Thermoelectric materials have received increasing attentions in the energy conversion field because of their ability to convert heat into electrical energy.^[31] The energy conversion capability of a thermoelectric system can be estimated by a dimensionless figure of merit: ZT = P · T/κ, where P, T, and κ are power factor, temperature, and thermal conductivity, respectively. The power factor P is defined as P = δS², in which δ is the electrical conductivity and S is the Seebeck coefficient. Accordingly, a high energy conversion capability requires a low thermal conductivity (κ) but a high electrical conductivity (δ). To achieve commercial applications of thermoelectric materials, a number of research efforts are being made to improve their efficiencies, and one way is to use nanostructured materials such as sintered powder nanocomposites.^[32–35] Nevertheless, the traditional process of experimental materials design in laboratory is often a painstaking trial-and-error process and is bound by high time- and cost-consumption. In 2006, Madsen reported the first search model for new thermoelectric materials using automated band structure calculations for all the Sb-based compounds based on inorganic crystal structure database.^[36] In this work, Madsen first extracted about 1630 Sb-containing compounds from the Inorganic Crystal Structure Database.^[37] Next, the authors performed an initial screening and removed all the undesired compounds on the basis of criteria: i) disordered compounds; ii) compounds containing lanthanide atoms; iii) compounds that contain highly electronegative elements N, O, F, and Cl. This initial screening reduced the dataset to 570 compounds. Third, the authors carried out electronic structure calculations for all these 570 compounds and extracted their transport coefficients to select thermoelectric materials, in which air-sensitive compounds were not considered. In this work, one selected material, LiZnSb, was presented in detail.

In 2011, Wang et al. evaluated thermoelectric properties of sintered compounds using high-throughput first-principle calculations.^[7] The fundamental reason to use sintered compounds is that the wide existence of grain boundaries reduces the thermal conductivity (κ) by reducing the phonon mean free path (λ). In this study, the authors have calculated the thermoelectric properties of more than 2500 sintered compounds from the online quantum materials repository AFLOWLIB^[20] and found 20 best candidate compounds with the highest power factor, see Fig. 2. To make the high-throughput calculations possible, several assumptions were made in this work: i) Diffusive electron scattering occurs at grain boundaries; ii) Grain sizes are smaller than the mean free path of the bulk compounds; iii) Constant-mean-free-path is equal to the grain size of the compound; and iv) The same grain size is used for all the compounds. This work also reveals some interesting correlations. That is, sintered thermoelectric compounds with large power factors tend to have large band gaps, heavy carrier effective masses, and many atoms per primitive cell.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. (color online) Selected 20 best nanosintered thermoelectric materials from high-throughput screening. (a) n-doped and (b) p-doped compounds, along with the calculated averaged power factor (P) and Seebeck coefficient at optimal doping. Adapted from Ref. [7].

Topological insulators (TIs) have great potential for nanoelectronics applications because of their novel materials properties; i.e., coexistence of conducting surface states protected by time-reversal-symmetry and an insulating bulk gap.^[38–41] To identify novel TIs, Lin et al. investigated ternary thermoelectric half-Heusler compounds.^[42] Half-Heusler compounds have a cubic lattice structure with a space group and a chemical formula of XYZ, where X and Y are transition metal elements and Z is a p-block element. The authors found that a large majority of the known Heuslers such as TiNiSn and LuNiBi are topological trivial, while the distorted LnPtSb-type compounds such as LnPtBi or LnPdBi (Ln = fⁿ lanthanides) are topological nontrivial. Similarly, Chadov et al. found around 50 half-Heusler compounds with a band inversion similar to that of HgTe, and proposed that the topological states in these zero-gap semiconductors can be achieved by applying strain or designing an appropriate quantum-well structure.^[43] These two works show that half-Heuslers can serve a new platform for the realization of multifunctional topological devices.

