The high-throughput highway to computational materials

innovating nanoscience

The high-throughput highway to computational materials design: finding new magnets Stefano Sanvito ([email protected]) School of Physics and CRANN, Trinity College Dublin, IRELAND

UCD 2015 January 2015

mailto:[email protected]

It is important to find new magnets

Novel rare-earth-free permanent magnets

US permanent magnets market ~10B$

4 Be 9.01

12Mg 24.21

2 He 4.00

10Ne 20.18

24Cr 52.00

19K 38.21

11Na 22.99

3 Li 6.94

37Rb 85.47

55Cs 132.9

38 Sr 87.62

56Ba 137.3

59Pr 140.9

1 H 1.00

5 B 10.81

9 F 19.00

17Cl 35.45

35Br 79.90

21Sc 44.96

22Ti 47.88

23V 50.94

26Fe 55.85

27Co 58.93

28Ni 58.69

29Cu 63.55

30Zn 65.39

31Ga 69.72

14Si 28.09

32Ge 72.61

33As 74.92

34Se 78.96

6 C 12.01

7 N 14.01

15P 30.97

16S 32.07

18Ar 39.95

39 Y 88.91

40 Zr 91.22

41 Nb 92.91

42 Mo 95.94

43 Tc 97.9

44 Ru 101.1

45 Rh 102.4

46 Pd 106.4

47 Ag 107.9

48 Cd 112.4

49 In 114.8

50 Sn 118.7

51 Sb 121.8

52 Te 127.6

53 I 126.9

57La 138.9

72Hf 178.5

73Ta 180.9

74W 183.8

75Re 186.2

76Os 190.2

77Ir 192.2

79Au 197.0

61Pm 145

70Yb 173.0

71Lu 175.0

90Th 232.0

91Pa 231.0

87Fr 223

88Ra 226.0

89Ac 227.0

62Sm 150.4 105

66Dy 162.5 179 85

67Ho 164.9 132 20

68Er 167.3 85 20

58Ce 140.1 13

8 O 16.00 35

65Tb 158.9 229 221

64Gd 157.3

63Eu 152.0 90

66Dy 162.5 179 85

Atomic symbol Atomic Number Atomic weight

Antiferromagnetic TN(K) Ferromagnetic TC(K)

Cost Periodic Table

80Hg 200.6

36Kr 83.80

54Xe 83.80

81Tl 204.4

82Pb 207.2

83Bi 209.0

84Po 209

85At 210

86Rn 222

Metal

Radioactive

Nonmetal

BOLD Magnetic atom

25Mn 55.85 96

20Ca 40.08

13Al 26.98

69Tm 168.9 56

312 96

36

78Pt 195.1

1043 1390 629

60Nd 144.2 19

292

< $10/kg $10 - 100/kg $100 - 1000/kg $1000 - 10000/kg >$10000/kg

92U 238.0

93Np 238.0

It is important to find new magnets

Data storage industry has multiple requirements

❑ High TC (>600K) ❑ High spin polarization (P~100%) ❑ Low Gilbert damping ❑ Low saturation magnetization ❑ Compatible with epitaxial growth of oxides

MRAM / STT Oscillators

Magnetism is complicated

SrMO3

SrCrO3 TN=-230C

SrMoO3

SrMnO3 TN=-10C

SrRuO3 TC=-100C

SrFeO3 TN=-140C

SrTcO3 TN=500C

C. Franchini, T. Archer, J. He, X.-Q. Chen, A. Filippetti and S. Sanvito, Phys. Rev. B 83, 220402(R) (2011)

Magnetism is rare

The discover a new useful magnet is a rare event

SrTcO3

Bottom line ….

We are looking for a needle in haystack

The magnetic genome project

with Stefano Curtarolo, Duke


Virtual Materials Growth 1) Simulating existing materials 2) Simulating new materials

Rational materials storage Creating searchable database where to store information

Materials selection Search the database for 1) new materials, 2) physical insights

Robust electronic structure method: density functional theory (VASP)

Database Creation (AFLOW)

Finding descriptors



Virtual Materials Growth (existing materials)


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/mistakes


Only ~150,000 are known to us


Duke calculated single elements, binary, ternary and some quaternary (about 500,000)

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)

Heusler alloys

~250 known …

~1200 claimed …

Heusler alloys

~236,000 calculated !!







Finding descriptors



Rational materials storage

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)

… and one theory for find them all

Comp. Mat. Sci. 49, 299-312 (2010)







Finding descriptors


Searching among transition metals

A look at the full database

Descriptor 0: Enthalpy of formation

Energy (Ni2MnAl) < Energy (2Ni + Mn +Al)

Property: Can be made ?

