Electron–phonon coupling and coherent energy superposition induce spin-sensitive orbital degeneracy for enhanced acidic water oxidation

The development of hydrogen economy is pivotal for the future of decarbonizing the energy landscape. The International Energy Agency predicts that global hydrogen production could reach 14% of final energy demand by 2050¹. Achieving this goal depends on producing green hydrogen affordably on an industrial scale. Proton exchange membrane water electrolysis (PEM-WE)² and alkaline water electrolysis (AWE)³ are the two primary technologies for splitting water into hydrogen and oxygen. However, both technologies suffer from sluggish oxygen evolution reaction (OER) at the anode. PEM-WE has a distinct advantage over AWE, delivering purer hydrogen at industrial current densities (1.0 A cm^–2) with superior energy conversion efficiency (70%~90%)^4,5. Currently, commercial PEM-WEs rely on iridium (Ir) catalysts, which cost approximately USD 160,500 per kg⁶, to support acidic OER owing to their notable electrochemical stability and activity under harsh acidic conditions^7,8. The high cost of Ir catalysts restricts the global use of PEM-WE technology. Ruthenium (Ru) with a greater abundance in earth and a lower cost of USD 9523 per kg⁶ is a promising alternative to partially replace Ir. Meanwhile, RuO₂ demonstrates higher activity than IrO₂ in acidic OER^9,10. However, RuO₂ suffers from overoxidation during acidic OER, leading to the formation of water soluble RuO₄ and subsequent corrosion^11,12. To address this, current research has focused on balancing electrochemical stability, reactivity, and cost of acidic catalyst.

Typically, electrochemical stability and reactivity of electrocatalysts are inversely proportional. Designing electronic structures to strengthen the bonding interactions between Ru sites and their coordination environments, stronger than the redox H₂O/O₂ energy, can inhibit the acidic dissolution of Ru catalysts by preventing overoxidation^13,14,15. However, this approach can increase the rate-limiting potential barrier by limiting the adsorption and dissociation of reactants, reducing catalytic activity. Current reports on acidic OER primarily address the thermodynamic process^16,17,18, overlooking the importance of spin-related orbital hybridization and charge transfer between metal sites and derivatives. In fact, the number of unpaired electrons at metal sites is not conserved as in the four-electron OER process, which provides a feasible strategy to simultaneously optimize stability and reactivity from the viewpoint of spin catalysis^19,20,21,22. In other words, controllable spin splitting at the Fermi level can regulate orbital degeneracy. In this case, spin-up bands with metallic characteristics can provide sufficient valence electrons to ensure catalytic activity, while spin-down bands with semiconducting characteristics can enter the bonding levels to prevent deleterious overoxidation (Supplementary Fig. 1).

Developing a suitable synthesis strategy for assembling spin-dependent catalysts is crucial to validating this proposal. Existing microstructural strategies for Ru catalysts such as doping, alloying, and amorphization^23,24,25 partially improve acidic OER activity but fail to deliver satisfactory overall performance. Key issues include: (1) The spin configuration of metal sites, formulated based on the lowest energy principle, cannot be easily rearranged by conventional synthesis methods^26,27,28,29. (2) While the random anchoring of Ru patterns onto catalyst surfaces can partially enhance the atomic utilization, their bonding interactions and orbital hybridization with the matrixes become uncontrollable^30,31, and some unstable Ru particles are readily dissociated into acidic electrolytes³². (3) Controlling Ru atomic distribution and diffusivity at catalyst surfaces is challenging with traditional strategies, which may unintentionally undervalue the contributions of spin-relevant symmetry breaking and orbital degeneracy^33,34. Overall, these traditional synthesis and assembly strategies for Ru catalysts cannot be separated from the solution conditions, which inspires us to implant an external microwave disturbance to timely modulate the Ru atomic bonding process. These findings can principally overcome the current technical bottlenecks. However, the microwave-mediated spin ___domain inversion and orbital splitting at Ru catalysts for acidic OER have yet to be addressed.

Based on the aforementioned considerations, we intentionally introduce some Cr atoms into MnO₂ hosts (Mn_1-xCr_xO₂) as anchor sites, followed by a microwave-mediated cation-exchange reaction in RuCl₃ solution to control Ru atomic assembly (Ru_MW-Mn_1-xCr_xO₂). This synthesis strategy offers several advantages: (1) Doped Cr atoms intentionally weaken the bonding strength of neighboring Mn–O bonds, facilitating orderly cation replacements by Ru atoms. Microwave stimulations decrease the formation probability of larger Ru particles, improving electrochemical stability and Ru atomic utilization, thereby reducing the catalyst cost. (2) Assembled Ru atoms coordinated by asymmetric Mn–O and Cr–O bonds change their orbital degeneracy and spin electron occupation, leading to a stronger bonding interaction than the redox energy of H₂O/O₂, thereby enhancing their stability. (3) The coherent energy superposition from microwave-mediated molecular frictions selectively assembles hydrated Ru ions and induces symmetry-breaking-dependent spin rearrangement, improving acidic OER activity. As a result, the intrinsic OER activity of Ru_MW-Mn_1-xCr_xO₂ is two orders of magnitude higher than that of the typical heating-assembled Ru catalyst (Ru_T-Mn_1-xCr_xO₂). As a proof of concept, an integrated PEM electrolyzer with the Ru_MW-Mn_1-xCr_xO₂ catalyst achieved an industrial OER current density of 1.0 A cm⁻² at 1.88 V cell voltage, substantially surpassing commercial RuO₂ (com-RuO₂) catalysts (2.49 [email protected] A cm⁻²). Moreover, the technique achieves superior electricity-to-hydrogen energy conversion efficiency (88.7%), stable operation (>300 h, 1.0 A cm⁻²), and a lower cost per gallon of gasoline equivalent for the produced H₂ (USD 0.87), suggesting that this approach holds immense potential for improving the hydrogen economy and reforming the energy landscape.

Catalyst design

Generally, the four-electron OER process mainly involves intermediates such as *OH, *O, *OOH, and *OO, whose reactivities are highly dependent on the electron occupation at half-filled d orbitals³⁵. For reactant chemisorption, the metal active sites should have empty t_2g orbitals to hybridize with the σ orbitals of *OH, determining the initiation of OER and accepting unpaired valence electrons. Meanwhile, separate d electrons can be easily donated to the antibonding orbitals between metal sites and adsorbed *OOH species, influencing the final rate-limiting potential barrier. The electron “acceptance-donation” process between metal sites and adsorbed derivatives is crucial in determining OER performance, and this charge transfer is strongly related to electron occupation and orbital splitting^36,37. The octahedral RuO₆ configuration (left panel of Fig. 1a) splits into higher e_g (d_x²_−y² and d_z²) and lower t_2g (d_xy, d_xz, and d_yz) orbitals, with energy splitting and electron occupation proportional to the electronegativity differences. In this case, the symmetrical coordination of Ru sites with six oxygen atoms increases crystal field contribution but decreases intra-atomic Coulomb interactions for orbital nondegeneracy (Supplementary Figs. 2 and 3). When partially replacing Mn sites in MnO₂ with Ru atoms (middle panel of Fig. 1a) breaks regional symmetry, degenerating the t_2g orbital into completely occupied e_g and empty a_1g orbitals. Adding spin-differentiating Cr atoms further breaks crystal symmetry, increasing intra-atomic Coulomb interactions (right panel of Fig. 1a). Cr doping reduces the theoretical formation energy for Ru to replace Mn sites from 2.41 to 1.92 eV, weakening Mn–O bonds at nearby Cr sites through spin-related symmetry breaking and orbital hybridization, while the higher formation energy for Ru to replace Cr sites (2.28 eV) compared to Mn sites (1.92 eV) suggests Ru preferentially substitutes Mn over Cr. The orbital degeneration induced by Jahn–Teller distortions in Ru-Mn_1-xCr_xO₂ decreases the orbital splitting energy and helps electrons hop onto a_1g orbitals from e_g orbitals via electron–phonon interactions (Supplementary Fig. 4), and this half-filled electron occupation leads to feasible catalytic activity and stability (Supplementary Fig. 1).

