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