Spin crossover d6 ES10

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Spin-state crossover in lower-mantle minerals and lanthanum cobaltite (LaCoO3) Han Hsu (徐翰) Department of Chemical Engineering and Materials Science University of Minnesota, Minneapolis, Minnesota 55455, USA UMN MRSEC

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People Renata Wentzcovitch (CEMS & MRSEC, UMN) Advisor Peter Blaha (TU Wien) APW+lo calculation for the EFG of Fe and Co Matteo Cococcioni (CEMS, UMN) LDA+U method in QUAMTUM ESPRESSO Chris Leighton (CEMS & MRSEC, UMN) Experimental works on LaCoO3

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Outline Spin state of 3d6 ions (e.g. Fe2+ and Co3+) Spin-state crossover and geophysics Pressure-induced spin-state crossover in (Mg,Fe)SiO3 Thermally-induced spin-state crossover in LaCoO3 Summary

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Spin states of 3d6 ions EC EX Low-spin (LS) S = 0 Intermediate-spin (IS) S = 1 High-spin (HS) S = 2 Compression Expansion

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Lower-mantle environment Depth: 600 – 2890 km Pressure: 23 - 135 GPa Temperature: 1900 – 4000 K Ferropericlase ~ 35 vol% Perovskite ~ 62 vol%

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Ferropericlase (Mg,Fe)O Rock salt 17% of iron

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Spin state of (Mg,Fe)O EC EX LS, S = 0 HS, S = 2 Tsuchiya et al. PRL (2006)

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Spin-state crossover and geophysics Tsuchiya et al., PRL (2006) Wentzcovitch et al., PNAS (2009) n: fraction of LS Fe PT = 35 GPa PT ~ 50 GPa

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(Mg,Fe)SiO3 (Pbnm) Most abundant mineral (lower mantle) Fe concentration: ~10%. Spin state of Fe directly may affect the transport, elastic, rheological properties of the host phase, as in Fp. More complicated than (Mg,Fe)O Fe3+/Fe2+ not well characterized. Spin-state crossover is proposed based on XES and Mössbauer spectroscopy, but detail mechanism remains controversial.

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Spin state probed with XES Kβ’ : signature of HS iron. HS  HS/LS (70 GPa)  LS (120 GPa) by Badro et al. HS  IS  LS by Li et al., PNAS (2004). Badro et al., Science (2004)

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Fe2+ with different nuclear QS Two types of Fe2+ QS ≈ 2.4 and 3.5 mm/s Low-QS  high-QS at ~30 GPa Spin state cannot be directly derived from QS HS  IS by McCammon et al. HS remains until 120 GPa by Jackson et al., Am. Mineral. (2005). HS  IS/LS by Li et al., Phys. Chem. Mineral. (2006) McCammon et al., Nature Geosci (2008)

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Hyperfine interaction in 57Fe Nuclear quadrupole moment. For 57Fe, Q = 0.16 barn. EFG tensor Vij ≣ ∂2V/∂xi ∂xj |r=0 Nuclear spin. For 57Fe, I = 3/2 Asymmetry parameter. η≣ (Vxx –Vyy)/ Vzz (usually small)

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Nuclear QS of 57Fe I = 3/2 I = 1/2 Vzz = 0 Vzz > 0 m = ±3/2 m = ±1/2 m = ±1/2 ΔEQ E = Eo+ eQVzz / 4 E = Eo - eQVzz / 4 14.4 keV Quadrupole Splitting (QS): ΔEQ = eQVzz / 2 QS can be measured with Mössbauer spectroscopy EFG (VZZ) can be computed with DFT codes (Wien2K)

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Searching for Fe sites in Pv Finding soft phonon modes in hypothetical cubic HS or LS (Mg0.75Fe0.25)SiO3 perovskite. (GGA) Displace atoms according to the soft modes Structural optimization Does the resultant equilibrium structure have soft phonon modes? Metastable structure is achieved! Metastable iron site is found! YES unstable NO

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(Mg0.75Fe0.25)SiO3 at 0 GPa From the soft mode of Si-O rotation about [100] of cubic Pv From the soft mode of horizontal shift of Mg and octahedra. ΔE = −1.8 mRy/Fe. ΔV/Vo=0.2% Two steps: (1) Si-O rotation about [100]; (2) displace Fe from mirror plane along z-axis HS (3.3) and HS (2.3) differ in Fe position IS Fe (QS=1.4) obtained by starting with HS structure Hsu et al., EPSL (2010)

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Fe site and orbital occupancy Orbital occupancy (↓) nx2-y2 = 0.45; nxy = 0.60 Orbital occupancy (↓) nyz = 0.97 Hsu et al., EPSL (2010)