In a later study, instead of screening a special class of compounds, Yang et al. scanned the electronic band structures of more than 15000 inorganic crystal structures and discovered 28 TIs (some of them already known) on the basis of the quantum materials repository AFLOWLIB.^[20] It is known that the fundamental mechanism of protected conducting surface states involves a band inversion caused by spin–orbit coupling (SOC).^[9] Accordingly, the central idea of high-throughput screening for TIs is to identify the key physical parameters that are related to the band inversion. In this work, by analyzing the fundamentals of TIs, Yang et al. developed a group of materials descriptors and implemented them into an algorithm for the efficient high-throughput search of TIs. The material descriptors include: (i) a relatively small band gap (less than 1.5 eV) calculated from noSOC density functional theory (DFT) calculations, because that SOC is more likely to lead to an inverted band order in a compound with a smaller band gap; (ii) the compounds should contain heavy elements, the underlying mechanism here is that the heavy elements have strong SOC effects and thus larger ability to flip a band order; and (iii) a “TI robustness descriptor” that measures the robustness of the TI, see Fig. 3. The initial motivation of developing TI robustness descriptor is to make effective use of the electronic structure data of more than 15000 inorganic compounds already available in the AFLOWLIB. Yang et al. studied band energy variations as the lattice strain using noSOC and SOC calculations, respectively; i.e., and . They found that the SOC band energy difference ( ) could change sign at some time-reversal invariant k-points when the lattice parameter crosses a critical value. This is a direct signal of band inversion. More interestingly, the authors found that the energy difference between and (ΔE_k) varies much less than and (even a constant for some compounds such as PbTe) over a wide range of surface strain. The fundamental reason behind this phenomenon is that most of the SOC effects come from core electrons and will not be affected (or less affected) during the bond strain. On the basis of this finding, the authors approximated

Fig. 3.

Figure Option ViewDownloadNew Window

Fig. 3. (color online) Material descriptor for the high-throughput screening of topological insulators.[9] The extraction of the TI robustness descriptor from band energy versus strain variations in SOC and noSOC calculations is shown. are are the band gaps (at k point) from SOC and noSOC calculations, and ΔEk is defined as the energy difference between are . (a) Bi2Te2S at k = Γ, and (b) PbTe at k = N of the body-centered tetragonal Brillouin zone.[27] The vertical green line shows the relaxed lattice constant from DFT calculations, a0, whereas the vertical blue line indicates the critical value, acrit, for the TI to non-TI transition. Adapted from Ref. [9]

Transparent conducting oxides (TCOs) have a wide range of applications in electronic devices, such as light-emitting diodes and solar cells. Compared to the currently commercialized n-type TCOs like Sn-doped In₂O₃ (ITO), F-doped SnO₂ (FTO),^[44] p-type TCOs have a slow development progress because of great challenges in realizing a combination of high hole conductivity and optical transparency.^[45] A fundamental reason of the difficulty of developing p-type TCOs with high mobility is because that 2p orbitals of oxygen anions in most oxides are rather localized and make the bands in the valence band very flat, thus leading to large hole effective masses.

In 2013, Hautier et al. reported a high-throughput computational search on binary and ternary oxides and identified several highly promising compounds as p-type host.^[11] In this work, the authors have calculated the electronic band structures for 3052 oxides using the relaxed crystalline structures in the Materials Project Database.^[30] The authors searched the database using effective mass (< 1.5) as a screening criterion and identified 20 oxides as TCO candidates. Figure 4 shows the effective mass versus the band gap for the 20 compounds. A good p-type TCO should have a large band gap and meanwhile a low hole effective mass, and thus the ideal TCOs should appear in the lower right corner. Next, the authors analyzed p-type dopability of the identified most promising candidates (Sb₄Cl₂O₅, K₂SnO₃, and K₂Pb₂O₃) by calculating their defect-formation energy as a function of the Fermi energy in oxidizing conditions. They found that Sb₄Cl₂O₅ is not likely to be p-type doped because oxygen and chlorine vacancies will form spontaneously and act as hole killers when the Fermi energy is close to valence band. In contrast, K₂Sn₂O₃ is one promising p-type TCO because oxygen vacancy will not compensate hole formation, and the presence of low-energy potassium vacancy can lead to an intrinsic p-type behavior. On the basis of the screening results, the authors further proposed two design principles for the p-type TCOs: i) hybridization of a d¹⁰ (3d¹⁰4s² or 4d¹⁰5s²) ion with oxygen; ii) presence of an anion (such as S², P³, Cl, or Br) with more delocalized p-orbitals than oxygen. These design principles serve as useful guidance for future searches for high-mobility p-type TCOs.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. (color online) Calculated effective mass versus band gap for the p-type TCO candidates. Adapted from Ref. [11].