a Top: Symmetry breaking of RuO₆ coordination polyhedron in the MnO₂ substrate mediated by Cr doping. Bottom: Splitting of the Ru 4d orbital for different symmetries. b Schematic diagram of 2.45 GHz microwave-mediated resonance of polar water molecules. c Comparison of dielectric loss tangent values of MnO₂ and Mn_1-xCr_xO₂ substrates with water molecules. d Top: Raman measurements of the OH stretching vibration of RuCl₃ aqueous solution at different energy modes. Bottom: Proportion of deconvolution Raman peak areas for hydrogen bond and hydrated Ru³⁺ species vibration under different energy modes. e Microwave-mediated coherent energy transfer (ET) and selective assembly of hydrated Ru ions on the Mn_1-xCr_xO₂ substrate. arb. units, arbitrary units; ε” and ε’, imaginary and real parts of the dielectric constant.

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The microwave modulation operating principle on cation-exchange reactions in RuCl₃ solution is schematically shown in Fig. 1b. Water molecules have a typical polar feature. The electric dipole interaction among water molecules will cause a molecular configuration with hydrated Ru-ionic statues that are dynamic combinations using hydrogen bonding interactions^38,39, which can be probed in subsequent Raman spectra of ionic solutions. The water molecule will bring tropism polarity under microwave stimulation, while the rotations and collisions of the water molecule will enforce the phonon vibrations of the H–O–H bond^40,41. Infrared thermal imaging and theoretical simulation results show that this specific resonance mode’s energy superposition rapidly increases the solution temperature (Supplementary Figs. 5–7). Subsequently, coherent energies (~400–450 meV) are spontaneously injected into hydrated Ru ions via Förster energy transfer⁴², making Ru ions replace Mn sites efficiently for electronic reconstruction. This microwave-triggered electron–phonon coupling uniformly activates each hydrated Ru-ion complex, inhibiting random agglomerations on Ru_T-Mn_1-xCr_xO₂ catalyst surfaces (Supplementary Fig. 8). Moreover, this operation must also consider the interface coherence between the aqueous solution and the exchange substrate, which depends on their dielectric loss tangent (tan δ) values. When the exchange substrate’s tan δ value is comparable to that of water molecules, a more available coherent energy superposition can be induced^43,44,45, facilitating the Ru-atomic implantation and then enhancing OER performance. Interestingly, the tan δ value of the exchange substrate can be regulated by the type and concentration of dopants, especially for Cr (Supplementary Fig. 9). The tan δ value of optimal Mn_1-xCr_xO₂ is similar to that in water molecules but higher than pristine MnO₂ (Fig. 1c). The relevant radar cross-section simulations in Supplementary Fig. 10 also indicate that Mn_1-xCr_xO₂ has a more sensitive microwave response than pristine MnO₂. Thus, Mn_1-xCr_xO₂ provides better Ru assembly than pristine MnO₂ under microwave modulation, which can enhance the electron-phonon coupling strength through effective coherent energy superposition.

Raman spectra of RuCl₃ solution under traditional and microwave heating were compared (top panel of Fig. 1d). The Raman signals can be attributed to the symmetrical and asymmetrical OH stretching vibrations of water molecules and hydrated Ru ions^46,47,48. The high concentration of Ru ions has a stronger hydration state and lower water activity, as indicated by the monotonous decrease in the intensity of Raman signals related to hydrogen bond interactions (Supplementary Fig. 11). Compared to traditional heating (blue line), the Raman signals were substantially enhanced with microwave modulations. The energy superposition from microwave-driven rotations and collisions makes the energetic OH-stretching strength further deviate from equilibrium position, and this noticeable change in response to the structural force constants in the excited state can be intuitively reflected by the Raman fingerprints. The deconvolution of Raman peak areas for hydrogen bonds and hydrated Ru ion species (Supplementary Fig. 12 and Table 1) and comparison (bottom panel of Fig. 1d) clarify their intrinsic differences. The OH stretching vibrations are substantially enhanced under microwave heating compared to traditional heating. Conversely, the proportion of hydrated Ru-ion species decreases due to microwave-induced energy transfer, facilitating Ru atom diffusivity by breaking the hydrated bonds.

To better understand the specific assembly of Ru patterns, the microwave-mediated cation-exchange reaction at Mn_1-xCr_xO₂ surfaces in RuCl₃ solution is schematically shown in Fig. 1e. Theoretically, the traditional cation-exchange reaction must overcome a minimum potential barrier of about 353 meV (Supplementary Fig. 13). The slower assembly kinetic rate leads to a longer reaction time (more than 12 h). In this process, some hydrated Ru ions may spontaneously congregate together by hydrogen bond interaction of the hydration layer and finally be adsorbed on Mn_1-xCr_xO₂ surfaces as unstable Ru particles. If molecular phonon vibration energies are coherently transferred into hydrated Ru ions via Förster energy transfer under microwave stimulation, the relative potential barrier for cation-exchange reactions will be transiently diminished, making the substitution of Ru atoms easier (less than 30 min). Experimentally, the relevant energy superposition process and the minimum energy required for the optimal Ru atomic assembly were revealed by further modulating the microwave time and power (Supplementary Figs. 14 and 15).

Structural characterization of catalysts

A series of structural characterizations confirm the Ru_MW-Mn_1-xCr_xO₂ proposal. Transmission electron microscopy (TEM) images (Fig. 2a) show that the nanofiber morphology of Ru_MW-Mn_1-xCr_xO₂ remained unchanged compared to pristine Mn_1-xCr_xO₂ and other samples (Supplementary Fig. 16). Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images (Fig. 2b) show that the Ru atoms are brighter than neighboring Mn and Cr atoms owing to their significant mass difference. The fast Fourier transform images of Ru_MW-Mn_1-xCr_xO₂ in the inset of Fig. 2b reveal good crystal structure with typical (301), (200), and (400) planes; slight lattice distortion can be observed comparing with the Mn_1-xCr_xO₂ host (Supplementary Fig. 17). Microwave-activated Ru atoms are successfully implanted onto Mn_1-xCr_xO₂ surfaces, primarily as single-atom sites or regular Ru atomic chains with a Ru–Ru interatomic distance of 2.91 Å (Fig. 2c). Although some sub-nanometer Ru clusters are detected, substantially different from massive Ru particles in traditional cation-exchange reactions (Supplementary Fig. 18). This microwave-mediated assembly pattern enhances Ru species’ utilization and stability. Peak fitting and Rietveld refinement analysis of powder X-ray diffraction patterns demonstrate a well-ordered I4/m symmetry, but differences in Ru atomic assembly cause some peak broadening (Supplementary Fig. 19 and Table 2). It can be easily understood that the implantation of Ru atoms into Mn_1-xCr_xO₂ could lead to localized structural distortion more readily than simply random deposition without microwave modulation, and the symmetry-breaking-dependent structure factor causes some slight differences in XRD and Raman fingerprints (Supplementary Fig. 20)^49,50. Element mappings (Fig. 2d) indicate the coexistence of Mn, Cr, Ru, and O elements in the Ru_MW-Mn_1-xCr_xO₂ sample, and the corresponding energy-dispersive spectrum (EDS) was provided (Supplementary Fig. 21 and Table 3). The element contents of different samples were further determined via inductively coupled plasma optical emission spectroscopy (ICP-OES), as detailed in Supplementary Table 4. It is observed that Mn content decreases with some Ru atoms being selectively implanted, while Cr content remains virtually unchanged. Based on the above ICP results and the Pauli electronegativity principle, we can conclude that Ru atoms prefer to occupy the Mn sites, which can be further elucidated by X-ray photoelectron spectroscopy (XPS) analysis (Supplementary Fig. 22).

