Spin transition in ferrous iron in MgSiO 3 perovskite under pressure Koichiro Umemoto  Spin transition of Fe 2+ Displacement of low-spin Fe Change of electronic structure  Transition pressure dependence on: Fe concentration Fe configuration  Gradual spin transition of Fe 2+ Minnesota Supercomputing Institute and Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA

Acknowledgments Supported by NSF/EAR , EAR , ITR (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 MgSiO 3 pv Experiments J. Badro et al., Science 305, 383 (2004) (Fe 0.1 Mg 0.9 )SiO 3 Two distinct spin transitions at 70 GPa (HS-mixed S) and 120 GPa (mixed S-LS) J. Li et al., PNAS 101, (2004) (Fe 0.09 Mg 0.92 )SiO 3 Gradual spin transition at wide pressure range up to 100 GPa intermediate spin states for Fe 2+ at A site, Fe 3+ at A and B sites J. Jackson et al., Am. Mineral. 90, 199 (2005) (Fe 0.1 Mg 0.9 )SiO 3 Continuous spin transition in Fe 3+ ends around 70 GPa.

First-principles calculations Li Li et al., Geophys. Res. Lett. 32, L17307 (2005) (FeMg 15 )(AlSi 15 )O 48 : HS-LS transition in Fe 3+ at GPa F. Zhang and A. R. Oganov, Earth Planet. Sci. Lett. 249, 436 (2006) (FeMg 31 )(FeSi 31 )O 96 : HS-LS transition in Fe 3+ at 76 GPa R. E. Cohen et al., Science 275, 654 (1997) FeSiO 3 : HS-LS transition in Fe 2+ at 1 TPa This study will investigate the spin transition in Fe 2+ with effects of Fe concentration and structural and magnetic ordering. S. Stackhouse et al., Earth Planet. Sci. Lett. 253, 282 (2007) (Mg Fe ) SiO 3, (Mg Fe )SiO 3, (Mg Fe )(Si Fe )O 3 : HS-LS transitions in Fe 2+ and Fe 3+ at GPa and GPa, respectively. Spin transition of Fe in MgSiO 3 pv According to these first-principles studies, Fe 3+ 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 (

12.5%25% 50% 75%100% Atomic configurations of Fe and Mg : Fe: Mg 40 atoms20 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

 H(Ry/Fe) Spin transition Calculated enthalpies w.r.t. the HS state LDA Spin transition from HS (4  B /Fe) to LS (0  B /Fe) No transition to Intermediate spin state (2  B /Fe) HS: 4  B /Fe IS: 2  B /Fe LS: 0  B /Fe

Fe concentration (%) Transition Pressure (GPa) HS(FM)-LS transition in Fe 2+

Displacement of A-site Fe atom by spin transition Å HSLS Number: Fe-O bond length ( Å ) : Fe: O Fe 12.5%, 120 GPa, LDA

Displacement of A-site Fe atom by spin transition HSLS : Fe: O Fe 12.5%, 120 GPa, LDA Bicapped trigonal prism (8-coordinated Fe) Distorted octahedron (6-coordinated Fe)

DOS (states/eV/spin/Fe) Electronic DOS at 120 GPa (LDA) HS LS z 2,yz,xy xz x 2 -y 2 xy z 2, yz xz x 2 -y 2 xz,xy,yzx 2 -y 2, z 2 LS: t 2g and e g -derived state, wider gap (blue shift)

Effect of ordering Fe 50% (Fe 0.5 Mg 0.5 SiO 3 ) : Fe: Mg Atomic ordering Magnetic ordering for HS state: Ferro- and Antiferro-magnetic 20 atoms 40 atoms

AFM1<AFM2AFM2<AFM3<AFM1 AFM2~<AFM1 AFM1<AFM2 H: Spin ordering for AFM-HS states

FM Fe 0.5 Mg 0.5 SiO 3 (LDA)  H (Ry/Fe 0.5 Mg 0.5 SiO 3 )

AFM Fe 0.5 Mg 0.5 SiO 3 (LDA)  H (Ry/Fe 0.5 Mg 0.5 SiO 3 ) Conf 1 Conf 2 Conf 3 Conf 5 Conf 4

