Spin-related symmetry breaking induced by half-disordered hybridization in BixEr2-xRu2O7 pyrochlores for acidic oxygen evolution

While acidic oxygen evolution reaction plays a critical role in electrochemical energy conversion devices, the sluggish reaction kinetics and poor stability in acidic electrolyte challenges materials development. Unlike traditional nano-structuring approaches, this work focuses on the structural symmetry breaking to rearrange spin electron occupation and optimize spin-dependent orbital interaction to alter charge transfer between catalysts and reactants. Herein, we propose an atomic half-disordering strategy in multistage-hybridized BixEr2-xRu2O7 pyrochlores to reconfigure orbital degeneracy and spin-related electron occupation. This strategy involves controlling the bonding interaction of Bi-6s lone pair electrons, in which partial atom rearrangement makes the active sites transform into asymmetric high-spin states from symmetric low-spin states. As a result, the half-disordered BixEr2-xRu2O7 pyrochlores demonstrate an overpotential of ~0.18 V at 10 mA cm−2 accompanied with excellent stability of 100 h in acidic electrolyte. Our findings not only provide a strategy for designing atom-disorder-related catalysts, but also provides a deeper understanding of the spin-related acidic oxygen evolution reaction kinetics.


The catalytic mechanism based on Jose Gracia rules.
The OER performance is strongly related with spin-dependent orbital hybridization in catalysts, in which the number of unpaired electrons during OER cannot be conserved. In OER process, the magnetic potentials via exchange interaction or spin-orbit coupling effect can directly affect the activation energy at rate-limiting step and carrier transfer ability. This is because that the bonding characteristic between catalysts and reactants can be reduced by the quantum spin exchange interactions, meanwhile the rate constant for charge transfer reaction and spin-dependent electron mobility can be enhanced by magnetic potentials acting as selective gates.
To understand the correlation between ferromagnetic (FM) configuration and catalytic activity, we should extend the spin-dependent mechanisms of electron tunneling to catalytic surface or interfaces, because the exchange coupling between different orbitals, in the catalysts and with the chemisorbed reactants, affects the kinetics of electron transfer reactions. In this regard, the Jose Gracia rules can be introduced to explain our experimental conclusions. To sum up, the Jose Gracia rules are as follows 1-3 : (1) The spin angular momentum is conserved during an electron transfer in the catalyst and with the reactants; (2) The intra-atomic and inter-atomic exchange interaction in the covalent framework are ferromagnetic in oxides with minimum ∆ ; (3) In the active metal atoms on the surface, the d-orbitals oriented towards the bonds with the reactants, anti-bonding d-orbitals at the fermi level, must be partially occupied; (4) The overall reduction of Coulomb interactions can facilitate the entrance of itinerant charge carriers at working conditions. Defects or dopants at the interstitial sites or cations with occupied f-or d-orbitals, increasing the covalence of frameworks, help to create active FM orderings, adaptable to redox variations and with minimum ∆ ; (5) At the transition state, the active cations on the surface at reaction conditions formally receive or lose electronic density during spin-selective steps with the reactants. Nevertheless, good electrocatalysts retain the overall FM exchange delocalization; (6) The reaction mechanism adapts to the response of the electronic free energy of activation, ∆ , towards maximum entropic gains.
According to these rules, it can be found that good catalysts need to be FM feature.
Generally speaking, the intra-atomic exchange interactions benefits for the configurations with more unpaired d electrons, leading to an appearance of high spin state. However, in crystal catalysts, the oriented metals and ligands are bonded together depending on the symmetry. The crystal field theory discloses that disorderedhybridization for Bi2Ru2O7 at room temperature makes the d manifolds split into completely filled eg orbital and empty a1g orbital, the latter one is higher in energy due to the larger electronic repulsions. Interestingly, the influence of spin-orbit coupling in BixEr2-xRu2O7 sample can contribute to trigger a magnetic splitting from d shells meanwhile the RuO6 coordination are changed into D'3d symmetry from D3d point group.
In these hybridized structures, the intra-atomic exchange interactions and crystal filed contribution becomes comparable strength, leading to a competing spin state. When the doped Er atoms lead to an uneven occupation at d shells as shown in Figure 1d, the electron-spin (e-spin) becomes localization by Jahan-Teller distortion. The electronic repulsions between the oxygen and metal orbitals decrease with the radial compression of the d orbitals that increase the intra-atomic exchange interaction but weak the crystal field effect, thus leading to a high-spin configuration as the magnetic characterization in Figure 3a-3b. Therefore, we can conclude that the magnetic existence is originated from the cooperative phenomenon influenced by inter-atomic exchange interactions and crystal field, which plays a decisive role in electro-catalysis because they can set the collective e-spin transport. Enough empty d orbitals at the Fermi level for BixEr2-xRu2O7 sample with D'3d point group can enforce the exchange of electrons to generate a ferromagnetism, which benefits for a fast and coherent e-spin transport with a zero band gap for the spin-up state. Instead, if the orbitals are symmetrically filled, the intraatomic interactions are antiferromagnetic configuration for D3d symmetry with a band gap, which can be confirmed by the difference in spin-resolved DOS as shown in Figure   1e.