a TEM image of the Ru_MW-Mn_1-xCr_xO₂ catalyst, showing nanowire morphology similar to that of α-MnO₂ and reference samples. b Aberration-corrected HAADF-STEM image of Ru_MW-Mn_1-xCr_xO₂ at low magnification. Inset: Electron diffraction image obtained by fast Fourier transform (FFT). c Aberration-corrected HAADF-STEM image of Ru_MW-Mn_1-xCr_xO₂ at high magnification. Insets on the right show the corresponding intensity profiles labeled with L1 and L2 boxes. d Corresponding EDS mappings of Ru_MW-Mn_1-xCr_xO₂. The scale bar represents 1 nm. Normalized Ru K-edge XANES (e) and k³-weighted Fourier transform EXAFS (f) spectra for Ru_T-Mn_1-xCr_xO₂ (blue line) and Ru_MW-Mn_1-xCr_xO₂ (red line). g Wavelet transform EXAFS of the Ru K-edge for Ru_T-Mn_1-xCr_xO₂ (top) and Ru_MW-Mn_1-xCr_xO₂ (bottom). Normalized Cr K-edge XANES (h) and k³-weighted Fourier transform EXAFS (i) spectra for Ru_T-Mn_1-xCr_xO₂ (blue line) and Ru_MW-Mn_1-xCr_xO₂ (red line). j Wavelet transform EXAFS of the Cr K-edge for Ru_T-Mn_1-xCr_xO₂ (top) and Ru_MW-Mn_1-xCr_xO₂ (bottom). arb. units, arbitrary units; k, wave vector.

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Ru atomic configurations and their interatomic interactions were studied using X-ray absorption spectroscopy. The Ru K-edge X-ray absorption near-edge structure (XANES) spectra and amplified absorption pre-edge shifts (the insert of Fig. 2e) indicate that the Ru species’ oxidation state in Ru_MW-Mn_1-xCr_xO₂ is higher than that in Ru_T-Mn_1-xCr_xO₂, with an average positive valence between Ru powder (0) and RuO₂ (+4), consistent with XPS analysis (Supplementary Fig. 23). The difference in Ru oxide state can be attributed to the microwave-mediated orderly Ru atomic assembly and electronic interaction of the neighboring lattice Cr sites⁵¹. The extended X-ray absorption fine-structure (EXAFS) spectrum of Ru_MW-Mn_1-xCr_xO₂ shows a prominent scattering path at ~1.48 Å and a weaker second-shell signal at ~2.51 Å (Fig. 2f), corresponding to the Ru–O and Ru–O–Cr units, respectively. In contrast, an obvious peak appears at ~2.35 Å in both Ru_T-Mn_1-xCr_xO₂ and Ru powder, which can be assigned to the metallic Ru–Ru coordination. The least-squares EXAFS curve fitting was conducted to further extract the fine configuration of Ru atomic assembly (Supplementary Fig. 24 and Table 5). Notably, the Ru–O coordination of Ru_MW-Mn_1-xCr_xO₂ displays a shorter radial distance (R) and a lower centrosymmetry degree compared to RuO₂, which may originate from the contribution of local lattice distortion induced by the Ru–O–Cr configuration with symmetry breaking⁵². These results reveal that microwave-mediated coherent energy superposition facilitates orderly Ru atomic assembly and reduces the formation probability of Ru particles, which is observed in the Morlet wavelet transform (WT) more clearly (Fig. 2g). More discussions regarding the structure differences of the Ru assembly were provided in Supplementary Fig. 25. To further elucidate the interaction between Ru and Cr sites, Cr K-edge XANES and EXAFS spectra were also conducted. The average Cr oxidation state in Ru_MW-Mn_1-xCr_xO₂ is slightly lower than that of Ru_T-Mn_1-xCr_xO₂, as indicated by the energy position of absorption pre-edges (Fig. 2h) and relevant XPS analysis (Supplementary Fig. 26). This suggests potential bonding interactions and charge transfer between Cr and Ru sites. The EXAFS spectra of both samples show a dominant Cr–O signal at ~1.49 Å with no Cr−Cr scattering peak, indicating atomic dispersion of Cr in the MnO₂ substrate (Fig. 2i). Notably, the second-shell signal in Ru_MW-Mn_1-xCr_xO₂ exhibits a slightly positive shift compared with Cr–O–Cr in Ru_T-Mn_1-xCr_xO₂, which may be related to the local Cr–O–Ru interactions^52,53. The WT-EXAFS spectra show that (Fig. 2j) the second-shell in Ru_MW-Mn_1-xCr_xO₂ is located at ~6.9 Å⁻¹ in k space, larger than ~6.4 Å⁻¹ for the Cr–O–Cr path in Ru_T-Mn_1-xCr_xO₂, due to the stronger back-scattering of Ru atoms compared to neighboring Cr atoms. The differences of k values further corroborate the contribution of the Cr–O–Ru configuration. In a word, microwave stimulation effectively modulates the assembly pattern and local coordination environment of Ru atoms, which will further affect reactive Ru sites’ spin-dependent electronic structure.

