High-Throughput Screening of Magnetic Antiperovskites - Chemistry of

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High Throughput Screening of Magnetic Antiperovskites Harish K. Singh, Zeying Zhang, Ingo Opahle, Dominik Ohmer, Yugui Yao, and Hongbin Zhang Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b01618 • Publication Date (Web): 19 Sep 2018 Downloaded from http://pubs.acs.org on September 23, 2018

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Chemistry of Materials

High Throughput Screening of Magnetic Antiperovskites Harish K. Singh,*,† Zeying Zhang,§,† Ingo Opahle,*,† Dominik Ohmer,† Yugui Yao,§ and Hongbin Zhang*,† † Institute of Materials Science, TU Darmstadt, Otto-Berndt-Str. 3, 64287 Darmstadt, Germany § Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China

ABSTRACT Like perovskite materials, antiperovskites display many intriguing physical properties. In this work, we carried out high throughput density functional theory calculations to evaluate the stability of magnetic antiperovskite compounds. We screened 630 cubic antiperovskites M3XZ (M = Cr, Mn, Fe, Co, and Ni; Z = C, N; and X is one of the elements from Li to Bi except noble gases and 4f rare-earth metals) in order to validate the experimentally known phases and to predict novel systems. Thermodynamical, mechanical, and dynamical stabilities are considered, which are obtained by evaluating the formation energy with convex hull, elastic constants, and phonon dispersion, respectively. Eleven antiperovskites so far not reported in the ICSD database fulfil all the above mentioned stability criteria, suggesting that their synthesis as bulk phases is likely. A softening of the above mentioned stability criteria results in more than 50 potentially new materials, where synthesis as thin film or in related structures may be possible. The chemical trends in the stability are analyzed based on the crystal orbital Hamilton population.

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INTRODUCTION Analogous to perovskites, the antiperovskites (APVs) are also one of the most commonly explored materials in recent years, due to their remarkable properties such as superconductivity,1-3 nontrivial topological nature,4-6 spin glass behavior,7-9 barocaloric effect,10,11 thermoelectric,12,13 magnetostriction,14,15 negative thermal expansion,16-20 and piezomagnetism.21-23 For instance, Ni3MgC1 is a well-known superconductor with a critical temperature of 8 K, which is unique as being the first oxygen-free superconductor with a crystal structure similar to perovskites. Moreover, Co3SnC12 is a thermoelectric with a Seebeck coefficient of about 50 μV/K, which was attributed to strong electronic correlations. Such a treasury of functionalities could be possibly further tailored by accommodating various combinations of chemical elements in the APV crystal structure (M3XZ, with space group Pm3̅m (see Figure 1), like the perovskite materials. Thus, there is a strong impetus to predict more stable APV compounds with follow-up experimental verifications and future applications. Particularly, magnetic APVs with transition-metal or rare-earth ions occupying the M-sites show many fascinating physical properties, resulting from the cooperative interplay among the lattice, spin, and charge degrees of freedom. A prominent example is the barocaloric effect observed in Mn3GaN,10 which is originated from the geometric frustration associated with the noncollinear antiferromagnetic spin configuration. Zemen et al. investigated the piezomagnetic effect (PME) in a couple Mn based nitrides.22 Likewise, magnetocaloric effect has been observed in Mn3SnC24 and Mn3GaC.25 Remarkably, most of the fascinating magnetic properties appeared in Mn-based APV materials,16,18,24-27 including piezomagnetism,21 magnetostriction,14 and spin-glass behavior.9 Furthermore, the strong magnetostructural coupling also leads to unusual properties in the lattice, such as negative thermal expansion16 and zero thermal expansion behaviour, where neither expansion nor contraction occurred over a certain range of temperature.28,29 The variety of properties observed in APVs has also attracted strong theoretical attention. Fe3RhN was theoretically predicted to be stable based on density functional calculations by von Appen and Dronskowski30 and shortly after synthesized.31,32 Bannikov et al. have performed calculations on the formation energies and elastic constants on some APVs, but there is no systematic study on a more complete set of APVs by considering other stability parameters.33-37 In this work, we focus on magnetic APVs (both carbides and nitrides) with 3d-transition metal ions (Cr, Mn, Fe, Co, Ni) occupying the M sites. We carried out high throughput (HTP) screening on 630 magnetic APV systems based on density functional theory (DFT), with systematic evaluation of the stabilities. The screening was performed by considering three stability criteria, including (a) thermodynamical stability by calculating the formation energy together with the convex hull, (b) mechanical stability by evaluating the elastic constants, and (c) the dynamical stability by determining the phonon dispersion. Interestingly, about 76 APVs in this group have been already synthesized (see Table S1, S2 and S3). These compounds were properly validated based on our DFT calculations. Based on our calculations, 11 new APVs are predicted to be stable. All the above mentioned stability criteria are discussed with a thoughtful comparison among experimental and theoretical observations. To understand the chemical trends in the stabilities, detailed analysis based on the crystal orbital Hamilton population (COHP) was conducted, resulting in a transparent picture combined with our DFT data. To the best of our knowledge this is the first high throughput screening of APVs, which echoes the high throughput investigation of perovskites materials reported in the literature.38,39 Computational Details An extended version of the high throughput environment (HTE)40,41 is used to determine the thermodynamical and mechanical stability of cubic M3XZ APVs, where M = Cr, Mn, Fe, Co, and Ni, Z = C and N, whereas X is an arbitrary element from Li to Bi without inert gas and 4f-rare-earth elements (Figure 4). Thermodynamical stability is evaluated by calculation of the formation energy Ef = E(M3XZ) ACS Paragon Plus Environment

