Conductive Mg sub-silicate mantles dictate the dynamo of super-Earths

Conductive Mg sub-silicate mantles dictate the dynamo of super-Earths | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Conductive Mg sub-silicate mantles dictate the dynamo of super-Earths Qingyang Hu, Yanlei Geng, Fangfei Li, Ho-kwang Mao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6920303/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract While bridgmanite and the post-perovskite MgSiO 3 dominate Earth-sized terrestrial mantles, the extreme pressures within larger terrestrial exoplanets may disrupt the archetypal ionic balance of rock-forming elements, forming non-stoichiometric magnesium silicates. Here, we predict the stabilization of magnesium (Mg) sub-silicates such as Mg 2 SiO 3 , Mg 3 SiO 4 and Mg 4 SiO 3 in exoplanetary interiors. These phases are thermodynamically stable as low as 100 GPa, and become gravitationally favorable at multi-megabar pressures, corresponding to the mantle depth of silicate super-Earths. We further reveal that Si atoms donate electrons to localized sites, reducing valence states to 2 + and even anionic 1- and substantially narrowing band gaps. Mg sub-silicates start to form layer in exoplanet with > 2 Earth’s mass, and potentially become the major constituents in the basal mantle of larger super Earth. Their high electrical conductivity creates an electrically conductive layer that suppresses core-mantle electromagnetic coupling and strongly attenuates the dynamo-generated magnetic field, including the massive super-Earth Kepler-725c. Earth and environmental sciences/Planetary science/Exoplanets Earth and environmental sciences/Planetary science/Mineralogy Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The discovery of over 5000 exoplanets with silicate-dominant interiors, such as Gliese 832c, Kepler-452b, and Kepler-10c 1–3 , has revolutionized our understanding of the universe and planetary diversity 4,5 . The interiors of greater sized exoplanets are either primarily silicates (super-Earth), or made of planetary ices (ice giant such as Neptune). For instance, at a typical mass of ~10 M ⊕ (Earth’s mass), some astrophysics preferred the formation of volatile-rich "mini-Neptunes" 6 . However, recent mass–radius–composition analyses suggest that rocky planets with radii below 1.8 Earth’s radius can sustain silicate mantles up to ~20 M ⊕ , with tenuous gaseous or icy envelopes and silicate-dominant interiors 7–10 . In these super-Earths, pressures at the core–mantle boundary (CMB) can surpass 1 TPa with temperatures exceeding 6000 K, giving rise to extended mineralogical compositions, unique mantle structure, and refreshed convective models 11–16 . Understanding the generation of sustainable magnetic fields within such extreme environments is paramount for assessing planetary habitability and evolution. The geodynamo of Earth is driven by turbulent convection in the liquid Fe-Ni outer core 17 , and the magnetic field strength hinges on the convective power and rotation rate 18,19 . For exoplanets and particularly massive super-Earths, the dynamo mechanism may be more complicated. The traditional core-mantle coupling should still be applicable 20 , and may generate even stronger magnetic fields since radioactive heat-producing elements become increasingly more siderophile with planetary size and produce greater internal heat 21 . On the other hand, if long-lived magma oceans exist in large super-Earths’ interiors, the excellent electrical conductivity of molten silicates can also develop magnetic dynamo from the magma oceans 22 . In fact, the appearance of exoplanetary magnetic fields was hinted by the observations of auroral radio emissions and stellar wind-magnetosphere interactions such as HD 189733b, HD 209458b 23 , and YZ Ceti b 24 . However, many mysteries persist regarding the origin, evolution, and specific characteristics of magnetic fields in these exoplanets 25 . The phase transitions and chemistry of magnesium (Mg) silicates hold the key to deciphering these mysteries 26 . On Earth, two pivotal phase boundaries dictate the mantle structure: the 660 km discontinuity, where ringwoodite decomposes into bridgmanite plus ferropericlase to separate the upper and lower mantles 27 , and Earth’s CMB (∼2900 km), where the bridgmanite transforms into a post-perovskite-type (PPv) silicate 15,16 . At Earth’s CMB, vigorous convective geodynamo is driven by the interactions between the liquid outer core and the MgSiO 3 -dominant silicate mantle 17 . However, within super-Earths’ interiors experiencing pressures exceeding 1 TPa, the stability fields of terrestrial mantle minerals are dramatically altered. Under such extreme conditions, theoretical works have suggested the dissociation of MgSiO 3 into Mg 2 SiO 4 , MgO, and MgSi 2 O 5 28,29 . To this end, Mg silicates are generally described by the combination of fixed ionic groups such as MgO and SiO 2 , although sub-oxides such as Mg 3 O 2 and SiO were predicted at multi-megabar regions 30,31 . It is worth noting that these stoichiometric silicate solids retain wide electronic bandgaps, rendering them electrical insulators even at super-Earth mantle pressure-temperature ( P-T )geotherms. Consequently, a mantle dominated by such insulating minerals would inhibit large-scale charge transport in solid mantles and impose negligible electromagnetic coupling, and surface magnetic fields should directly reflect core dynamics. This stands in stark contrast to the anomalous radio signature reported for YZ Ceti b, suggesting that physical processes are still unaccounted for in simplified, fluid-core oriented dynamo frameworks. This work focuses on the dominant Mg-silicates in super-Earth’s interiors. In contrast to stoichiometric silicates, we introduce sub-silicates, in which the rock-forming elements (Mg 2+ , Si 4+ , etc.) shift to lower valence states, featuring intermediate stoichiometry of Mg x SiO 3 ( x > 1). We show that these non-stoichiometric compounds are candidates as major compositions in large exoplanetary interiors, and they play a pivotal role in generating planetary dynamos. Results and Discussion Mg sub-silicates in super-Earth mantles Building upon the conventional MgO-SiO 2 binary system, we added a Mg-endmember and performed an open-ended crystal structure search in the Mg-MgO-SiO 2 ternary system under super‐Earth conditions using the CALYPSO code integrated with density-functional-theory. The goal is to identify stable Mg sub-silicates and assess their thermodynamic stability fields across pressures relevant to super-Earth interiors (100–1500 GPa). We systematically surveyed compositions by varying Mg / Si ratios across three series: Mg x SiO 3 , MgO·Mg y SiO 3 and Mg z SiO 3 ·SiO 2 (with x , y , z > 1). Their formation enthalpies were calculated relative to decomposition into the products of MgO, SiO 2 , and Mg: ∆ H = [ H (Mg a Si b O c ) – ( p ) H (Mg) – ( q ) H (MgO) – ( r ) H (SiO 2 )] / ( a + b + c ) (1) Here, ∆ H represents the formation enthalpy per atom, H denotes the enthalpy of each constituent species, and the coefficients p , q , r are determined by elemental conservation: r = b , q = c – 2 r , p = a – q . Ternary convex hull analyses based on formation enthalpy reveal at least seven Mg sub-silicates at 500 GPa, and five phases at 1500 GPa (Figs. 1 a&b). By integrating our computational results with well-known endmember mineral phases, a thermodynamic phase diagram of sub-silicates was established in Fig. 2 with reference to super-Earth masses. The crystal structures of the predicted stable phases, as well as their phonon properties, are provided in Supplementary Figs. S1, S2 and Table S1 . We should note that literature has explored the Mg-Si-O ternary system up to ~ 3 GPa, yet their focus has concentrated on pseudo-binary (MgO) x ·(SiO 2 ) y compounds (e.g., Mg 2 SiO 4 and MgSi 2 O 5 ) or oxygen-rich compositions (e.g., MgSiO 6 and MgSi 3 O 12 ). In contrast, the Mg-rich regime has received little attention, likely because Mg-rich binary Mg-O compounds (e.g., Mg 2 O and Mg 4 O) are themselves unstable under high pressure, making Mg-rich chemistries appear unlikely 30 , 31 . To refine our predictions, we further filtered the candidate structures based on their density and compatibility with the high-pressure conditions of planetary interiors (details in Supplementary Fig. S3). In principle, only Mg 2 SiO 3 , Mg 4 SiO 3 , and Mg 3 SiO 4 have comparable density to the terrestrial silicate mantle and are likely