Idea Transcript
Large scale ab initio simulations of functional magnetic materials M. E. Gruner Department of Physics, University of Duisburg-Essen, 47048 Duisburg, Germany
G. Rollmann, A. Hucht, A. Dannenberg, P. Entel A.T. Zayak, W. A. Adeagbo
Functional magnetic materials by DFT
The Quest for Ultra-High-Density Magnetic Recording •
Exponential increase in storage densities in the past → still going on Recent values: ~ 600 GBit/in2 → long term goal: 10-50 TBit/in2
•
Major obstacle for media: Superparamagnetic limit
High-anisotropy recording materials: Increasing Ku to decrease V
Ku V kBT
N 0 exp
Ku: Anisotropy V: Grain volume
Patterned media: One particle per bit Current media:
Fe, Co Pt
c
a
L10: Fct layered along c-axis with c/a < 1
L10-FePt: Ku 7 · 107 erg/cm3 L10-CoPt: Ku 5 · 107 erg/cm3
0
1
1
Sun et al., Science 287, 1989 (2000)
Functional magnetic materials by DFT
FePt-Nanoparticles from Gas-Phase Experiments Cuboctahedron: Single crystalline fct
Decahedron: Multiply twinned fct
2 nm
2 nm HRTEM images of ordered Fe-Pt nanoparticles (O. Dmitrieva, et al.)
Multiple twinning incompatible with large magnetocrystalline anisotropy! Fabrication of fct L10-FePt nanoparticles increasingly difficult with decreasing sizes
Functional magnetic materials by DFT
Surface vs. volume energy Toy model: Potential energy in Lennard-Jones particles [E. g.: Doye, Miller and Wales, J. Chem. Phys. 111, 8417 (1999); Doye and Calvo, PRL 86, 3570 (2001)]
•
Icosahedron: lower surface energy
•
Cuboctahedron (fcc): No twinning, lower core energy MEG, G.Rollmann, A. Hucht, P. Entel, in: Advances in Solid State Physics, vol. 47, Springer, Berlin (2008) p. 117
→ Competition of structures as a function of particle size
Functional magnetic materials by DFT
Density functional theory calculations of large systems
[Kresse and Furthmüller, PRB 54, 11169 (1996); Kresse and Joubert, PRB 59, 1758 (1999)]
•
Plane wave basis (Ecut = 268 eV)
•
Reciprocal space integration restricted to Γ-point
•
PAW method for interaction with core and nuclei
•
GGA exchange correlation functional (PW91)
•
Colinear spin moments
•
Structure optimization on the Born-Oppenheimer surface using conjugate gradient method
Fe561: • • •
Diameter: Valence electrons: Memory requirement:
2.5 nm 4488 66 GByte
Functional magnetic materials by DFT
Scaling of the numerical demand on a single CPU IBM Blue Gene/L, PPC440d
JUGENE (#6 on top500.org)
Functional magnetic materials by DFT
Efficiency of VASP on the BlueGene/L: Scaling of Fe561 IBM Blue Gene/L
1024 nodes in one rack 2xPPC440d @ 700MHz (double FPU) per node 512 MBytes per node 3-fold high-speed communication network No virtual memory, restricted OS on nodes Air cooled…
IBM Blue Gene/P
1024 nodes in one rack 4xPPC450d @ 850MHz (double FPU) per node 2 GByte per node SMT on node possible
BG/L Reasonable scaling up to1024 cores
Functional magnetic materials by DFT
Efficiency of VASP on the BlueGene/L: Scaling of Fe561 IBM Blue Gene/L
1024 nodes in one rack 2xPPC440d @ 700MHz (double FPU) per node 512 MBytes per node 3-fold high-speed communication network No virtual memory, restricted OS on nodes Air cooled…
35 %
Quad-Opteron: Good scaling only up to ~100 cores
BG/L: Reasonable scaling up to1024 cores
Functional magnetic materials by DFT
Structure of nanoclusters: Size dependence • N O (102): Systematical scan of potential energy surface impossible Educated guess of favorable structures Restriction to “magical” cluster numbers: Na = 1/3 ( 10 n3 + 15 n2 + 11 n + 3) = 13, 55, 147, 309, 561, 923…
