Spin transition in ferrous iron in MgSiO3 perovskite under pressure

1
Spin transition in ferrous iron in MgSiO3
perovskite under pressure
Koichiro Umemoto
Minnesota Supercomputing Institute and Department
of Chemical Engineering and Materials Science,
University of Minnesota, Minneapolis, MN 55455,
USA

• Spin transition of Fe2
• Displacement of low-spin Fe
• Change of electronic structure
• Transition pressure dependence on
• Fe concentration
• Fe configuration
• Gradual spin transition of Fe2

2

• Collabolators
• Renata Wentzcovitch (University of Minnesota)
• Yonggang Yu (University of Minnesota)
• Ryan Requist (Friedrich Alexandre University,
  Germany)

• Acknowledgments
• Supported by NSF/EAR-0135533, EAR-0230319,
  ITR-0426757 (VLab)
• Computations were performed at Minnesota
  Supercomputing Institute
• and Indiana Universitys BigRed system

3
Spin transition of Fe in MgSiO3 pv
Experiments

• J. Badro et al., Science 305, 383 (2004)
• (Fe0.1Mg0.9)SiO3
• Two distinct spin transitions at 70 GPa
  (HS-mixed S) and 120 GPa (mixed S-LS)

• J. Li et al., PNAS 101, 14027 (2004)
• (Fe0.09Mg0.92)SiO3
• Gradual spin transition at wide pressure range
  up to 100 GPa
• intermediate spin states for Fe2 at A site,
  Fe3 at A and B sites

• J. Jackson et al., Am. Mineral. 90, 199 (2005)
• (Fe0.1Mg0.9)SiO3
• Continuous spin transition in Fe3 ends around
  70 GPa.

4
Spin transition of Fe in MgSiO3 pv
First-principles calculations

• R. E. Cohen et al., Science 275, 654 (1997)
• FeSiO3 HS-LS transition in Fe2 at 1 TPa

• Li Li et al., Geophys. Res. Lett. 32, L17307
  (2005)
• (FeMg15)(AlSi15)O48 HS-LS transition in Fe3
  at 97-126 GPa

• F. Zhang and A. R. Oganov, Earth Planet. Sci.
  Lett. 249, 436 (2006)
• (FeMg31)(FeSi31)O96 HS-LS transition in Fe3
  at 76 GPa

• S. Stackhouse et al., Earth Planet. Sci. Lett.
  253, 282 (2007)
• (Mg0.9375Fe0.0625)SiO3, (Mg0.8750Fe0.1250)SiO3,
  (Mg0.9375Fe0.0625)(Si0.9375Fe0.0625)O3 HS-LS
  transitions in Fe2 and Fe3 at 130-145 GPa and
  60-160 GPa, respectively.

According to these first-principles studies, Fe3
is responsible for spin transition in the lower
mantle pressure range.
This study will investigate the spin transition
in Fe2 with effects of Fe concentration and
structural and magnetic ordering.
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Method

• LDA (Ceperlay-Alder) and GGA (Perdew-Burke-Ernzer
  hof)
• Vanderbilt ultrasoft pseudopotentials for Fe,
  Si, and O
• Von-Barth Car pseudopotential for Mg
• Plane wave cut-off energy 40 Ry
• Variable Cell Shape Molecular Dynamics for
  structural search
• Supercell (up to 160 atoms)
• Quantum-ESPRESSO package (www.pwscf.org)

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Effect of Fe concentration
Atomic configurations of Fe and Mg
The largest distance between Fe atoms in the
smallest unit cell for each Fe concentration.
12.5
25
Fe 6.25
80 atoms
40 atoms
20 atoms
50
75
100
20 atoms
20 atoms
20 atoms
High-spin state Ferromagnetic
Fe
Mg
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Calculated enthalpies w.r.t. the HS state
LDA
HS 4mB/Fe
IS 2mB/Fe
LS 0mB/Fe
DH(Ry/Fe)
Spin transition

• Spin transition from HS (4mB/Fe) to LS (0mB/Fe)
• No transition to Intermediate spin state (2mB/Fe)

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HS(FM)-LS transition in Fe2
Transition Pressure (GPa)
Fe concentration ()
9
Displacement of A-site Fe atom by spin transition
Fe 12.5, 120 GPa, LDA
HS
LS
2.186 Å
1.830
1.878
1.765
2.060
1.903
1.869
1.781
1.918
1.855
1.943
1.878
2.060
2.416
2.186
2.561
Fe
O
Number Fe-O bond length (Å)
10
Displacement of A-site Fe atom by spin transition
Fe 12.5, 120 GPa, LDA
HS
LS
Bicapped trigonal prism (8-coordinated Fe)
Distorted octahedron (6-coordinated Fe)
Fe
O
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Electronic DOS at 120 GPa (LDA)
HS
LS
xz,xy,yz
x2-y2, z2
z2,yz,xy
xz
x2-y2
DOS (states/eV/spin/Fe)
xy
xz
z2, yz
x2-y2

LS t2g and eg-derived state, wider gap (blue
shift)
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Effect of ordering
Fe 50 (Fe0.5Mg0.5SiO3)

• Atomic ordering

20 atoms
20 atoms
20 atoms
40 atoms
40 atoms

• Magnetic ordering for HS state Ferro- and
  Antiferro-magnetic

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• Spin ordering for AFM-HS states

