Metallized ε-FeOOH and the heterogeneous electrical conductivity structure in the lower mantle

Electrical heterogeneity at the depth of 900-1400 km in Earth’s interior is a key factor to constrain the minor phase composition of the lower mantle. However, prevailing mineralogical models including Fe- or Al-enriched silicates or ferropericlase are insucient to explain the ultra-high electrical conductivity in local areas of subduction slabs. Here, we measure the electrical conductivity of ε-FeOOH up to 61 GPa. A 3-order abrupt jump of electrical conductivity is observed in 45-50 GPa, reaching 1.24±0.19 × 10 3 S/m at 61 GPa. Density mean eld theory simulations suggest that ε-FeOOH undergoes a Mott-type electronic transition, which leads the conduction mechanism to switch from small polaron conduction to free electron conduction. Compared with bridgmanite, ferropericlase and conventional mantle compositional models, the electrical conductivity of the metallic ε-FeOOH is 1-3 orders of magnitude higher. Minor or moderate incorporation of metallic ε-FeOOH into the ambient lower mantle could reproduce the observed electrical heterogeneity derived from geomagnetic data at 900-1400 km depth.


Introduction
The lower mantle occupies more than half of the solid Earth by volume. Its mineral composition has attracted enormous research interests as it holds key to understand the Earth's bulk structure, dynamics and physicochemical properties 1 . Based on mineral physics experiments, the lower mantle is dominated by bridgmanite (Brg) and ferropericlase (Fp) with a small amount of Ca-perovskite 2, 3 . However, recent seismological measurement 4 , electromagnetic tomography 5 and deep diamond inclusion 6 suggest the lower mantle can be locally heterogeneous and thus not fully covered by popular mineralogical models 2,7 .
Using a combination of global three-dimensional (3D) and one-dimensional (1D) induction studies 5,8,9,10,11,12 , pioneers have mapped out the electrical conductivity (EC) pro les and have located a couple of areas with very high EC. For example, Constable and Constable constructed a 1-D conductivity model by Occam smooth inversion and showed the EC values surge to 10 2 S/m at around 1300 km depth in the lower mantle 11 . Those high conductivity regions are observed at depths of 900-1400 km beneath Eastern Africa, South-East Asia and Eurasia in stark contrast to the large low conductivity areas under Australian region, Western Africa, near Japan, North and Central America 5,12 . The high conductivity number, which is almost two orders of magnitude greater than the mean value, agreed with the 1D conductivity pro le obtained with the global earth response and a synthetic 3D model 5 13,14,15,16 , even considering temperature effects 17 .
As a transport property, EC is mainly controlled by pressure, temperature, oxygen fugacity 18 , phase transitions 14,19,20 and is also sensitive to factors like water solubility 21 and partial melting 22 . The large variations of EC in the lower mantle indicate that multiple conductivity mechanisms may co-exist at similar depth. For example, applying high pressure and hydration effect promote the EC of nominal anhydrous olivine by orders of magnitude due to the onset of proton conduction 23 . Wüstite (FeO) enters an exotic metallic state when pressure increases above 70 GPa and temperature is higher than 1900 K 24 . Those observations provide potential mechanisms to explain the electrical conductivity pro les in the transition zone and the lower mantle.
In this work, we focus on the EC of ε-FeOOH, a high-pressure phase found to form solid solution with δ-AlOOH and phase H under the CaCl 2 -type hydroxide 25 . FeOOH is also a major component of band iron formations, which were largely subducted with deep ocean during the Archaean era by plate tectonic process 26 . It is reported that ε-FeOOH is a potential water carrier into the deep mantle in the recycled subduction slabs 27,28 . For its possible minor presence in the lower mantle, we rst measured the EC of ε-FeOOH up to 61 GPa, which is then compared against those of γ-AlOOH (boehmite) and δ-AlOOH to provide a holistic view on the effect of iron. Our in-situ measurements indicate that Fe 3+ in ε-FeOOH metalizes at 45-50 GPa and the electronic transition pushes EC above 10 3 S/m. This is approximately 2 to 2.5 orders of magnitude higher than that of pyrolite or Mid-Ocean Ridge Basalt (MORB) composition and may signi cantly contribute to the high conductivity observed at the corresponding 900-1400 km depth.