Two-dimensional electron gas (2DEG) at the interface of perovskite oxide heterostructures has recently attracted much interest because of its potential applications in the next-generation of nanoelectronics.^[46–49] The 2DEG at polar/nonpolar LaAlO₃/SrTiO₃ heterointerface was firstly reported by Hwang et al. in 2004,^[46] though the fundamental formation mechanism of the interfacial 2DEG has been on debate since its discovery.^[49–57] In spite of the controversy, the polar nature of the overlayer in the perovskite oxide heterostructure still plays an important role in the formation of the 2DEG in a direct or indirect way.^[50,51,57] In fact, with motivations either to search for novel heterostructures with better electron transport property or to explore the roles of the polar perovskite oxides, a series of experimental efforts have been made to explore the interfacial electronic properties in the novel polar/nonpolar perovskite oxide heterostructures such as

(i) The polar catastrophe mechanism requires that the heterostructure consists of polar and non-polar perovskite oxides. Note that in this work, for convenience, by using the same naming convention for the polar/nonpolar (LaO)⁺/(TiO₂)⁰ interface in the LaAlO₃/SrTiO₃ heterostructure, the authors defined the charged layer of a perovskite oxide along [001] direction like (LaO)⁺ as polar and the neutral layer like (TiO₂)⁰ as nonpolar. Accordingly, the polar oxides have a formula like A⁺B⁺⁵O₃ or A⁺³B⁺³O₃, and the nonpolar oxides have a formula like A⁺²B⁺⁴O₃.

(ii) The lattice constant of the perovskite oxide film should be close to that of the substrate (SrTiO₃) so that a close lattice mismatch between the epitaxially grown film and its substrate is helpful to minimize defects and to improve the electron mobility.

(iii) The nature of 2DEG requires that the perovskite heterostructure should be conductive along the in-plane direction but insulating in the direction perpendicular to the interfacial plane. This condition requires that the 2DEG must be formed at the interface between two wide-band-gap oxides.

(iv) According to the polar catastrophe mechanism, the 2DEG at the interface of SrTiO₃-based heterostructure was caused by the charge transfer from the polar film to the interfacial TiO₂ layer of the SrTiO₃ substrate. This requires that the conduction band bottom of SrTiO₃ should be lower than that of the electron-donor oxide, i.e., polar oxide, so that the transferred electrons can be accumulated near the conduction band bottom, forming n-type interfacial conductivity.

Equipped with these combinatorial descriptors, Yang et al. carried out a screening of all the polar perovskite compounds, uncovering 42 compounds of potential interests (some of them are already known), see the high-throughput screening procedure in Fig. 5. These candidate perovskite oxides include Ga-based, Al-based, Sc-based, In-based, and Ag-based compounds. By building heterostructure models using these candidate perovskite oxides, the authors further studied their interfacial electronic states, and predicted that Al-, Ga-, Sc-, and Ta-based compounds can form the 2DEG with the SrTiO₃ substrate, while In-based compounds cannot. This happens because the compressive-strain-induced polarization in the film neutralizes the polar catastrophe and prevent the formation of 2DEG. This work opens new avenues for the discovery of perovskite-oxide-based functional interface materials in a high-throughput fashion by defining materials descriptors solely based on the bulk materials properties on the basis of the perovskite-oriented quantum materials repository. In addition, as one reference for designing future functional materials, several gene elements can be identified: Al, Ga, and Sc, are gene elements for designing polar/nonpolar interface to produce 2DEG, while In could be one key gene element for designing piezoelectric materials.