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– 3E(M) – E(X) – E(Z), where E denotes the DFT ground state energy for M3XZ and the individual components M, X, and Z. To obtain the distance to the convex hull, all competing phases stored in our in-house HTE database are considered. It contains among others about 3900 different experimentally reported binary and ternary phases relevant for the calculation of ternary phase diagrams with the magnetic 3d elements M = Cr, Mn, Fe, Co and Ni. In addition, about 5200 relevant phases available in the Materials Project database42 for these systems are included. In the cubic APV structure (space group 221, Pm3̅m), the M atoms occupy the face centers (Wyckoff position (½, ½, 0)), while the X and Y atoms are located at the corner (0, 0, 0) and body center (½, ½, ½) of the cube (Figure 1). DFT calculations are performed with the projector augmented wave method as implemented in the VASP package.43,44 The energy cut-off is taken to be 500 eV and 14x14x14 kpoints are used for the Brillouin zone integrations. For structural optimizations the Monkhorst–Pack scheme is used, while for the final evaluation of energies, magnetic moments, and elastic constants the tetrahedron method with the Blochl corrections is used. The exchange-correlation functional is approximated using the generalized gradient approximation (GGA) as parameterized by Perdew−Burke−Ernzerhof (PBE).45 For all competing phases the same computational setup as for the APVs is used to ensure the consistency. The calculations for APVs are carried out on both the nonmagnetic and ferromagnetic states. It is noted that due to the geometric frustration, noncollinear magnetic ground states can develop in APVs.22,23 We considered only the ferromagnetic configuration, which should be sufficient to evaluate the stabilities, whereas the magnetic ground state will be studied in a succeeding work. The lattice dynamics of APVs is studied in the framework of the harmonic approximation, where the phonon spectra are obtained using the frozen phonon approach with the Phonopy46 and VASP codes. Within this scheme, the forces on every atom are calculated based on the Hellmann-Feynman theorem by explicitly displacing atoms. 2 × 2 × 2 supercells are used to calculate the force constant matrix,47 with convergence tested by comparing to larger supercells and the density function perturbation theory (DFPT) methods. We cross checked our phonon calculations also by comparing with the Quantum Espresso package.48 Chemical bond analysis is performed based on crystal orbital Hamilton population (COHP)49,50 using the Lobster code,51 which provides information of the bond strength by giving access to the contribution of the chemical bonds with respect to the one-particle energies via partitioning the band structure energy.

Figure 1: Crystal structure of antiperovskite in the Pm3̅m space group with chemical formula M3XZ. Results and discussion Thermodynamical stability: Formation energy and convex hull The thermodynamic stability criteria Gf < 0 and ΔGh = 0 are the basic requirements in order to predict stable materials at given temperature and pressure, where Gf and ΔGh are the formation enthalpy and distance to the convex hull which can be evaluated from the Gibbs free energy. The first criterion, G f < 0 ensures that the compound is stable against decomposition into the elements according to the reaction ACS Paragon Plus Environment


