Dynamical Mean Field Theory on FeO under pressure Ronald Cohen Geophysical Laboratory
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2012 Summer School on Computational Materials Science Quantum Monte Carlo: Theory and FundamentalsJuly 23–-27, 2012 • University of Illinois at Urbana–Champaignhttp://www.mcc.uiuc.edu/summerschool/2012/
Dynamical Mean Field Theory on FeO under pressure
Ronald CohenGeophysical Laboratory
Carnegie Institution of [email protected]
2012 Summer School on Computational Materials Science Quantum Monte Carlo: Theory and FundamentalsJuly 23–-27, 2012 • University of Illinois at Urbana–Champaignhttp://www.mcc.uiuc.edu/summerschool/2012/
QMC Summer School 2012 UIUC
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Cohen QMC Summer SChool 2012 UIUC 2
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Background: FeO
• At ambient pressure FeO is an antiferromagnetic insulator with a rock salt structure
• Iron 3d states partially filled, but localized
• Borderline between charge transfer and Mott insulator
• Difficult to make stoichiometric FeO in the lab at low pressures (vacancies yield Fe1-xO where x ~ 0.07) but stoichiometric under pressure
Cohen QMC Summer SChool 2012 UIUC 3
The phase diagram as of1994 (Fei and Mao, Science, 266, 1678, 1994)
Knittle and Jeanloz, JGR 1991
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FeO wüstite is an insulator at ambient conditions
• LDA/GGA etc. make it a metal
Cohen QMC Summer SChool 2012 UIUC 4Cohen et al. (1998) High-Pressure Materials Research. Materials Research Society. 499.
• LDA+U does open a gap in AFM rhombohedral or lower symmetry FeO and predicts a metal insulator transition under pressure, but not a high-spin low-spin transition. (Gramsch, Cohen, and Savrasov, Am. Mineral., 88, 257 (2003).
• LDA+U is a model, and how accurate it is unknown.
• LDA+U cannot give a gap in paramagnetic FeO.
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Extended Stoner modelIncrease in bandwidth causes spin collapse:
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Magnetic collapse vs. High-spin low-spin transition vs. Orbital ordering in
FeO
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Moment 4μB
4 t2g 2 eg
Moment 0
6 t2g
t2g t2g
t2g
eg eg
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LDA-DMFT
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Lattice Problem (DFT) LAPW
Atomic Problem (Many-body theory: DMFT)
Lattice Problem (contains geometry)
Impurity Model (CTQMC)
HDFT
GimpNew density
Fully self-consistent, finite temperature
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DFT-DMFT
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Crystal problem
“Impurity” problem
Self-consistency conditionKristjan Haule DFT-DMFT code:
integrates wien2k LAPW code for Crystal with Continuous Time Quantum Monte Carlo (CTQMC) for impurity
Fully self-consistent in charge density ρ, chemical potential μ, impurity levels Eimp, hybridization Δ, and self-energy Σ.
Calculations are done on imaginary frequency ω axis, and analytically continued to real axis.
No down folding, fully self-consistent
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Haule
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Continuous Time Quantum Monte Carlo (CTQMC)QMC over Feynman diagrams
Imaginary time (frequency)
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Haule
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CTQMC
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β 0
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Histogram of number of kinks on Feynman diagrams
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300K
2000K
Number of kinks10000 500
V/V0=1, High Spin
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Experimental evidence of metallization at high P and T
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Ohta, Cohen, et al., PRL 2012Kenji Ohta, Katsuya Shimizu, Osaka
University, Yasuo Ohishi, Japan Synchrotron Radiation Research Institute, Kei Hirose, Tokyo Institute of Technology
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FeO Density of States
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Ohta et al., 2011
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DC conductivity versus pressure
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DMFT orbital occupancy transition (HS-LS crossover)
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Using experimental equation of state: from Fischer et al. EPSL 2011
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Spectral Function A(k,ω)
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V=405 au, V/V0=0.75, 68 GPa 300K V=405 au, V/V0=0.75, 88 GPa 2000K
Low spin insulator -> low spin metal
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High spin at low P
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V=540 au, V/V0=1
eg2 t2g4HS
d5 d7
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Spin fluctuations metallization
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V=405 au, V/V0=0.75, 68 GPa 300K V=405 au, V/V0=0.75, 88 GPa 2000K
eg0 t2g6
eg2 t2g4
LS
HS
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FeO phase diagram 1/12
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Ohta, Cohen, et al., PRL, 2012
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A new kind of metal in the deep Earth - Worldnews.comarticle.wn.com/view/ A_new_kind_of_metal_in_the_deep_Earth/Dec 19, 2011 – Read full article. Back to 'A new kind of metal in the deep Earth' .... 10 years ago, Ronald Cohen had made a name for himself in private equity.
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Summary
• DFT-DMFT computations show metallization in FeO at high P and T– Temperature is crucial.– Metallization is due to fluctuations between high-and
low-spin states. – Self-consistency is crucial.– Excellent agreement with experiment.
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