Supplementary Figure 1. EDS spectrum of the BERO nanoparticles.
No noticeable impurities are introduced unintentionally in the preparation process.  To explore the fine structure characteristic of different samples, we conducted the synchrotron radiation XRD and further make the Rietveld refinements at 50K and 300K.
To distinguish the degree of disorder of A site (the ideal Ru-based pyrochlores can be marked by A2Ru2O7), we pay much attentions on the thermal parameters, which can be used to reflect the atom vibrations around the equilibrium positions. Apparently, the Uiso(Bi) in BRO is higher than Uiso(Er) in ERO whether at 50 K or 300 K, demonstrating that a higher degree of disorder happened in BRO than ERO and the 6s lone pair electrons of Bi 3+ cations are responsible for the A-site disorder. Interestingly, the thermal parameters are differently changed in BRO and ERO as increasing temperature from 50 K to 300 K, because the thermal response to atomic disordered-hybridization of Er element is weaker than Bi that makes the changes in Uiso(Bi) become more drastic than Uiso(Er). Therefore, the symmetry breaking induced by atomic disorderedhybridization in pristine BRO sample can be effectively restricted by implanting some Er atoms, and the transition of Uiso(A-site) in BERO also can be easily understood from this viewpoint. We can imagine that atomic occupation of Ru and O atoms will be changed correspondingly. Notably, the provided thermal parameters are isotropic, because a, b, c orientations are equivalent in the cubic structure that cannot give a reasonable reliability factors (Rp, Rwp (%) >10%) 4,5 . In addition, a little negative occupation at Bi site in pristine BRO at 300 K can be found, which only can be attributed to the disorder of Bi atoms 4 . In the whole, the atomic disorderedhybridization in BERO can be effectively alleviated by implanting Er atoms comparing to the BRO. Interestingly, the RuO6 coordination octahedron will be changed as the degree of symmetry breaking and finally demonstrate a distinguishing physical characteristic.
Generally, the ideal RuO6 octahedron resulting a local point symmetry of Ru coordination is Oh, which is usually present in perovskite-based structures. Interestingly, the RuO6 coordination polyhedron in BRO cannot be simply described as an ideal octahedron, because the interstitial Bi 3+ cation with 6s long pair electrons will increase the Ru-O-Ru bond angle and finally lead to a distortion of octahedral RuO6 coordination by trigonal compression along a three-fold axis. This local structural deformation will cause a symmetry transition from Oh to D3d, as shown in Supplementary Figure 5 and Furthermore, this symmetry-breaking-dependent structure is expected to reconfigure the orbital degeneracy and spin-related electron occupation. In a distorted RuO6 octahedron (D3d or D'3d -symmetry), the partially filled t2g orbitals will be further degenerated to a 2-fold eg band and a singlet a1g band, which are described in Figure   1d. In addition, the catalytic mechanism about this symmetry breaking contribution is also provided in the former. In conclusion, the symmetry breaking transition from Oh and D3d could be reflected by the changes in distorted RuO6 octahedron and electronic band structure, which plays a determining role in efficient acidic OER.