Available morphologies:
n: number of complete geometrical shells
perfect icosahedra perfect cuboctrahedra (fcc) truncated decahedra bcc (Bain-transformed cuboctahedra)
• For binary particles: Compositional degrees of freedom…
Functional magnetic materials by DFT
Structural Transformations: Bain and Mackay Path
FCC↔BCC: Bain-transformation
Ico↔Cubo: Mackay-transformation
E. C. Bain, Trans. Am. Inst. Min. Met. Eng. 70, 25 (1924)
A. L. Mackay, Acta Cryst. 15, 916 (1962)
Functional magnetic materials by DFT
Ground-State Properties of Fe-Nanoparticles
ΔE 290 K
G. Rollmann, MEG, A. Hucht et al., PRL 99, 083402 (2007)
• •
Exp.: Billas et al., PRL 71, 4067 (1993)
Lowest energy for BCC (Bain transformed Cubo) for N ≥ 147 Ico and Cubo unstable against transformation along Mackay-path
Functional magnetic materials by DFT
Shell-wise Mackay transformation (SMT) in Fe561
Gradual transformation from icosahedron to cuboctahedron towards the center
Functional magnetic materials by DFT
Common Neighbor Analysis of SMT Fe561 Standard tool for structure identification:
Jónsson and Andersen, PRL 60, 2295 (1988) Faken and Jónsson, Comp. Mat. Sci. 2, 279(1994)
body centered cubic
cuboctahedron (fcc)
•
icosahedron
Outermost shells prefer bcc-like coordination, the core remains fcc G.Rollmann, MEG, A. Hucht et al., PRL 99, 083402 (2007)
Functional magnetic materials by DFT
Size dependent properties of Fe-Pt Nanoparticles • Binary system → variety of morphologies to be considered: Cuboctahedra, icosahedra, decahedra, ordered/disordered,core-shell • Calculations iso-stoichiometric (for each size), composition according to L10-ordered cuboctahedron • Two [001] surfaces covered by one element: cPt≠cFe • [001] surfaces preferred by Pt → cPt>cFe MEG, J. Phys. D: Appl. Phys., 41, 134015
Functional magnetic materials by DFT
Morphologies of Fe-Pt Particles
L10-Ordered Cuboctahedron
Disordered Cuboctahedron
Disordered Icosahedron
Disordered Decahedron
Core-Shell Icosahedra Ordered Decahedron
ΔE 300 K
MEG, G.Rollmann, P. Entel, M. Farle, PRL 100, 087203 (2008)
Ordered Icosahedron
“Alternating” Icosahedra
Functional magnetic materials by DFT
Larger particle sizes: Preliminary results
Functional magnetic materials by DFT
Magnetism of Fe-Pt Particles
Disordered Cuboctahedron
Disordered Icosahedron
L10-Ordered Cuboctahedron
Ordered Icosahedron
Core-Shell Icosahedron
Ferrimagnetism in core-shell structures
Ordered Decahedron
Functional magnetic materials by DFT
Ferrimagnetism in Core-Shell Isomers
Core-Shell isomers: Shell-wise alternating Moments in the pure Fe-core
MEG, G.Rollmann, A. Hucht, P. Entel, in: Advances in Solid State Physics, Vol. 47, Springer, Berlin (2008), p. 117 MEG, G. Rollmann, S. Sahoo, P. Entel, Phase Transitions 79, 701 (2006)
Functional magnetic materials by DFT
Antiferromagnetism in L10 FePt Bulk calculations: AF and FM solutions very close in energy Zeng, Sabirianov, Mryasov et al., PRB 66, 184425 (2002) Brown, Kraczek, Janotti et al., PRB 68, 052405 (2003)
Similar situation in perfectly L10 ordered cuboctahedra! MEG, J. Phys. D: Appl. Phys., 41, 134015
Functional magnetic materials by DFT
Multiple twinning: Exploring chemical trends
Functional magnetic materials by DFT
Co-Pt
L10-Ordered Cuboctahedron
Disordered Cuboctahedron
Disordered Icosahedron
Disordered Decahedron “Alternating” Icosahedra
Ordered Decahedron ΔE 1000 K!