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M3XZ → 3M + X + Z, while the second (more restrictive) criterion ΔGh = 0 ensures the stability of the compound against decomposition into any combination of other known phases. While this does not exclude the existence of a more stable unknown (e.g. distorted) structure, it ensures the existence of a new phase. The latter point will be addressed in more detail in the next Section. At T = 0 K the above mentioned stability criteria reduce to Ef < 0 and ΔEh = 0, where Ef is the formation energy defined in the Computational details and ΔEh the corresponding distance from the convex hull calculated from the DFT ground state energies. While the calculation of the thermodynamical potentials G(P,T) is possible for a few selected competing phases within a given thermodynamical model and approximation to DFT,52 it is infeasible in a high-throughput study like the present one, where a large number of competing phases have to be considered. We considered the convex hull tolerance of ΔEh < 50 meV/atom by taking into account the approximate temperature effects as well as systematic errors in DFT calculations due to approximations in the exchange-correlation XC functional and numerics. Critical tolerance with comparable values for the convex hull has been adopted also in other highthroughput41,107 studies. To verify the above mentioned stability criterion for the present APVs, we first discuss the compounds which have been already synthesized (see Table S1). All stoichiometric bulk compounds reported with the Pm3̅m space group symmetry fulfill the Ef < 0 criterion, with exception of Mn3InC53 (0.02 eV/atom) and Fe3ZnC54 (0.01 eV/atom). The related energies are small (below kBT at room temperature) and well within the range where details of the magnetic structure, temperature effects, or systematic errors in the DFT methods are expected to play a role. The majority of these compounds fulfill also the more stringent ΔEh < 50 meV/atom condition, with exceptions of Mn3XN (X= Al,54,55 Ni,56 Cu,57,58 Rh,59 Ag,58 In,60 Ir), Mn3InC,53 Mn3SnC,61 Cr3XN59 (X= Sn, Pd), and Ni3GeC.62 For the Mn and Cr alloys, the non-collinear magnetic structures due to geometrical frustration may be expected22,23 and lead to a reduction of the total energy and ΔEh. An unusually large distance from the convex hull is found for Ni3GeC62 (0.318 eV/atom), which also shows an unusually large 6% deviation between reported and calculated lattice parameters. The reported lattice parameter (3.58 Å) is close to the one of Ni3Ge (3.57 Å), which is stable according to our HTE database. This may be an indication that the reported Ni3GeC phase is C deficient. In general, our calculated lattice parameters deviate less than 2% from the experimentally reported values (see Table S1), with exception of Ni3GeC,62 Mn3GaN,58,63 Mn3SnN,64 Ni3GaC,65 Co3GeN,8 where the deviation is about 2-6%. Table S2 and S3 list APV compounds, which are reported in a non-cubic structure, as thin films and as non-stoichiometric alloys. For such alloys larger deviations from the above mentioned stability criteria are expected (when calculated as stoichiometric M3XZ compounds in the cubic Pm3̅m structure). The reported non-cubic APVs such as Cr3AsN,66 Cr3GeC,67 Cr3GeN,67,68 and Mn3GeC66,68 have a lower formation energy compared to Pm3̅m cubic structure in our HTE database and are found to be thermodynamically stable (see Table S2). In addition, from our calculations we confirmed that the reported non-cubic structure of Mn3GeN57 and Cr3AsC68 have lower formation energy than the cubic Pm3̅m and are thermodynamical stable (see Table S2). Figure 2 shows exemplary the calculated formation energies and distances from the convex hull for Mn3XC and Mn3XN, similar plots for the other M3XZ APVs are included in Figure S1. In total we find more than 200 M3XZ cubic APVs with formation energy Ef 0, C11 > 0, C44 > 0, and C11 + 2C12 > 0. These second-order elastic constants can be calculated as described by Soderlind.69 Our calculated elastic constants are in an overall good agreement with previous calculations by Bannikov 35 and Shein70,71 for Ni3XC (X = Y – Ag, Zn, Mg, and Cd), see Table S6. In most cases the agreement is within 10%, somewhat larger deviations are found for C44, especially when the absolute value of C44 is small as in the case of X = Y, Nb, and Mo. Such differences may be due to the use of different electronic structure codes. Further, the elastic constants for all synthesized APVs obey the mechanical stability conditions, except for Mn3CuN,63 Mn3InC,53 and Mn3InN,60 where deviations from the assumed ferromagnetic structure may play a role. In our calculations Mn3CuN63 and Mn3InC53 do not satisfy C11 − C12 > 0, while Mn3InN60 does not obey C44 > 0. Overall, our high throughput screening of mechanical stability is in good agreement with the experimental findings. Especially, none of the novel compounds predicted to be thermodynamically stable is found to be mechanically unstable. Phonon dispersions provide information about the dynamical stability of the specific crystal structure under consideration, where possible imaginary phonon modes indicate the crystal structure is unstable with respect to the ionic displacements following the phonon eigen modes. For cubic APVs with the Pm3̅m space group, there are 15 vibrational modes for any chosen q-point, as there are five atoms in the unit cell. We performed the systematic phonon calculations for 123 APVs by considering only the existing APVs and the novel APVs which satisfy the thermodynamical and mechanical stability criteria. Our calculated phonon spectra for Ni3CdC71 and Ni3MgC72 are in good agreement with earlier results (see Figure S7), especially they have no imaginary mode throughout the Brillouin zone, indicating that both are dynamically stable. For the compounds reported to be stoichiometric in space group Pm3̅m (Table S1), we do not observe imaginary modes except for seven compounds Cr3RhN59 (G, R), Mn3CuN58 (X, M), Mn3InN60 (M), Ni3GaC65 (M), Mn3CoN73 (X-M, R), Ni3GeC62 (TBZ), and Cr3IrN59 (G, R-M-R) where letters in parentheses denote the q-points with imaginary modes. Ni3GeC was already found to be thermodynamically unstable, while for the Mn and Cr compounds the assumed ferromagnetism may be responsible for the observed instability. Overall, our calculations are in good agreement with experiment. In addition, we found imaginary phonon frequencies for Ni3AlC (M point), Co3GaC (M point), Mn3CoN and Co3GeC (all over the Brillouin zone), which are reported to be nonstoichiometric in experiments (see Table S3). Apart from these 11 systems, no imaginary mode is observed for the other experimentally reported APVs, confirming their dynamical stability. ACS Paragon Plus Environment

