spin transition in ferrous iron in mgsio 3 perovskite under pressure koichiro umemoto spin...
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Spin transition in ferrous iron in MgSiO3 perovskite under pressure
Koichiro Umemoto
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+
Minnesota Supercomputing Institute and Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Acknowledgments• Supported by NSF/EAR-0135533, EAR-0230319, ITR-0426757 (VLab)
• Computations were performed at Minnesota Supercomputing Institute
and Indiana University‘s BigRed system
Collabolators• Renata Wentzcovitch (University of Minnesota)
• Yonggang Yu (University of Minnesota)
• Ryan Requist (Friedrich Alexandre University, Germany)
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.
First-principles calculations
• 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
• R. E. Cohen et al., Science 275, 654 (1997)
FeSiO3 : HS-LS transition in Fe2+ at 1 TPa
This study will investigate the spin transition in Fe2+ with effects of Fe concentration and structural and magnetic ordering.
• 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-L
S transitions in Fe2+ and Fe3+ at 130-145 GPa and 60-160 GPa, respectively.
Spin transition of Fe in MgSiO3 pv
According to these first-principles studies, Fe3+ is responsible for spin transition in the lower mantle pressure range.
Method
LDA (Ceperlay-Alder) and GGA (Perdew-Burke-Ernzerhof)
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)
12.5% 25%
50% 75% 100%
Atomic configurations of Fe and Mg
: Fe : Mg
40 atoms 20 atoms
20 atoms 20 atoms 20 atoms
The largest distance between Fe atoms in the smallest unit cell for each Fe concentration.
High-spin state: Ferromagnetic
Fe 6.25%
80 atoms
Effect of Fe concentration
-0.02
0
0.02
0.04
0.06
0 20 40 60 80 100 120 140
P (GPa)
Fe 12.5%
LS
IS
HS
H(R
y/F
e)
Spin transition
Calculated enthalpies w.r.t. the HS stateLDA
• Spin transition from HS (4B/Fe) to LS (0B/Fe)• No transition to Intermediate spin state (2B/Fe)
HS: 4B/Fe
IS: 2B/Fe
LS: 0B/Fe
Fe concentration (%)
Tra
nsiti
on P
ress
ure
(GP
a)HS(FM)-LS transition in Fe2+
Displacement of A-site Fe atom by spin transition
2.186 Å
1.869
1.918
2.186
2.060 1.878
2.0601.878
1.830
1.781
1.855
2.561
2.416
1.943
1.9031.765
HS LS
Number: Fe-O bond length (Å) : Fe : O
Fe 12.5%, 120 GPa, LDA
Displacement of A-site Fe atom by spin transition
HS LS
: Fe : O
Fe 12.5%, 120 GPa, LDA
Bicapped trigonal prism (8-coordinated Fe)
Distorted octahedron (6-coordinated Fe)
DO
S (
stat
es/e
V/s
pin/
Fe)
Electronic DOS at 120 GPa (LDA)
HS LS
z2,yz,xyxz x2-y2
xy
z2, yzxz
x2-y2
xz,xy,yz x2-y2, z2
LS: t2g and eg-derived state, wider gap (blue shift)
Effect of ordering
Fe 50% (Fe0.5Mg0.5SiO3)
: Fe : Mg
• Atomic ordering
• Magnetic ordering for HS state: Ferro- and Antiferro-magnetic
20 atoms 20 atoms 20 atoms 40 atoms 40 atoms
AFM1<AFM2AFM2<AFM3<AFM1AFM2~<AFM1AFM1<AFM2AFM1<AFM2H:
• Spin ordering for AFM-HS states
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 20 40 60 80 100 120 140
P (GPa)
HS-FM Fe0.5Mg0.5SiO3 PV (LDA-CA, 3s,3p:valence)
Conf.4
Conf.3
Conf.1
Conf.2
Conf.5
FM Fe0.5Mg0.5SiO3 (LDA)H
(R
y/F
e 0.5M
g 0.5S
iO3)
-0.001
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0 20 40 60 80 100 120 140P (GPa)
HS1_AFM1
HS4_AFM2
HS2_AFM1
HS3_AFM2
HS5_AFM1
AFM Fe0.5Mg0.5SiO3 (LDA)H
(R
y/F
e 0.5M
g 0.5S
iO3)
Conf 1
Conf 2
Conf 3
Conf 5
Conf 4
0
0.002
0.004
0.006
0.008
0.01
0 20 40 60 80 100 120 140
P (GPa)
LS Fe0.5Mg0.5SiO3 PV (LDA-CA, 3s&3p:valence)
Conf.4
Conf.3
Conf.1
Conf.2
LS Fe0.5Mg0.5SiO3 (LDA)H
(R
y/F
e 0.5M
g 0.5S
iO3)
-0.004
-0.002
0
0.002
0.004
0 20 40 60 80 100 120 140
P (GPa)
HS1_AFM1
HS4_FM
HS4_AFM2
HS3_FM
LS4
HS-LS transition in Fe0.5Mg0.5SiO3 (LDA)H
(R
y/F
e 0.5M
g 0.5S
iO3)
Conf4_FMConf3_FM
Conf4_AFM
Conf1_AFM
Conf4_LS
Conf. 4
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.
