MaX Conference, Trieste January 2018 innovating nanoscience High-throughput electronic structure theory: are all calculations useful ? Stefano Sanvito (sanvitos@tcd.ie) School of Physics and CRANN, Trinity College Dublin, IRELAND
My objectives for this talk Demonstrate that HTEST works and that new magnets can be discovered Show that, as databases grow, we will become more clever in creating and using them
Finding new magnets: why ? US permanent magnets market ~22.6B$ (2021) Cost Periodic Table 1 H 2 He 1.00 4.00 Atomic Number Atomic symbol 66 Dy Atomic weight 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 162.5 Antiferromagnetic T N (K) Ferromagnetic T C (K) 6.94 9.01 10.81 12.01 14.01 16.00 19.00 20.18 179 85 36 35 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 26.98 28.09 30.97 32.07 22.99 24.21 35.45 39.95 32 Ge 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 33 As 34 Se 35 Br 36 Kr 38.21 44.96 47.88 50.94 52.00 55.85 55.85 58.69 63.55 65.39 69.72 72.61 74.92 78.96 83.80 40.08 58.93 79.90 96 312 96 1043 1390 629 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 87.62 88.91 91.22 92.91 95.94 97.9 101.1 102.4 106.4 107.9 112.4 114.8 118.7 121.8 127.6 126.9 83.80 85.47 56 Ba 57 La 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 55 Cs 78 Pt 79 Au New tech. 137.3 138.9 178.5 180.9 183.8 186.2 190.2 192.2 200.6 204.4 207.2 209.0 209 210 222 197.0 195.1 132.9 87 Fr 88 Ra 89 Ac to deploy 223 226.0 227.0 66 Dy 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 162.5 140.1 140.9 144.2 145 150.4 152.0 157.3 158.9 164.9 167.3 168.9 173.0 175.0 13 105 229 221 179 85 132 20 85 20 56 19 90 292 91 Pa 93 Np 90 Th 92 U 231.0 238.0 232.0 238.0 < $10/kg $10 - 100/kg Nonmetal $100 - 1000/kg Metal $1000 - 10000/kg >$10000/kg Radioactive BOLD Magnetic atom
Magnetism is rare ~2,000 The discover a new useful magnet is a rare event SrTcO 3 Fe 3 O 4
The magnetic genome project with Stefano Curtarolo, Duke
The magnetic genome project Finding descriptors Materials selection Search the database for 1) new materials, 2) physical insights Database Creation (AFLOW) Rational materials storage Creating searchable database where to store information Virtual Materials Growth 1) Simulating existing materials 2) Simulating new materials Robust electronic structure method: density functional theory (VASP)
The magnetic genome project Finding descriptors Materials selection Search the database for 1) new materials, 2) physical insights Database Creation (AFLOW) Rational materials storage Rational materials storage Creating searchable database Creating searchable database where to store information where to store information Virtual Materials Growth Virtual Materials Growth 1) Simulating existing materials 1) Simulating existing materials 2) Simulating new materials Robust electronic structure method: 2) Simulating new materials density functional theory (VASP)
The magnetic genome project Virtual Materials Growth (existing materials) Only ~150,000 are known to us ICSD: Inorganic Crystal Structure Database � • 1,616 crystal structures of the elements • 28,354 records for binary compounds • 55,436 records for ternary compounds • 54,144 records for quarternary and quintenary • About 113,000 entries (75.6%) have been assigned a structure type. • There are currently 6,336 structure prototypes. � • Lots of redundancy
The magnetic genome project Virtual Materials Growth (existing materials) Duke calculated single elements, binary, ternary and some quaternary (about 100,000) Calculations: � • AFLOW manages the run (large code) • DFT done with VASP (pseudo-potential, plane-wave) • Calculations at the DFT GGA-PBE level � • Relaxation performed à new space group worked out • Basic electronic structures collected (including: spin- polarization, effective mass, magnetic moment, etc.) S. Curtarolo, W. Setyawan, G. L. W. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy, M. Mehl, H. T. Stokes, D. O. Demchenko, and D. Morgan, Comp. Mat. Sci. 58 , 218 (2012)
The AFLOW consortium www.aflowlib.org S. Curtarolo, W. Setyawan, S. Wang, J. Xue, K. Yang, R.H. Taylor, L.J. Nelson, G.L.W. Hart, S. Sanvito, M. Buongiorno-Nardelli, N. Mingo, O. Levy, Comp. Mat. Sci. 58 , 227 (2012)
Heusler alloys ~250 known … ~1000 claimed … ~90 magnetic …
Heusler alloys ~236,000/0.5M calculated !!
