Synthesis methods
Preparation of Fe–LMS, Fe@Ga–In, Fe@Ga–Sn and Fe@Ga
The synthesis Fe–LMS must be performed in a nitrogen atmosphere throughout to prevent oxygen oxidation.
Gallium (99.999%) was first melted at 50 °C in a beaker. Subsequently, 7 g molten gallium metal was mixed with 2 g indium powder (99.999%) and 1 g tin powder (99.999%), followed by vigorous stirring at 160 °C for 5 h. Different amounts of iron powder (0.1–2 g, 99.999%) were added into the liquid metal alloy followed by manual stirring until the iron powder was entirely dissolved. Then, 100 µl of 5% hydrochloric acid was added to keep the alloy in a liquid state. The obtained liquid metal catalyst Fe–LMS was stored in an oxygen-free container.
After adjusting the feeding ratio to Fe:Ga:In to 0.1:7:3 (w/w/w/), the aforementioned process was repeated to obtain Fe@Ga–In. After adjusting the feeding ratio to Fe:Ga:Sn to 0.09:7:1 (w/w/w/), the aforementioned process was repeated to obtain Fe@Ga–Sn. After adjusting the feeding ratio to Fe:Ga to 0.1:10 (w/w) and adjusting the temperature to 200 °C, the aforementioned process was repeated to obtain Fe@Ga.
Preparation of Fe–LMS@H2O
First, 10 mg of prepared Fe–LMS was added to 20 ml of deionized water, and the mixture was then placed in a room-temperature water bath and agitated ultrasonically for 30 min until the solution became turbid. The synthesis of Fe–LMS@H2O does not require a protective atmosphere. Fe–LMS@H2O is a suspension, and the prepared Fe–LMS@H2O must be used immediately to avoid sedimentation.
Catalytic performance evaluation
Methane oxidation by Fe–LMS with no magnetic field
Oxidation of CH4 was performed in a stainless-steel Teflon-lined autoclave with a volume of 100 ml. Typically, 10 mg catalyst Fe–LMS, 20 ml deionized water and 5 ml H2O2 (30%) were added to the autoclave. Hydrochloric acid was added dropwise until the pH of the solution approached 4. The autoclave was flushed three times with methane and then pressurized with methane to the desired pressures (0.5–3.0 MPa CH4, 99.999%). The reaction proceeded for 1 h at room temperature. The autoclave with obtained products was cooled in ice water for 20 min prior to analysis. Liquid products were quantified by 1H and 13C NMR spectroscopy. The gas-phase products are discharged through the reactor’s exhaust valve and collected in a gas bag, which is subsequently transferred to the GC for analysis.
Methane oxidation by Fe–LMS with a magnetic field
The CH4 oxidation reaction was carried out in a closed high-pressure autoclave. The high-pressure reactor was placed between two parallel permanent magnets, and the intensity of the magnetic field was controlled by an external distance-adjustment device. About 10 mg catalyst, 20 ml deionized water and 5 ml H2O2 (30%) were added to the autoclave. Hydrochloric acid was added dropwise until the solution pH approached 4. The autoclave was flushed three times and then pressurized with methane to the desired pressure (0.5–3.0 MPa CH4, 99.999%). The reaction mixture was left at room temperature for 1 h. The magnetic field can be regulated over the range 0–1,200 G. The autoclave with obtained products was cooled in ice water for 20 min prior to analysis. Liquid products were quantified by 1H and 13C NMR spectroscopy. The gas-phase products are discharged through the reactor’s exhaust valve and collected in a gas bag, which is subsequently transferred to the GC for analysis.
Methane oxidation by Fe–LMS@H2O with magnetic field switching
The CH4 oxidation reaction was carried out in a closed high-pressure autoclave. The high-pressure reactor was placed between two parallel permanent magnets, and the intensity of the magnetic field was controlled by an external distance-adjustment device. First, 2 ml Fe–LMS@H2O solution, 20 ml deionized water and 5 ml H2O2 (30%) were added to the autoclave. Hydrochloric acid was added dropwise until the solution pH approached 4. The autoclave was flushed three times and then pressurized with methane to the desired pressure (2.0 MPa CH4, 99.999%). The reaction mixture was left at room temperature for 1 h. Tests were conducted under magnetic fields of 0, 50, 100, 150, 175, 200, 210, 250, 300, 400 and 500 G. The autoclave with obtained products was cooled in ice water for 20 min prior to analysis. Liquid products were quantified by 1H and 13C NMR spectroscopy. The gas-phase products are discharged through the reactor’s exhaust valve and collected in a gas bag, which is subsequently transferred to the GC for analysis.
