Reversible hydrogen control of antiferromagnetic anisotropy in α-Fe2O3

Antiferromagnetic insulators are a ubiquitous class of magnetic materials, holding the promise of low-dissipation spin-based computing devices that can display ultra-fast switching and are robust against stray fields. However, their imperviousness to magnetic fields also makes them difficult to control in a reversible and scalable manner. Here we demonstrate a novel proof-of-principle ionic approach to control the spin reorientation (Morin) transition reversibly in the common antiferromagnetic insulator α-Fe2O3 (haematite) – now an emerging spintronic material that hosts topological antiferromagnetic spin-textures and long magnon-diffusion lengths. We use a low-temperature catalytic-spillover process involving the post-growth incorporation or removal of hydrogen from α-Fe2O3 thin films. Hydrogenation drives pronounced changes in its magnetic anisotropy, Néel vector orientation and canted magnetism via electron injection and local distortions. We explain these effects with a detailed magnetic anisotropy model and first-principles calculations. Tailoring our work for future applications, we demonstrate reversible control of the room-temperature spin-state by doping/expelling hydrogen in Rh-substituted α-Fe2O3.

Similarly, high quality epitaxial thin films of α-Fe1.97Rh0.03O3 were also grown on α-Al2O3 substrates (Fig. S2.2a), at the same growth conditions. The magnetism and anisotropy properties of α-Fe1.97Rh0.03O3 films studied via magnetometry and XLD revealed the anisotropy reversal across the Morin transition (Fig. S2.2b) which is now elevated relative to non-Rh substituted samples.  Discontinuous platinum (Pt) grown after sputter deposition, formed spheroidal nano-structures (NSs) of diameter slightly more than ~2 nm on the top surface of the sample (Fig. S3.1a). Due to Zcontrast of the HAADF mode, Pt appears brightest. The ratio of the Pt areal density obtained from the RBS measurements to the theoretical value expected from a continuous Pt layer was much less than unity, confirming partial surface coverage of Pt nano-structures. Magnetometry of Pt NS-covered α-Fe2O3 film (Fig. S3.1b) showed the comparable () MT and X-ray dichroism as the undoped α-Fe2O3

Reversibility
After an H-doping step, the AFM-state can be restored as observed in the α-Fe2O3 (see Figs. 1g-i) as well as in α-Fe1.97Rh0.03O3 (Figs. S4.3a,b) samples. The restoration process resulted in a slightly

S5. Control annealing experiments Argon annealing of α-Fe2O3 films
Ar-annealing experiments, where Pt NS-covered undoped α-Fe 2 O 3 films were exposed to 100% Ar for the same annealing conditions continued to exhibit the Morin transition, Fig. S5.1, in sharp contrast to the behaviour of H-doped films (Fig. 1e,f), implying that merely having an oxygen-absent atmosphere (as in 100% Ar) at elevated temperatures is insufficient to mimic H-spillover effects.

Absence of magnetic contribution before and after H-annealing of substrates (α-Al2O3)
To rule out the presence of spurious magnetic artefacts of the α-Al2O3 substrates (without any α-Fe2O3 films), we performed magnetometry of bare and H-annealed substrates. For accuracy, these control substrates were taken through the entire growth process involved in PLD film growth (heating, annealing, etc.), with one major exception that no α-Fe2O3 film was deposited on them. We found that α-Al2O3 trends are essentially diamagnetic where the () MT and () MH curves did not show any magnetic transition features (unlike α-Fe2O3), as Al 3+ -cations have no net moment due to their fullyfilled valence shell. H-doping also does not affect α-Al2O3 as the Al 3+ -cations cannot accommodate excess electrons. These results, over and above the element specific X-ray dichroic experiments (see Supplementary-S6), clearly establish that our magnetometry data originate from α-Fe2O3 and its Hdoped state and not the substrates or the Pt catalyst layer. To discern whether the observed modulation of magnetic properties is because of H incorporation or O-vacancy creation during our H-spillover treatment (see Supplementary-S4), we performed the restoration of the H-doped samples in 100% Ar atmosphere, Fig. S5.2a. The Morin transition could be retrieved to a similar condition as the sample restored in 100% O2 atmosphere, Fig.   S5.2b, suggesting that the H-annealing step essentially adds H-dopants to the system, creating only negligible fraction of O-vacancies, as the latter cannot be healed in an O-poor atmosphere (in this case 100% Ar) at higher temperature. Here, the H-dopants certainly can undergo excorporation from the oxide in H-poor atmospheres as they are weakly bound dopants. This is consistent with other oxide Hdoping studies in the literature [2][3][4] . We also remark that it is possible to suppress the Morin transition by growing α-Fe2O3 samples at 700 °C in an oxygen-poor atmosphere. However, these oxygen-deficient samples have markedly different magnetic properties from our H-doped α-Fe2O3 samples (not shown here). Both these results unequivocally establish that H-doping plays a distinctive role in modifying the magnetism in α-Fe2O3 which cannot be reproduced by merely creating O-vacancies. XLD signals of α-Fe2O3 sample, with Xray in grazing incidence at room temperature. RCP, LCP, LHP, LVP correspond to right-circular, leftcircular, linear-horizontal, linear-vertical polarizations, respectively. (c) XMCD of undoped and Hdoped α-Fe2O3 films, compared against the XMCD signal 5 of Fe3O4. Inset shows magnified XMCD spectra of undoped and H-doped α-Fe2O3 films that are translated vertically for clarity. These α-Fe2O3 signals lack any systematic ferromagnetic spectral features, as is well known in literature 6 .