to exist in super-Earth interiors (Figs. 1 c-e). Coincidently, all three Mg sub-silicates have the same orthorhombic space group of Cmmm . We should note that the ternary phase diagram encodes the thermodynamic relationships among all possible compounds under a given pressure condition and static conditions. In these systems, it is necessary to compare formation enthalpy between different sub-silicates by drawing tie lines. Taking Mg 2 SiO 3 (Fig. 2 , 1500 GPa) for example, its stability is strengthened by connecting the MgSi 2 O 5 - Mg 2 SiO 3 - Mg 5 SiO 4 - Mg 3 O tie line, indicating its robustness and resistance to decomposition in super-Earth interiors (Supplementary Fig. S4). Mantle mineralogy within super-Earth interiors The stabilities of Mg sub-silicates suggest an altered mineralogical model in super-Earths’ interiors. Compared to bridgmanite and post-perovskite MgSiO 3 , the Si-O and Mg-O building blocks and the electronic structures of Mg sub-silicates are prominently changed, featuring unprecedented hypo-coordination geometries (Figs. 1 c-e). For instance, the Cmmm phase of Mg 2 SiO 3 is built upon face-sharing MgO 8 cuboids that interconnect with an unusual e − -SiO 4 polyhedron, where silicon adopts a planar four-coordinated configuration. Coincidentally, the Cmmm -type Mg 3 SiO 4 shares analogous structural characteristics with Mg 2 SiO 3 , providing a structural foundation for the potential formation of solid solutions of MgO x ·MgSiO 3 (0 < x < 1) in deep mantle environments of super-Earths. Despite having the same space group, Mg 4 SiO 3 demonstrates a distinct architecture, in which edge-/plane-sharing MgO 6 trigonal prisms interweave with quasi-1D Si-O chains. This systematic reduction of Si coordination number (6→4→2) reveals a pressure-driven structural evolution of cations, and implies that increasing Mg/Si ratios induce progressive collapse of silicon’s coordination environment from octahedral to planar to linear configurations. We further perform Bader charge analysis to quantify the valence collapse of silicon and its pressure-dependent evolution, and demonstrate that the valence state of Si transitions from + 3.3 in MgSiO 3 , reducing to + 1.9 in Mg 2 SiO 3 or Mg 3 SiO 4 , and eventually inverting to an anionic − 1.1 in Mg 4 SiO 3 (Supplementary Fig. S5). This anomalous reduction in oxidation state results from pressure-mediated asymmetric charge redistribution, and has profound impacts on the electronic properties. For example, Mg 2 SiO 3 and Mg 3 SiO 4 exhibit localized electron density between adjacent Si ions, which is a hallmark of high-pressure electrides (Figs. 3 a&b). In contrast, Mg 4 SiO 3 exhibits an unprecedented electronic topology, characterized by quasi-2D electron-rich domains localized around Si ions. These domains form anisotropic conductive pathways through overlapping Si 3 p orbitals, enabling delocalized electron transport along the [001] crystallographic axis (Fig. 3 c). Moreover, Mg 2 SiO 3 and Mg 3 SiO 4 are narrow-bandgap semiconductors with narrow widths of 0.96 eV and 2.89 eV at 1,000 GPa, respectively. Their Fermi levels are primarily dominated by hybridized O 2 p , Si 3 p , and ISQ states (Figs. 3 d&e). On the other hand, Mg 4 SiO 3 is metal with a nonzero electron density of states at the Fermi level (Fig. 3 f). The evolution of electronic structures suggests that as the Mg / Si ratio increases, the super Earth’s mantles become more electrically conductive, especially in Mg 4 SiO 3 , whose metallic properties provide a pathway for the flow of electric current in the mantle (Fig. 3 g). This potentially suppresses electromagnetic coupling between the mantle and the core. Implications for super-Earth interiors and planetary dynamos The chemical composition ( e.g. the Mg/Si ratio), coupled with extreme pressure and temperature condition, governs the mantle mineralogy of super-Earths and influences both their internal structure and magnetic field dynamics. Whereas solar and bulk Earth compositions favor MgSiO 3 dominated mantles 32 , our thermodynamic calculations reveal a paradigm shift to Mg sub-silicates for super-Earths, whose interiors can reach several megabar pressures. The stability of Mg sub-silicates hinges on the formation free energy (Fig. 2 ), density (Fig. 3 h), and chemical compositions. We therefore derive their high-temperature properties through both quasiharmonic approximation and ab initio molecular dynamics simulations (Supplementary Fig. S6). After confirming the thermal and kinetic stability of Mg x SiO 3 ( x = 2 and 4) and Mg 3 SiO 4 in super-Earths 33 , we calculate their thermal expansions and densities to evaluate the gravitational stability. These factors were combined to established a hierarchical mantle model in Figs. 4 a&b, in which Mg sub-silicates become dominant in the mid-lower portion of super-Earth’s deep mantles. For example, Mg 3 SiO 4 is both energetically and gravitationally at above approximately 280 GPa and 3500 K, which may co-exist with PPv-MgSiO 3 . At 750 GPa, PPv-MgSiO 3 is thought to decompose into Mg 2 SiO 4 and MgSi 2 O 5 , indicated by the green dashed line in Fig. 4 a. Coincidently, the Mg 2 SiO 3 becomes stable and possibly forms a continuous solid solution with Mg 3 SiO 4 . Our computational results suggest that in the range of 1500–4400 km depth, semiconducting Mg 3 SiO 4 and Mg 2 SiO 3 will progressively become the major silicates in super-Earth’s mantles. Although the conductivity of semiconducting Mg sub-silicate ( σ ≈ 10 3 − 10 4 S/m) is lower than that of metallized Mg 4 SiO 3 or liquid Fe cores (Supplementary Fig. S7), the thickness of this layer can exceed thousands of kilometers and enables effective skin-effect attenuation​ of core-generated magnetic fields. Using the skin depth formula: $$\:\delta\:=\:\sqrt{\frac{2}{{\mu\:}_{0}\sigma\:\omega\:}}$$ 2 where \(\:{\mu\:}_{0}\) is the ​​vacuum permeability (4π × 10 − 7 H/m, a fundamental constant), \(\:\sigma\:\) is the electrical conductivity, and \(\:\omega\:\) is the angular frequency of the time-varying magnetic field. For Earth, the internally generated secular-variation field exhibits most of its power on timescales of several years to several decades, corresponding to angular frequencies ω ≈ 10 − 8 to 10 − 7 rad/s 34,35 . Since larger cores are expected to produce slower magnetic variations, the magnetic field frequency ω is estimated in the range of 10 − 9 to 10 − 8 rad/s 36 . This Mg sub-silicates layer yields a skin depth δ of approximately 180 km. We further defined the magnetic field penetration ratio as: $$\:\gamma\:={B}_{surf}/{B}_{core}\approx\:{e}^{-d/\delta\:}$$ 3 Our results suggest that for a thick sub-silicate mantle ( d refers to the thickness, and d > δ ), core-generated magnetic fields will undergo exponential attenuation. This demonstrates that super-Earths with > 2M ⊕ may be influenced by skin effects and experience substantial magnetic damping (Fig. 4 c). For example, at 10 − 9 rad/s, the magnetic-field penetration ratios for 2.5 M ⊕ , 5 M ⊕ , and 7.5 M ⊕ planets are ~ 36%, 1.1%, and 0.18%, respectively. At more realistic magnetic field frequency of 10 − 8 rad s − 1 , over 96% of the field is attenuated for a 2.5 M ⊕ super-Earths. For massive super-Earths (> 10 M ⊕ ; CMB > 1300 GPa) such as Kepler-725c 37 (10 ± 3 M ⊕ ), the stability of Mg 2 SiO 3 and Mg 4 SiO 3 in deep interiors or CMB promotes an interconnected metallized layer. Similar to the previously proposed electrically conducting mantle layer, this metallized rocky layer shield magnetic fields on planetary surfaces through the skin effect 20 , 36 , 38 – 41 . The exceptionally high conductivity (σ ≈ 10 5 ~ 10 6 S/m), combined with the low-frequency nature of planetary magnetic fields, yields extremely small skin depth ( δ shrinks to a few to several tens of kilometers). This results in all time-varying core-generated fields, including the low-frequency dipole, decaying sharply as they propagate through the metallized mantle layer. Similar to the silicate-dominant Earth’s lower mantle 42 , the deep mantles of massive super-Earths are expected to become progressively more reducing toward to the core, favoring more reduced Mg sub-silicates over their stoichiometric counterparts. By varying the fraction of Mg 4 SiO 3 , we estimate efficiency of a conductive mantle layer in shielding the magnetic field. When Mg 4 SiO 3 constitutes ∼50% of the assemblage, a conductive mantle layer with only ~ 260 km thick can achieve ≥ 99% shielding. For even more conservative