Methane oxidation by Fe–LMS with additional CO and applying a magnetic field
The CH4 oxidation reaction was carried out in a closed high-pressure autoclave. The high-pressure reactor was placed between two parallel permanent magnets, and the intensity of the magnetic field was controlled by an external distance-adjustment device. About 100 µl catalyst, 19 ml deionized water and 1 ml H2O2 (30%) were added to the autoclave. Hydrochloric acid was added dropwise until the pH of the solution approached 4. The autoclave was flushed three times and then pressurized with CO to the desired pressure (0.1–1.0 MPa), and 2 MPa CH4 was then added into the reaction system. The reaction proceeded for 1 h at room temperature, under 0 or 500 G. The obtained products were cooled in ice water for 10 min prior to analysis. Liquid products were quantified by 1H and 13C NMR spectroscopy. Gas products were quantified by GC.
Reproducibility of liquid product conversion
First, 100 µl fresh catalyst, 20 ml deionized water and 5 ml H2O2 (30%) were added to the autoclave, which was flushed three times with deionized water and then pressurized with 2.0 MPa methane. Hydrochloric acid was added dropwise until the pH of the solution approached 4. The reaction was performed while switching the magnetic field on–off 11 times at 1-h intervals. The catalyst was washed with hydrochloric acid (pH 4) after each 1-h reaction to remove the oxidation film on the catalyst. The reactants and washed catalyst were then placed back into the autoclave for the next reaction. The obtained products were cooled in ice water for 10 min prior to analysis. Liquid products were quantified by 1H and 13C NMR spectroscopy.
Characterization methods
X-ray diffraction measurements were recorded on a Rigaku Miniflex-600 diffractometer using Cu Kα radiation (λ = 0.15406 nm) with a step size of 0.02° and a counting time of 0.5 s. Transmission electron microscopy images were recorded on a Hitachi H-7700 operated at 100 kV. Scanning electron microscopy images were recorded on a Supra 40. A Quantum Design MPMS3 was used for magnetic moment testing. Elemental analysis was performed by inductively coupled plasma atomic emission spectrometry using an Optima 7300 DV spectrometer. Liquid products were quantified by NMR spectroscopy. Measurements were conducted on a Bruker Avance-Ⅲ 400 spectrometer. 1H NMR spectra were recorded with a 2-s recycle delay, for 64 scans, using dimethyl sulfoxide as an internal standard. 13C NMR spectra were recorded with a 10-s recycle delay, for 2,048 scans. Gaseous products were quantified by a GC equipped with a 5-Å molecular sieve, a Porapak Q 80/100 mesh, and SE-30 and HP-Al2O3/S columns using helium (ultrahigh purity) as carrier gas.
In situ electron microscopy and corresponding atomic-level EDS mapping
Aberration-corrected HAADF-STEM images and corresponding EDS maps were recorded on a FEI-Titan Cubed Themis G2 300 STEM. Frozen sample rods were used to load samples, allowing for cooling with liquid nitrogen during testing. Before electron microscopy imaging, the samples were subjected to magnetic fields of 0 G and 500 G and frozen with liquid nitrogen for 10 min to fix the structure.
In situ X-ray 3D CT
In situ X-ray 3D CT was carried out at beamline BL07W of the National Synchrotron Radiation Laboratory. The sample holder, containing the nickel grid, was transferred to the chamber of a transmission soft X-ray microscope, where an elliptical capillary condenser focused the soft X-ray beam onto the cells for observation. In the sample chamber, the magnetic field is adjusted by controlling the distance between the natural magnet and the sample holder. For the generation of 3D volumes, the cells were rotated from −60° to +60°, capturing a continuous series of 121 projected images at 1° intervals with a 2-s exposure time. X-ray energies is 706 eV and 715 eV (covering the Fe L3 edge) were used. Alignment of the tilt series was performed using XMController, and 3D CT reconstruction was carried out using XMReconstruction.
In situ Mössbauer spectroscopy
Mössbauer spectroscopy measurements were conducted using a Wissel MR-2500 spectrometer. For the Fe–LMS sample under a 500-G magnetic field, the field strength at the sample location was adjusted by placing a natural magnet outside the measurement chamber. Each sample weighed 100 mg, and measurements were performed at room temperature in a vacuum environment. The spectral range was set to ±12 mm s−1, with a measurement duration of 24 h.
ESR
ESR was performed at the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, using the following parameters: temperature, 173 K; power, 0.01 mW; central field, 7,000 G; sweep width, 14,000 G; modulation frequency, 100 kHz; modulation amplitude, 2.00 G. The samples were frozen at 173 K for 10 min under magnetic fields of 0 G and 500 G, respectively, and the iron powder standard samples were frozen at 0 G and 173 K for 10 min before testing.