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. (color online) High-throughput design of two-dimensional electron gas systems via polar catastrophe mechanism from large-scale first-principles calculations. Adapted from Ref. [14].

In addition to the polar catastrophe, another possible mechanism to produce 2DEG is via polarization discontinuity.^[71–73] The polarization has been found to lead to 2DEG in traditional semiconductor materials such as ZnMgO/ZnO,^[16,17] but few efforts have been made to explore possibility of producing 2DEG in the perovskite-oxide heterostructures through polarization discontinuity. In 2016, Chen et al. have observed a highly mobile 2DEG in the nonpolar/nonpolar CaZrO₃/SrTiO₃ perovskite oxide heterostructures.^[74] Later first-principles computational study has confirmed that the 2DEG can be created by the lattice-mismatch-induced polarization discontinuity between the film and substrate.^[64] Compared to the great success of producing 2DEG in the polar/nonpolar perovskite heterostructure systems,^[14,57–61] the two-dimensional electron gas at the nonpolar/nonpolar perovskites interface remains rarely explored. Moreover, the polarization-discontinuity-induced 2DEG has a great advantage as compared to that induced by polar catastrophe. That is, the polarization in the film can be controlled by external electrical filed more efficiently, thus bringing enhanced functionalities. In addition, many perovskite oxides are equipped with ferroelectric/piezoelectric property, so to search for perovskite-based 2DEG systems via polarization discontinuity is of great fundamental and practical interest.

In a recent study, Cheng et al. carried out a high-throughput design of perovskite-oxide-based 2DEG systems via polarization discontinuity mechanism using large-scale first-principles calculations, see the screening procedure in Fig. 6. In this work, by using a group of combinatorial materials descriptors including band gap, piezoelectric property, and nonpolar character, and high-throughput first-principles calculations, the authors have successfully identified 34 nonpolar piezoelectric perovskite oxides. These oxides can be divided into six groups based on their constituents: Ti-, Zr-, Hf-, Si-, Ge-, and Sn-based oxides. These results indicate that Ti, Zr, Hf, Si, Ge, and Sn, are the key gene elements for the piezoelectric oxide materials, which could be an important reference in future design of piezoelectric materials. It is noted that Armiento et al. has carried out an early work on the high-throughput screening of bulk perovskite alloys,^[12] in which the discovered relevant compounds are also well consistent with our heterostructure calculations. Note that, in this work, only the nonpolar oxides are considered, and thus the trivalent elements such as In are not highlighted here. However, as discussed in the section of high-throughput of 2DEG via polar catastrophe mechanism, In and Ta are also effective gene elements for designing piezoelectric oxide materials. The authors have further built 1122 unique heterostructures by combining these 34 compounds. Next, by using a simple but critical material descriptor, lattice mismatch 0 < f < 6%, they were able to shrink the screening space of the heterostructures from 1122 to 311. It is worth mentioning that the lattice mismatch here is defined as f = (a_f − a_s)/a_s, and the positive f means that the film will experience a compressive strain from the substrate during the epitaxial film growth process, a necessary condition to produce polarization in the film. Cheng et al. further performed first-principles electronic structure calculations for 70 selected heterostructures and validated the formation of the 2DEG in most of the selected heterostructures. This work demonstrates an efficient way to accelerate the design of perovskite-based functional materials.

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. (color online) High-throughput design of two-dimensional electron gas systems via polarization discontinuity from large-scale first-principles calculations. Adapted from Ref. [15].