Spin-related properties of catalysts

To display microwave-induced spin-dependent electronic reconfiguration, the magnetization of Mn_1-xCr_xO₂ as a function of magnetic field (M-H) with different assembly strategies was compared using a superconducting quantum interference device (SQUID) at room temperature (Fig. 3a). For pristine Mn_1-xCr_xO₂ sample, the M-H loop is linear without remanent magnetization, indicating paramagnetic behavior. The magnetic domains are randomly distributed due to room-temperature thermal disturbance (low spin: LS). When Ru patterns are selectively assembled onto Mn_1-xCr_xO₂ surfaces, the slope of M-H loop decreases, especially in the Ru_MW-Mn_1-xCr_xO₂ sample. Compared with random Ru particle deposition on Ru_T-Mn_1-xCr_xO₂, the bonding interaction and orbital hybridization in Ru_MW-Mn_1-xCr_xO₂ will be changed as symmetry breaking induced by selective Ru-atomic implantation. The corresponding multistage orbital degeneracy causes a spin ___domain flipping to a certain extent (the insert of Fig. 3a), leading to a more ordered spin configuration (high spin: HS) and distinguishable magnetic structure. Notably, the unchanged magnetic susceptibility of MnO₂-based samples shows the critical role of Cr incorporation in modulating spin structures (Supplementary Fig. 27). According to Heisenberg model⁵⁴, the energy difference between HS and LS configurations can be quantitatively expressed as follows: \(\Delta {{\rm{E}}}={E}_{{LS}}-{E}_{{HS}}={\sum}_{{ij}}{J}_{{ij}}{S}_{i}{{\cdot S}}_{j}\), where J_ij is the spin-exchange interaction strength, and S_i and S_j are the magnetic moments at the spin nets. The calculations show that HS configuration is more stable than LS configuration (ΔE is ~0.363 eV). The paramagnetic response difference shows that the orderly Ru atomic assembly at Ru_MW-Mn_1-xCr_xO₂ can also lead to a spin-related electronic reconfiguration, as confirmed by the temperature-dependent magnetization (M-T) curves (Fig. 3b). Generally, the relative magnetization intensity decreases with increasing temperature, but a cross point between Ru_MW-Mn_1-xCr_xO₂ and Ru_T-Mn_1-xCr_xO₂ was observed at ~350 K, indicating a stronger spin-exchange interaction induced by spin-flop transition.

a Room-temperature magnetic hysteresis loops of Mn_1-xCr_xO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂. Insets show magnetic ordering patterns in low-spin (LS) and high-spin (HS) states. b ZFC (zero field-cooled) and FC (field-cooled) magnetization curves of Mn_1-xCr_xO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂ as a function of temperature with a 5000 Oe external magnetic field. c EELS spectra of the Ru M-edge for Ru_MW-MnO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂. d Spin-resolved PDOS for the Ru element in Ru-MnO₂ and Ru-Mn_1-xCr_xO₂. E_F represents Fermi level. e ESR spectra of Mn_1-xCr_xO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂ recorded at room temperature. ΔH represents line width of the spectrum. f Electrical conductivity (σ) as a function of temperature for Mn_1-xCr_xO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂. Inset: Schematic of the electrode resistance measured by the four-terminal sensing method. arb. units, arbitrary units.

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The electron energy loss spectroscopy (EELS) was performed to determine the spin-dependent electronic reconfigurations (Fig. 3c and Supplementary Fig. 28). Typically, the fingerprint feature of Ru M-edge is primarily determined by the structural symmetry and spin electron occupation⁵⁵. The partial replacement in Ru_MW-Mn_1-xCr_xO₂ makes some electrons of Ru donate to the nearby Cr sites and a larger Ru-d half-filled electron density will increase the M₃ intensity. The integral peak area ratio (I_w) between the Ru M-edges after removing the baselines (I_w = M₃/(M₂ + M₃)) was calculated to gain insights into the Ru spin-state. Compared with the Ru_MW-MnO₂ and Ru_T-Mn_1-xCr_xO₂, the I_w value of Ru_MW-Mn_1-xCr_xO₂ sample increased, while the peak position blue-shifted to the high-energy region, corresponding to HS configuration. This is because the multistage orbital hybridizations induced by the microwave-mediated symmetry-breaking-dependent Ru-atomic patterns can facilitate valence electron hopping from the e_g orbital to the a_1g orbital, leading to a spin-electronic reoccupation.

Spin-resolved projected density of state (PDOS) of Ru sites was determined to comprehend spin-dependent electron occupation (Fig. 3d). Based on the Goodenough–Kanamori rule⁵⁶, the spin-exchange interaction between two neighboring t_2g orbitals will give rise to antiferromagnetic (AFM) behavior. When electrons at the lower t_2g orbital are easily hopped onto a higher half-filled a_1g orbital, the strong spin-exchange interaction will lead to a conversion from AFM to ferromagnetic (FM) behavior. Therefore, the electronic occupation at the Fermi level plays a crucial role in triggering a spin-flop transition. For the Ru-MnO₂ configuration, no obvious spin-polarized electrons populate at the Fermi level. Conversely, the Fermi level of Ru-Mn_1-xCr_xO₂ is fully occupied by the spin-up state, in which some electrons can be energetically exchanged between t_2g and a_1g orbitals. This is why the spin-flop transition preferentially occurs in the Ru-Mn_1-xCr_xO₂ configuration.

The spin-flop transition from LS to HS configuration is generally accompanied by changing the unpaired electrons. To further unveil their spin-dependent electron transition, the electron spin resonance (ESR) spectra of different samples were compared at room temperature (Fig. 3e). A distinguishable peak at g = 2.00 was observed for Ru_MW-Mn_1-xCr_xO₂ sample that corresponds with a partial spin-flop transition at the HS configuration. The electron occupation at multiple half-filled d orbitals with HS state leads to complex Zeeman splitting and resonance energy absorption⁵⁷, broadening the region of signal response. Combining the O 1s XPS results from Supplementary Fig. 29, we can conclude that the primary differences in ESR signals stem from spin-state transition. As a comparison, the signal response decreased for Ru_T-Mn_1-xCr_xO₂, further indicating that microwave-mediated coordinatively distorted π-donor ligands enhance the d-orbital degeneracy and electron pairing energy.

Temperature-related conductivity (σ) of different samples was measured to establish the relationship between electron–phonon couplings and microwave-mediated atomic assembly (Fig. 3f). Ru_MW-Mn_1-xCr_xO₂ showed higher conductivity than Mn_1-xCr_xO₂ and Ru_T-Mn_1-xCr_xO₂. The conductivity linearly increases with increasing temperature owing to the thermal excitation from phonon–electron interaction, indicating semiconductor behavior. In principle, the high-energy hot carriers at Ru_MW-Mn_1-xCr_xO₂ mainly confront lattice symmetry-breaking-induced single electron–phonon scattering (Supplementary Fig. 30). Conversely, randomly deposited Ru particles on Ru_T-Mn_1-xCr_xO₂ cause multiple electron–phonon scattering as interparticle interaction can partially hinder the migration of hot carriers. The temperature-dependent conductivity differences also demonstrate the advantage of microwave-mediated Ru atomic assembly in accelerating carrier migration.