NAP-XPS measurements
NAP-XPS measurements were performed using a system located at Shanghai Tech University. This system was manufactured by SPECS Surface Nano Analysis (Supplementary Fig. 28). The facility consists of a main chamber, a preparation chamber and a load–lock chamber. The analysis chamber is equipped with a PHOIBOS NAP hemispherical electron energy analyser, a microfocus monochromatized Al Kα X-ray source with a beam diameter of 300 μm, a SPECS IQE-11A ion gun and an infrared laser heater. Fe1–LMS (1.1 wt%) was dropped onto a clean silicon wafer and dried at room temperature. Having installed the sample in the analysis chamber, high-purity CH4 was fed into the chamber up to a pressure of 0.4 mbar. After collecting the C 1s spectra, a flask containing 30% H2O2 solution was connected to the XPS testing chamber (see Supplementary Fig. 29 for photographs). The negative pressure within the chamber ensured the controlled evaporation of H2O2 into the atmosphere, and a new series of C 1s spectra were acquired. The above results were recorded as the dispersed state. We then replaced the iron content to give a concentration of 9.8 wt%, repeated the above experiment, and recorded the results as the aggregated state.
It should be noted that due to the stringent pressure requirements of NAP-XPS, the testing conditions represent a compromise compared with those of the actual catalytic experiments. Below, we provide a detailed justification for these compromises:
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(1)
The primary objective of NAP-XPS is to capture reaction intermediates. Given the technique’s qualitative nature and operational constraints, direct introduction of a liquid-phase environment was unfeasible. Instead, we used a 0.13-mbar H2O2 (30% solution) vapour atmosphere to approximate the H2O2 liquid environment present in the actual catalytic reaction. Although this substitution differs from the exact reaction conditions, it enables the identification of key intermediates under operando conditions.
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(2)
As discussed elsewhere (Supplementary Figs. 20–24), HCl serves to prevent complete oxidation of the catalyst surface in the catalytic reaction. However, during the NAP-XPS measurement timeframe, the oxidative capacity of the H2O2 atmosphere is insufficient to fully oxidize the catalyst surface; thus, its absence does not alter the observed reaction pathway. Furthermore, due to the pressure limitations of NAP-XPS, the concentrations of the primary reactants (CH₄ and H2O2) were already lower than those in the catalytic process. Introducing HCl would further reduce reactant concentrations, adversely affecting the signal-to-noise ratio and the reliability of the measurements. Consequently, HCl was deliberately excluded from the NAP-XPS experiments to preserve data quality.
In situ XAFS measurements
Fe K-edge (7,112 eV) XAFS spectra were recorded at the 1W1B beamline of the Beijing Synchrotron Radiation Facility. The storage ring was operated at 2.5 GeV, with a maximum electron current of 250 mA. The hard X-ray beam was monochromatized with a Si(111) double-crystal monochromator. For the removal of higher-order harmonics, the X-ray was detuned by 30% for the Fe K-edge. The detection system consists of a 19-element germanium solid-state detector and a Lytle detector. In situ XAFS measurements were performed using a homemade reactor (10 ml) with a vitreous carbon window (diameter, 6 mm; Supplementary Fig. 30). A catalyst-coated carbon-fibre paper (diameter, ∼5 mm) was sealed behind the window. Spectra were collected in fluorescence mode. The spectrum of a iron metal foil was collected concomitantly for internal energy calibration. Three spectra were averaged for each dataset. The catalysts used in the measurements are Fe–LMS–1% and Fe–LMS–10%, with precise iron loadings of 1.1 wt% and 9.8 wt%, respectively. To investigate the influence of the self-absorption effect, test samples were collected at incidence angles of 45° and 15°, respectively.
XAFS data analysis
Extended X-ray absorption fine structure (EXAFS) data were processed and analysed following standard procedures within the ATHENA module implemented in the IFEFFIT library software package. The Fe K-edge k3-weighted χ(k) data in the k-space were Fourier-transformed to the real space (R) with Hanning windows (dk = 1.0 Å−1) to separate out EXAFS contributions from different coordination shells. Effective backscattering amplitudes and phase shifts were calculated using the ab initio code FEFF8.054. For the FeGa sample, a k-rage of 2.5–12.1 Å−1 (Δk) was used and the curve fittings in the R space were carried out within the range 1.0–3.0 Å (ΔR). The number of independent points was: Nipt = 2Δk × ΔR/π = 2 × (12.1 − 2.5) × (3.0 − 1.0)∕π ≈ 12. The fitting ranges of all the other samples are listed below Supplementary Table 2, and the numbers of their independent points were calculated similarly; all the samples had more than nine independent points.