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EFG and orbital occupancy nxy, nyz, … are the orbital occupancies of dxy, dyz, … etc. nxy, nx2-y2, and nz2 contribute twice more in EFG nx2-y2 = 0.45; nxy = 0.60  higher QS nyz = 0.97  lower QS

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Hubbard U (Mg0.875Fe0.125)SiO3 Hubbard U is computed with linear response theory (Cococcioni & de Gironcoli, PRB 2005) UHS < UIS < ULS in both cases. Hsu et al., EPSL (2010)

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Effect of EXC and Hubbard U Hsu et al., EPSL (2010) 24 GPa 15 GPa 4 GPa 7 GPa QS = 2.4 mm/s QS = 3.5 mm/s (Mg0.875Fe0.125)SiO3 The low UHS further stabilize HS Fe. QS improved by U No HS-to-IS The two competing HS indistinguishable in 10-150 GPa in LDA(+U). No HS-to-IS

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(Mg,Fe)SiO3 Using phonon calculation as a guidance, many metastable iron equilibrium sites in (Mg,Fe)SiO3 were found. In the relevant energy range, Two sites for HS iron (QS = 2.3-2.4 and 3.3-3.5 mm/s) One site for IS iron (QS = 1.4 mm/s) One site for LS iron (QS = 0.8 mm/s) The crossover from low-QS HS to high-QS HS occurs at pressures between 4-25 GPa, depending on the exchange-correlation functional. The “transition” at ~30 GPa observed using Mössbauer spectroscopy is more likely a change of iron position than a spin-state crossover. Decreasing of Kβ’? An open question…..

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Lanthanum cobaltite (LaCoO3) Co O La Two transitions: (1) ~ 80K (2) ~ 500 K Metallic: T > 500 K For 0 < T < 80 K, LS  IS? LS  HS? English et al., PRB (2002) Controversial !! View from [111]

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How controversial? LS  HS LS  IS Bulk calculations

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Hyperfine interaction in 59Co ΔEQ (or vQ) can be measured by Mössbauer or NMR spectroscopy Nuclear quadrupole moment. For 59Co, Q = 0.42 barn. EFG tensor Vij ≣ ∂2V/∂xi ∂xj |r=0 Nuclear spin. For 59Co, I = 7/2 Asymmetry parameter. η≣ (Vxx –Vyy)/ Vzz (usually small)

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Computations LS Isolated IS/HS ion IS or HS (FM) IS or HS (AFM) 40-atom cell for isolated HS or IS ion (12.5%). LDA+U with U = 5 and 8 eV Hsu et al. PRB (2009), EPSL (2010) Lattice constants at T = 5 K, relaxed internal structure. Confirmed by plane-wave pseudopotential (PWscf) and all-electron APW+lo (Wien2k) calculations. EFG calculated with Wien2k.

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EFG and spin state of Co3+ Calculated EFG (1021 V/m2) (MHz) IS: 12.79±1.09 HS: -20.28±2.01 LS: -0.88±0.06 Bose et al., PRB (1982); Itoh & Natori, JPSJ (1995)

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Rhombohedral perovskite Compressed along the [111] direction z-axis≣[111] Doublet eg character Doublet Singlet (3z2-r2)/r2

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Spin state of Co3+ in LaCoO3 EC EX LS IS HS All Co(IS)-O bond have the same length.

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Isolated IS Co3+  Metallic! Isolated IS Co (U = 5 eV) Partially occupied eg-like doublet  half-filled band

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1.6% of IS Co (320-atom cell) Half-fill band (eg-like orbitals) Bandwidth ~0.1 eV

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LaCoO3 With LDA+U method, we have stabilized - single isolated HS or IS Co ion in an array of LS Co - pure HS and IS LaCoO3 in FM and AFM state. EFG is calculated - Computed EFG is not sensitive to Hubbard U - EFG only depends on the spin state of Co Mössbauer or NMR spectroscopy can be used to probe the spin state of Co at early, middle, or late stage of the spin-state crossover. LS  IS is unlikely.

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Summary Using DFT(+U) method, we can stabilize transition-metal ions to the desired spin states. EFG can be calculated. Combination of first-principles calculation and NMR/Mössbauer measurement can clarify the controversial spin-crossover phenomenon in the earth or in the labs.

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THANK YOU!!

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XES of HS: Kβand Kβ’ 3d 3p 1s 3d 3p 1s 3d 3p 1s X-ray is emitted when 3p  1s occurs One 1s hole is created by x-ray absorption

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XES of LS: no satellite 3d 3p 1s 3d 3p 1s 3d 3p 1s One 1s hole is created by x-ray absorption X-ray is emitted when 3p  1s occurs

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