H
AFM1ltAFM2
AFM2ltAFM3ltAFM1
AFM1ltAFM2
AFM1ltAFM2
AFM2ltAFM1
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FM Fe0.5Mg0.5SiO3 (LDA)
DH (Ry/Fe0.5Mg0.5SiO3)
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AFM Fe0.5Mg0.5SiO3 (LDA)
Conf 2
Conf 3
Conf 5
DH (Ry/Fe0.5Mg0.5SiO3)
Conf 4
Conf 1
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LS Fe0.5Mg0.5SiO3 (LDA)
DH (Ry/Fe0.5Mg0.5SiO3)
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HS-LS transition in Fe0.5Mg0.5SiO3 (LDA)
Conf4_FM
Conf3_FM
Conf4_AFM
Conf1_AFM
DH (Ry/Fe0.5Mg0.5SiO3)
Conf. 4
Conf4_LS
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Atomic structure of Configuration 4

• Fe atoms are placed on the (110) plane.
• The same kind of cations prefer to be in the
  same column.

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Fe/Mg configurations in Fe0.125Mg0.875SiO3 (12.5
Fe)
80 atoms/unit cell 2 Fe 14 Mg
20
80 atoms/unit cell 2 Fe 14 Mg
80 atoms/unit cell 2 Fe 14 Mg
160 atoms/unit cell 4 Fe 28 Mg
similar to Conf4 in Fe50
similar to Conf3 in Fe50
similar to Conf5 in Fe50
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Enthalpies of Fe0.125Mg0.875SiO3 at 0 GPa (LDA)
0.03 Ry/Fe
0.01Ry/Fe
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Enthalpies of Fe0.125Mg0.875SiO3 at 150 GPa (LDA)
0.02Ry/Fe
0.04Ry/Fe
Conf 10 is the lowest-enthalpy configuration for
AFM-HS and LS.
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HS-LS transition in Fe0.125Mg0.875SiO3 (LDA)
FM10
FM11
DH (Ry/Fe0.125Mg0.875SiO3)
AFM10
LS10
56 GPa
P (GPa)
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HS-LS transition in Fe2
With Fe-(110) plane configurations
Transition Pressure (GPa)
Fe concentration ()
25
HS-LS transition in Fe2
With separated-iron configurations Highest
transition pressure
Transition Pressure (GPa)
With Fe-plane configurations Lowest transition
pressure
Fe concentration ()
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Configuration vs HS-LS transition pressure in
Fe0.125Mg0.875SiO3 (LDA)
With separated-iron configurations
With Fe-plane configurations
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At high temperature

• All configurations with different transition
  pressures should appear locally.
• Fe planes (conf. 10) with different sizes should
  exist locally. The larger (smaller) size of Fe
  plane gives the lower (higher) spin transition
  pressure.

Possibility of gradual spin transition in Fe2 at
the A site
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Electronic DOS of Fe 12.5 at 150 GPa (LDA)
With separated-iron configuration
With Fe-plane configuration
FM
AFM
LS
LS
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Summary

• FexMg1-xSiO3 shows tendency to display atomic
  and magnetic (AFM) order at 0 K. This tendency
  decreases with temperature.
• Spin transition in Fe2 occurs at 0 K in the
  pressure range found experimentally, i.e., at
  lower mantle pressures. At high temperature, this
  transition should be broad and pass through mixed
  spins states.
• In highly-ordered structures, where Fes are
  close to each other and they are on the (110)
  plane, the spin transition pressure is the
  lowest. This is consistent with the transition
  pressure dependence on Fe concentration.
• In the LS state, electronic structure of Fe at
  the A site becomes similar to that of Fe at the
  octahedron (t2g and eg-derived states) with a
  large gap.

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Spin transition of Fe in MgSiO3 pv
Experiments

• J. Badro et al., Science 305, 383 (2004)
• (Fe0.1Mg0.9)SiO3
• Two distinct spin transitions at 70 GPa
  (HS-mixed S) and 120 GPa (mixed S-LS)

• J. Li et al., PNAS 101, 14027 (2004)
• (Fe0.09Mg0.92)SiO3
• Spin transition at wide pressure range up to 100
  GPa
• intermediate spin states for Fe2 at A site,
  Fe3 at A and B sites

• J. Jackson et al., Am. Mineral. 90, 199 (2005)
• (Fe0.1Mg0.9)SiO3
• Continuous spin transition in Fe3 ends around
  70 GPa.

Calculations

• R. E. Cohen et al., Science 275, 654 (1997)
• FeSiO3 HS-LS transition in Fe2 at 1 TPa

• Li Li et al., Geophys. Res. Lett. 32, L17307
  (2005)
• (FeMg15)(AlSi15)O48 HS-LS transition in Fe3
  at 97-126 GPa

• F. Zhang and A. R. Oganov, Earth Planet. Sci.
  Lett. 249, 436 (2006)
• (FeMg31)(FeSi31)O96 HS-LS transition in Fe3
  at 76 GPa

• S. Stackhouse et al., Earth Planet. Sci. Lett.
  253, 282 (2007)
• (Mg0.9375Fe0.0625)SiO3, (Mg0.8750Fe0.1250)SiO3,
  (Mg0.9375Fe0.0625)(Si0.9375Fe0.0625)O3 HS-LS
  transitions in Fe2 and Fe3 at 130-145 GPa and
  60-160 GPa, respectively.

This study will investigate the spin transition
in Fe2 with effects of Fe concentration and
structural and magnetic ordering.
34
DH (Ry/f.u.)
P (GPa)
LDA-CA, 3s3pvalence