Results
The high-pressure phases of ε-FeOOH and δ-AlOOH are synthesized using a large volume multi-anvil press (MAP, see Materials and Methods for details). The pressure-temperature (P-T) conditions for MAP experiments are summarized in Table 1. We conducted a set of MAP experiments to synthesize highpressure samples as well as to constrain the phase stability elds of FeOOH, as shown in Fig. 1. At low pressure (< 7 GPa), FeOOH dehydrates along a steep P/T curve 28,29,30,31 . At higher pressure, our results generally agree with previous MAP results by Yoshino,et al 29 . Also plotted in Fig. 1 are four different subduction slab geotherms from Kirby et al 32 . Although the high-pressure ε-FeOOH dehydrates at the conditions of mantle geotherm and not considered as a superior stable phase to survive all categories of subducting slabs, it bears the P-T conditions of subducting slabs with relatively older age and faster sinking conditions. Once ε-FeOOH descends to deeper mantle, it bene ts from improved thermal stability ( Fig. 1) such that it is capable to carry hydrous and ferric iron enriched fragments deeper. On the other hand, partially dehydrated ε-FeOOH may possibly rehydrate in wet local regions of the mantle transition zone 33 . Therefore, ε-FeOOH is a potential minor phase transporting water down to the lower mantle through cold subducting slabs.  Table 2). The high-pressure in situ EC numbers are calculated by the van der Pauw method 34 (Details in Methods). In Fig. 2, the EC of γ-AlOOH is almost invariantly correlated with pressure, while those of γ-AlOOH and ε-FeOOH climb with pressure.
Speci cally, the EC of ε-FeOOH exhibits an abrupt jump at ~ 45 GPa and reaches 1.24 ± 0.19 × 10 3 S/m at 61.2 GPa. We note that a similar trend of change is also observed in goethite α-FeOOH within similar pressure range 35,36 . In contrast, the EC of γ-AlOOH shows a small kink between 30 and 40 GPa but the increment of EC is less than one order of magnitude.  View software 37 and the tting errors are generally less than 1%. Up to 53.5 GPa, only one semi-circle exists in the high frequency region (inset in Fig. 3a). Below 45 GPa, ε-FeOOH is well de ned as an insulating phase. It has the same small polaron hopping conduction as many other insulating hydroxide or hydrous minerals 38 . At 53.5 GPa, a second semi-circular arc appears in the low frequency region next to the main circle (Fig. 3b). The onset of the second arc is often attributed to grain boundary resistance 39 .
This is previously regarded as a symbol of anisotropy of the charge carrier transportation in the crystallites 40 . While both our x-ray diffraction experiment and literature data indicate that ε-FeOOH is a stable phase throughout the pressure range we have investigated 27,41,42 , the appearance of the second arc coincides with the spin-paring of Fe 42 . The spin transition of Fe may create grain boundaries between the high-spin and low-spin domains. Above the critical pressure, the EC of ε-FeOOH sharply increases and is comparable to metal, for example the metallic FeO 24 and FeH 43 . Upon further compression, the arc at the low-frequency region becomes insigni cant while the high-frequency arc dominates. Such wax and wane imply the progression of spin transition. From 53.5 to 61.7 GPa, it is possible to have two conduction mechanisms competing with each other.
In Fig. 3c, we calculate the relationship between pressure and relaxation frequency for the conduction of grain and grain boundary by tting the impedance spectra with an equivalent-circuit method (Fig. 3a, 3b insert) 44 . The characteristic relaxation frequency (f) can be obtained by the equivalent circuit model of a constant phase element (CPE) using the equations 45 : where R is the resistance (intercept of the semiarc with the imaginary axis); C is the capacitance, C = (Rt) 1/H /R (t is a tting parameter that equals to the capacitance of the CPE when it behaves as an ideal capacitor and H is a value between 0 and 1 depending on the suppression angle of the semi-circle). Similar to EC, f gradually increases with the compression and spikes at 40-45 GPa due to the electronic transition of Fe. At about 52 GPa, f for grain interior signi cantly drops and that for grain boundary emerges. This is consistent with measured EC value which soars at the same pressure range. The lowspin con guration may play a signi cant role in the high EC.