S6. Fe L edge X-ray linear and circular dichroism
In α-Fe2O3, XMCD is negligible 6 whereas XLD is evident (Figs. S6.1a,b). According to the α-Fe 2 O 3 literature, XLD has a magnetic origin here (and negligible structural or orbital contributions), as it reverses sign across the Morin transition and vanishes above the Néel temperature 7,8 . Hence, the magnetic anisotropy and Néel vector orientation (i.e. in-plane vs out-of-plane direction) can be readily determined from the Fe L edge XLD. Moreover, XMCD signals were absent in both undoped and Hdoped α-Fe2O3 (Fig. S6.1c), due to the smallness of the canted moment 6 . This negligible XMCD signal also confirms the purity of our iron oxide samples and strongly suggests that the presence of any ferro/ferrimagnetic iron-oxide inclusions (for which XMCD is a strong tell-tale signal 9 ) should be negligible in the H-doped samples prepared at optimal H-spillover temperatures used in this work (also see Supplementary-S4,S10).

S7. Selective ion beam techniques: Proof of H incorporation
Elemental analysis to study hydrogen and oxygen stoichiometry in the oxide was performed by elastic recoil detection analysis (ERDA) and oxygen resonant Rutherford backscattering (RRBS), respectively, performed in tandem (see 'Methods').

O-Detection: oxygen resonant RBS
RRBS with He-ions incident at oxygen resonance dramatically increases the back-scattering cross-section of He-ions from the surface oxygen atoms (to depths corresponding well with film thickness). Hence, He ions back-scattered from α-Fe2O3 contributed to the sharp O resonance peak, whereas He ions back-scattered from α-Al2O3 appeared as the usual oxygen hump, see  Table S7.1. These results confirm negligible difference in oxygen content between undoped, H-doped and Ar-annealed samples. This is consistent with the higher formation energies of O-vacancies as compared to H-interstitials obtained by our first principles calculations, which are discussed in Supplementary-S15.

H-Detection: ERDA
By contrast, differences in hydrogen content can be easily detected by ERDA (see Fig. S7.2), where the outgoing He ions and the recoiling H leave the sample in a grazing geometry. To distinguish these ion species, we placed an aluminium (Al) absorber-foil following to the standard protocol, thereby allowing only H to pass to the detector. While the foil provides selectivity, it also increases the energy straggling 11 . This increases the full-width at half-maximum (FWHM) of the surface peaks in ERDA 12 , causing the signal from the surface hydrogen (either surface water 13 or hydrocarbon layer) to be as prominent as the bulk H inside the films. We subtracted the pure surface contribution (using the control undoped sample as the reference, Fig. S7.2a) from the total ERDA signals to extract the effective Hconcentration in the bulk (for H-doped sample see Fig. S7.2b). The H areal density (in atoms/cm 2 ) was then obtained by fitting the experimental ERDA curves followed by an integration over the energy axis. A quantitative summary of the effective bulk H-concentration for all samples is given in Table S7.1. We observed that while the undoped and Ar-annealed samples have a small hump (coming essentially from surface adsorbed H), the H-annealed samples had a significantly higher signal, indicating the incorporation of hydrogen into the films, which is consistent with our Fourier transform infrared spectroscopy (FTIR experiments, Supplementary-S8). From the quantitative results in Table S7.1 we conclude: ➢ H-annealing led to incorporation of H-dopants into the α-Fe2O3 films with Pt NSs, by a fraction that was an order of magnitude greater than H incorporation in films without Pt NSs on the surface. This confirms that catalytic H-spillover is indeed at play in our experiments. ➢ Comparing samples H-annealed at 150 °C, 170 °C, 250 °C reveals that H-annealing at higher temperatures allowed greater H incorporation in the lattice. This thermodynamic activation of H incorporation follows previous reports in spillover studies 14 . ➢ Moreover, control undoped samples with Pt nanostructures on the surface (without performing Hspillover) or those that are Ar-annealed had negligible amount of natural hydrogen adsorption.