Electrocatalytic performance

To disclose the relationship between spin-sensitive Ru atomic assembly and acidic OER activity, the linear sweep voltammetry (LSV) curves of different samples were measured in 0.1 M HClO₄ (Fig. 4a). All electrode potentials have been converted into the reversible hydrogen electrode (RHE). The catalytic activities of pristine MnO₂ and Mn_1-xCr_xO₂ are inferior to com-RuO₂, indicating that superficial Mn or Cr sites cannot easily trigger an acidic OER (Supplementary Fig. 31). When Ru atoms are selectively assembled onto electrode surfaces using a microwave-mediated strategy, the reactivities can be substantially enhanced, especially for Ru_MW-Mn_1-xCr_xO₂ sample. Cr doping in Mn_1-xCr_xO₂ optimizes the microwave-mediated Ru atomic assembly, making Ru_MW-Mn_1-xCr_xO₂ superior to Ru_MW-MnO₂. More interestingly, traditional heating-regulated Ru atomic assembly (Ru_T-MnO₂ and Ru_T-Mn_1-xCr_xO₂) does not achieve ideal OER behavior (Supplementary Fig. 32) due to randomly deposited Ru particles’ inability to provide half-filled d orbitals for optimal orbital hybridization and bonding interaction with O 2p orbitals of intermediates.

a LSV polarization curves (iR-corrected) of MnO₂, Mn_1-xCr_xO₂, RuO₂, Ru_MW-MnO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂ in 0.1 M HClO₄. The solution resistance (R) is about 10 ± 0.8 Ω. b Comparison of overpotential (10 mA cm⁻²), Tafel slopes, mass activities, specific activities, and TOF at a voltage of 1.45 V vs. RHE for RuO₂, Ru_T-Mn_1-xCr_xO₂, and Ru_MW-Mn_1-xCr_xO₂. Data are presented as mean values ± s.d. (n = 3). c Section of the pulse voltammetry protocol (black) showing an oxidative and reductive pulses of Ru_T-Mn_1-xCr_xO₂ and Ru_MW-Mn_1-xCr_xO₂ with the current response. d Total charge (integral anodic charge) of Ru_T-Mn_1-xCr_xO₂ and Ru_MW-Mn_1-xCr_xO₂ versus potential from pulse voltage induced current (PVC). e Response of the phase angle to the applied potential of Ru_T-Mn_1-xCr_xO₂ and Ru_MW-Mn_1-xCr_xO₂. The applied potentials in c, d, and e were without iR correction.

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Specific electrochemical metrics were measured or calculated to comprehensively compare the OER performance of different samples (Fig. 4b and Supplementary Table 6). The lower overpotential and Tafel slope of Ru_MW-Mn_1-xCr_xO₂ indicate its superior OER dynamics (Supplementary Figs. 33 and 34), including 1–3 orders of magnitude higher mass activity, specific activity, and turnover frequency than other samples (Supplementary Figs. 35–38). Ru_MW-Mn_1-xCr_xO₂ is one of the most active electrocatalysts among the state-of-the-art Ru/Ir-based materials reported in literature (Supplementary Table 7). Moreover, Ru_MW-Mn_1-xCr_xO₂ operated at 10 mA cm⁻² for over 200 h with a negligible increase in potential in sharp contrast to Ru_T-Mn_1-xCr_xO₂ and com-RuO₂ (Supplementary Fig. 39). Long-term ICP measurements of Ru and Mn elements in the electrolyte show that the disparity in stability stems from the rapid dissolution of unstable Ru particles on Ru_T-Mn_1-xCr_xO₂ during acidic OER (Supplementary Fig. 40). Moreover, the structural evolution, magnetic structure and electronic state transition of the catalysts during the acidic OER process were further probed by XPS, TEM, XRD, SQUID, and in-situ Raman measurements (Supplementary Figs. 41−46). All these results indicate that the microwave-mediated Ru_MW-Mn_1-xCr_xO₂ catalyst has superior OER activity and structural stability in acidic media.

The differences in catalytic activity can be quantitatively assessed using pulse voltammetry (PV) (Supplementary Fig. 47). The oxidation of active sites under bias in PV tests will form an oxidative charge involved in acidic OER⁵⁸. The degree of oxidation reflects changes in the pseudo-capacitance of Ru catalysts, related to the symmetry-breaking-dependent electronic reconfiguration. Figure 4c shows the partial redox pulse currents of Ru_T-Mn_1-xCr_xO₂ (blue) and Ru_MW-Mn_1-xCr_xO₂ (red), followed by the PV protocol (black). Generally, the decay behavior in the current response of Ru_MW-Mn_1-xCr_xO₂ is slower than that of Ru_T-Mn_1-xCr_xO₂ because the multilevel orbital splitting and spin transition induced by asymmetric Ru atomic patterns provides more half-filled d orbitals for the electronic “acceptance-donation” process (Supplementary Fig. 48). Conversely, randomly deposited Ru particles on Ru_T-Mn_1-xCr_xO₂ display metallic behavior, and the delocalization of electronic state makes the current response more sensitive. The instantaneous charge storage in different catalysts as a function of the applied voltage pulse is quantified by integrating the response currents after deducting the OER background current (Supplementary Fig. 49). The relationship between charge storage and applied potentials shows a bilinear behavior for different electrochemical process, indicating that capacitance values vary with slope (Fig. 4d). When reactants are adsorbed onto active sites and slowly become saturated, the instantaneous electronic reconfiguration compels the charge storage capacity to change with increase in potential. Compared with Ru_T-Mn_1-xCr_xO₂, Ru_MW-Mn_1-xCr_xO₂ exhibits a faster oxidative charge accumulation and dissipation behavior, lowering the OER activation energy and facilitating the deprotonation coupling electron transfer process. The difference in charge in this synchronized short-time transient as a function of log OER current (Supplementary Fig. 50) shows that oxidative charge accumulation on catalysts may directly affect the OER rate^59,60.

To further analyze the differences in reaction kinetics, in-situ electrochemical impedance spectroscopy (EIS) tests were performed at various applied biases. Ru_MW-Mn_1-xCr_xO₂ exhibited an accelerating trend of phase angle decline at low-frequency regions, indicating that the charge transfer between catalyst surfaces and electrolyte is substantially enhanced due to microwave-mediated spin-sensitive Ru atomic assembly (Fig. 4e and Supplementary Fig. 51). Meanwhile, the carrier migration in Ru_MW-Mn_1-xCr_xO₂ becomes easier than in Ru_T-Mn_1-xCr_xO₂ (Supplementary Fig. 52) because the multiple electronic scattering from random Ru interparticles can be avoided. The lower charge transfer resistance of Ru_MW-Mn_1-xCr_xO₂ facilitates the adsorption and activation of oxygen-containing species, leading to faster reaction kinetics for acidic OER applications.

Insights into OER mechanism

The reaction mechanism of acidic OER was elucidated from in-situ attenuated total reflectance surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS) (Fig. 5a and Supplementary Fig. 53) owing to its sensitivity to dynamic surface reconstitution with adsorbed intermediates. The intrinsic ATR-SEIRAS signals of Ru_MW-Mn_1-xCr_xO₂ sample merged with increasing potential (1.0–1.8 V vs. RHE), while oxygen bubbles slowly appeared at the electrodes. The intensity of two distinct adsorption bands at 960 cm⁻¹ and 1108 cm⁻¹ substantially increased with potential exceeding the OER region potential (≥1.3 V). This can be attributed to the formation of surface-adsorbed *OOH and linearly bonded superoxol species (*OO)⁶¹, where *OOH is a typical intermediate for adsorbate-evolving mechanism (AEM) (Supplementary Fig. 54). Moreover, the Ru_T-Mn_1-xCr_xO₂ sample exhibited similar FTIR signals, suggesting the same AEM pathway as Ru_MW-Mn_1-xCr_xO₂. However, the weaker intensity and higher threshold potential observed indicate slower OER kinetics (Supplementary Fig. 55). Owing to this distinctive FTIR signal response, their catalytic properties were quantitatively evaluated by calculating the relative peak area (R_A) of intermediates as follows: \({R}_{A}=\int {I}_{E}/\int {I}_{\max }\), where I_E is the peak intensity of *OOH intermediate at different applied potentials and I_max is the maximum value of I_E. The normalized peak areas of *OOH in Ru_T-Mn_1-xCr_xO₂ and Ru_MW-Mn_1-xCr_xO₂ with varying potential were compared (right panel of Fig. 5a). The signal area of Ru_MW-Mn_1-xCr_xO₂ with intermediates rapidly increased at ~1.35 V and then slowly reached a maximum value, demonstrating a typical OER process. However, the relative signal area of Ru_T-Mn_1-xCr_xO₂ is less than that of Ru_MW-Mn_1-xCr_xO₂, and the potential for initiating OER blue-shifted to 1.45 V. This ATR-SEIRAS signal response between Ru_MW-Mn_1-xCr_xO₂ and Ru_T-Mn_1-xCr_xO₂ reveals their differences in reaction kinetics during acidic OER.