80 atoms/unit cell2 Fe + 14 Mg
Fe/Mg configurations in Fe0.125Mg0.875SiO3 (12.5% Fe)
160 atoms/unit cell4 Fe + 28 Mg
80 atoms/unit cell2 Fe + 14 Mg
80 atoms/unit cell2 Fe + 14 Mg
similar to Conf4 in Fe50% similar to Conf3 in Fe50% similar to Conf5 in Fe50%
-1104.80
-1104.79
-1104.78
-1104.77
-1104.76
-1104.75
-1104.74
-1104.73
-1104.72
1 2 3 4 5 6 7 8 9 10 11 12
Configuration
LS
AFM
FM
Enthalpies of Fe0.125Mg0.875SiO3 at 0 GPa (LDA)
~0.03 Ry/Fe
~0.01Ry/Fe
Enthalpies of Fe0.125Mg0.875SiO3 at 150 GPa (LDA)
1 2 3 4 5 6 7 8 9 10 11 12
Configuration
LS
AFM
FM
-1086.31
-1086.30
-1086.29
-1086.28
-1086.27
-1086.26
-1086.25
-1086.24
-1086.23
Conf 10 is the lowest-enthalpy configuration for AFM-HS and LS.
~0.04Ry/Fe
~0.02Ry/Fe
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0 20 40 60 80 100 120 140
HS-LS transition in Fe0.125Mg0.875SiO3 (LDA)
LS10
AFM10
FM10
FM11
P (GPa)
H (
Ry/
Fe 0
.12
5M
g 0.8
75S
iO3)
56 GPa
Fe concentration (%)
Tra
nsiti
on P
ress
ure
(GP
a)HS-LS transition in Fe2+
With Fe-(110) plane configurations
Fe concentration (%)
Tra
nsiti
on P
ress
ure
(GP
a)HS-LS transition in Fe2+
With separated-iron configurationsHighest transition pressure
With Fe-plane configurationsLowest transition pressure
50
60
70
80
90
100
110
0 1 2 3 4 5 6 7 8 9 10 11 12Configuration
Configuration vs HS-LS transition pressure in Fe0.125Mg0.875SiO3 (LDA)
With separated-iron configurations
With Fe-plane configurations
Possibility of gradual spin transition in Fe2+ at the A site
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.
Conf10 LS
EF
0
4
8
12
16
-2 0 2 4 6 8
Energy (eV)
Conf10 AFM
EF
EF
Conf0 FM
0
4
8
12
16
EF
Conf0 LS
-2 0 2 4 6 8
Energy (eV)
Electronic DOS of Fe 12.5% at 150 GPa (LDA)With separated-iron configuration With Fe-plane configuration
FM
LS
AFM
LS
Summary• FexMg1-xSiO3 shows tendency to display atomic and magnetic (AF
M) order at 0 K. This tendency decreases with temperature.
• Spin transition in Fe2+ occurs at 0 K in the pressure range found e
xperimentally, 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 Fe‘s are close to each other a
nd they are on the (110) plane, the spin transition pressure is the lo
west. This is consistent with the transition pressure dependence on
Fe concentration.
• In the LS state, electronic structure of Fe at the A site becomes si
milar to that of Fe at the octahedron (t2g and eg-derived states) with
a large gap.
-0.6
-0.55
-0.5
-0.45
-0.4
-0.35
-0.3
0 20 40 60 80 100 120 140
P (GPa)
Volume difference of Fe 12.5 % (LDA)
Conf.10
Conf. 0
-1.5
-1
-0.5
0
0.5
1
0 20 40 60 80 100 120 140
P (GPa)
Bulk modulus difference of Fe 12.5 % (LDA)
Conf.10
Conf. 0
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
0 20 40 60 80 100 120 140P (GPa)
Volume difference of Fe 12.5 % (LDA)
Conf.10
Conf. 0
Spin transition of Fe in MgSiO3 pvExperiments
• 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
• 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
• R. E. Cohen et al., Science 275, 654 (1997) FeSiO3 : HS-LS transition in Fe2+ at 1 TPa
This study will investigate the spin transition in Fe2+ with effects of Fe concentration and structural and magnetic ordering.
• 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 transi
tions in Fe2+ and Fe3+ at 130-145 GPa and 60-160 GPa, respectively.
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0 40 80 120 0 40 80 120 0 40 80 120 0 40 80 120 0 40 80 120
Conf1 Conf2 Conf3 Conf4 Conf5
AFM1 AFM1 AFM1 AFM1 AFM1
AFM2
AFM2
AFM2
AFM2
AFM2
AFM3
P (GPa)
H (
Ry/
f.u.
)
LDA-CA, 3s&3p:valence