Database Rational materials storage www.aflowlib.org S. Curtarolo, W. Setyawan, S. Wang, J. Xue, K. Yang, R.H. Taylor, L.J. Nelson, G.L.W. Hart, S. Sanvito, M. Buongiorno-Nardelli, N. Mingo, O. Levy, Comp. Mat. Sci. 58 , 227 (2012)
The magnetic genome project Finding descriptors Materials selection Materials selection Search the database for 1) new Search the database for 1) new materials, 2) physical insights materials, 2) physical insights Database Creation (AFLOW) Rational materials storage Creating searchable database where to store information Virtual Materials Growth 1) Simulating existing materials 2) Simulating new materials Robust electronic structure method: density functional theory (VASP)
Back to the magnets … .. S. Sanvito et al., Accelerated discovery of new magnets in the Heusler alloy family , Science Advances 3 , e1602241 (2017)
A look at the full database Property : Can be made ? Descriptor 0: Enthalpy of formation Energy (Ni 2 MnAl) < Energy (2Ni + Mn +Al) Total Unique Possible Possible Magnetic 235,253 105,212 35,602 6,778
Stability analysis Descriptor 1: Enthalpy of formation Mn Ni 2 MnAl 2 Ni + Mn + Al 2 Ni + MnAl MnAl Ni 2 MnAl 1/2 (MnNi 3 + NiAl + MnAl) MnNi 3 Ni 2 MnAl Al NiAl Ni
Stability analysis (e)$ This is very much on-going Ni - Mn - Al
TM 3 Look at the transition metal intermetallics 36,540
In summary … 36,540 possible à 248 stable à 8 Robust ( ∆ 30 criterion) 22 magnetic Extrapolating 236,000 possible à 1550 stable 138 magnetic à 50 Robust For real … . 70 80 magnetic magnetic predicted known
Critical temperature magnetism Descriptor 2: Critical temperature Known Heusler ferromagnets Co 2 XY Generalized regression model based on valence, volume, spin decomposition Fe 2 Mn Y Ni 2 Mn Y Prediction of T C Mn 2 XY Material V (Å) µ Δ E (eV) T … .. T Rh 2 Mn Y Co 47.85 2.0 -0.30 3007 352 Mn 48.93 2.0 -0.32 3524 760 Cu 2 Mn Y … … … … … … Pd 2 Mn Y Mn 54.28 9.03 -0.17 1918 ? Au 2 Mn Y
Analysis Co 2 XY Mn 2 XY X 2 Mn Y
Co 2 YZ 6 Co 2 FeSi 1200 Co 2 FeSi Co 2 FeGa Co 2 YZ Co 2 AB 1 5 Co 2 FeAl 1000 Co 2 MnTi Co 2 MnTi Co 2 MnSi Co 2 MnTi Co 2 MnGe Co 2 MnAl/Co 2 MnGa 4 Co 2 MnSn 800 m ( µ B ) T C (K) Co 2 MnAl/Co 2 MnGa Co 2 CrGa Slater- 3 600 Pauling Co 2 VZn Co 2 CrGa Co 2 NbZn Co 2 VGa/Co 2 TiGe Co 2 VGa/Co 2 TiGe 2 Co 2 TaZn Co 2 TaZn Co 2 NbAl 400 Co 2 VAl Co 2 CrAl Co 2 NbAl Co 2 VZn Co 2 VAl Co 2 CrAl Co 2 NbZn Co 2 TaAl Co 2 VSn 1 200 Co 2 TiGa Co 2 AB 3 Co 2 TiGa Co 2 TiAl Co 2 NbSn Co 2 NbSn Co 2 TiAl Co 2 TaZn Co 2 VSn Co 2 AB 2 0 0 25 26 27 28 29 30 25 26 27 28 29 30 N V N V m X 2 YZ = N V -24
X 2 Mn Z 5 600 X 2 Mn Z 4 Rh 2 MnTi Rh 2 MnZr Rh 2 MnSc Pd 2 MnCu 3 400 Pd 2 MnZn m ( µ B ) T C (K) Rh 2 MnHf Rh 2 MnZn Pt 2 MnZn N V = 27 Ru 2 MnV Pd 2 MnAu = 28 Ru 2 MnTa = 29 2 Ru 2 MnNb = 27 = 28 = 29 200 = 30 1 = 31 = 32 Castelliz- = 33 Kanomata 0 curve 4.2 4.3 4.4 4.5 4.2 4.3 4.4 4.5 d Mn-Mn (A) d Mn-Mn (A)
X 2 Mn Z X 2 Mn Z K. Shirakawa et al., J. Magn. Magn. Mater. 70 , 421 (1987)
Mn 2 YZ 200 Inverse Heusler 100 Mn 2 YZ Mn 2 PtGa (2236) Mn 2 PtIn (841) 0 Regular Heusler ∆ H (meV) Mn 2 CoCr (529) -100 Mn 2 PtV (3353) -200 Mn 2 PtPd (3218) Mn 2 PtCo (1918) -300 Mn 2 PtRh (3247) Co 2 XY -400 Mn 2 XY -500 45 50 55 60 65 3 ) V (A
Mn 3 Ga Mn 3 Ga K. Rode et al., Phys. Rev. B 87 , 184429 (2013)
Machine learning workflow 1000 used for DFT + ML 250,000 candidates 80 used for DFT + ML 2000 candidates 80 used for DFT + ML 229 candidates 249,000 remaining 1920 remaining 149 remaining ML TPR 60% (50:50 population) Don’t calculate 30% = 50 Don’t calculate 30% = ~650 Don’t calculate 30% = ~80,000
OK, but does all that work? S. Sanvito et al., Accelerated discovery of new magnets in the Heusler alloy family , Science Advances 3 , e1602241 (2017)
Co 2 MnTi Co 2 MnTi T Cmeasured = 940K T Cpredicted = 938K Prepared by arc melting in an Ar atmosphere Courtesy J.M.D. Coey’s Lab (P. Tozman, M. Venkatesan)
Mn 2 PtPd T N1measured = 67K T N1measured = 350K Complex antiferromagnetic order Courtesy J.M.D. Coey’s Lab (P. Tozman, M. Venkatesan)
Bottom line … . Demonstrate that HTEST works and that new magnets can be discovered Yes, it works!! But a massive effort is needed! Show that, as databases grow, we will become more clever in creating and using them Maybe … the algorithm will be clever if the researcher is
Duke Team: TCD Team: Tom Archer, Anurag Tiwari, Mario Stefano Curtarolo, Junkai Xue, Kevin Zic, James Nelson Rasch, Corey Oses
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