S8. Structural evolution with H-doping
Precise lattice constants were obtained by measurement of reciprocal space vectors (RSVs) via HR-XRD of α-Fe2O3 referenced against the substrate. Transformation from RSVs to real space vectors was performed (following Ref 15 ) to obtain lattice constants in     FTIR experiments (see 'Methods') performed in an evacuated chamber helped to identify hydrogen related bonds in H-doped α-Fe2O3, Fig. S8.3. Firstly, the lower wavenumber peak C, which was present in undoped as well as H-doped samples, may be attributed to OH in monomeric water molecules or bonds at the surface. Peak B (~3664 cm -1 ), which was strong in the H-doped samples but also manifested as a shoulder in undoped sample, may arise likely from surface OH groups 16,17 than Hdoping. Lastly, we saw a singular peak A (~3740 cm -1 ), which uniquely manifested after H-doping and was absent in the undoped sample. We postulate this may be a signature of the new OH bonds formed after H-doping in α-Fe2O3. Such singular peaks related to internal OH bonds have also been reported in other hydrogenated oxide systems in the literature 18,19 . We note that this is consistent with our DFT calculations of H-dopants optimised in α-Fe2O3 super-cells, which revealed that incorporated H form interstitial dopants in the system and migrate to the nearby oxygen to form OH bonds (Supplementary-S14). To further verify our experimental results, we investigated another H-doped α-Fe2O3 sample, which was month aged. We found that all the peak positions were comparable to those in the freshly H-doped counterpart, with peaks B, A slightly weakened in intensity presumably due to aging, as also observed previously in H-doping literature 18 . This result seems to substantiate our peak assignment.  Figs. 3a,b) was to red-shift the main edge and pre-edge shoulder which was not observed in the control Ar-annealed samples (i.e. within experimental error margin). In Fe K edge XANES literature, red-shifts are associated with a reduction of the Fe-cation valence 20 . Coupled with the fact that excess electronic charge in a polar lattice (such as α-Fe2O3) is self-trapped as small-polarons at the Fe-cations, these red-shifts correspond to a mild conversion of Fe valence from +3 towards +2. The atomic fraction of Fe 2+ -species has been shown in Table S9

Local changes in molecular bonding around Fe: EXAFS
Fourier transformed spectra of the extended X-ray absorption fine structure (EXAFS) revealed the minor changes in the Fe-O bonding after H-doping, Fig. S9.2. Firstly, the averaged Fe-O bond length peak, which includes the contribution of both Fe-O1 and Fe-O2 type bonds (see Supplementary-S14 for definition) changed by ~ 1% from 1.98 ± 0.02 Å to 2.00 ± 0.02 Å, lying at the error margin.
However, the mean-square displacement ( 2  ) increased systematically after hydrogen doping, from 0.0089 ± 0.0009 Å 2 to 0.0101 ± 0.0010 Å 2 , implying that H-doping causes bond distortions in the host lattice. This result is in line with our first-principles calculations (see Supplementary-S16).

S10. Effect of hydrogenation on canted magnetism
In the absence of external field, above the Morin transition, in-plane spins form randomlydistributed trigonal domains 21 . Bulk DMI results in a small canting between the antiparallel sublattices. Application of an in-plane field reorganizes the domains with the canted moment increasingly aligning till saturation. Evolution of the canted-magnetism through field dependent magnetometry, is shown in  Fig. S10.1a,e) the canted moment and associated hysteresis disappeared abruptly due to spin reorientation.
In optimal H-doped α-Fe2O3 samples, suppression of the Morin transition caused a persistence of the canted moment and its hysteresis to cryogenic temperatures (Fig. S10.1c). Although the hysteresis near room-temperature remained similar to that in undoped α-Fe2O3, two-step hysteresis loops with enhanced saturation magnetization, H S m , manifested at lower temperatures (dashed yellow line, Fig. S10.1e) , Figs. S10.1d,e), with temperature. We postulate that H-dopants introduce local distortions in their neighbourhood (discussed in Supplementary-S9,S16), which may affect domain propagation via magneto-elastic effects 1,22,23   We did not observe magnetite peaks either in the Fe L edge XMCD measurements (see Fig.  S6.1c), or in HR-XRD (Fig. S4.1a) of these H-doped samples, suggesting that Fe3O4 nuclei, if any, should be very small in size. Moreover, small-sized magnetite nuclei are expected to exhibit superparamagnetism at room temperature 9,24-27 , which was not observed in our magnetometry results (see Figs. S10.1c-e). This indicates that the presence of Fe3O4 after low-temperature H-spillover here, although impossible to rule out completely, is below the limit of experimental detection, and that its contribution to the magnetization be at most ~ 0.2 emu/cc. Moreover, thickness-dependent experiments ruled out any surface effects (Fig. S10.2) , Fig. S10.1d). This suggests that the secondary signal may come from localized regions, distributed through the film, not involving largescale domain reorientation. One possibility is an increase of canting between the sublattices due to short-range lattice distortions in the vicinity of H-dopants (see Supplementary-S16) which may increase the effective local DMI 28 . As the temperature lowers, electron hopping would freeze and phonon populations reduce, allowing the local distortions to be imprinted in the lattice. This may lead to increased relative canting between Fe-spins, thereby increasing the canted moment after H-doping.