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Figure 3: The calculated phonon dispersion for Cr3GeC in Pm3̅m (left) and in Cmcm (right) space group. We note that the distorted structures with displaced atoms can also be stabilised following the imaginary phonon eigen modes of the Pm3̅m space group. For instance, there are 12 APVs reported in other space groups (Fm3m, Cmcm, I4/mcm, P421m, and P4/mmm) (see Table S2). The space groups Cmcm and I4/mcm are subgroups of Pm3̅m, originated from the imaginary mode of the R4+ and M3+-R4+ types, respectively. There are four APVs (Mn3GeC,66 Mn3GeN,59,66 Fe3GeN66 and Cr3AsN59,66) with the I4/mcm structure and four (Cr3AsC,68 Cr3GeC,67 Cr3PN68,76 and Cr3PC68,76) with the Cmcm space group. It is observed that the Mn3GeC and Mn3GeN display imaginary mode at the R point and Cr3AsN the imaginary modes extend in the whole BZ for the cubic Pm3̅m structure. The imaginary mode throughout the BZ for Cr3AsN might be due to strong phonon coupling between the R4+ and other phonon modes. For APVs in the Cmcm space group, only Cr3GeC67 have the M3+-R4+ imaginary modes, while all other Cmcm APVs exhibit imaginary modes in the whole BZ. Taking Cr3GeC67 as an example, it is confirmed that there is no imaginary phonon mode in the phonon dispersions calculated using the Cmcm crystal structure, as shown in Figure 3. In this regard, for those compounds which are predicted to be thermodynamically stable based on the formation energy and the distance to the convex hull but dynamically unstable (Table S5), they can probably be synthesized in other crystal structures than Pm3̅m. Finally based on the stability criteria, we have verified the stability of existing APVs and identified newly designed APVs. The 22 (58) potentially novel APVs predicted to be stable based on thermodynamical and mechanical stability reduced to 11 (33) after considering the lattice dynamical stability. It is noted that the number of stable APVs is reduced by one order of magnitude when going from cases with negative formation energies to cases with ΔEh < 50 meV/atom for the convex hull, and further by a factor of two after considering the dynamical stability. Therefore, we believe that all four stability criteria (formation energy, convex hull, elasticity, and phonons) should be investigated systematically for valid high throughput screening of novel compounds. The dynamically unstable compounds may be stabilized in other structures, awaiting further experimental and theoretical exploration. The 11 APVs which are not reported in the ICSD database and fulfil all stability criteria are listed in Table 1. All compounds are magnetic, and with exception of Ni3LiC all are nitrides. Co3ZnN, Co3PdN, Co3PtN, Co3AuN, and Ni3LiC are on the convex hull (ΔEh = 0), indicating that their synthesis is most likely. Fe3IrN30 was already proposed in earlier calculations to be potentially stable, which is confirmed by our calculations. Further, we noted that Co 3GaN, Co3SnN, and Co3ZnN are mentioned in Landolt-Börnstein.77 The distribution of potentially novel APVs (including those with ACS Paragon Plus Environment