fractions of 5%, approximately 750 km thick layer is required to reach similar attenuation (Fig. 4 d). Higher frequencies, such as ω ≈ 10 − 8 rad/s, will further enhance the shielding effects (Supplementary Fig. S8). Notably, the interiors of massive super-Earths are easily capable of forming conductive layers several hundred kilometers thick (Supplementary Fig. S9), which will eliminate global dynamo. While recent geochemistry work suggests that the radioactive heat generation in the core of massive super-Earth such as Kepler-725c fuels an amplified dynamo 21 , a layer made of metallized Mg sub-silicates may confine magnetic flux within the core, making its surface magnetic fields nearly undetectable. In summary, our study reveals the high-pressure stability of Mg sub-silicates in super-Earth interiors and demonstrates their profound influence on the attenuation of planetary magnetic fields. In super-Earths exceeding ~ 2M ⊕ , semiconducting or metallized layers in the mid-to-lower mantle induce exponential decay of core-generated magnetic fields through the skin effect, while in more massive super-Earths, fully metallized conductive layers can produce more effective or even near-complete magnetic shielding. These findings might revise the conventional view of magnetic-field evolution in super-Earths and provide a key theoretical framework for understanding the interior structure and magnetic environments of terrestrial exoplanets. Methods Structural searching using CALYPSO We conducted an extensive global structure search for Mg x SiO 3 , Mg y SiO 4 and Mg z Si 2 O 5 ( x , y , z > 1) across the pressure range of 100 – 1500 GPa, employing simulation cells containing 1–8 formula units. To predict stable structures for a given chemical composition, we utilized the CALYPSO code 43 , 44 along with the particle swarm optimization algorithm. This approach is based on ab initio total-energy calculations and implemented within the framework of density functional theory 45 . Geometric optimization and free energy calculation Geometric optimization and electronic property calculations were performed in the framework of the density functional theory within the generalized gradient approximation Perdew − Burke − Ernzerhof 46 in the Vienna Ab initio Simulation Package (VASP) code 47 . The projector-augmented-wave 48 (PAW) method was applied with the appropriate pseudopotentials for magnesium, silicon, and oxygen, reflecting their respective valence electrons: 3 s 2 , 3 s 2 3 p 4 , 2 s 2 2 p 6 . These pseudopotentials were sourced from the VASP library. To achieve convergence within 1 meV/atom, we employed a plane-wave energy cutoff of 600 eV and a Monkhorst-Pack 49 k -point grid with a spacing of 0.02 Å −1 . Charge transfer was analyzed using Bader’s quantum theory 50 . Phonon calculations are carried out using the supercell approach, as implemented in the PHONOPY code 51 . First-principles molecular dynamic Ab initio molecular dynamics (AIMD) simulations were performed using the Vienna Ab initio Simulation Package (VASP) 47 with the projector augmented wave (PAW) method 48 . A [3×1×4] supercell containing 144 atoms was constructed for Mg 2 SiO 3 ( Cmmm ), a [2×1×4] supercell containing 128 atoms was constructed for Mg 3 SiO 4 ( Cmmm ), and a [1×2×4] supercell containing 128 atoms was used for Mg 4 SiO 3 ( Cmmm ). NVT ensemble simulations were carried out using the Nosé–Hoover thermostat 52 , 53 . The DFT calculations were carried out with a Γ-centered k-point and the simulations temperature adopts 7000 K. Each MD simulation step used a time step of 2 fs, with a total of 10000 steps, corresponding to 20 ps of simulation time. Electrical conductivity calculation Electrical conductivity was calculated based on the semi-empirical Boltzmann transport theory. The group velocity of an electron is expressed as: $$\:{v}_{\alpha\:}\left(i,k\right)=\frac{1}{h}\frac{\partial\:{\epsilon\:}_{i,k}}{\partial\:{k}_{\alpha\:}}$$ 4 where \(\:{\epsilon\:}_{i,k}\) denotes the energy eigenvalue at the \(\:i\) band, point \(\:k\) ; \(\:\alpha\:\) means along the direction \(\:\alpha\:\) . The electrical conductivity tensor is given by: $$\:{\sigma\:}_{\alpha\:\beta\:}\left(i,k\right)=\:{e}^{2}{\tau\:}_{i,k}{v}_{\alpha\:}\left(i,k\right){v}_{\beta\:}\left(i,k\right)$$ 5 Here, \(\:{v}_{\alpha\:}\left(i,k\right){v}_{\beta\:}\left(i,k\right)\) is the group velocity; \(\:{\tau\:}_{i,k}\) is the relaxation time. In most cases, \(\:{\tau\:}_{i,k}\) can be treated as a constant without affecting the accuracy of the calculation (relaxation time approximation, RTA). Although the constant relaxation time approximation is limited, it simplifies the carrier transport mechanism within the material. In this case, the electrical conductivity depends on the transport distribution function: $$\:{\sigma\:}_{\alpha\:\beta\:}\left(\epsilon\:\right)=\:\frac{1}{N}\sum\:_{i,k}{\sigma\:}_{\alpha\:\beta\:}(i,k)\frac{\delta\:(\epsilon\:\:-\:{\epsilon\:}_{i,k})}{d\epsilon\:}$$ 6 where \(\:N\) is the number of k points set in the calculation. The electrical conductivity \(\:\sigma\:\) is obtained by integrating the distribution function over the whole space: $$\:{\sigma\:}_{\alpha\:\beta\:}\left(T,\mu\:\right)=\:\frac{1}{{\Omega\:}}\int\:{\sigma\:}_{\alpha\:\beta\:}\left(\epsilon\:\right)\left[-\frac{\partial\:{f}_{\mu\:}\left(T,\epsilon\:\right)}{{\partial\:}_{\epsilon\:}}\right]d\epsilon\:$$ 7 Here, \(\:{f}_{\mu\:}\left(T,\epsilon\:\right)\) is the Fermi-Dirac distribution function, \(\:\mu\:\) is the chemical potential, and \(\:T\) is the temperature. Given a known constant relaxation time, the electrical conductivity at a certain chemical potential and temperature can be obtained from the band structure calculations performed with VASP. In addition, the VASP calculation data were processed using the VASPKIT code 54 . However, due to the extreme pressure and temperature in the context, the calculated electrical conductivity of Mg sub-silicates is discussed in qualitative terms. We define the generalized electrical conductivity as the electrical conductivity (in units of relaxation time) at the Fermi level ( \(\:\mu\:\) = 0). The generalized conductivity curves of these Mg sub-silicates with temperature varying from 1000 K to 7000 K under a pressure of 1000 GPa are presented in Supplementary Fig. S10. Declarations Competing interests The authors declare no competing interests. Author Contributions: Conceptualization: Q.H., Y.G. and H.M. Methodology: Y.G. and Q.H. Investigation: Y.G. and Q.H. Visualization: Y.G. Formal analysis: Y.G. F.L. H.M. and Q.H. Validation: Y.G. and Q.H. Funding acquisition: F.L. and Q.H. Resources: F.L., H.M. and Q.H. Project administration: Q.H. Writing—original draft: Y.G. Writing—review and editing: Y.G. F.L. H.M. and Q.H. ACKNOWLEDGMENTS. Natural Science Foundation of China (NSFC) with grant number T2425016, Jilin Provincial Science and Technology Development Project (SKL202502017JC), and NSFC grants (#42150101, 12274168 and 42472065). The computational work was supported by the High Performance Computing Platform of Nanjing University of Aeronautics and Astronautics. References Wittenmyer RA et al (2014) GJ 832c: A super-earth in the habitable zone. Astrophys J 791:114 Jenkins JM et al (2015) Discovery and validation of Kepler-452b: A 1.6 R ⊕ super earth exoplanet in the habitable zone of a G2 star. Astron J 150:56 Dumusque X et al (2014) The kepler-10 planetary system revisited by harps-n: A hot rocky world and a solid neptune-mass planet. 