S11. Phenomenological magnetic anisotropy model
The evolution of the Morin transition can be investigated from the magnetic anisotropy energy , as defined in the main text. The higher-order terms are much weaker 23 . The anisotropy constant results from competing 1,23,29 magnetic-dipolar and single-ion interactions: . Their temperature dependence 29,30 is given as, Here, the term 3 () Fe ZT + is obtained later from a transcendental equation (see Supplementary-S12), using a mean-field treatment. In the following, we discuss the specific consequences of H-doping.

Effect of H-dopants on the magnetic-dipolar term
The magnetic-dipolar term involves a summation of the classical dipole-dipole interactions and can be constructed from an effective mean-field acting on a local moment 29 as Our XANES results revealed that the addition of H-dopants leads to electron injection to the Fe 3+ -cations, reducing their valence. This causes the effective contribution of the Fe 3+ dipole moments to be reduced in proportion with the H-concentration ( x ). A simple Taylor analysis up to lowest order (given that we are in the low H-doping regime) reveals that the magnetic-dipolar anisotropy weakens as per the relation, where, () Eq. [S1]. In this estimation, we ignore averaged changes to the geometrical factor MD D , as we experimentally find that the overall structure, apart from local changes, remains mostly similar after H-doping (see Supplementary-S8).

MD K T is defined in
a is the factor to convert atomic concentration ( x ) to a fraction with respect to total Fe-species, see main text.

Effect of H-dopants on the single-ion term
The single-ion interaction term results from the combined action of crystal-field-splitting and relativistic spin-orbit-coupling (SOC), as discussed in the main text. In α-Fe2O3, the FeO6 octahedra undergo a small trigonal distortion, lowering the symmetry of the half-filled (3d 5 ) Fe-orbitals to generate a weak magneto-crystalline anisotropy. The single-ion anisotropy constant, owing to the axial symmetry of the cation environment, can be obtained from the spin Hamiltonian 29,30 : 1 .
Adopting a phenomenological approach outlined in the literature 29 , the single-ion anisotropy is found to be positive, favouring spins to reach a stable minimum out-of-plane, 0 Upon H-doping, there are two Fe-species. Hence, the overall single-ion contribution approximately evolves as the sum of decreasing Fe 3+ -and increasing Fe 2+ -cation contributions, The single-ion anisotropy contributed by the Fe 2+ -cations, i.e.

S, DSI and g-factor of Fe 2+ -cation
In Supplementary-S13, we discuss a quantum mechanical crystal-field model to is treated as an adjustable parameter to obtain a good match to our experimental data in Fig. 2. We roughly estimated its value to be ~ +3 cm -1 (which is comparable to but slightly smaller than its counterpart for Fe 2+ -cations in α-Al2O3 (Ref [31][32][33], which is usually in the range ~ +4 cm -1 ). We believe such a reduction could result from (i) atomic positions and trigonal distortions being different in haematite and corundum, and (ii) local distortion effects of H-dopants in α-Fe2O3, which add further bond and octahedral distortions in their immediate vicinity, where the Fe 2+ -cations are expected to be located (see Supplementary-S9,S16  [31][32][33] . Crucially, this equivalence validates the quantum mechanical approach outlined later in Supplementary-S13.

S12. Temperature evolution of the Fe 3+ and Fe 2+ species
To obtain the temperature evolution of the Fe 3+ and Fe 2+ -cation related anisotropy terms we formulated a modified two-sublattice model 34 . For the sake of brevity, we shall refer to Fe 3+ magnetic sublattices as 1 or 2, and Fe 2+ -sublattice as 3, in this section. Hence, 3 1  33 N is absent as the Fe 2+ -cation density is very low (in this work). The temperature evolution of the sublattices following a mean-field approach is given by the corresponding Brillouin

S13. Single-ion in-plane anisotropy of the Fe 2+ -cation
In this section, following Ref 37,38 , we obtain the single-ion contribution of the Fe 2+ -cation, which is in a 3d 6 configuration. The orbital triplet can be constructed from d-orbitals to manifest the trigonal symmetry about the quantization axis of the FeO6-octahedron, where, the value 2 Fe SI D + is defined as the level-splitting between ground and excited states (see Fig.   S13.1b). As discussed before (see Supplementary-S11), we found that 2 Fe SI D + can be set to allow good correspondence with experimental transition results, and its positive sign implies that the ground state