1. Spin-state Crossover and Hyperfine Interactions of Iron in MgSiO3 Perovskite
Han Hsu (徐翰)
Department of Chemical Engineering & Materials Science
Materials Research Science & Engineering Center (MRSEC)
University of Minnesota
Good afternoon. I’d like to thank Prof Kim for inviting me over. I am really glad to be here today to give this talk, spin-state crossover in Earth materials and complex oxides.
UMN MRSEC

2. Iron in lower-mantle minerals
Iron-bearing MgSiO3 Pv
(Mg,Fe)O
ferropericlase +
Ferropericlase ~ 20 vol%
Perovskite ~ 75 vol%
Iron is the most abundant transition metal in the Earth, It can incorporate into many minerals, including MgSiO3 Pv, which constitutes 75% of LM, and MgO, which constitute 20% of LS.
Depth: 660 – 2890 km
Pressure: GPa
Temperature: 1900 – 4000 K

3. Spin states of Fe2+ and Fe3+
High spin
Intermediate spin
Low spin
?????????? EC
Fe2+
S = 2
S = 1
S = 0
When iron is incorporated in minerals, its five degenerate 3d orbitals. When the Hund’s exchange energy dominates, which usually happens at low P, the electron spin moment tend to align as much as possible, and the iron is in HS state. When crystal field splitting dominates, which usually happens at high P, Fe is in the LS spin. As the pressure in the Earth increases with the depth, it is possible for iron to undergo a crossover from HS to LS. Does the IS state play any role, or is there an IS state at all? It is highly debated, not only in Fe-bearing minerals, but also in other transition-metal oxides. EC
Fe3+
S = 5/2
S = 3/2
S = 1/2
Compression

4. Spin matters!
Crowhurst et al., Science (2008)
Wentzcovitch et al., PNAS USA (2009)
A HS-LS crossover in (Mg,Fe)O directly affects its structural, elastic, optical and conducting properties.
T. Tsuchiya et al, PRL (2006) J. Crowhurst et al., Science (2008) A. F. Goncharov et al., Science (2006) J.-F. Lin et al., GRL (2007) R. M. Wentzcovitch et al., PNAS (2009) Z. Wu et al., PRB (2009) and many more…
K (GPa)
So, iron spin state changes with pressure. The question is, does it matter? The answer is yes. After lots of theoretical and experimental studies, we relized that iron in (Mg,Fe)O undergoes a HS-LS crossover, and this crossover directly affects the strucutral,. … properties of (Mg,Fe)O.

5. Iron-bearing MgSiO3 (Pbnm)
Fe2+  (Mg,Fe)SiO3
Fe3+  (Mg,Fe)(Si,Fe)O3
Unfortunately, the spin-state crossover in iron-bearing Pv has been highly controversial. This controversy mainly arises from two reasons. One is the complexity of this mineral. Iron incorporated in Pv can be ferrous, which substitute Mg at the A site. It can be ferric, which substitute bohh Mg and Si. So we have to treat three different iron, and each of them can have three spin states.
Most abundant mineral (~ 75 vol%), with ~ 10% Fe.
Fe3+/Fe2+ not well characterized (Fe3+/∑Fe = )
Controversial spin-state crossover

6. XES and Mössbauer spectra
Badro et al., Science (2004)
McCammon et al., Nature Geosci. (2008)
Unfortunately, it is really difficult to directly measure current iron spin state. Experimental techniques, such as XES and Mossbauer spectroscopy, do tell us that some crossover is occurring. But they do not tell us which iron, ferrous or ferric, A-site B-site is undergoing what kind of crossover, HS-LS, or HS-IS-LS.
Catalli et al., EPSL (2010)

7. QS of Fe in MgSiO3 Pv (Mg,Fe)SiO3 (Mg,Fe)(Si,Fe)O3
So how are we gonna solve this problem with first-principles calcualtions? Our strategy is quite straight forward. We try to find out as many spin states as we can, calculate their QS, and compare with experiments. For Fe2+.we find LS., IS, and two distinct HS states. For Fe3+, we als find these spin at both A and B site, except for IS and at the B-site. By comparing with experiments, we can easily see that as the pressure increases, Fe2+ changes is QS, not not spin. Fe3+ does. But which ferric iron? We can’t tell just based on QS. Further information is needed.
Exp McCammon et al., Nature Geosci. (2008); Jackson et al., Am. Mineral. (2005); Catalli et al., EPSL (2010).
Hsu et al., PRL (2011)

8. (Mg,Fe)SiO3 High-QS Low-QS Spin-down nx2-y2 = 0.45 nxy = 0.60
24 GPa
15 GPa
Spin-down nx2-y2 = nxy = 0.60
Spin-down nyz = 0.97
Hsu et al., EPSL (2010)

9. (Mg,Fe)(Si,Fe)O3 Self-consistent USC (eV) Hsu et al., PRL (2011)
So we calculate the equation of state of each possible state and compare their enthalpies. We adopt different methods, LDA+U, GGA+U, a trial U or self-consitent U. They all give the same result, qualitatively. At low P, both A and B site iron are Hs. As P increases, the B-site ferric rion undergoes a HS-LS crossover while A-site Ferric iron remains in HS state.

10. Anomaly in (Mg,Fe)(Si,Fe)O3
Our calclations also predict that accompanying with the B-sitate spin-state crossover, we have a volume reduction, in good agreement with experimental data. This volume reduction leads to a anomaloues sofeting in bulk moduls. This anomalie is still prominent at 2000 K. This result implies that spin-sttate crossover of B-site ferric iron can be a possible source of seismic anomaly.
Hsu et al., PRL (2011)

11. Iron-bearing MgSiO3 Pv Ferrous iron in (Mg,Fe)SiO3
- HS in the lower-mantle pressure range ( GPa)
- At ~30 GPa, a crossover from QS = 2.4 to 3.5 mm/s
- Neither HS-LS nor HS-IS crossover
Ferric iron in (Mg,Fe)(Si,Fe)O3
- A-site iron remains in HS state in GPa.
- B-site iron undergoes a HS-LS crossover in GPa.
- B-site HS-LS crossover may lead to seismic anomalies.

12. Thank you!!! Physics Today May 2011 (pp. 12)
Physical Review Letters Vol. 106 Iss. 11

13. Future work Fe-bearing MgSiO3 post perovskite
Fe with QS= 4.0 mm/s IS state? Lin et al., Nature (2008)