Supplementary Figure 6. Raman spectra of the (a) BRO and (b) ERO samples under different temperature.
The F2g mode in BRO sample can be shifted as temperature but this change cannot occur at ERO sample.
When the RuO6 coordination polyhedron in BERO is changed into D'3d symmetry from D3d point group, the splitting energy between eg and a1g orbital is slowly decreased. Therefore, the electrons at eg orbitals can easily hop onto a1g orbital due to electronphonon interaction.

Supplementary Figure 8. The simplified QSEI energy plots for catalysts with predominant with AFM (left) and FM (right) couplings.
To further disclose the correlation between magnetic structure and OER activity, the spin energic terms depending on QSEI comprise two possible spatial interactions, as displayed in Supplementary Figure 8, where the extra on-site interactions takes place with the same atomic boundary and the extra interatomic interactions take place among different atoms. In the system with dominant AFM coupling, the strong intra-atomic QSEI will localize in space with 4d-5f pen shells that allow a stable low-spin orbital configurations by decreasing exclusively the on-site electronic configuration. It is important to note that no extra interatomic QSEI between AFM-coupled spinconfigurations can be triggered and the interatomic Coulomb repulsions are intact in the catalyst. In this case, AFM Jahan-Teller elongations emerge to help reduce the electronic repulsions, which might appear along the direction of the highest occupied antibonding orbitals. Generally speaking, the OER reactive activity in AFM configuration will be reduced by the stabilization and additional localization of the electron pairs, Fermi heaps between metal centers and the relative destabilization at the lowest unoccupied orbitals. This fact is likewise related with the enhanced electronic localization in space as shown in Figure  The efficiency of "acceptance-donation" process of electrons between the metal site and reactants is responsible for improving the OER catalytic activity, regulating the electronic occupation at d orbital is a feasible strategy to accelerate this process.
Compared with the disordered atomic configuration (D3d), the degenerated t2g orbitals in D'3d point group split into a half-filled a1g band and eg band, which are advantages to accelerate "acceptance-donation" process and improve the OER performance.  Figure 10, the rate coefficient of e-spin transfer towards the catalyst during OER can be described as equation (1), in which ∆ !" and ∆ !" is electronic enthalpy and entropy at transition state, respectively.
The OER cannot be triggered by vibrational oscillations but change in free energy at TS: As shown in Figure 5, the differentiated free energy for OER demonstrates that  Table 5.
The compared results confirm that the OER performance for BERO sample is obviously better than BRO and ERO, which are independent of normalization methods.
However, the slight changes in current values as normalization method cannot affect our conclusion. From this result, it is convincible to confirm that BERO catalyst with half-disordered hybridization has a higher intrinsic activity than BRO and ERO, in which the spin-related symmetry breaking plays a critical role in accelerating the catalytic kinetics.

Supplementary
Then the loading amount of catalysts on carbon paper for electrochemical tests are about 0.83±0.12 mg/cm 2 . To exclude the contribution of loading amount difference onto catalytic performance, the mass activity curves are displayed in Supplementary Figure   12, in which the BERO sample also demonstrates the best reaction activity. We can conclude that the spin-related symmetry breaking induced by half-disordered hybridization in BERO plays the key role to accelerate the electrochemical reactive activity, which is independent of assessment method.

Supplementary Figure 13. Mass activity and BET surface area-normalized specific activity of BRO, ERO and BERO catalysts at η = 0.27 V (1.5V vs. RHE).
To display a fair comparison in OER performance, mass activity (normalized to the loading amount) and specific activity (normalized to the sample surface area as estimated from BET values) are obtained and shown in Supplementary Figure 13, respectively. Interestingly, BERO shows the excellent OER performance in acid, and the mass activity of BERO at 270 mV overpotential is about 6.1 and 74.4 times higher than that of BRO and ERO. Furthermore, the specific activity is also significantly higher than the other reports. The excellent OER activity only can be attributed to the spin-related symmetry breaking induced by half-disordered hybridization in BERO pyrochlores. In addition, the mass activity (normalized by catalysts) of BERO is superior to many reported state-of-the-art catalysts, as shown in Supplementary Table   14.