a Left: In-situ ATR-SEIRAS measurements in the range of 900−1200 cm⁻¹ at various applied potentials vs. RHE for Ru_MW-Mn_1-xCr_xO₂. Right: Potential-dependent normalized *OOH peak areas of Ru_T-Mn_1-xCr_xO₂ (grey line) and Ru_MW-Mn_1-xCr_xO₂ (black line). b Top: DEMS signals of O₂ products for Ru_MW-Mn_1-xCr_xO₂ in the electrolyte using H₂¹⁶O as the solvent during three cycles of LSV in the potential range of 1.1–1.75 V vs. RHE, with a scan rate of 5 mV s⁻¹. Bottom: The ³⁴O₂:³²O₂ and ³⁶O₂:³²O₂ signal ratios of Ru_MW-Mn_1-xCr_xO₂ during the OER process with H₂¹⁶O as the electrolyte solvent. c Computed free energies of intermediates for the AEM-type OER at different reactive sites and spin states. U = 1.23 V vs. RHE. Charge density difference (d) and relative COHP of adsorbed *OOH (e) onto the Ru site at Ru_MW-Mn_1-xCr_xO₂ with LS and HS states. The yellow regions in d show charge depletion, while the blue regions show charge accumulation. MS mass spectrometry, arb. units, arbitrary units, LS low spin, HS high spin, E_F fermi level.

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To further monitor the acidic OER behaviors, in-situ differential electrochemical mass spectrometry (DEMS) measurements were performed using the isotope¹⁸O-labeling method (Supplementary Fig. 56). Ru_MW-Mn_1-xCr_xO₂ was first labeled with ¹⁸O by performing LSV cycles in H₂¹⁸O electrolyte (Supplementary Fig. 57a). The relative XPS measurement shows that abundant ¹⁶O species spontaneously adsorbed onto the catalyst surface (before ¹⁸O-labeling operation) (Supplementary Fig. 29)⁶¹. Therefore, the corresponding ³²O₂ (¹⁶O + ¹⁶O), ³⁴O₂ (¹⁶O + ¹⁸O), and ³⁶O₂ (¹⁸O + ¹⁸O) species were formed from H₂¹⁸O and intrinsic ¹⁶O species through AEM pathway, with ³⁶O₂ being the dominant product along with trace amounts of ³⁴O₂ and ³²O₂ for each OER cycle. Distinct signals of these gaseous products indicate that the catalyst surfaces are labeled with large amounts of ¹⁸O if the acidic OER process is promoted by lattice oxygen mechanism (LOM). The labeled catalyst was thoroughly washed with abundant deionized water, and the DEMS measurements for OER cycles in H₂¹⁶O electrolyte were repeated (top panel of Fig. 5b). The signal response of ³²O₂ is obviously higher than that of ³⁴O₂ and ³⁶O₂. And the corresponding MS signals as a function of potentials (Supplementary Fig. 57b) show a typical initiation behavior of AEM-type OER. Ru_T-Mn_1-xCr_xO₂ sample showed similar signal distributions, but with magnitude differences (Supplementary Fig. 58). More importantly, the relative signal ratio of ³⁴O₂: ³²O₂ (black line) within the OER working windows (1.2–1.6 V vs. RHE) hardly unchanged (bottom panel of Fig. 5b) and is comparable to that of the abundance of ¹⁸O in natural water or residual ¹⁸O adsorbates at the previous step within experimental uncertainty⁶², indicating that the LOM cannot happen over Ru_MW-MmCrO₂. Meanwhile, the relative signal ratio of ³⁶O₂: ³²O₂ (gray line) gradually decreased with increasing potential, further confirming the dominance of AEM pathway during acidic OER⁶³.

Comprehensive comparison of free energies for each intermediate in the AEM pathway (Fig. 5c and Supplementary Fig. 59) were conducted to reveal the correlation between reactivity and microwave-mediated symmetry-breaking-dependent spin electronic reconfiguration. The relative difference in free energy between successive derivatives plays a crucial role in determining the activation energy at rate-limiting steps. For pristine MnO₂ surface, the rate-determining intermediate originates from the generation of *OOH (top panel), requiring additional energy of 1.0 eV to continue follow-up reactions. When Cr atoms are doped into MnO₂ surface to construct Mn_1-xCr_xO₂ slab, the potential barrier with the formed *OOH increases to 1.28 eV. This comparison shows that the OER preferably occurs in MnO₂ sample instead of Mn_1-xCr_xO₂. Interestingly, the assembled Ru atoms on MnO₂ (middle panel) or Mn_1-xCr_xO₂ (bottom panel) will cause a spin-dependent electronic arrangement, greatly optimizing the corresponding catalytic activity. For Ru-MnO₂ sample (middle panel), the rate-limiting intermediate *OOH remains unchanged, but the activation energy decreased from 1.19 eV (LS) to 0.67 eV (HS) with the flipping of a spin state electron. If Ru atoms are selectively assembled onto Mn_1-xCr_xO₂ surface (bottom panel), the activation energy further decreased to 0.63 eV at HS, because microwave-mediated spin-dependent symmetry-breaking leads to a multilevel orbital hybridization and electron rearrangement facilitating the electronic “acceptance-donation” process. By the way, the possibility that the Mn sites around the Ru atoms act as adsorption-activating centers has been ruled out (Supplementary Figs. 60 and 61).

Spin-dependent orbital hybridization and charge transfer were compared from the charge density difference for Ru-Mn_1-xCr_xO₂ with adsorbed *OOH species (Fig. 5d). The charge reconfiguration is mainly delocalized at the formed Ru–OOH bonds, especially for the HS state. The Ru site with HS configuration donates sufficient unpaired d-electrons to the formed Ru–OOH bonds, leading to an energetic bonding interaction from d-p orbital hybridization. Bader charge analysis also confirms that the Ru sites at HS lead to a charge transfer of 0.034 e, larger than the charge transfer of LS (0.022 e). To better understand this process, the crystal orbital Hamilton population (COHP) was compared (Fig. 5e). Unlike the HS configuration, an obvious antibonding interaction appears at the Fermi levels. This makes the LS configuration challenging to optimize the electron donation process, leading to a higher rate-limiting potential barrier. The differences in bonding interactions can also be quantitatively evaluated from the integrated area of COHP (ICOHP). The higher electron orbital overlap (lower ICOHP) at HS (–1.07 eV) than LS (–0.96 eV) indicates stronger Ru–OOH orbital interaction. Meanwhile, an easier charge transfer and orbital hybridization preferably choose the HS configuration. The experimental and theoretical analyses confirm that microwave-mediated symmetry-breaking-dependent orbital degeneracy and spin electronic rearrangement play a crucial role in enhancing the reaction kinetics and stability of acidic OER (Supplementary Fig. 62).