MEG, G.Rollmann, P. Entel, M. Farle, PRL 100, 087203 (2008) Ordered Icosahedron
Core-Shell Icosahedra
Functional magnetic materials by DFT
Electronic structure of Fe265Pt296 Fe-Pt Co-Pt Fe Co
Pt
Mn: [Ar] 3d5 4s2 Fe: [Ar] 3d6 4s2 Co: [Ar] 3d7 4s2
Stability of icosahedral structures influenced by filling of 3d minority states
Functional magnetic materials by DFT
Mn-Pt
L10-Ordered Cuboctahedron
Disordered Cuboctahedron
Disordered Icosahedron
Disordered Decahedron “Alternating” Icosahedra
Ordered Decahedron
Ordered Icosahedron
Antiferromagnetic L10 Cuboctahedra
Functional magnetic materials by DFT
Structural instability of the ordered Mn-Pt icosahedron
Geometric optimization procedure leads to tranformation into ordered cuboctahedral L10 structure along the Mackay-path
Functional magnetic materials by DFT
Magnetic shape change by field induced reorientation Archetypical system: Ni-Mn-Ga }
+ + +
Entirely in the martensitic phase Strain up to10% (Ni-Mn-Ga) High frequencies possible
6…10 %
Ullako et al., Appl. Phys. Lett. 69, 1966 (1996)
Functional magnetic materials by DFT
Magnetic shape change by field induced reorientation Requirements:
Archetypical system: Ni-Mn-Ga
• Ferromagnetic, martensitic phase stable around (and above) room temperature • Considerable magnetocrystalline anisotropy energy (MAE)
• Highly mobile martensitic twin boundaries • Single crystals benefical for large strains Goal:
Understanding phase stability, MAE and twin boundary mobility from microscopic (electronic structure) point of view
}
6…10 %
Ullako et al., Appl. Phys. Lett. 69, 1966 (1996)
Functional magnetic materials by DFT
Density functional theory electronic structure calculations • Energy surfaces and twin boundary motion: Vienna Ab initio Simulation Package (VASP) – GGA exchange correlation functional (PW91,PBE) – PAW method for interaction with core and nuclei. – Valence: Ga → 3d104s2p1/4s2p1, Mn → 3d64s1, Ni → 3d94s1. Ecutoff = 337 eV. – Ab initio molecular statics/dynamics on the Born-Oppenheimer surface
JUGENE: Rank #6 on top500.org
• Phonon dispersions: VASP + PHONON (K. Parlinski) – Direct (supercell) approach: 1 x 5 x 1 unit cells (40 atoms)
• Magnetocrystalline anisotropy energy (MAE): Full-potential localized-orbital minimum-basis code (FPLO) – In cooperation with I. Opahle and M. Richter, IFW Dresden
Functional magnetic materials by DFT
Martensitic phases in the MSM Heusler system Ni-Mn-Ga
Parent phase: Cubic L21
Experiment: V. V. Khovailo et. al., Phys. Rev. B 72, 224408 (2005)
a
5M modulated martensitic phase:
Relevant for the MSM effect!
c
Functional magnetic materials by DFT
Phonon softening in the parent L21 phase
Mañosa et al.
Experiment (e.g.): Zheludev et al., PRB 54, 15045,(1996) Mañosa et al., PRB 64, 024305 (2001)
Symbols (exp.): T. Mehaddene et al.
Theory, DFT, T=0 (e.g.): Zayak et al., PRB 68, 132402 (2003)
Functional magnetic materials by DFT
Nesting features of the Fermi surfaces (e.g.): Lee, Rhee, Harmon, PRB 66, 054424 (2002) Bungaro, Rabe, Dal Corso, PRB 68, 134104 (2003)
L21 Ni2MnGa M = 4.05 μB/f.u.