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ΔEh < 100 meV/atom) is summarized in Table 1 and Figure S4. The electronic band structure for the novel APVs exhibiting metallic nature (not shown). Moreover, we also summarized the overall trend of X elements (M3XZ) which stabilize the APVs (including existing and novel APVs) in the Pm3̅m space group (see Figure 4). Li and Mg are the only s-block elements which forms the stable APV compounds. The predicted Li-based APVs (Co3LiN and Ni3LiC) could be interesting for Li-ion battery applications. While the p-block elements as X corresponding to the 13th and 14th groups form the stable APV compounds where Ga, In and Sn each form four stable APV nitrides (see Figure 4) and it is also reported that Ga and Sn based APVs also display many interesting properties.10,12,21,25 Further, it could be seen from Figure 4, that the X elements belonging to d-block transition metals (7th–12th group) form the most number of stable APVs. Among these transition metals, the most number of stable APVs nitrides are designed as X element comprise Rh, Ir, Pd, Pt, Cu, and Au and each of them form four stable APVs. Table 1. APVs which satisfy all three stability criteria (thermodynamical, mechanical, and dynamical) and are not listed in the ICSD. The calculated distance to the convex hull ΔEh, lattice parameter a, formation energy Ef, and magnetic moment M are given. The calculated nonmagnetic lattice constant aNM is given for comparison. Compound

ΔEh (eV/atom)

a (Å)

Ef (eV/atom)

M (µB/f.u.)

aNM (Å)

Co3LiN

0.031

3.72

-0.134

2.90

3.69

Co3AuN

0.000

3.83

-0.051

4.36

3.80

Co3GaN

0.040

3.75

-0.230

2.60

3.73

Co3PdN

0.000

3.80

-0.084

5.13

3.76

Co3PtN

0.000

3.80

-0.103

5.14

3.77

Co3RhN

0.041

3.78

-0.007

6.07

3.74

Co3SnN

0.009

3.85

-0.077

2.22

3.84

Co3ZnN

0.000

3.74

-0.184

2.85

3.72

Fe3CuN

0.036

3.79

-0.105

6.96

3.71

Fe3IrN

0.037

3.83

-0.104

7.81

3.75

Ni3LiC

0.000

3.75

-0.063

0.70

3.76

Figure 4. Distribution of the stable novel and experimental APVs M3XZ for the Pm3̅m space group. The upper and lower triangular corner represents APV carbides and nitrides respectively. Each element in the periodic table corresponds to the X for the chemical formula M3XZ where M = Cr, Mn, Fe, Co, and Ni, whereas Z = C and N. The color indicates the number of stable phases for each X element. ACS Paragon Plus Environment

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Trends in the stability To understand the trends observed in the stabilities of the APV compounds, a detailed analysis on the chemical bonds is done, in order to find out which bond is responsible for the stability. To this aim, the integrated chemical orbital Hamilton population (ICOHP) is calculated using the LOBSTER code. 51, 78 Four different bonds, i.e., bonds between M-M, M-C, M-X, and X-C, are considered. Mn3XC with X being elements in the fifth period are chosen, which show typical trends observed also for other series of elements in the periodic table (not shown). The averaged ICOHP and the bond resolved ICOHP are shown in Figure S8. The averaged ICOHP shows qualitatively the same trend as the formation energy (Figure 2) with respect to elements as X in the same row of the periodic table. For instance, according to ICOHP, the most stable composition is reached with elements from the fourth and fifth groups (Zr and Nb), and a downturn occurs at the thirteenth group (In). Furthermore, the Mn-C bonds have the strongest contribution to the ICOHP, while the X-C bonds are the weakest link, i.e., contribute the least to the stability of the Mn3XC compounds. The Mn-Mn bonds have more significant contribution to the ICOHP than the Mn-X bonds for X ranging from Rb to Mo, while the Mn-X bonds become more dominant for more covalent X such as In, Sn, Sb, and Te. For other X elements from Tc to Cd, such two bonds have comparable contributions. In comparison with the SrTiO3, the ICOHP values for the Ti-O, Ti-Sr, O-Sr, and O-O bonds are -3.12, -0.96, -0.69, and -0.033 eV/bond, respectively. That is, the bonds between the face centered ions and body centered ions are the most stable bonds for both APVs (M-C) and perovskites (Ti-O), whereas the least stable bonds in SrTiO3 is the O-O bonds and for APVs the X-C bonds.

