Viscosity jump in the lower mantle inferred from melting curves of ferropericlase

Convection provides the mechanism behind plate tectonics, which allows oceanic lithosphere to be subducted into the mantle as “slabs” and new rock to be generated by volcanism. Stagnation of subducting slabs and deflection of rising plumes in Earth’s shallow lower mantle have been suggested to result from a viscosity increase at those depths. However, the mechanism for this increase remains elusive. Here, we examine the melting behavior in the MgO–FeO binary system at high pressures using the laser-heated diamond-anvil cell and show that the liquidus and solidus of (MgxFe1−x)O ferropericlase (x = ~0.52–0.98), exhibit a local maximum at ~40 GPa, likely caused by the spin transition of iron. We calculate the relative viscosity profiles of ferropericlase using homologous temperature scaling and find that viscosity increases 10–100 times from ~750 km to ~1000–1250 km, with a smaller decrease at deeper depths, pointing to a single mechanism for slab stagnation and plume deflection.

. e Intensity data of thermal radiation saturated in all four wavelengths. Temperature calculated by the power ratio used for Fp800180GA and Fp800180GB and the inverse modeling T m of Fp800180GB. f The chemical composition of the melt is estimated from the degree of melting which is determined by the areas of coexisting solid and melt from the optical images. g The melt is too small (< 1 μm) to measure precisely using WDS. In order to get a estimate of the composition, we compare the melt and (Mg 0.09 Fe 0.81 )O under BSE. The melt tends to be "brighter" than (Mg 0.09 Fe 0.81 )O, which indicates that it is more iron-rich than (Mg 0.09 Fe 0.81 )O. Table 2. Best-fitting thermodynamic parameters using the ideal solution model. Uncertainties in pressure and fitted parameters at each region are shown in parentheses.

Supplementary Note 3: Comparison with linearly extrapolated solidus melting temperatures of ferropericlase
As pointed out in the main text, the solidus temperatures of ferropericlase that we measure are much smaller than those extrapolated by a linear reduction of melting curves of pure MgO and FeO by up to ~3000 K. We plot the temperature differences in

Supplementary Note 4: Interpretation of local maxima in melting temperatures
In order to interpret the melting temperature variations in ferropericlase, we look to the spin transition of Fe 2+ in (Mg,Fe)O. While it is unknown how the spin transition in iron affects the melting of (Mg,Fe)O, the spin transition has been found to influence many physical, chemical and transport properties including density 21 , elastic moduli 21 , element partitioning 22 and thermal/electrical conductivities 23,24 . Nevertheless, we can make a qualitative estimate based on Lindemann's law 25 . Lindemann's law provides a simple relationship between the melting temperature and thermo-elastic properties of materials, T m ∝ C / ρ , where C is some combination of elastic moduli and ρ is the density 26,27 . Both experiments and first principles computations have shown that the spin transition softens and densifies (Mg,Fe)O 28,29 . Therefore, we expect that the spin transition tends to lower the melting temperatures based on Lindemann's law. We take (Mg 0.9 Fe 0.10 )O as an example and use the bulk modulus as the elastic constant of interest for simplicity which has been shown to decrease over a broad range (40 -70 GPa) due to the spin transition and reach a local minimum at ~50 GPa 28 . The local minimum bulk modulus is ~220 GPa compared with ~360 GPa if there were no spin transition.
Additionally, the spin transition also increases the density of ferropericlase by ~2.4% in this pressure range 28 . As such, an overall decrease in T m will occur between 40 -70 GPa with the decrease peaking at ~50 GPa. After the mid-point of the spin crossover, the moduli will monotonically increase at values greater than those in the high-spin state, thus setting up a local maximum in the melting curves 28,29 . For Earth-relevant compositions, this local maximum in T m occurs at ~40 GPa based on the spin-state crossover range 3 . Note that the above spin-state crossover pressure range is experimentally obtained at 300 K and so high temperatures may additionally influence this analysis 30,31,32 .
Previous ambient temperature experimental studies suggest that the elasticity of simulations study 30  For the Fe-rich samples, we use MgO as insulation and a pressure media so that we are able to heat, without which, laser heating would be difficult. We find diffusion between the MgO and Fe-rich ferropericlase and therefore do need to take this into account when applying the temperature correction due to wavelength-dependent absorption. Fortunately, in terms of contamination, MgO is fine since it is already part of the binary system we are investigating. Using a noble gas such as argon, for example, may cause lowered melting temperatures due to incorporation in to melts of this composition 2 . Additionally, due to the high temperatures anticipated for ferropericlase melting, we avoided alkali halides due to strong changes in the optical properties, which cause a rapid increase in temperature near their melting points 36 .
Although there exists large temperature gradients within the sample during the laser heating due to the absence pressure media for some experiments, the correction of the effects of temperature gradients on temperature deviation is already incorporated in proper boundaries conditions to obtain the 1D axial temperature gradient. More rigorous temperature profiles can be calculated using the TempDAC code 37 with the knowledge of thermodynamic properties of materials at corresponding conditions. But unfortunately, those parameters are poorly constrained for most Earth materials at elevated pressures and temperatures. Nevertheless, the fine structure of the temperature profile obtained by rigorous thermodynamic simulation is not expected to change the axial temperature distribution within the melt much while it does alter the fine structure of the temperature profile of the solid part. As such, temperature correction will not be influenced largely by the rigorous temperature profile calculation since the hottest part (melt) dominates the effects of the temperature.