We conducted rst-principles simulation to study the underlying electronic transition. For the strong- In Fig. 4, the Fermi level comes across the valence band when unit cell volume is below 51.27 Å 3 , which is a clear evidence of metallization (band structures in Supplementary Fig. 1-3). The metallization is mainly associated with Fe d orbitals and the Fermi level shifts to the valence bands. This is due to the weakening of the Mott-Hubbard energy. Thermal uctuations between the high-spin and low-spin states of Fe 3+ trigger the insulator-metal transition. The same transition mechanism is also found in BiFeO 3 , which carries ferric iron 50 . It is worth noting that the metallic ε-FeO 2 H is in the low-spin con guration.
Consequently, for low-spin ε-FeOOH, small-polaron hopping model converts to the free electron model that is often found in metal.

Discussion
The jump of EC is absent in Al endmember γ-AlOOH or δ-AlOOH up to 55 GPa. This is reasonable since Al atom has no d electrons in the valence band, thus is unlikely to metalize through a spin transition (Fig. 2). Similar to the incorporation of Mg to wüstite, adding Al to ε-FeOOH is expected to scale down the EC changes during electronic transition. Here, our results on the end members may bracket the upper and lower limits of EC.
For the large-scale electrical structure of the lower mantle, a more comprehensive mineral system should be taken into account. In Fig. 5, we compare the EC of ε-FeOOH with a variety of lower mantle components including Brg, Fp, and mineral phases in MORB compositional model. Also plotted in Fig. 5 are the high and average 1D EC pro le from frequency dependent impedance response functions of the geomagnetic eld by Constable and Constable 11 and Ohta et al. 51 , respectively. When pressure is below 45 GPa, EC numbers from the majority of mineral phases are varying within a modest 1-2 orders of magnitude. One exception is the semiconducting wüstite which leaves a signi cant gap with other compositions. The mineralogy data is generally consistent with geomagnetic models which regard the top later of the lower mantle is relatively homogeneous 5 (Fig. 5). The divergence of EC in different mineral phases above 45 GPa may give rise to the lateral conductivity heterogeneity in the deep lower mantle due to their chemical (phase) heterogeneity. While the major components of the lower mantle like Brg and Fp feature low EC in their insulating phases, ε-FeOOH is among the few phases to establish signi cantly higher EC. ε-FeOOH, owning to the electronic transition, would be a candidate to explain the electrically heterogenous lower mantle.
In Fig. 6, we overlay a synthetic 3D conductivity structure 5 at 1220 km depth on a map of tectonics plates in the South China Sea region 57 . The separation of high EC and low EC regions have an intriguing relation with the plot of tectonic plates. A large portion of the high EC regions are located at the stagnant slab beneath subduction zones, which is enriched in water and ferric iron 58,59 . Mineral physics experiments also support the concentration of Fe 3+ and water content is positively correlated 33 . We also notice in some local regions, the EC values may surge to the level of 10 2 S/m, which is not fully covered by the highly conductive mid-oceanic ridge basalt (MORB) segments. Here, we assume a scenario of mixing ε-FeOOH to a MORB composition at the bottom of subduction slabs. Using the simple averaging theorem 60 , mixing 25% of ε-FeOOH to a MORB composition yields a total EC of 18.1 ± 2.7 S/m at 50 GPa. This is 7 times higher than the average EC pro le shown in Fig. 5 and in line with the higher variation of electrical heterogeneity estimated by the 3D synthetic model 5 in the range of 1200-1400 km depth, e.g.
at the Java subduction slab 61, 62 (Fig. 6). In addition, when hydrous ε-FeOOH meets hotter regions in the mantle, it causes dehydration melting that would further boost the overall transport properties 63 . We therefore suggest that those localized domains with topped 10 2 S/m EC may have incorporated higher concentration of ε-FeOOH, or the enrichment of other superior EC components.
To sum up, high pressure alters the electron conduction mechanism in ε-FeOOH from insulator to metal at about 45 GPa. This transition is accompanied with a nearly 3 orders of magnitude increase in EC. The metallic ε-FeOOH has much higher EC than major lower mantle compositions. Minor to moderate presence of the metallic ε-FeOOH causes the overall EC in a conventional mineral assemblage to approach the high EC pro les of the lower mantle 57 , giving rise to a possible EC heterogeneity in the deep lower mantle. Future studies of seismology and deep diamond inclusions are on-demand to detect and constrain the availability of iron-enriched hydrous materials in the lower mantle.
boehmite samples were checked by electron microscope analysis. The result shows boehmite contains 0.03 wt.% of hematite ( Supplementary Fig. 4). The powder samples were grounded in an agate motor with alcohol for 1 hour.