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J Chem Phys 81:511–519 Hoover WG (1985) Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A 31:1695–1697 Wang V, Xu N, Liu J-C, Tang G, Geng W-T (2021) VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code. Comput Phys Commun 267:108033 Additional Declarations There is NO Competing Interest. Supplementary Files SuppInfo.docx Supplementary Information Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6920303","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":579460185,"identity":"ef8b879d-9481-424f-81c5-b4218a520250","order_by":0,"name":"Qingyang 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05:36:18","extension":"html","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":110660,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/f5f891a17fc253880ea7e8ba.html"},{"id":101184371,"identity":"cc474627-8a35-4037-bab1-02e37db8cc41","added_by":"auto","created_at":"2026-01-27 05:36:18","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":175219,"visible":true,"origin":"","legend":"\u003cp\u003eThermodynamics stability and crystal structures of the Mg-Si-O compounds. (\u003cem\u003eA\u003c/em\u003e), Convex hull of formation enthalpies for Mg-Si-O compounds at 500 GPa. (\u003cem\u003eB\u003c/em\u003e), Convex hull of formation enthalpies for Mg-Si-O compounds at 1500 GPa. Crystal structures of (\u003cem\u003eC\u003c/em\u003e), \u003cem\u003eCmmm\u003c/em\u003e-Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e. (\u003cem\u003eD\u003c/em\u003e), Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e and (\u003cem\u003eE\u003c/em\u003e), Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/d316823c27b97046422d4d42.jpg"},{"id":101297209,"identity":"707e5f3a-46ea-45fe-b45b-c5681ca6059a","added_by":"auto","created_at":"2026-01-28 09:25:56","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":131509,"visible":true,"origin":"","legend":"\u003cp\u003ePhase stability fields of terrestrial mantle constituents at ultrahigh pressures. Blue dashed lines show expected core–mantle boundary pressures for terrestrial super-Earths of different sizes based on the model of Wagner et al. (2012) \u003csup\u003e33\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/410aaadcb100c2fca0152c86.jpg"},{"id":101207125,"identity":"5d721e57-aaf3-41c9-ad33-878973ea2df2","added_by":"auto","created_at":"2026-01-27 09:57:39","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":167104,"visible":true,"origin":"","legend":"\u003cp\u003eThe electronic properties and density profiles of the Mg sub-silicates. Calculated electron localization function for (\u003cem\u003eA\u003c/em\u003e), Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e at 1000 GPa; (\u003cem\u003eB\u003c/em\u003e), Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e at 1000 GPa; and (\u003cem\u003eC\u003c/em\u003e), Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e at 1200 GPa. (\u003cem\u003eD\u003c/em\u003e-\u003cem\u003eF\u003c/em\u003e), The projected density of states for the Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e, and Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e structure at selected pressures. (\u003cem\u003eG\u003c/em\u003e), The band gap of Mg sub-silicates. (\u003cem\u003eH\u003c/em\u003e), Density differences Δ\u003cem\u003eρ\u003c/em\u003e of Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e, and Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e structure relative to PPv-MgSiO\u003csub\u003e3\u003c/sub\u003e as a function of pressure and under static condition. Open symbols represent metastable phases.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/a5fca89031ac401ddcbe02df.jpg"},{"id":101184374,"identity":"d4464dde-4786-466a-9e4d-3eac66d32e21","added_by":"auto","created_at":"2026-01-27 05:36:18","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":229596,"visible":true,"origin":"","legend":"\u003cp\u003eStratified mantle structure in massive super-Earths’ mantle. (\u003cem\u003eA\u003c/em\u003e), Pressure-temperature (\u003cem\u003eP-T\u003c/em\u003e) phase diagram, which divides the mantle into silicate mantle, sub-silicate mantle, and conductive mantle according to mineral composition. The red solid line and blue solid line respectively represent the temperature-pressure distributions inside Earth-like planets with 10 M\u003csub\u003e⊕\u003c/sub\u003e and 5 M\u003csub\u003e⊕ \u003c/sub\u003e\u003csup\u003e33\u003c/sup\u003e. The green dashed line is the decomposition pressure curve of PPV-MgSiO\u003csub\u003e3 \u003c/sub\u003e\u003csup\u003e31\u003c/sup\u003e. (\u003cem\u003eB\u003c/em\u003e), Schematic illustration of the layered structure, showing the sub-silicate mantle and conductive mantle. (\u003cem\u003eC\u003c/em\u003e), Magnetic field penetration (γ) induced by the skin effects of semiconducting Mg sub-silicate mantles. (\u003cem\u003eD\u003c/em\u003e), Shielding of magnetic field in metalized Mg sub-silicate layer. In both (\u003cem\u003eC\u003c/em\u003e) and (\u003cem\u003eD\u003c/em\u003e): Dashed lines correspond to an angular frequency \u003cem\u003eω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e identical to that of Earth (1 × 10\u003csup\u003e-8\u003c/sup\u003e rad/s), while solid lines represent \u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e = 10\u003csup\u003e-9\u003c/sup\u003e rad/s, as adopted in this work for super-Earths. Dot-dashed lines corresponding to the size of super-Earths. In (\u003cem\u003eD\u003c/em\u003e), different colors denote the content of Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e in the mantle: orange for 50%, blue for 10%, and green for 5%. The black dot-dashed line marks the threshold corresponding to a 1% magnetic field penetration rate.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/db9b54891419253f3c03496a.jpg"},{"id":101299240,"identity":"5541655d-7582-4132-8bb4-cffb311a9cf7","added_by":"auto","created_at":"2026-01-28 09:41:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1394195,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/e8fedcce-605a-495b-bf09-44da18dcbcf4.pdf"},{"id":101297078,"identity":"4228bdeb-0b7d-42a7-afa2-214b70184919","added_by":"auto","created_at":"2026-01-28 09:24:59","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1345553,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"SuppInfo.docx","url":"https://assets-eu.researchsquare.com/files/rs-6920303/v1/0e8d8db24ecd65fb847765bd.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Conductive Mg sub-silicate mantles dictate the dynamo of super-Earths","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe discovery of over 5000 exoplanets with silicate-dominant interiors, such as Gliese 832c, Kepler-452b, and Kepler-10c\u003csup\u003e1–3\u003c/sup\u003e, has revolutionized our understanding of the universe and planetary diversity\u003csup\u003e4,5\u003c/sup\u003e. The interiors of greater sized exoplanets are either primarily silicates (super-Earth), or made of planetary ices (ice giant such as Neptune). For instance, at a typical mass of ~10 M\u003csub\u003e⊕\u003c/sub\u003e(Earth’s mass), some astrophysics preferred the formation of volatile-rich \"mini-Neptunes\"\u003csup\u003e6\u003c/sup\u003e. However, recent mass–radius–composition analyses suggest that rocky planets with radii below 1.8 Earth’s radius can sustain silicate mantles up to ~20\u0026nbsp;M\u003csub\u003e⊕\u003c/sub\u003e, with tenuous gaseous or icy envelopes and silicate-dominant interiors\u003csup\u003e7–10\u003c/sup\u003e. In these super-Earths, pressures at the core–mantle boundary (CMB) can surpass 1 TPa with temperatures exceeding 6000 K, giving rise to extended mineralogical compositions, unique mantle structure, and refreshed convective models\u003csup\u003e11–16\u003c/sup\u003e. Understanding the generation of sustainable magnetic fields within such extreme environments is paramount for assessing planetary habitability and evolution.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe geodynamo of Earth is driven by turbulent convection in the liquid Fe-Ni outer core\u003csup\u003e17\u003c/sup\u003e, and the magnetic field strength hinges on the convective power and rotation rate\u003csup\u003e18,19\u003c/sup\u003e. For exoplanets and particularly massive super-Earths, the dynamo mechanism may be more complicated. The traditional core-mantle coupling should still be applicable\u003csup\u003e20\u003c/sup\u003e, and may generate even stronger magnetic fields since radioactive heat-producing elements become increasingly more siderophile with planetary size and produce greater internal heat\u003csup\u003e21\u003c/sup\u003e. On the other hand, if long-lived magma oceans exist in large super-Earths’ interiors, the excellent electrical conductivity of molten silicates can also develop magnetic dynamo from the magma oceans\u003csup\u003e22\u003c/sup\u003e. In fact, the appearance of exoplanetary magnetic fields was hinted by the observations of auroral radio emissions and stellar wind-magnetosphere interactions such as HD 189733b, HD 209458b\u003csup\u003e23\u003c/sup\u003e, and YZ Ceti b\u003csup\u003e24\u003c/sup\u003e. However, many mysteries persist regarding the origin, evolution, and specific characteristics of magnetic fields in these exoplanets\u003csup\u003e25\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe phase transitions and chemistry of magnesium (Mg) silicates hold the key to deciphering these mysteries\u003csup\u003e26\u003c/sup\u003e. On Earth, two pivotal phase