The Fourier-transformed curves for Fe–LMS, Fe–LMS–B, Fe–LMS–H2O2–B and Fe–LMS–H2O2–CH4–B showed a wide peak at 2.30 Å, which can be assigned to the combination of two kinds of Fe–Ga coordination with different structures, and a two-shell structure model with two different kinds of Fe–Ga scattering paths was used for fitting. For Fe–LMS–H2O2 and Fe–LMS–H2O2–CH4, besides the wide peak at 2.30 Å from the Fe–Ga coordination, two distinct peaks at 1.50 Å and 1.58 Å arise due to Fe–O and Fe–C bonds. Consequently, a three-shell structure model with one Fe–O/C path and two different Fe–Ga scattering paths was used to fit the data of both samples.
During curve fittings, the amplitude reduction factor S02 was fixed at a value of 0.78 as determined by fitting the data for a iron foil. For the Fe–LMS sample, the coordination numbers, interatomic distances (R) and energy shifts (ΔE0) for both Fe–Ga paths were treated as adjustable parameters, and the energy shifts (ΔE0) for the two paths were considered to be the same.
Disorder factor (Debye–Waller factor, σ²)
A single σ² value is used for one or two Fe–Ga paths within the same sample, set as an adjustable parameter. For Fe–LMS–B samples, the Fe–Fe path is set as an adjustable parameter. To reduce the number of adjustable parameters in subsequent sample fittings, especially for Fe–LMS–H2O2 and Fe–LMS–H2O2–CH4, where three paths are utilized, the σ² value for the Fe–Fe path is set to be the same as that of Fe–LMS–B. The Fe–C/O paths in the remaining samples are set as adjustable parameters.
The actual number of adjustable parameters, Npara = 5, was lower than the maximum number Nipt = 12. All of the other samples were treated similarly, and their actual numbers of adjustable parameters were all lower than their independent points. The structural parameters obtained from fitting are listed in Supplementary Table 1. The R factor obtained for every fit is not larger than 0.031, indicating a good quality of the fitting.
Self-absorption correction
Based on iron mass fractions of 1% and 10% in the GaInSn alloy, self-absorption correction was applied using the self-absorption correction function in Athena. The incident and exit angles were set at 45°, reflecting the actual testing conditions, and the fluo-μ(E) algorithm and troger-χ(k) algorithm were used for XANES and EXAFS corrections, respectively.
DFT calculations
A vacuum spacing of 10 Å was applied in three directions for all constructed models to prevent interactions between periodic images. All DFT calculations were performed with the Vienna Ab initio Simulation Package (VASP)30. The exchange-correlation interactions were treated using the Perdew–Burke–Ernzerhof functional31 within the generalized gradient approximation. The projector augmented wave32 was used to treat the inert core electrons. Spin polarization was implemented in all calculations. To simulate the presence of an external magnetic field, noncollinear magnetic calculations were carried out, with the direction of spin moment fixed along the positive x axis, while allowing the magnitude of the magnetic moments to relax. A plane-wave kinetic energy cut-off of 400 eV was used throughout all calculations. The Brillouin zone was sampled with a 1 × 1 × 1 Monkhorst–Pack k-point mesh. The strongly localized 3d orbitals of iron were treated by the DFT + U method with an effective U value of 3 eV (refs. 33,34). The electronic energy convergence criteria were set to 10−5 eV, and the force convergence threshold was 0.02 eV Å−1. The climbing-image nudged elastic band method35 was used to identify transition state structures. All optimized structures were confirmed as ground states (zero imaginary frequency) or transition states (one imaginary frequency) by performing vibrational frequency analysis. Long-range dispersion interactions were included using Grimme’s DFT-D3 method36. Solvent effects were considered by applying an implicit solvation model for water via the VASPsol module37,38. Bader charge analysis was performed to quantify electron transfer. PDOS calculations and orbital interaction analyses were conducted using the VASPKIT toolkit39.
AIMD simulations
The structural changes and dynamic properties of the Fen–LMS were investigated with AIMD simulations using VASP. The same computational settings were used as in the static DFT calculations, including convergence criteria, plane-wave kinetic energy cut-off, k-point mesh, exchange-correlation functional, spin treatment, DFT-D3 dispersion correction, and the DFT + U correction. Canonical NVT ensemble and Nosé–Hoover thermostats40 were adopted at 298.15 K with a time step of 1 fs.