The organic-inorganic halide perovskites are an emerging class of semiconductor materials that have many promising optoelectronic applications.^[75–81] In spite of their exceptional optoelectronic properties, particularly for photovoltaic applications, the organic-inorganic halide perovskites face major challenges because of their poor stability and presence of toxic lead, which limits their large-scale applications. To overcome these challenges, one solution is to search for novel hybrid materials with potentially superior properties beyond or like that of lead-based organohalide perovskites.^[82,83]

In 2015, Filip et al. screened all the possible homovalent metal ions over the entire periodic table for replacing the lead in the perovskite halide structural configuration.^[16] The screening process is shown in Fig. 7. In this work, as the first step, the authors selected 29 possible metal ions with +2 oxidation state and generated a total of 116 possible metal–halide combinations by excluding all rare-earth and radioactive metals. Next, the authors performed the structural relaxations from five ideal unit cells constructed with five types of metal-halide-metal bond angles, and the compound with the lowest energy configuration was selected for further electronic structure calculations because structural optimizations of CH₃NH₃PbI₃ are sensitive to the starting point geometry.^[84–86] The third step is to select semiconductor compounds with band gaps less than 3.5 eV, which reduces the total number of the compounds to 40. The authors next probe the dynamic stability of these newly formed compounds by displacing the atomic positions and lattice parameters of each unit cell randomly and relaxing the structures. The difference between the maximum and minimum metal-halide distance (Δ) within an octahedron of the lowest energy structures was calculated to evaluate the degree of distortion. By excluding all structures with Δ > 0.5 Å, the total number of compounds was further reduced to 32. They next calculated the band gaps of remaining structures using DFT calculations including spin–orbit coupling and lowered the band gap threshold from 3.5 eV to 2 eV. After an analysis of the compounds that satisfy this criterion, the elements Ge²⁺, Sn²⁺, Mg²⁺, V²⁺, Mn²⁺, Ni²⁺, Cd²⁺, Hg²⁺, Ca²⁺, and In²⁺ were considered as novel candidates for the replacement of Pb in metal-halide perovskites. Next, by considering band gap types (direct band gap only) and the criterion for reducing toxicity, Mg, Mn, V, and Ni were selected as potential alternatives to Pb in lead-halide perovskites. In particular, the magnesium-iodine perovskite was proposed to be an efficient electron conductor due to low electron effective masses.

Fig. 7.

	Figure Option ViewDownloadNew Window
	Fig. 7. (color online) Scheme of the computational screening process. The initial input elements and selected candidate elements are shown in the blue shading on the periodic table. The numbers 1, 2, and 3 mark the steps of the screening process, with the screening criteria. Adapted with permission from Ref. [16] Copyright (2015) American Chemical Society.

In a later research work, Jain et al. screened lead-free pe-rovskite-like materials with compositions A₂BB′X₆, ABX₄, and A₃B₂X₉ for optoelectronic performance using high-throughput DFT calculations.^[87] In this research, the monovalent A and B′ cations were selected from Na, Ka, Rb, Cs, Cu, and Ag, and trivalent B cations were chosen from Ga, In, and Sb, with monovalent anions X = Cl, Br, and I. The authors employed two material descriptors including formation energy and hybrid HSE06 band gaps and found 10 compounds with bandgaps in the range of 1.5 eV–2.5 eV from more than 480 compounds. To evaluate their optoelectronic applications, the authors further characterize effective masses, density of states, and absorption coefficients of all these selected compounds.