boundaries dictate the mantle structure: the 660 km discontinuity, where ringwoodite decomposes into bridgmanite plus ferropericlase to separate the upper and lower mantles\u003csup\u003e27\u003c/sup\u003e, and Earth’s CMB (∼2900 km), where the bridgmanite transforms into a post-perovskite-type (PPv) silicate\u003csup\u003e15,16\u003c/sup\u003e. At Earth’s CMB, vigorous convective geodynamo is driven by the interactions between the liquid outer core and the MgSiO\u003csub\u003e3\u003c/sub\u003e-dominant silicate mantle\u003csup\u003e17\u003c/sup\u003e. However, within super-Earths’ interiors experiencing pressures exceeding 1 TPa, the stability fields of terrestrial mantle minerals are dramatically altered. Under such extreme conditions, theoretical works have suggested the dissociation of MgSiO\u003csub\u003e3\u003c/sub\u003e into Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e, MgO, and MgSi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u003csup\u003e28,29\u003c/sup\u003e. To this end, Mg silicates are generally described by the combination of fixed ionic groups such as MgO and SiO\u003csub\u003e2\u003c/sub\u003e, although sub-oxides such as Mg\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e and SiO were predicted at multi-megabar regions\u003csup\u003e30,31\u003c/sup\u003e. It is worth noting that these stoichiometric silicate solids retain wide electronic bandgaps, rendering them electrical insulators even at super-Earth mantle pressure-temperature (\u003cem\u003eP-T\u003c/em\u003e)geotherms. Consequently, a mantle dominated by such insulating minerals would inhibit large-scale charge transport in solid mantles and impose negligible electromagnetic coupling, and surface magnetic fields should directly reflect core dynamics. This stands in stark contrast to the anomalous radio signature reported for YZ Ceti b, suggesting that physical processes are still unaccounted for in simplified, fluid-core oriented dynamo frameworks.\u003c/p\u003e\n\u003cp\u003eThis work focuses on the dominant Mg-silicates in super-Earth’s interiors. In contrast to stoichiometric silicates, we introduce sub-silicates, in which the rock-forming elements (Mg\u003csup\u003e2+\u003c/sup\u003e, Si\u003csup\u003e4+\u003c/sup\u003e, etc.) shift to lower valence states, featuring intermediate stoichiometry of Mg\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eSiO\u003csub\u003e3\u003c/sub\u003e (\u003cem\u003ex\u003c/em\u003e \u0026gt; 1). We show that these non-stoichiometric compounds are candidates as major compositions in large exoplanetary interiors, and they play a pivotal role in generating planetary dynamos.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003eMg sub-silicates in super-Earth mantles\u003c/h2\u003e \u003cp\u003eBuilding upon the conventional MgO-SiO\u003csub\u003e2\u003c/sub\u003e binary system, we added a Mg-endmember and performed an open-ended crystal structure search in the Mg-MgO-SiO\u003csub\u003e2\u003c/sub\u003e ternary system under super‐Earth conditions using the CALYPSO code integrated with density-functional-theory. The goal is to identify stable Mg sub-silicates and assess their thermodynamic stability fields across pressures relevant to super-Earth interiors (100\u0026ndash;1500 GPa). We systematically surveyed compositions by varying Mg / Si ratios across three series: Mg\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, MgO\u0026middot;Mg\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e and Mg\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e\u0026middot;SiO\u003csub\u003e2\u003c/sub\u003e (with \u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e, \u003cem\u003ez\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;1). Their formation enthalpies were calculated relative to decomposition into the products of MgO, SiO\u003csub\u003e2\u003c/sub\u003e, and Mg:\u003c/p\u003e \u003cp\u003e∆\u003cem\u003eH\u003c/em\u003e = [\u003cem\u003eH\u003c/em\u003e (Mg\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003eSi\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003eO\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e) \u0026ndash; (\u003cem\u003ep\u003c/em\u003e) \u003cem\u003eH\u003c/em\u003e (Mg) \u0026ndash; (\u003cem\u003eq\u003c/em\u003e) \u003cem\u003eH\u003c/em\u003e (MgO) \u0026ndash; (\u003cem\u003er\u003c/em\u003e) \u003cem\u003eH\u003c/em\u003e (SiO\u003csub\u003e2\u003c/sub\u003e)] / (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eb\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003ec\u003c/em\u003e) (1)\u003c/p\u003e \u003cp\u003eHere, ∆\u003cem\u003eH\u003c/em\u003e represents the formation enthalpy per atom, \u003cem\u003eH\u003c/em\u003e denotes the enthalpy of each constituent species, and the coefficients \u003cem\u003ep\u003c/em\u003e, \u003cem\u003eq\u003c/em\u003e, \u003cem\u003er\u003c/em\u003e are determined by elemental conservation: \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e, \u003cem\u003eq\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ec\u003c/em\u003e \u0026ndash; 2\u003cem\u003er\u003c/em\u003e, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ea\u003c/em\u003e \u0026ndash; \u003cem\u003eq\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eTernary convex hull analyses based on formation enthalpy reveal at least seven Mg sub-silicates at 500 GPa, and five phases at 1500 GPa (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea\u0026amp;b). By integrating our computational results with well-known endmember mineral phases, a thermodynamic phase diagram of sub-silicates was established in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e with reference to super-Earth masses. The crystal structures of the predicted stable phases, as well as their phonon properties, are provided in Supplementary Figs. S1, S2 and Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e. We should note that literature has explored the Mg-Si-O ternary system up to ~\u0026thinsp;3 GPa, yet their focus has concentrated on pseudo-binary (MgO)\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u0026middot;(SiO\u003csub\u003e2\u003c/sub\u003e)\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e compounds (e.g., Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e and MgSi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e) or oxygen-rich compositions (e.g., MgSiO\u003csub\u003e6\u003c/sub\u003e and MgSi\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e12\u003c/sub\u003e). In contrast, the Mg-rich regime has received little attention, likely because Mg-rich binary Mg-O compounds (e.g., Mg\u003csub\u003e2\u003c/sub\u003eO and Mg\u003csub\u003e4\u003c/sub\u003eO) are themselves unstable under high pressure, making Mg-rich chemistries appear unlikely\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. To refine our predictions, we further filtered the candidate structures based on their density and compatibility with the high-pressure conditions of planetary interiors (details in Supplementary Fig. S3). In principle, only Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, and Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e have comparable density to the terrestrial silicate mantle and are likely to exist in super-Earth interiors (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec-e). Coincidently, all three Mg sub-silicates have the same orthorhombic space group of \u003cem\u003eCmmm\u003c/em\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe should note that the ternary phase diagram encodes the thermodynamic relationships among all possible compounds under a given pressure condition and static conditions. In these systems, it is necessary to compare formation enthalpy between different sub-silicates by drawing tie lines. Taking Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, 1500 GPa) for example, its stability is strengthened by connecting the MgSi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e - Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e - Mg\u003csub\u003e5\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e - Mg\u003csub\u003e3\u003c/sub\u003eO tie line, indicating its robustness and resistance to decomposition in super-Earth interiors (Supplementary Fig. S4).