A. Hucht et al.
Functional magnetic materials by DFT
Magnetism and stability of the austenitic phase
Energy
M = 3.8 μB/f.u.: unstable
M = 3.6 μB/f.u.: ~ stable
Stability of phases affected by magnetism (temperature)
E(c/a,M) by fixed-spin-moment approach
M. E. Gruner et al., Eur. Phys. J. – Special Topics 158, 193 (2008) P. Entel et al., Mater. Sci. Forum 583, 21 (2008)
Functional magnetic materials by DFT
Magnetocrystalline Anisotropy in Ni2MnGa FPLO (LSDA): •
Magnetocrystalline anisotropy energy (MAE) largest for c/a1.2
•
Change of direction: [001] is easy axis for c/a1 (easy plane instead)
Enkovaara et al., PRB 65, 134442 (2002) M. E. Gruner, P. Entel, I. Opahle, M. Richter, J. Mater. Sci. 43, 3825 (2008)
Functional magnetic materials by DFT
Ab initio modelling of twin boundary motion 3d periodic boundary conditions
• Line defects important for realistic description of twin boundary motion Pond, Celotto, Int. Mater. Rev. 48, 225 (2003); Müllner, Kostorz, Mater. Sci. Forum 583, 43 (2008)
x1 F x c
eˆ z nˆ
nˆ eˆ z
x2 G x d
Very large systems required: Not possible by ab initio so far! • Instead: Construction of perfect twin boundary
• Direct simulation of MSM effect requires spin-orbit terms → too expensive • But simulation of shear induced twin boundary motion is feasible
Austenite
Martensite
Ball, James, Arch. Rat. Mech. Anal. 100, 13 (1987) Bhattacharya, Microstructure of martensite, Oxford (2003)
Shear
Relaxation
Functional magnetic materials by DFT
Example of a double L10 Twin Boundary (c/a=1.25)
256 atoms (2x2x4 unit cells), doubled in each direction
Functional magnetic materials by DFT
256 atom supercell (4x replicated) with two twin boundaries
Activation energy in L10 phase (c/a=1.25) more than one order of magnitude larger than total MAE M. E. Gruner, P. Entel, I. Opahle, M. Richter, J. Mater. Sci. 43, 3825 (2008)
Functional magnetic materials by DFT
Simplified twin boundary motion in L10 Ni2.2Mn0.8Ga Ni2.2Mn0.8Ga, 512 atoms (2x2x8 unit cells)
Comparison with MSM-relevant (modulated) phases will help to understand origin of high mobility from first principles (…but they are rather difficult to stabilize)
Functional magnetic materials by DFT
Conclusions • Ab initio determination of materials properties of nano-objects with more than 900 spin-polarized atoms on state-of-the-art supercomputers → Blue Gene/P: 1400 TM atoms or more: Ø of 3.5 - 4 nm possible!
• Fe nanoparticles: – Size dependence of structures (bcc from 100…150 atoms on) – New conformation discovered (shell-wise Mackay-transformed structure)
• Binary TM nanoparticles for magnetic data recording (FePt, CoPt): – Multiple twinning and segregation may prevent formation of high uniaxial magnetocrystalline anisotropy – Multiply twinned structures lower in energy up to 3 nm – Relative stability can be controlled by filling of 3d minority states
• Magnetic Shape Memory materials: – Simplified models of twin boundary motion can be handled with first principles methods on contemporary supercomputers
Functional magnetic materials by DFT
Acknowledgements O. Dmitrieva (now@MPIE), D. Sudfeld (now@FEI), M. Spasova, C. Antoniak, N. Friedenberger, M. Farle, Universität Duisburg-Essen K. Albe,
TU Darmstadt
U. Wiedwald Universität Ulm M. L. Tiago, ICES, Univ. of Texas, Austin A. T. Zayak, J. R. Chelikowsky,
I. Opahle (now@Frankfurt), M. Richter, U. K. Rössler, S. Fähler IFW, Dresden
W. A. Adeagbo
MPI Halle
A. T. Zayak,
ICES, Univ. of Texas, Austin
M. Acet, S. Aksoy, E. F. Wassermann, Universität Duisburg-Essen M. Ogura, H. Akai, Osaka University
John von Neumann Institute for Computing and JSC @ FZ Jülich for computational resources and support P. Vezolle,
IBM Montpellier
Deutsche Forschungsgemeinschaft: SPP
1239:
Change of Microstructure and Shape of Solid Materials by External Magnetic Fields
SFB
445:
Nanoparticles from the Gas-Phase: Formation, Structure, Properties
Functional magnetic materials by DFT
Three good reasons for doing more computational materials science on world leading supercomputers: • It is more reliable than a weather forecast • It has more technological relevance than QCD • It is (potentially) much less harmful than simulations of military devices making use of nuclear reactions There is plenty of room at the TOP500!