, its poor air stability^34,35,36,37 along with the low T_C present major obstacles for practical applications.

Fig. 1

Band diagram schematics of spin-polarised electron injection using a ferromagnetic (FM)/non-magnetic (NM) n–n heterojunction a and of spin filtering achieved with an FM tunneling barrier sandwiched between two NM metal contacts b. For the ferromagnetic semiconductor, the exchange splitting of the conduction band amounts to 2Δ_ex and is depicted by dashed lines

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 In₂Mn₂O₇ 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) functional³⁸ 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 ($m_e^ \ast$) smaller than 1.5 m₀. In comparison, typical semiconductors (e.g. GaAs, Si, and ZnO) present $m_e^ \ast$ ranging from 0.05 to 0.5 m₀.⁴⁰ Figure 2a shows the distribution of $m_e^ \ast$ for materials exhibiting a finite magnetisation compared to non-magnetic materials. It is clear that low $m_e^ \ast$ 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 $m_e^ \ast$ materials are mainly of s character. The poor effective mass and strong ferromagnetism are, for instance, present in CrBr₃ and certain manganites such as LaMnO₃, where a predominant 3d character in the lowest conduction band leads to a high $m_e^ \ast$ of over 10 m₀. At variance, the low $m_e^ \ast$ of EuO (0.4 m₀) 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

Fig. 2

a Violin plot of electron effective masses for semiconductors in the FM and non-FM configurations. The vertical lines refer to the median value along with the first and third quartiles. b Probability distribution of the orbital characters in the conduction band minimum for FM semiconductors with an electron effective mass smaller than 1.5 m₀

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 non-collinear 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 ordering²⁴). 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 approximation⁴⁶ 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 chalcogenides, Bi manganites, Mn pyrochlore oxides, and Mn double perovskites. 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, CdCr₂Se₄, and BiMnO₃. Less traditionally associated to spintronics are the Mn pyrochlores (e.g., In₂Mn₂O₇).

Table 1 Properties of identified ferromagnetic semiconductors evaluated with HSE hybrid functional, including the exchange splitting of the conduction band (2Δ_ex), electron effective mass (m_e), and Curie–Weiss temperature (θ_CW)

Fig. 3

Spin-polarised band structures of the five representative ferromagnetic semiconductors obtained with HSE hybrid-functional calculations. The majority and minority spin channels are shaded by the blue and light red colours, respectively

To compare the performances of these different compounds, we plot in Fig. 4 $m_e^ \ast$ 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 LaBMnO₆ (B = Ni, Co). In particular, La₂NiMnO₆ shows near room-temperature ferromagnetism arising from the strong ferromagnetic superexchange interactions between the Mn⁴⁺ and Ni²⁺.⁴⁷ However, the large $m_e^ \ast$ of over 1.1 m₀ could be a limiting factor for high mobility applications. Following La₂NiMnO₆, the sulfide and selenide spinels ACr₂X₄ (A = Hg, Cd, Zn, and Mg; X = S, Se) show θ_CW up to 200 K. The prevalence of Cr³⁺ can be related to the high magnetic moment of its d³ configuration. The strongest ferromagnetism is observed in CdCr₂Se₄ in accordance with experiment.⁴⁸ MgCr₂Se₄, which has been overlooked as a ferromagnetic spinel in literature, shows comparable ferromagnetism as CdCr₂Se₄ 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 Eu²⁺ is easily oxidised to Eu³⁺.^34,35,36,37 The remaining oxides are the pyrochlores and BiMnO₃. Among the pyrochlores, In₂Mn₂O₇ is especially noteworthy as it shows the highest θ_CW and the lowest $m_e^ \ast$. While showing similar electronic and magnetic properties as BiMnO₃, In₂Mn₂O₇ exhibits a higher air stability thanks to their high stability of the oxidation states of its cations: In³⁺ and Mn⁴⁺. In comparison with EuO, it offers an even lower $m_e^ \ast$ (0.29 m₀), better air stability, and a significantly higher θ_CW (155 K vs 76 K).

Fig. 4

Figure of merit of the ferromagnetic semiconductors identified through the computational screening. $\Delta \mu _{{\rm{O}}_2}$ indicates the oxygen chemical potential (referred to the isolated molecule) below which the compound is stable in an oxidising atmosphere. Oxidisation is more likely for compounds with a more negative $\Delta \mu _{{\rm{O}}_2}$

The calculated exchange splitting of the conduction band shown in Table 1 for the candidates confirms the good performance in spin filtering with EuO¹² and BiMnO₃.²⁵ Table 1 implies that In₂Mn₂O₇ 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 corrections⁴⁹ to calculate the electronic structure of In₂Mn₂O₇. 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 In₂Mn₂O₇ for efficient spin filtering.