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eMantle mineralogy within super-Earth interiors\u003c/h2\u003e \u003cp\u003eThe stabilities of Mg sub-silicates suggest an altered mineralogical model in super-Earths\u0026rsquo; interiors. Compared to bridgmanite and post-perovskite MgSiO\u003csub\u003e3\u003c/sub\u003e, the Si-O and Mg-O building blocks and the electronic structures of Mg sub-silicates are prominently changed, featuring unprecedented hypo-coordination geometries (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec-e). For instance, the \u003cem\u003eCmmm\u003c/em\u003e phase of Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e is built upon face-sharing MgO\u003csub\u003e8\u003c/sub\u003e cuboids that interconnect with an unusual e\u003csup\u003e\u0026minus;\u003c/sup\u003e-SiO\u003csub\u003e4\u003c/sub\u003e polyhedron, where silicon adopts a planar four-coordinated configuration. Coincidentally, the \u003cem\u003eCmmm\u003c/em\u003e-type Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e shares analogous structural characteristics with Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, providing a structural foundation for the potential formation of solid solutions of MgO\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u0026middot;MgSiO\u003csub\u003e3\u003c/sub\u003e (0\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1) in deep mantle environments of super-Earths. Despite having the same space group, Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e demonstrates a distinct architecture, in which edge-/plane-sharing MgO\u003csub\u003e6\u003c/sub\u003e trigonal prisms interweave with quasi-1D Si-O chains. This systematic reduction of Si coordination number (6\u0026rarr;4\u0026rarr;2) reveals a pressure-driven structural evolution of cations, and implies that increasing Mg/Si ratios induce progressive collapse of silicon\u0026rsquo;s coordination environment from octahedral to planar to linear configurations. We further perform Bader charge analysis to quantify the valence collapse of silicon and its pressure-dependent evolution, and demonstrate that the valence state of Si transitions from +\u0026thinsp;3.3 in MgSiO\u003csub\u003e3\u003c/sub\u003e, reducing to +\u0026thinsp;1.9 in Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e or Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e, and eventually inverting to an anionic \u0026minus;\u0026thinsp;1.1 in Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e (Supplementary Fig. S5).\u003c/p\u003e \u003cp\u003eThis anomalous reduction in oxidation state results from pressure-mediated asymmetric charge redistribution, and has profound impacts on the electronic properties. For example, Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e and Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e exhibit localized electron density between adjacent Si ions, which is a hallmark of high-pressure electrides (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea\u0026amp;b). In contrast, Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e exhibits an unprecedented electronic topology, characterized by quasi-2D electron-rich domains localized around Si ions. These domains form anisotropic conductive pathways through overlapping Si 3\u003cem\u003ep\u003c/em\u003e orbitals, enabling delocalized electron transport along the [001] crystallographic axis (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). Moreover, Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e and Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e are narrow-bandgap semiconductors with narrow widths of 0.96 eV and 2.89 eV at 1,000 GPa, respectively. Their Fermi levels are primarily dominated by hybridized O 2\u003cem\u003ep\u003c/em\u003e, Si 3\u003cem\u003ep\u003c/em\u003e, and ISQ states (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed\u0026amp;e). On the other hand, Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e is metal with a nonzero electron density of states at the Fermi level (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef). The evolution of electronic structures suggests that as the Mg / Si ratio increases, the super Earth\u0026rsquo;s mantles become more electrically conductive, especially in Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, whose metallic properties provide a pathway for the flow of electric current in the mantle (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg). This potentially suppresses electromagnetic coupling between the mantle and the core.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eImplications for super-Earth interiors and planetary dynamos\u003c/h3\u003e\n\u003cp\u003eThe chemical composition (\u003cem\u003ee.g.\u003c/em\u003e the Mg/Si ratio), coupled with extreme pressure and temperature condition, governs the mantle mineralogy of super-Earths and influences both their internal structure and magnetic field dynamics. Whereas solar and bulk Earth compositions favor MgSiO\u003csub\u003e3\u003c/sub\u003e dominated mantles\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e, our thermodynamic calculations reveal a paradigm shift to Mg sub-silicates for super-Earths, whose interiors can reach several megabar pressures. The stability of Mg sub-silicates hinges on the formation free energy (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), density (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eh), and chemical compositions. We therefore derive their high-temperature properties through both quasiharmonic approximation and \u003cem\u003eab initio\u003c/em\u003e molecular dynamics simulations (Supplementary Fig. S6). After confirming the thermal and kinetic stability of Mg\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 and 4) and Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e in super-Earths\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, we calculate their thermal expansions and densities to evaluate the gravitational stability. These factors were combined to established a hierarchical mantle model in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea\u0026amp;b, in which Mg sub-silicates become dominant in the mid-lower portion of super-Earth\u0026rsquo;s deep mantles. For example, Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e is both energetically and gravitationally at above approximately 280 GPa and 3500 K, which may co-exist with PPv-MgSiO\u003csub\u003e3\u003c/sub\u003e. At 750 GPa, PPv-MgSiO\u003csub\u003e3\u003c/sub\u003e is thought to decompose into Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e and MgSi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e, indicated by the green dashed line in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. Coincidently, the Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e becomes stable and possibly forms a continuous solid solution with Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e. Our computational results suggest that in the range of 1500\u0026ndash;4400 km depth, semiconducting Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e and Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e will progressively become the major silicates in super-Earth\u0026rsquo;s mantles.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAlthough the conductivity of semiconducting Mg sub-silicate (\u003cem\u003eσ\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;10\u003csup\u003e3\u003c/sup\u003e \u0026minus;\u0026thinsp;10\u003csup\u003e4\u003c/sup\u003e S/m) is lower than that of metallized Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e or liquid Fe cores (Supplementary Fig. S7), the thickness of this layer can exceed thousands of kilometers and enables effective skin-effect attenuation​ of core-generated magnetic fields. Using the skin depth formula:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\delta\\:=\\:\\sqrt{\\frac{2}{{\\mu\\:}_{0}\\sigma\\:\\omega\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{0}\\)\u003c/span\u003e\u003c/span\u003e is the ​​vacuum permeability (4π\u0026thinsp;\u0026times;\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;7\u003c/sup\u003e H/m, a fundamental constant), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e is the electrical conductivity, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:\\)\u003c/span\u003e\u003c/span\u003e is the angular frequency of the time-varying magnetic field. For Earth, the internally generated secular-variation field exhibits most of its power on timescales of several years to several decades, corresponding to angular frequencies \u003cem\u003eω\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e to 10\u003csup\u003e\u0026minus;\u0026thinsp;7\u003c/sup\u003e rad/s\u003csup\u003e34,35\u003c/sup\u003e. Since larger cores are expected