LS Fe 0.5 Mg 0.5 SiO 3 (LDA)  H (Ry/Fe 0.5 Mg 0.5 SiO 3 )

HS-LS transition in Fe 0.5 Mg 0.5 SiO 3 (LDA)  H (Ry/Fe 0.5 Mg 0.5 SiO 3 ) Conf4_FM Conf3_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 cell 2 Fe + 14 Mg Fe/Mg configurations in Fe Mg SiO 3 (12.5% Fe)

160 atoms/unit cell 4 Fe + 28 Mg 80 atoms/unit cell 2 Fe + 14 Mg 80 atoms/unit cell 2 Fe + 14 Mg similar to Conf4 in Fe50%similar to Conf3 in Fe50% similar to Conf5 in Fe50%

Enthalpies of Fe Mg SiO 3 at 0 GPa (LDA) ~0.03 Ry/Fe ~0.01 Ry/Fe

Enthalpies of Fe Mg SiO 3 at 150 GPa (LDA) Conf 10 is the lowest-enthalpy configuration for AFM-HS and LS. ~0.04 Ry/Fe ~0.02 Ry/Fe

HS-LS transition in Fe Mg SiO 3 (LDA) LS10 AFM10 FM10 FM11 P (GPa)  H (Ry/Fe Mg SiO 3 ) 56 GPa

Fe concentration (%) Transition Pressure (GPa) HS-LS transition in Fe 2+ With Fe-(110) plane configurations

Fe concentration (%) Transition Pressure (GPa) HS-LS transition in Fe 2+ With separated-iron configurations Highest transition pressure With Fe-plane configurations Lowest transition pressure

Configuration vs HS-LS transition pressure in Fe Mg SiO 3 (LDA) With separated-iron configurations With Fe-plane configurations

Possibility of gradual spin transition in Fe 2+ 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.

Electronic DOS of Fe 12.5% at 150 GPa (LDA) With separated-iron configurationWith Fe-plane configuration FM LS AFM LS

Summary Fe x Mg 1-x SiO 3 shows tendency to display atomic and magnetic (AFM) order at 0 K. This tendency decreases with temperature. Spin transition in Fe 2+ 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 Fe ‘ s 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 (t 2g and e g -derived states) with a large gap.

Spin transition of Fe in MgSiO 3 pv Experiments J. Badro et al., Science 305, 383 (2004) (Fe 0.1 Mg 0.9 )SiO 3 Two distinct spin transitions at 70 GPa (HS-mixed S) and 120 GPa (mixed S-LS) J. Li et al., PNAS 101, (2004) (Fe 0.09 Mg 0.92 )SiO 3 Spin transition at wide pressure range up to 100 GPa intermediate spin states for Fe 2+ at A site, Fe 3+ at A and B sites J. Jackson et al., Am. Mineral. 90, 199 (2005) (Fe 0.1 Mg 0.9 )SiO 3 Continuous spin transition in Fe 3+ ends around 70 GPa. Calculations Li Li et al., Geophys. Res. Lett. 32, L17307 (2005) (FeMg 15 )(AlSi 15 )O 48 : HS-LS transition in Fe 3+ at GPa F. Zhang and A. R. Oganov, Earth Planet. Sci. Lett. 249, 436 (2006) (FeMg 31 )(FeSi 31 )O 96 : HS-LS transition in Fe 3+ at 76 GPa R. E. Cohen et al., Science 275, 654 (1997) FeSiO 3 : HS-LS transition in Fe 2+ at 1 TPa This study will investigate the spin transition in Fe 2+ with effects of Fe concentration and structural and magnetic ordering. S. Stackhouse et al., Earth Planet. Sci. Lett. 253, 282 (2007) (Mg Fe ) SiO 3, (Mg Fe )SiO 3, (Mg Fe )(Si Fe )O 3 : HS-LS transitions in Fe 2+ and Fe 3+ at GPa and GPa, respectively.

P (GPa)  H (Ry/f.u.) LDA-CA, 3s&3p:valence