Phosphor-converted white light-emitting diodes (pc-LEDs) are emerging as an important light source for solid-state lighting because of their high efficiency and long lifetime.^[88] To produce a white light LED with a better performance, an efficient red-emitting phosphor is desired^[17] Wang et al. recently reported a high-throughput search for new narrow-band red-emitting phosphors by developing a group of quantitative descriptors for Eu²⁺-activated emission on the basis of the electronic structure database Materials Project.^[17] An ideal red-emitting phosphor host material should have properties such as high phase stability, red-orange-light emission, high thermal quenching resistance, and high photoluminescence quantum efficiency. In light of these material properties, the authors set a group of materials descriptors: i) E_hull < 50 meV, whereas E_hull is defined as the energy above the linear combination of stable phases in the phase diagram; ii) calculated band gap (E_g) at the Perdew–Burke–Ernzerhof (PBE) functional^[89] level should be in the range from 2.42 eV to 3.58 eV, this criterion was chosen based on the analysis of the band gap data of 10 well-known red-emitting phosphor hosts; iii) energy splitting, ΔE_S > 0.1 eV, whereas ΔE_S is defined as the energy gap between the highest and the second highest Eu²⁺4f band. This feature leads to a narrow-band emission; and iv) the authors calculated the Debye temperature (Θ_D) using quasi-harmonic approximation for estimating structural rigidity and band gap using screened hybrid Heyd–Scuseria–Ernzerhof (HSE) functional,^[90] which is in much better agreement (within 0.3 eV) with the experimental values.

The flowchart of the high-throughput screening procedure for narrow-band red-emitting phosphor hosts is shown in Fig. 8. By using this procedure, the authors screened 2259 materials (including 203 ternary, 156 quaternary, and 1900 nitridosilicate and nitriodoaluminate quarternary structures), and eventually found a total of eight narrow-band-emitting phosphor hosts. Three of them have already been previously reported experimentally, and five of identified hosts are new.

Fig. 8.

	Figure Option ViewDownloadNew Window
	Fig. 8. (color online) (a) Flowchart of the high-throughput screening for narrow-band red-emitting phosphor hosts, and (b) scheme of the narrow-band electron emission of Eu2+5d–4f. Adapted with permission from ref.[17] Copyright (2016) American Chemical Society.

A high-throughput virtual screening and experimental approach was also employed to design high-performance molecular organic light-emitting diodes.^[18] In this work, the authors explored a search space of 1.6 million molecules and screened over 4 × 10⁵ of them using time-dependent density functional theory calculations, and eventually identified nearly one thousand of molecules across the visible spectrum for light-emitting diode applications. The workflow of materials discovery for this work is shown in Fig. 9.

Fig. 9.

Figure Option ViewDownloadNew Window

Fig. 9. (color online) Workflow of materials discovery. (a) As shown is the diagram of collaborative materials discovery approach, whereas the search space reduces by over five orders of magnitudes with the screening process. It involves different theoretical and computational approaches and experimental input and testing from left to right. (b) Dependency graph of the quantum chemistry calculations in this study. Adapted from Ref. [18].

This project involves several consequent steps. First, library generation of molecules. The authors produced more than 1.6 million candidates in their library by setting two major conditions: First, the molecules should have a low enough singlet-triplet energy gap. Second, molecular size should be less than 1100 g·mol⁻¹, limited by the requirement for vapor processing. Second, machine learning for pre-screening. Owning to the large size of over 1.6 million candidate molecules, it is not possible or necessary to screen all of them with quantum simulation. To speed up the screening efficiency, by using results from previous calculations as training data, the authors employed machine learning approach to do a pre-screening, which is able to predict molecules with a high probability to have good outcomes and prioritize the molecules for next-step simulation. Third, quantum chemical calculations. The authors estimated the emission color via vertical absorption energies using time-dependent density functional theory (TD-DFT) calculations. Fourth, experimental calibrations. To get accurate excitation energy of charge-transfer excitations, the authors employed B3LYP functional by including an amount of exact Hartree–Fock exchange, since the standard TD-DFT calculations often underestimate the excitation energy because of the semi-local nature of the exchange–correlation functional.^[91,92] The authors further confirmed the accuracy of this approach by using a linear calibration scheme on 46 experimental data points from the past literature, and their calibration against 17 in-house measurements were verified. Finally, analysis and lead discovery. The authors’ quantum calculations revealed thousands of candidate emitters with potentially high efficiency, with about 900 as extremely promising. At this step, it is possible to make human tractable decision to choose candidate materials, and the authors used a web-based selection process including data visualization and sorting interfaces to do this. Eventually, a small consensus set of molecules was selected for further experimental synthesis and characterization in devices.