to produce slower magnetic variations, the magnetic field frequency \u003cem\u003eω\u003c/em\u003e is estimated in the range of 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e to 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e rad/s\u003csup\u003e36\u003c/sup\u003e. This Mg sub-silicates layer yields a skin depth \u003cem\u003eδ\u003c/em\u003e of approximately 180 km. We further defined the magnetic field penetration ratio as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\gamma\\:={B}_{surf}/{B}_{core}\\approx\\:{e}^{-d/\\delta\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eOur results suggest that for a thick sub-silicate mantle (\u003cem\u003ed\u003c/em\u003e refers to the thickness, and \u003cem\u003ed\u0026thinsp;\u0026gt;\u0026thinsp;δ\u003c/em\u003e), core-generated magnetic fields will undergo exponential attenuation. This demonstrates that super-Earths with \u0026gt;\u0026thinsp;2M\u003csub\u003e\u0026oplus;\u003c/sub\u003e may be influenced by skin effects and experience substantial magnetic damping (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). For example, at 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e rad/s, the magnetic-field penetration ratios for 2.5 M\u003csub\u003e\u0026oplus;\u003c/sub\u003e, 5 M\u003csub\u003e\u0026oplus;\u003c/sub\u003e, and 7.5 M\u003csub\u003e\u0026oplus;\u003c/sub\u003e planets are ~\u0026thinsp;36%, 1.1%, and 0.18%, respectively. At more realistic magnetic field frequency of 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e rad s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, over 96% of the field is attenuated for a 2.5 M\u003csub\u003e\u0026oplus;\u003c/sub\u003e super-Earths.\u003c/p\u003e \u003cp\u003eFor massive super-Earths (\u0026gt;\u0026thinsp;10 M\u003csub\u003e\u0026oplus;\u003c/sub\u003e; CMB\u0026thinsp;\u0026gt;\u0026thinsp;1300 GPa) such as Kepler-725c\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e (10\u0026thinsp;\u0026plusmn;\u0026thinsp;3 M\u003csub\u003e\u0026oplus;\u003c/sub\u003e), the stability of Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e and Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e in deep interiors or CMB promotes an interconnected metallized layer. Similar to the previously proposed electrically conducting mantle layer, this metallized rocky layer shield magnetic fields on planetary surfaces through the skin effect\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan additionalcitationids=\"CR39 CR40\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The exceptionally high conductivity (σ\u0026thinsp;\u0026asymp;\u0026thinsp;10\u003csup\u003e5\u003c/sup\u003e ~ 10\u003csup\u003e6\u003c/sup\u003e S/m), combined with the low-frequency nature of planetary magnetic fields, yields extremely small skin depth (\u003cem\u003eδ\u003c/em\u003e shrinks to a few to several tens of kilometers). This results in all time-varying core-generated fields, including the low-frequency dipole, decaying sharply as they propagate through the metallized mantle layer.\u003c/p\u003e \u003cp\u003eSimilar to the silicate-dominant Earth\u0026rsquo;s lower mantle\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, the deep mantles of massive super-Earths are expected to become progressively more reducing toward to the core, favoring more reduced Mg sub-silicates over their stoichiometric counterparts. By varying the fraction of Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, we estimate efficiency of a conductive mantle layer in shielding the magnetic field. When Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e constitutes \u0026sim;50% of the assemblage, a conductive mantle layer with only\u0026thinsp;~\u0026thinsp;260 km thick can achieve\u0026thinsp;\u0026ge;\u0026thinsp;99% shielding. For even more conservative fractions of 5%, approximately 750 km thick layer is required to reach similar attenuation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). Higher frequencies, such as \u003cem\u003eω\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e rad/s, will further enhance the shielding effects (Supplementary Fig. S8). Notably, the interiors of massive super-Earths are easily capable of forming conductive layers several hundred kilometers thick (Supplementary Fig. S9), which will eliminate global dynamo. While recent geochemistry work suggests that the radioactive heat generation in the core of massive super-Earth such as Kepler-725c fuels an amplified dynamo\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, a layer made of metallized Mg sub-silicates may confine magnetic flux within the core, making its surface magnetic fields nearly undetectable.\u003c/p\u003e \u003cp\u003eIn summary, our study reveals the high-pressure stability of Mg sub-silicates in super-Earth interiors and demonstrates their profound influence on the attenuation of planetary magnetic fields. In super-Earths exceeding\u0026thinsp;~\u0026thinsp;2M\u003csub\u003e\u0026oplus;\u003c/sub\u003e, semiconducting or metallized layers in the mid-to-lower mantle induce exponential decay of core-generated magnetic fields through the skin effect, while in more massive super-Earths, fully metallized conductive layers can produce more effective or even near-complete magnetic shielding. These findings might revise the conventional view of magnetic-field evolution in super-Earths and provide a key theoretical framework for understanding the interior structure and magnetic environments of terrestrial exoplanets.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eStructural searching using CALYPSO\u003c/h2\u003e \u003cp\u003eWe conducted an extensive global structure search for Mg\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, Mg\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e and Mg\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e (\u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e, \u003cem\u003ez\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;1) across the pressure range of 100\u003cb\u003e\u0026ndash;\u003c/b\u003e1500 GPa, employing simulation cells containing 1\u0026ndash;8 formula units. To predict stable structures for a given chemical composition, we utilized the CALYPSO code\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e along with the particle swarm optimization algorithm. This approach is based on ab initio total-energy calculations and implemented within the framework of density functional theory\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eGeometric optimization and free energy calculation\u003c/h3\u003e\n\u003cp\u003eGeometric optimization and electronic property calculations were performed in the framework of the density functional theory within the generalized gradient approximation Perdew\u0026thinsp;\u0026minus;\u0026thinsp;Burke\u0026thinsp;\u0026minus;\u0026thinsp;Ernzerhof\u003csup\u003e46\u003c/sup\u003e in the Vienna \u003cem\u003eAb initio\u003c/em\u003e Simulation Package (VASP) code\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. The projector-augmented-wave\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e (PAW) method was applied with the appropriate pseudopotentials for magnesium, silicon, and oxygen, reflecting their respective valence electrons: 3\u003cem\u003es\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e, 3\u003cem\u003es\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e3\u003cem\u003ep\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, 2\u003cem\u003es\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e2\u003cem\u003ep\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. These pseudopotentials were sourced from the VASP library. To achieve convergence within 1 meV/atom, we employed a plane-wave energy cutoff of 600 eV and a Monkhorst-Pack\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e \u003cem\u003ek\u003c/em\u003e-point grid with a spacing of 0.02 \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e. Charge transfer was analyzed using Bader\u0026rsquo;s quantum theory\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. Phonon calculations are carried out using the supercell approach, as implemented in the PHONOPY code\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eFirst-principles molecular dynamic\u003c/h2\u003e \u003cp\u003e \u003cem\u003eAb initio\u003c/em\u003e molecular dynamics (AIMD) simulations were performed using the Vienna \u003cem\u003eAb initio\u003c/em\u003e Simulation Package (VASP)\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e with the projector augmented wave (PAW) method\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. A [3\u0026times;1\u0026times;4] supercell containing 144 atoms was constructed for Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e (\u003cem\u003eCmmm\u003c/em\u003e), a [2\u0026times;1\u0026times;4] supercell containing 128 atoms was constructed for Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e (\u003cem\u003eCmmm\u003c/em\u003e), and a [1\u0026times;2\u0026times;4] supercell containing 128 atoms was used for Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e (\u003cem\u003eCmmm\u003c/em\u003e). NVT ensemble simulations were carried out using the Nos\u0026eacute;\u0026ndash;Hoover thermostat\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. The DFT calculations were carried out with a Γ-centered k-point and the simulations temperature adopts 7000 K. Each MD simulation step used a time step of 2 fs, with a total of 10000 steps, corresponding to 20 ps of simulation time.