Total

235,253

Possible

35,602

Unique

105,212 6,778

Possible Magnetic

Stability analysis

Descriptor 1: Enthalpy of formation

Al Ni

Mn

Ni2MnAl

2 Ni + Mn + Al

Ni2MnAl

2 Ni + MnAlMnAl

MnNi3

NiAl

1/2 (MnNi3 + NiAl + MnAl)

Stability analysis

Ni - Mn - Al

This is very much on-going

TM3

Look at the transition metal intermetallics

36,540

In summary …

36,540 possible à 249 stable

23 magnetic

236,000 possible à 1550 stable

138 magnetic

Extrapolating

Entropic temperature

Descriptor 2: Entropic temperature

Entropic temperature

Descriptor 2: Entropic temperature

N=8776 N=249

TS TS

Critical temperature magnetism

Descriptor 3: Critical temperature

Known Heusler ferromagnets

Co2XY

Mn2XY

Ni2MnY

Rh2MnY

Cu2MnYPd2MnYAu2MnY

Fe2MnYGeneralized regression model based on valence, volume, spin decomposition

Prediction of TC

Material V (Å) µ ΔE (eV) T ….. T

Co 47.85 2.0 -0.30 3007 352

Mn 48.93 2.0 -0.32 3524 760

… … … … … …Mn 54.28 9.03 -0.17 1918 ?

Analysis

Co2XY

Mn2XY

X2MnY

25 26 27 28 29 30

NV

0

1

2

3

4

5

6

m (µ

B)

25 26 27 28 29 30

NV

0

200

400

600

800

1000

1200

T C (K

)

Co2MnTi

Co2FeSi

Co2AB 1

Co2CrGa

Co2MnAl/Co2MnGa

Co2NbAl

Co2VSn

Co2NbSn

Co2VZnCo2NbZnCo2TaZn

Co2VGa/Co2TiGe

Co2VAl

Co2AB 2

Co2TiGaCo2TiAl

Co2FeSi

Co2MnTi Co2MnTi

Co2FeGa

Co2FeAlCo2MnSi

Co2MnGe

Co2MnSn

Co2MnAl/Co2MnGa

Co2CrGa

Co2NbAl

Co2NbSn

Co2CrAl

Co2VSn

Co2VGa/Co2TiGe

Co2VAlCo2TaAlCo2AB 3

Co2VZnCo2NbZn

Co2TaZn

Co2TaZnCo2TiAlCo2TiGa

Co2CrAl

Co2XY

Slater-Pauling

mX2YZ=NV-24

Co2XY

Co2XY

Slater-Pauling

X2MnY

52 54 56 58 60 62 64 66 68

V (A3)0

100

200

300

400

500

600

700

T C(K

)

NV = 23 = 27 = 28 = 29 = 27 = 28 = 29 = 30 = 31 = 32 = 33

52 54 56 58 60 62 64 66 68

V (A3)0

1

2

3

4

5

m (µ

B)

X2MnY

40 45 50 55 60 65 70

V (A3)

-500

-400

-300

-200

-100

0

100

200

ΔH

(meV

)

Co2XYMn2XY

Full Heusler

Inverse Heusler

Mn2YZ

Mn2YZMn2PtGa

Mn3Ga

Mn3Ga

K. Rode et al., Phys. Rev. B 87, 184429 (2013)

Is that all ?

?

Tetragonal distortion

Mn3Ga Mn3Ge

Ni2MnGa Ni2MnSn Ni2MnIn

Mn2NiGa !Co2NbSn

Rh2VSn Rh2CrSn Rh2FeSn Rh2CoSn

Pd2NbSn Pd2TbSn Pd2DySn


Little magnetic anisotropy in cubic symmetry. Tetragonal distortion does not much better!

T. Graf et al., in Handbook of Magnetic Materials, Elsevier (2013)


Mechanism for tetragonal distortionD

OS

Energy

EF

Non-magnetic & non-distorted

DO

S

Energy

EF

Magnetic & non-distorted

DO

S

Energy

EF

Magnetic & Distorted

Stoner Criterion vs band Jahn-Teller distortion


Among our 23:

2 turn diamagnetic

Co2NbZnCo2TaZn

3 remain magnetic

X2MnY

PF~0, TC~300-400, TN~2000-5000

OK, but does all that work?

Co2MnTi

Courtesy J.M.D. Coey’s Lab

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Bottom line ….

Did we find one ?

TCD Team: Duke Team:Tom Archer, Anurag Tiwari, Mario Zic

Stefano Curtarolo, Junkai Xue, Kevin Rasch

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The high-throughput highway to computational materials