Calculations clarify the role of minerals’ electron spins in Earth’s mantle

When a transition-metal compound is subject to high pressure, its electronic spin state can change, which in turn can change its material properties. That spin-state crossover is of geophysical relevance because of the iron-bearing minerals in Earth’s mantle and because material properties affect the speed of seismic waves. But the most abundant mantle mineral—Fe-bearing magnesium silicate perovskite (Pv)—is a challenge to study, because it contains three nonequivalent types of Fe atom.

Experiments on spin states under pressure probe the electron configuration only indirectly, so computational studies are necessary to resolve experimental ambiguities and to connect measurements with the correct interpretations and implications. Researchers led by Renata Wentzcovitch (University of Minnesota) have now done a computational study of Fe atoms in Pv. ¹ They found that one of the three types of Fe undergoes a spin-state crossover, which has a significant effect on seismic waves and on mantle convection.

Go for a spin

Spin-state crossover arises from the behavior of electrons in a transition metal’s partially filled d subshells. In an isolated atom, all five d orbitals are degenerate, but the degeneracy is lifted in the anisotropic environment of a crystal. For example, in an octahedral complex, as shown in figure 1, the two orbitals that point directly at the surrounding atoms are higher in energy than the three that point between the atoms. When that crystal-field splitting is not too great, the d electrons find it energetically favorable to spread out among the orbitals so their spins can align. Putting the material under pressure tends to increase the splitting; when it becomes great enough, the electrons tend instead to fill the lower-energy orbitals before occupying any of the higher-energy ones. Because the spin crossover involves the migration of electrons between distinguishable orbitals, rather than being just a spin flip, it can noticeably affect the length and strength of chemical bonds.

Iron in Pv can be either ferrous (Fe²⁺) or ferric (Fe³⁺). Ferrous Fe can replace Mg in the crystal structure, and ferric Fe can replace either Mg or silicon. Ferric Fe has five d electrons, so its spin state, as shown in figure 1, can change between S = 5⁄2 and S = 1⁄2. Ferrous Fe has six d electrons, so it can undergo a crossover from spin S = 2 to S = 0.

Ferrous wheel

The principal experimental techniques to study spin-state crossover are Mössbauer spectroscopy and x-ray spectroscopy on laboratory samples. Both techniques probe not the electrons but the Fe nuclear energy levels, which are affected by the electric field gradient at the nucleus and thus by the electron configuration. In 2008 two experimental groups studying ferrous Fe in Pv found a crossover between two electric field gradients that were too high to result from the low-spin, S = 0 configuration. ² The experimenters thought, then, that they were seeing a crossover between high spin (S = 2) and intermediate spin (S = 1). But according to theory, such a spin-state change should be impossible.

Using techniques pioneered by Wentzcovitch, Matteo Cococcioni, and Peter Blaha, the computational team resolved the mystery. ³ The change in the electric field gradient, they found, was due not to a spin-state crossover but instead to a structural change in which an Fe atom shifts position within a cage of surrounding oxygen atoms. The d electrons remain in the high-spin state all the while.

Ferric crossover

The situation with ferric Fe in Pv is more complicated because it can occupy two nonequivalent sites in the crystal lattice. Last year an experimental study, at odds with the computational studies to date and with other experiments, found that ferric Fe that replaces Si undergoes a spin-state crossover between 50 and 60 GPa (equivalent to subterranean depths of 1400–1700 km), and that ferric Fe that replaces Mg remains in the high-spin state at all pressures relevant to Earth’s mantle. ⁴ Using the same method they’d applied to ferrous Fe, Wentzcovitch and colleagues verified that interpretation unambiguously, and they explored its geophysical consequences. ¹

The team found that for ferric Fe on the Si site, the change from S = 5⁄2 to S = 1⁄2 causes the unit cell to shrink in volume by about 1%. And the spin-state crossover isn’t abrupt as a function of pressure; at nonzero temperature, there is a range of pressures over which high-spin and low-spin unit cells coexist. At those pressures, which in Earth’s mantle correspond to depths from about 1000 km to 2200 km, the material is significantly more compressible than it would be in the absence of a crossover, because it’s relatively easy to nudge a few more unit cells into the low-spin state. As shown in figure 2, the higher the temperature, the wider the crossover’s pressure range, but the less significant the softening. In contrast, for ferric Fe on the Mg site, a change in spin causes almost no change in volume, so even if those Fe atoms did undergo spin-state crossover, it would have little effect.