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eElectrical conductivity calculation\u003c/h3\u003e\n\u003cp\u003eElectrical conductivity was calculated based on the semi-empirical Boltzmann transport theory. The group velocity of an electron is expressed as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{v}_{\\alpha\\:}\\left(i,k\\right)=\\frac{1}{h}\\frac{\\partial\\:{\\epsilon\\:}_{i,k}}{\\partial\\:{k}_{\\alpha\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{i,k}\\)\u003c/span\u003e\u003c/span\u003e denotes the energy eigenvalue at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e band, point \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e means along the direction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e. The electrical conductivity tensor is given by:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\sigma\\:}_{\\alpha\\:\\beta\\:}\\left(i,k\\right)=\\:{e}^{2}{\\tau\\:}_{i,k}{v}_{\\alpha\\:}\\left(i,k\\right){v}_{\\beta\\:}\\left(i,k\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{v}_{\\alpha\\:}\\left(i,k\\right){v}_{\\beta\\:}\\left(i,k\\right)\\)\u003c/span\u003e\u003c/span\u003e is the group velocity; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{i,k}\\)\u003c/span\u003e\u003c/span\u003e is the relaxation time. In most cases, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{i,k}\\)\u003c/span\u003e\u003c/span\u003e can be treated as a constant without affecting the accuracy of the calculation (relaxation time approximation, RTA). Although the constant relaxation time approximation is limited, it simplifies the carrier transport mechanism within the material. In this case, the electrical conductivity depends on the transport distribution function:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\sigma\\:}_{\\alpha\\:\\beta\\:}\\left(\\epsilon\\:\\right)=\\:\\frac{1}{N}\\sum\\:_{i,k}{\\sigma\\:}_{\\alpha\\:\\beta\\:}(i,k)\\frac{\\delta\\:(\\epsilon\\:\\:-\\:{\\epsilon\\:}_{i,k})}{d\\epsilon\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\)\u003c/span\u003e\u003c/span\u003e is the number of \u003cem\u003ek\u003c/em\u003e points set in the calculation. The electrical conductivity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e is obtained by integrating the distribution function over the whole space:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\sigma\\:}_{\\alpha\\:\\beta\\:}\\left(T,\\mu\\:\\right)=\\:\\frac{1}{{\\Omega\\:}}\\int\\:{\\sigma\\:}_{\\alpha\\:\\beta\\:}\\left(\\epsilon\\:\\right)\\left[-\\frac{\\partial\\:{f}_{\\mu\\:}\\left(T,\\epsilon\\:\\right)}{{\\partial\\:}_{\\epsilon\\:}}\\right]d\\epsilon\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{\\mu\\:}\\left(T,\\epsilon\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e is the Fermi-Dirac distribution function, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e is the chemical potential, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e is the temperature. Given a known constant relaxation time, the electrical conductivity at a certain chemical potential and temperature can be obtained from the band structure calculations performed with VASP. In addition, the VASP calculation data were processed using the VASPKIT code\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. However, due to the extreme pressure and temperature in the context, the calculated electrical conductivity of Mg sub-silicates is discussed in qualitative terms. We define the generalized electrical conductivity as the electrical conductivity (in units of relaxation time) at the Fermi level (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e = 0). The generalized conductivity curves of these Mg sub-silicates with temperature varying from 1000 K to 7000 K under a pressure of 1000 GPa are presented in Supplementary Fig. S10.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contributions:\u003c/h2\u003e \u003cp\u003eConceptualization: Q.H., Y.G. and H.M. Methodology: Y.G. and Q.H. Investigation: Y.G. and Q.H. Visualization: Y.G. Formal analysis: Y.G. F.L. H.M. and Q.H. Validation: Y.G. and Q.H. Funding acquisition: F.L. and Q.H. Resources: F.L., H.M. and Q.H. Project administration: Q.H. Writing\u0026mdash;original draft: Y.G. Writing\u0026mdash;review and editing: Y.G. F.L. H.M. and Q.H.\u003c/p\u003e\u003ch2\u003eACKNOWLEDGMENTS.\u003c/h2\u003e \u003cp\u003eNatural Science Foundation of China (NSFC) with grant number T2425016, Jilin Provincial Science and Technology Development Project (SKL202502017JC), and NSFC grants (#42150101, 12274168 and 42472065). The computational work was supported by the High Performance Computing Platform of Nanjing University of Aeronautics and Astronautics.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWittenmyer RA et al (2014) GJ 832c: A super-earth in the habitable zone. Astrophys J 791:114\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJenkins JM et al (2015) Discovery and validation of Kepler-452b: A 1.6 R\u003csub\u003e\u0026oplus;\u003c/sub\u003e super earth exoplanet in the habitable zone of a G2 star. 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Comput Phys Commun 267:108033\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6920303/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6920303/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWhile bridgmanite and the post-perovskite MgSiO\u003csub\u003e3\u003c/sub\u003e dominate Earth-sized terrestrial mantles, the extreme pressures within larger terrestrial exoplanets may disrupt the archetypal ionic balance of rock-forming elements, forming non-stoichiometric magnesium silicates. Here, we predict the stabilization of magnesium (Mg) sub-silicates such as Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, Mg\u003csub\u003e3\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e and Mg\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e in exoplanetary interiors. These phases are thermodynamically stable as low as 100 GPa, and become gravitationally favorable at multi-megabar pressures, corresponding to the mantle depth of silicate super-Earths. We further reveal that Si atoms donate electrons to localized sites, reducing valence states to 2 + and even anionic 1- and substantially narrowing band gaps. Mg sub-silicates start to form layer in exoplanet with \u0026gt; 2 Earth’s mass, and potentially become the major constituents in the basal mantle of larger super Earth. Their high electrical conductivity creates an electrically conductive layer that suppresses core-mantle electromagnetic coupling and strongly attenuates the dynamo-generated magnetic field, including the massive super-Earth Kepler-725c.\u003c/p\u003e","manuscriptTitle":"Conductive Mg sub-silicate mantles dictate the dynamo of super-Earths","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-27 05:36:10","doi":"10.21203/rs.3.rs-6920303/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"46981680-4b2b-4131-9835-f8d63b83b2f6","owner":[],"postedDate":"January 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61656182,"name":"Earth and environmental sciences/Planetary science/Exoplanets"},{"id":61656183,"name":"Earth and environmental sciences/Planetary science/Mineralogy"}],"tags":[],"updatedAt":"2026-01-27T05:36:10+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-27 05:36:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6920303","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6920303","identity":"rs-6920303","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}