Supplementary Figure 14. The structural characterization. (a) The SEM image and (b) TEM images of BERO catalyst after OER test.
The stability of catalysts can be reflected by the microstructure of the catalysts that after OER test. The BERO catalyst maintains the original morphology and high crystallinity. No obvious amorphization can be observed by the TEM images.

Supplementary Figure 15. XRD patterns of BERO catalyst after OER test.
Nor variation in XRD peaks can be observed after OER test, indicating there were no structural destruction.

Supplementary Figure 16. XPS characterizations of BERO before and after OER
test.
The high stability of BERO is also supported by XPS measurements after OER test. No visible changes in the positions of XPS core level peaks can be found on this sample before and after OER test.

Supplementary Figure 17. X-ray absorption spectroscopy (XAS) results. (a) Ru Kedge XAS spectra of BERO before and after OER test. (b) Corresponding FT-EXAFS spectra.
To exclude the existence of Bi and Er cations leaching or small rutile-type particles, the X-ray absorption spectroscopy (XAS) measurements were conducted to reveal the stability of BERO after 100 hours OER test. As shown in Supplementary Figure 15a Figure   16a. Because, the transformation from Ru 4+ to Ru>4 + at high voltages will lead to the decomposition of the pyrochlore, following by the dissolution of Bi element. This similar phenomenon also occurs at ERO and RuO2 system, as shown in Supplementary   Figure 16b. Remarkably, it is amazing to note that the stability region of BERO (Labels 6) is much larger than BRO, ERO and RuO2, which can overlap the whole region of oxygen evolution potentials. This conclusion is consisting with our electrochemical tests, demonstrating the BERO with an excellent electrochemical stability. Including Bi1.8Er0.2Ru2O7, Bi1.0Er1.0Ru2O7, Bi0.5Er1.5Ru2O7 and Bi0.2Er1.8Ru2O7.
To explore the optimal OER performance in BixEr2-xRu2O7 with different disordered-hybridization, the OER performance of various BixEr2-xRu2O7 are compared and shown in Fig. 4a, Fig. 4f and Supplementary Fig. 20. Importantly, we further clarify this intriguing spin-related electronic reconfiguration induced by symmetry breaking is strongly related with the doping Er elements. Interestingly, both Bi and Pb element including lone-pair cations can lead to an atomic disorder, in which the degenerated dxy, dxz and dyz orbitals in Oh symmetry split into a completely filled eg band and an empty a1g band for D3d symmetry as shown in Figure 1b. However, the "acceptance-donation" cannot be realized easily to display a good catalytic activity, because the splitting energy between eg and a1g orbital is too larger and valence electron cannot easily hop onto a1g levels by electron-phonon interaction according to Goodenough-Kanamori rule. To realize this particular halffilled occupation at a1g orbital, the Er cations, not sensitive to this symmetry breaking, should be introduced to control the atomic disorder degree in BixEr2-xRu2O7 sample (named as half-disorder). As atomic disordering operation to eliminate orbital degeneracy, the spin electron occupation at a1g and eg orbitals will be reconfigured with symmetry-breaking-generated orbital splitting. In the view of this, the introduced Er plays a critical role in improving catalytic activity. As a universal law, the OER performances for PbxEr2-xRu2O7 are also conducted as shown in Supplementary Figure   19. The compared results also confirm that the doping Er element can enhance the OER performance in the PbxEr2-xRu2O7, similar to that of BixEr2-xRu2O7. According to the similar method, the Pb2Ru2O7 and Pb1.5Er0.5Ru2O7 samples are successfully fabricated,

Supplementary
is the activation energy needed to create an itinerant TS in conduction band of the catalyst, which is relevant with conductivity 2 . For good catalysts, and #$ should be comparable for similar reaction mechanisms and conditions. Theoretical studies on oxides surface conclude that the OER activity cannot be enhanced beyond noble diamagnetic metal oxides by tuning the binding energies ( ). Hence, the decisive differences between good electro-catalysts appear due to changes in ∆ and , both sensitive to magnetic forces. Therefore, the presence of high-spin orbital configurations induced by reconfiguring orbital degeneracy in BixEr2-xRu2O7 pyrochlores is responsible for the enhanced OER activity.