High pressure synthesis of ε-FeOOH started with grounded goethite powder. The powder was packed in a gold capsule which is rolled in a rhenium heater, and placed in a Kawai-type multi-anvil press at the Geophysical Laboratory, Carnegie Institution of Washington. Synthesis experiments were conducted at 12 or 14 GPa and in the temperature range of 600-1000 o C and kept those conditions for up to 4 hours. Since ε-FeOOH is heated to dehydrate even upon Raman laser, the recovered products were characterized by xray diffraction ( Supplementary Fig. 5 and 6). The grain size of ε-FeOOH is around 50 μm ( Supplementary   Fig. 7). We varied our experimental P-T conditions to constrain the stability elds of ε-FeOOH up to 14 GPa (Fig. 1). δ-AlOOH sample was synthesized in a Kawaii-type multi anvil press available at Jilin University. The starting composition is Al(OH) 3 and the sample was sealed in a platinum capsule during synthesis. The synthesis was performed at 18 GPa and 900 o C, and then held for 2 hours. We measured the Raman spectroscopy of the synthesized sample to con rm that the product is pure.
In situ high-pressure EC measurements using impedance spectroscopy High-pressure EC experiment was performed by a Solartron-1260 AC impedance spectroscopy with frequencies between 0.1 Hz and 10 MHz incorporation with a 300-μm anvil culet symmetrical-style DAC.
A T-301 steel gasket was pre-indented to a thickness of 50 µm then a hole with diameter d = 280 µm was drilled at the center of the indentation and lled in the mixed powder of boron nitride-epoxy. The lled hole was then compressed to ~15 GPa. Afterwards, a 100-µm hole was drilled at the center to act as the insulating sample chamber. Four Pt foils were chosen serving as the electrodes with a thickness of less than 4 μm, which can determine the resistivity of an arbitrary-shaped sample with an even thickness and minimize the resistivity effect from the contact resistance ( Supplementary Fig. 8). To avoid impurities and ensure good electrode contact, no pressure medium was used for the EC measurement.
The thickness (t) of the sample in Table 2 was estimated using a simple interpolation method 64 . We compressed a few standard samples to different pressures (P = 0, 10, 20, 30, 40, 50 GPa respectively) and calibrated the gasket thickness by a Vernier caliper. The sampling results were tted to a parabolic relation between pressure and gasket thickness. We calculated the thickness shrinkage rate as the slope (δ t = dt/dP) of parabolic relation. Using the same gasket material and sample assemblage, the thickness at arbitrary pressure is interpolated by the formula: t(P) = t min + P·δ t where t min is the thickness of the gasket when pressure is fully released in the experiment run. The thickness of the sample is comparable to that of the gasket. The error in thickness includes measured and systematic error, which is estimated to be about 20%.
First principles simulation based on DFT+DMFT

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We rst relaxed the crystal structure of ε-FeOOH using conventional DFT. The simulation was performed by Quantum Espresso version 6.3 (ref. 65 ). The kinetic energy cutoff is 70 Ry for wavefunctions and 600 Ry for charge density. Both lattice parameters and atomic positions were relaxed to the target pressures.
We noticed the crystal structure has symmetric hydrogen bonding at 50 GPa.
To proceed with the electronic structure calculation, we used the DFT + DMFT method as was implemented in the DCore code. A noninteracting GGA Hamiltonian, which includes the Fe 3d and O 2p states, was constructed by the Wannier function projection 66 . The quantum impurity problem was handled by a continuous-time hybridization expansion solver from TRIQS/cthyb 67,68 . The calculation is performed by DCore version 2.1 69 . We used the same set of Coulomb parameters (U = 6 eV and J H = 0.89 eV) for all the structures 47 . All calculations were performed at inverse temperature β = 40 eV -1 (~290 K). Figure 1 Stability elds of FeOOH. Colors of red, blue and yellow correspond to Fe2O3+H2O, ε-FeOOH and α-FeOOH. Dot dashed curves are thermokinetic model results of four slabs representing subducting lithosphere in different trenches by Kirby et al.32. From A to D, slabs are older and faster sinking.

Figure 2
Electrical properties of ε-FeOOH, γ-AlOOH and δ-AlOOH versus pressure at ambient temperature. The EC of ε-FeOOH showed a huge jump at ~45 GPa. The errors were estimated to be ~15%.