Fig. 5

Electron density distributions of the lowest conduction band at the Γ point and QSGW band structures for In₂Mn₂O₇ a and Y₂Mn₂O₇ b in the ferromagnetic configuration. The electron density is plotted on the (111) plane centered at an In (Y) atom, whereas the characters associated with the states are resolved by the fat bands mapped onto the atoms. The significant s character in the lowest conduction band of In₂Mn₂O₇ is absent in Y₂Mn₂O₇

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 3d³ 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 BiMnO₃ and LaMnO₃. The anomalously strong ferromagnetism of La₂NiMnO₆ stems from the fully occupied e_g state of Ni²⁺, which is unique to this type of material. In comparison, the e_g state is either partially occupied for the Mn³⁺ in BiMnO₃, or simply empty for the Mn⁴⁺ and Cr³⁺ in the case of pyrochlores and spinels.

Our results confirm the challenge in combining adequate air stability, effective mass, and Curie temperature. In₂Mn₂O₇ offers an exceptional compromise between these three metrics. Among the ferromagnetic pyrochlore materials, In₂Mn₂O₇ shows a very low $m_e^ \ast$ of 0.29 m₀, 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 Y₂Mn₂O₇, 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 In₂O₃.

The s character in the conduction band is also at the origin of the strong ferromagnetism present in In₂Mn₂O₇, leading to the highest T_C among all pyrochlore oxides. Apparently, the semi-empirical Goodenough–Kanamori rules of superexchange^52,53 do not fully account for such strong ferromagnetism as all the pyrochlore oxides considered in Table 1 show Mn–O–Mn bond angles between 130° and 133°. Longer Mn–O bond lengths reduce the AFM t_2g–t_2g interactions among neighbouring Mn atoms, yet this does not explain the higher T_C of In₂Mn₂O₇ (d_Mn−O = 1.89 Å) compared to Y₂Mn₂O₇ (d_Mn−O = 1.91 Å). Indeed, the hybridisation among Mn(t_2g)–O(p)–In(s) states is key to the strong ferromagnetism of In₂Mn₂O₇. Specifically, the In–O covalency mixes with the Mn-t_2g–O-p states, stabilising the ferromagnetic configuration by shifting the In–O states upward (downward) in the majority (minority) channel.⁵⁴ This is supported by the band-resolved crystal orbital Hamilton population (COHP) analysis,^{55,56,57,58,59} showing the antibonding nature of In(5s)–O and Mn–O interactions at the CBM of the minority spin channel (see Table S2 and Fig. S2 of Supplementary Information). More intuitively, the enhanced ferromagnetism can be understood by the indirect-exchange mechanism⁶⁰ 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 Tl₂Mn₂O₇ 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 In₂Mn₂O₇ (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 In₂Mn₂O₇, among which Sn and Mo are found to incorporate on the In site while acting as shallow donors, analogous to that in In₂O₃.^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 In₂Mn₂O₇ can be effectively n-type 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 In₂Mn₂O₇ 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 In₂Mn₂O₇ 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 In₂Mn₂O₇, 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 Curie temperature as it has been demonstrated for EuO and BiMnO₃.^{68,69,70,71,72}

Methods

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 projector-augmented-wave (PAW) method.^75,76 We use the Pymatgen package⁷⁷ 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 method⁸⁴ 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.

Band-resolved COHP calculations are carried out with a development version of the LOBSTER package.^{55,56,57,58,59} The pbeVaspFit2015 basis is used with the following basis functions: O: 2s, 2p; In: 5s, 5p, and 4d; Mn: 4s, 3p, and 3d. The wavefunctions are obtained using the PBE + U functional.

Effective mass calculation

The reported effective mass is defined as the conductivity effective mass

$$(m^ \ast )^{ - 1} = \frac{{\sigma (T,\mu )}}{{n(T,\mu )e^2\tau }},$$

(1)

where the electrical conductivity σ and the charge carrier concentration n are computed directly from the Boltztrap calculations⁸⁵ with T = 300 K and a chemical potential μ leading to n = 10¹⁸ cm⁻³. The relaxation time τ is assumed to be independent of T and μ following previous high-throughput works.^41,86