Magnetic materials have played an important role in modern technologies from data storage to energy conversion.^[19,93] Recently, Sanvito et al. demonstrated a high-throughput materials design approach to search for novel magnetic materials based on Heusler alloys (HAs).^[19] In this study, on the basis of an extensive electronic structure library of HAs, the authors employed a series of material descriptors including magnetic order and materials stability, and eventually found about 20 novel magnetic materials. Figure 10 shows the high-throughput design procedure of Heusler-based magnets. In this work, the high-throughput materials design strategy consists of three main steps:

(I) The authors built an extensive electronic structure database that contains 236115 compounds based on the structure prototype of HAs. The authors choose to search for new magnets from HAs based on two reasons. First, many HAs contain magnetic ions and therefore it is likely to find candidate magnets from HAs. Second, HA is one large class of materials that can be formed from a wide variety of chemical compositions, which corresponds to a large number of prototypical compounds. These two features give authors a high chance to find new magnets.

Fig. 10.

	Figure Option ViewDownloadNew Window
	Fig. 10. (color online) High-throughput design of Heusler-based magnets. Structural models of (a) regular Heusler, (b) inverse Heusler, and (c) half Heusler. (d) Primitive unit cell to construct electronic structure database. (e) Convex hull diagram for Al–Mn–Ni. (f) High-throughput workflow for searching for Heusler-based magnets. Adapted and redesigned from Ref. [19]

(II) The authors performed a preliminary screening using two materials descriptors: formation enthalpy and magnetic moment. They analyzed the formation enthalpy for all the 236115 calculated compounds and set the first screening criterion of ΔH = H_X2YZ − (2H_X + H_Y + H_Z) > 0. This screening condition gives authors 35602 compounds, in which 6778 carry a magnetic moment. This number could be much larger than the actual number of stable magnetic HAs since this preliminary screening did not assess the stability of a given X₂YZ structure against decomposition over all the possible binary and ternary prototypes. After some preliminary analysis, the authors found that it is an extremely challenging task to map the stability of every calculated HA because it requires the calculation of approximately 15 million prototypes.

(III) The authors employed an alternative approach to screen the entire database after the preliminary screening. They narrowed down the entire database to intermetallic HAs consisting of elements of 3d, 4d, and 5d periods, with the number reduction from original 23615 to 36540. Next, on the basis of available energy data of corresponding binaries and known ternary compounds in the AFLOWLIB, the authors conducted a convex hull analysis, and found that, among the 36540 compounds, only 248 are thermodynamically stable.

(IV) Last, the authors found 22 compounds having a magnetic ground state among the 248 compounds from first-principles electronic structure calculations. Interestingly, 20 new magnetic HAs belong to the Co₂YZ, Mn₂YZ, and X₂MnZ classes, implying an important role of Co and Mn elements. Accordingly, Co and Mn can be considered as gene elements of magnets in future high-throughput search of new magnets.

In this work, the employed screening strategy is to first search for thermodynamically stable HAs instead of HAs with ferromagnetic ground state, which significantly improves the screening efficiency. In addition, to validate the computational predication, the authors attempted the synthesis of four HAs: two of them (Co₂MnTi and Mn₂PtPd) have been successfully synthesized, whereas the other two (Mn₂PtCo and Mn₂PtV) are decomposed into binary compounds. Notably, the authors found that the Co₂MnTi has a Curie temperature (T_C) as high as 938 K. This remarkable finding has proven that a new high-temperature ferromagnetic can be discovered using high-throughput approach.