PEM–WE device performance

Motivated by the superior acidic OER activity and stability of Ru_MW-Mn_1-xCr_xO₂, we proceeded to assess its practical water-splitting potential. Herein, Ru_MW-Mn_1-xCr_xO₂ was used as the anode catalyst for OER, commercial Pt/C as the cathode catalyst for HER, and a PEM to construct a PEM-WE electrolyzer (Fig. 6a and Supplementary Fig. 63). The membrane electrode assembly (MEA) was prepared using the catalyst-coated membrane (CCM) method (Supplementary Figs. 64 and 65). The SEM image and corresponding EDS mapping (Fig. 6b) clearly show the microstructure of MEA composed of Pt/C and Ru_MW-Mn_1-xCr_xO₂ catalysts, tightly and uniformly distributed on both sides of PEM. The zero-gap electrode interface is beneficial for accelerating proton migration and charge transport between the anode and cathode. The steady-state current–voltage (I–V) polarization curves (without iR compensation) (Fig. 6c) clearly show that Ru_MW-Mn_1-xCr_xO₂ had greater water electrolysis activity compared to the com-RuO₂ catalyst. At 80 °C, cell voltages of only 1.67 and 1.88 V were required to reach current densities of 0.5 and 1.0 A cm⁻², respectively, far superior to those achievable with com-RuO₂ (1.99 [email protected] A cm⁻² and 2.49 [email protected] A cm⁻²). More importantly, the Ru_MW-Mn_1-xCr_xO₂ cell can be operated stably at 0.2 and 1.0 A cm⁻² over 300 h (Fig. 6d), with a negligible degradation rate (~0.18 mV h⁻¹), substantially better than the com-RuO₂ electrolyzer (0.2 A cm⁻², <30 h). The Ru_MW-Mn_1-xCr_xO₂ electrolyzer exhibits stronger stability at higher current densities compared to the other state-of-the-art electrocatalysts (Supplementary Table 8). In addition, there was no apparent change in the morphology and electronic structure of the catalysts on MEA after long-term operation in the PEM electrolyzer (Supplementary Figs. 66 and 67), further corroborating the notable durability of the Ru_MW-Mn_1-xCr_xO₂ catalyst under industrially relevant harsh scenarios.

a Schematic of the stack structure and operation principle for the PEM electrolyzer. b The SEM image and corresponding elemental mapping of the MEA prepared by the CCM process. c Polarization curves of the PEM electrolyzer using Ru_MW-Mn_1-xCr_xO₂ or com-RuO₂ as the anodic catalyst and commercial Pt/C as the cathodic catalyst, at room temperature (RT) and 80 °C. No cell voltages were iR compensated. d Top panel: Chronopotentiometry curves of the PEM electrolyzer using Ru_MW-Mn_1-xCr_xO₂ or com-RuO₂ catalyst operated at 200 mA cm⁻². Bottom panel: Chronopotentiometry curve of the PEM electrolyzer using Ru_MW-Mn_1-xCr_xO₂ catalyst operated at 1000 mA cm⁻². e Comprehensive comparison of the PEM electrolyzer using Ru_MW-Mn_1-xCr_xO₂ (red line) and com-RuO₂ catalysts (blue line) in terms of the W, ETH (500 mA cm⁻²), j (at 1.8 V), R, T, and per GGE H₂ price. W, power consumption per cubic meter of hydrogen yield; ETH, electricity-to-hydrogen energy conversion efficiency; j, current density; R, hydrogen production rate; GGE, gallon of gasoline equivalent.

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Subsequently, we compared the energy indicators of different electrolyzers to quantify their application value, as electricity costs account for 50–90% of the overall levelized cost of hydrogen production. As shown in Fig. 6e, the well-designed Ru_MW-Mn_1-xCr_xO₂ cell exhibits substantial improvements in energy utilization, including power consumption per cubic meter of hydrogen yield (W) of 3.65 kW h Nm⁻³, electricity-to-hydrogen energy conversion efficiency (ETH) of 88.7%, hydrogen production rate (R) of 3.64 Nm³ h⁻¹ m⁻², and current density at 1.8 V ( j) = 797 mA cm⁻². These values are notably superior compared to a typical com-RuO₂ electrolyzer, which has W of 4.35 kW h Nm⁻³, ETH of 74.4%, R of 1.36 Nm³h⁻¹ m⁻², and j of 298 mA cm⁻². More importantly, the cost per gallon of gasoline equivalent (GGE) for the H₂ produced using a Ru_MW-Mn_1-xCr_xO₂ electrolyzer is only USD 0.87, far below the U.S. Department of Energy’ s 2026 target of US$ 2.00⁶⁴. Additionally, the scalability and cost of electrocatalysts are crucial for practical applications. The Ru_MW-Mn_1-xCr_xO₂ catalyst can be synthesized on a gram scale using a custom microwave reactor (Supplementary Fig. 68), with a calculated cost of approximately USD 2001 per kg. This is only 4.9% of the cost of com-RuO₂ (approximately USD 40,383 per kg) and 0.47% of IrO₂ (approximately USD 428,000 per kg) (Supplementary Tables 9 and 10). Considering both cell performance and noble metal cost, the advantages of the microwave-mediated orderly Ru atomic assembly and spin renormalization are clear. Moreover, owing to its intrinsic fast proton transport, the PEM-WE has a much faster start-up and shut-down response than other electrolyzer types like alkaline water electrolyzers and anion exchange membrane electrolyzers. Consequently, our Ru_MW-Mn_1-xCr_xO₂ cell performs well with variable energy sources such as wind, photovoltaic, and thermoelectric power in experiments (Supplementary Fig. 69). More crucially, utilizing these clean energy sources to drive the PEM-WE can further reduce carbon emissions, promoting a closed-loop carbon footprint and sustainable social development.

To summarize, we developed a microwave-mediated strategy that selectively assembles Ru patterns onto the Mn_1-xCr_xO₂ surface. Microwave-modulated coherent energy superposition avoids random agglomerations in Ru atomic assembly while inducing localized spin ___domain renormalization, enhancing Ru sites’ reactivity and preventing deleterious overoxidation in acidic OER. The obtained Ru_MW-Mn_1-xCr_xO₂ catalyst possesses a high mass activity of 1014.5 A g_Ru⁻¹, which is about 33-fold higher than the Ru_T-Mn_1-xCr_xO₂ processed through traditional heating. Moreover, Ru_MW-Mn_1-xCr_xO₂ demonstrates an industrial current density of 1.0 A cm⁻² at 1.88 V cell voltage and operates stably over 300 h in a PEM electrolyzer. The higher electrolysis efficiency and lower comprehensive cost further demonstrate that the PEM system using the Ru_MW-Mn_1-xCr_xO₂ catalyst has great future potential in practical water splitting to produce green hydrogen. From both theoretical research and practical application perspectives, this work suggests an intriguing nanotechnology to realize the orderly assembly and spin configuration optimization of Ru atomic patterns, thereby boosting the acidic water oxidation performance.