Figure 5: The non-spin polarized chemical orbital Hamilton population (COHP) curves of the (a) Co3PdN and (c) Mn3MoN. The upper and lower part of figure (a) and (c) separated by the horizontal blue dotted line represents the bonding and antibonding states respectively. Total and atom-projected density of states (DOS) of (b) Co3PdN and (d) Mn3MoN. The fermi-energy Ef lies at the 0 eV which is represented by the vertical dotted line (black). Magnetic properties Last but not least, it is observed that not all APV compounds with magnetic atoms show a magnetic ground state. To acquire the physical insight into the magnetic ground state of APVs, we did detailed analysis on COHP and DOS for Co3PdN and Mn3MoN in the nonmagnetic state. As suggested by Landrum106 et al., for systems with magnetic ground state, there exists a peak of COHP of antibonding ACS Paragon Plus Environment


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nature located at the Fermi energy (Ef) in the non-spin-polarized calculations. Obviously, the COHP for Co3PdN displays a strong antibonding peaks at Ef (Figure 5(a)). This indicate that Co3PdN should have a magnetic ground state, which is consistent with our explicit calculation where the ferromagnetic ground state is about 0.12 eV/atom lower in energy than the nonmagnetic state. Such an observation is consistent with the magnetic instability of itinerant magnetism following the Stoner criterion N(Ef) I > 1, which says that a large density of states (DOS) at Ef is favorable for the occurrence of a magnetic ground state.108 According to Figure 5(b), the total DOS at Ef is as large as 16.20 states/eV/u.c. in the NM state, which is originated mostly from the Co 3d state. The calculated N(Ef) of Co 3d state is 4.57 states/eV/atom and an approximate Stoner parameter I of Co is 0.40 eV109,110 which lead to N(Ef) I = 1.82 > 1. Thus, peaks at Ef in COHP and DOS provide essential information about whether a compound is magnetic or not. This can be also verified using Mn3MoN as a counter example. As shown in Figure 5(c) and Figure 5(d), the COHP and DOS of Mn3MoN are vanishing at Ef, resulting in a nonmagnetic state, as confirmed by our DFT calculations as well. This picture can be applied to all the 11 newly predicted APVs (Table 1), and they are all with a magnetic ground state based on DOS, COHP (cf. Figure S9 in the Supplementary), and explicit DFT calculations. We note that the arguments based on DOS and COHP can only be used to justify whether the system would have a magnetic ground state or not, but provide limited information about the real magnetic ground state. As discussed in the introduction, the magnetic APVs can adopt noncollinear magnetic states leading to interesting barocaloric and piezomagnetic effects, which will be investigated in the future. Conclusion: In summary, we carried out systematic high throughput screening on 630 APV systems using firstprinciples calculations. In our screening procedure, three stability parameters were evaluated such as thermodynamical stability, mechanical stability, and dynamical stability. After validating our calculations on 76 existing APV materials, it is identified that 11 novel compounds can be stabilized in the cubic APV structure. This paves the way to design more magnetic materials, and we hope our work will stimulate more experimental and theoretical efforts to investigate the interesting properties of APV compounds. Acknowledgement The authors acknowledge support from the NOVAMAG project, under Grant Agreement No. 686056, EU Horizon 2020 Framework Programme, and also the LOEWE project RESPONSE funded by the Ministry of Higher Education, Research and the Arts (HMWK) of the Hessen state. The Lichtenberg high performance computer of the TU Darmstadt is gratefully acknowledged for the computational resources where the calculations were conducted for this project. Z. Zhang and Y. Yao acknowledge the financial support from the NSF of China Grant No 11734003. Zeying also thanks the financial support from the Chinese scholarship council (CSC). Supporting Information The SI consist of lattice constants, formation energy and convex hull tables for novel and experimental APVs. The plot of formation energy and convex hull trends are added to SI together with various other figures (Phonon dispersion, novel and experimental periodic table).

Corresponding Authors Harish K. Singh E-mail: [email protected] Ingo Opahle E-mail: [email protected] Hongbin Zhang E-mail: [email protected] Harish K. Singh and Zeying Zhang contributed equally to this manuscript. ACS Paragon Plus Environment

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