Synthesis of α-MnO₂ and Cr-doped MnO₂

To synthesize α-MnO₂ nanofibers, 0.02 mol of MnSO₄·H₂O, 0.02 mol of (NH₄)₂S₂O₈, and 0.06 mol of K₂SO₄ were dissolved in 70 mL of H₂O. The mixture was stirred vigorously for 1 h, transferred to an autoclave, and heated at 140 °C for 12 h. After cooling to room temperature, the resulting dark brown powders were washed alternately five times with deionized water and ethanol, separated via vacuum filtration, and dried overnight in an oven at 60 °C. To generate Cr-doped MnO₂, varying amounts of CrCl₃ (0.5%, 1%, 3%, and 5% of Mn’s molar mass) were added to the solution. These were designated as Mn_1-xCr_xO₂ (x represents 0.005, 0.01, 0.03, and 0.05, respectively). Unless otherwise stated, 1% Cr-doped MnO₂ was referred to as Mn_1-xCr_xO₂ in this work. The precise Cr content in bulk MnO₂ was determined using ICP-OES.

Microwave-mediated Ru atomic pattern assembly

For the assembly of Ru atomic patterns, 50 mg of as-prepared Mn_1-xCr_xO₂ nanofibers and 40 mg of RuCl₃·xH₂O were each dispersed in 10 mL of H₂O and sonicated for 30 min. The two solutions were then thoroughly mixed and injected into a polytetrafluoroethylene microwave reactor. The mixture was heated in a microwave oven (2.45 GHz, 900 W) for 0.5 h. The microwave time and microwave power were optimized in Supplementary Fig. 13. After naturally cooling to room temperature, the product was separated by vacuum filtration, washed alternately with ethanol and deionized water, and dried overnight in a vacuum oven at 80 °C to obtain microwave-assisted Ru-assembled Mn_1-xCr_xO₂ (Ru_MW-Mn_1-xCr_xO₂). Microwave-assisted Ru assembly on MnO₂ substrates (Ru_MW-MnO₂) followed a similar process. To differentiate the effects of microwave-mediated coherent energy superposition from traditional heating on Ru pattern assembly, thermal-assisted Ru assembly samples (Ru_T-MnO₂ and Ru_T-Mn_1-xCr_xO₂) were prepared using an oil bath device at 100 °C, matching the theoretical temperature of microwave heating.

Electrochemical measurements

The OER tests were conducted through a standard three-electrode system on an electrochemical workstation (Autolab PGSTAT302N, Metrohm). The O₂-saturated HClO₄ electrolyte of 0.1 M was freshly prepared before each test and stored at room temperature. All glassware was sonicated in ultrapure water before electrochemical treatment. Ag/AgCl (saturated KCl) served as the reference electrode, and a graphite rod (99.99%, Ledonlab) as the counter electrode. The reference electrode was calibrated in hydrogen-saturated 0.01 M HClO₄. The calibrated value for Ag/AgCl in 3.5 M AgCl–KCl was equal to 0.211 (close to the theoretical value of 0.205). The catalyst ink was prepared by dispersing the as-prepared catalyst (5 mg) with Vulcan XC-72 (2.5 mg) into 1 mL of mixed solution (5% Nafion® solution/deionized water/ethanol = 2:73:25 by volume). The effect of adding carbon black was discussed in detail in Supplementary Fig. 70. After 1 h of sonication, 50 μL of homogeneous ink was dropped onto a carbon paper electrode (geometric area: 0.5 cm²), resulting in a catalyst loading of 0.5 mg cm⁻², and dried fully in air at room temperature to serve as the working electrode. LSV with a scanning rate of 5 mV s⁻¹ was conducted in the potential range of 1.15–1.75 V versus RHE. Measurements were repeated at least three times using freshly deposited catalysts to assess reproducibility. All potentials measured against Ag/AgCl were converted to the RHE scale using: E (potential, versus RHE) = E (versus Ag/AgCl) + E⁰ (versus Ag/AgCl) + 0.059 × pH. In 0.1 M HClO₄ electrolyte, pH values are ~0.9 ± 0.04. E-iR represents 95% iR-corrected, where i is the measured current and R is the uncompensated solution resistance (~10 ± 0.8 Ω) as obtained from EIS. EIS measurements were carried out in the frequency range of 100 kHz to 0.1 Hz, applying different overpotentials. Stability tests were performed using chronopotentiometry (CP) measurements at 10 mA cm⁻² for 200 h. During LSV and CP tests, the electrolyte was stirred magnetically at 900 rpm to accelerate the detachment of oxygen bubbles on the working electrode surface. The Tafel plot was obtained by converting the J-V curves to potential (V versus RHE) versus the logarithm of current density (log |J|). Pulse voltammetry was performed to monitor the current over time. The potential was maintained at a low potential (E_low = 1.15 V versus RHE) for 5 s, then switched to a higher potential (E_high) for 5 s, before returning to E_low for 5 s. This cycle was repeated, increasing E_high from 1.27 V to 1.59 V in 20 mV increments. The charge related to the potential step was calculated by integrating the current pulse over time after subtracting the background current signal (OER current). The OER current was recorded at the end of the 5 s anodic potential segment.

PEM water electrolyzer tests

The MEA was prepared using the classical CCM method. Ru_MW-Mn_1-xCr_xO₂ or commercial RuO₂ (a typical OER catalyst) was used as the OER anode catalyst, and commercial Pt/C (40 wt%) was used as the HER cathode catalyst. Catalysts were dispersed in a mixture of isopropanol and distilled water (7:1) with 20 wt.% Nafion 117 ionomer for the cathode and 30 wt.% for the anode. The mixture was sonicated in a low-temperature water bath for at least 1 h and filtered through a 500-mesh filter to obtain a homogeneous catalyst ink. Then, around 1 mg cm⁻² of commercial Pt/C and 2.5 mg cm⁻² of Ru_MW-Mn_1-xCr_xO₂ with carbon black catalysts (3:1) were uniformly air-sprayed onto both sides of the Nafion 115 membrane (thickness: ~130 μm) under heating conditions. Finally, platinized titanium fiber felt (0.4 mm) and carbon paper were used as the porous transport layers in the anode and cathode, which were hot-pressed together with MEA (135 °C, 30 MPa) for 8 min. Deionized water was circulated in the anode using a peristaltic pump at 10 rpm. The electrolyzer’s operating temperature is regulated by the thermostat water bath and resistance heating element. Steady-state polarization curves and chronopotentiometric curves were obtained using a programmable direct-current power supply (DAHUA, DH1790-1).

Computational details

All DFT calculations were performed by the Vienna Ab initio Simulation Package⁶⁵. The electronic structures of materials were described by the generalized gradient approximation exchange-correlation function with Perdew–Burke–Ernzerhof (PBE)⁶⁶. Monkhorst–Pack k-points grid of 9 × 9 × 1 was applied to expand the Kohn–Sham wave functions. The plane wave basis set had a cutoff energy of 500 eV. A vacuum space of 20 Å was used for all the slab models (Supplementary Data 1) to ensure the periodic images were well separated. The bottom two layers of atoms in the slabs were fixed to mimic bulk, and then the surface relaxations were performed. The geometry relaxation and energy convergence tolerance for the electronic structure were 0.01 eV Å⁻¹ and 10⁻⁵ eV per atom, respectively. Spin polarization was applied to all structures. More computational details about formation energy and solvation effects were provided in the Supplementary Methods.