J.-P Rueff

V Balédent

K Higashi

H Kageyama

Spin transition in SrFeO 2 under Pressure by X-ray spectroscopy

We have investigated the local Fe electronic changes in the square planar Fe(II) compound SrFeO2 by x-ray emission (XES) and x-ray absorption spectroscopy (XAS) through the pressure-induced spin transition up to 60 GPa. The analysis of Fe Kβ XES confirms the transition under pressure from a high spin to intermediate spin state at Pc = 43 GPa while XAS at the Fe K-edge reveals the spectral signatures of the lattice compression under pressure. Simulations of the XAS spectra point to significant changes in Fe p-d states across Pc through the hybridization with the O p states eventually leading to the magnetic instability.

I. INTRODUCTION

Spin transitions are widely observed, important phenomena with potential use for ultrafast switches, data storage devices, and optical displays [START_REF] Létard | Towards spin crossover applications[END_REF]. Spin transitions are generally found in octahedrally coordinated 3d transition metal (TM) ions such as oxides [START_REF] Mattila | Metal-ligand interplay in strongly-correlated oxides:a parametrized phase diagram for pressure induced spin transitions[END_REF][START_REF] Pasternak | High pressure collapse of magnetism in Fe0.94O: Mössbauer spectroscopy beyond 100 GPa[END_REF], metal-organic complexes [START_REF] Vankó | Probing the 3d Spin Momentum with X-ray Emission Spectroscopy: The Case of Molecular-Spin Transitions[END_REF][START_REF] Pollock | Insights into the geometric and electronic structure of transition metal centers from valence-to-core x-ray emission spectroscopy[END_REF] or molecular magnets [START_REF] Cafun | Room-temperature photoinduced electron transfer in a prussian blue analogue under hydrostatic pressure[END_REF][START_REF] Papanikolaou | X-ray illumination induced fe(ii) spin crossover in the prussian blue analogue cesium iron hexacyanochromate[END_REF]. In the presence of the crystal electric field in O h symmetry, the 3d orbitals are split into t 2g and e g orbitals, whose energy gap depends on the crystal field strength. The filling of these orbitals by the 3d electrons governs the TM spin state and is determined by the competition between the crystal field strength and the intra-atomic exchange interaction. External perturbations such as temperature, pressure, magnetic field or light pulses can modify the relative strength of these interactions, eventually inducing a spin state transition. The stability of the spin state has profound consequences on the materials behavior as it affects its structural stability, magnetic ordering and transport properties, which explains its broad interest in condensed matter physics, molecular chemistry or mineralogy.

Recently, Kawakami et al. [START_REF] Kawakami | Spin transition in a four-coordinate iron oxide[END_REF] have reported a spin state transition in the Fe(II) SrFeO 2 compound under pressure. As illustrated in Fig. 1, the structure of SrFeO 2 consists of FeO 2 2D layers separated by Sr atoms [START_REF] Tsujimoto | Infinite-layer iron oxide with a square-planar coordination[END_REF] with Fe sitting in a square planar site with D 4h symmetry. Using Mössbauer spectroscopy, x-ray diffraction, and transport measurements, the authors showed that the Fe spin changes from high spin (HS, S = 2) to intermediate spin state (IS, S = 1) state around P c = 33 GPa ; the spin transition is accompanied by a transition from an antiferromagnetic (AFM) insulating state to likely a ferromagnetic (FM) half-metallic state ; at the same time, an anomalous drop of the lattice parameters is found at P c . This makes SrFeO 2 the first example of a four-fold coordinated TM compound undergoing a spin transition. Similar results were more recently observed in the structurally related two-legged spin ladder compound Sr 3 Fe 2 O 5 where Fe also occupies in a square planar site Kageyama et al. [START_REF] Kageyama | Spin-ladder iron oxide: Sr3fe2o5[END_REF]. Akin to SrFeO 2 , Sr 3 Fe 2 O 5 undergoes a pressure-induced spin state transition, an insulator to metal transition, and AFM to FM transition with a magnetic transition at 34 GPa [START_REF] Yamamoto | Pressure-induced structural, magnetic, and transport transitions in the two-legged ladder sr3fe2o5[END_REF].

In this article, we provide a detailed view at the local Fe level of the transition mechanism and change of the electronic structure under pressure in SrFeO 2 as observed by X-ray Emission Spectroscopy (XES) at the Fe Kβ emission line and X-ray Absorption Spectroscopy (XAS) at the Fe K-edge [START_REF] Rueff | Spin-transitions in metal oxides[END_REF]. Thanks to the resonant excita-tion, x-ray spectroscopy in the hard x-ray range is an effective element and orbital selective probe of the electronic properties in transition metal compounds, while being compatible with high pressure environment. The results confirm the spin state transition from HS to IS state at high pressure and demonstrate that significant changes in Fe p-d states occur across P c through the hybridization with the O p states eventually leading to the magnetic instability.

II. RESULTS AND DISCUSSION

A. Methodology SrFeO 2 sample was synthesized at Kyoto University as described in Ref. [START_REF] Kawakami | Spin transition in a four-coordinate iron oxide[END_REF]. The sample was prepared as powder and loaded in a membrane driven diamond anvil cell (DAC) with 300 µm culet size. We used Rh as gasket material with a 150 µm hole. The in-situ pressure was estimated from the photo luminescence of ruby chips that were placed in the sample chamber. We performed two successive loadings of the pressure cell to cover the entire pressure range with two different pressure transmitting medium : Neon gas (for the 0-60 GPa pressure range) and 1:4 methanol-ethanol mixture (for 50-60 GPa). The two datasets were eventually combined as no visible difference could be detected between them, either in the XAS and XES spectral shape or behavior under pressure.

The experiment has been carried out the GALAX-IES x-ray spectroscopy beamline at Synchrotron SOLEIL [START_REF] Rueff | The GALAXIES Beamline at SOLEIL Synchrotron: Inelastic X-ray Scattering and Photoelectron Spectroscopy in the Hard X-ray Range[END_REF]. The incident photons were monochromatized by a cryogenically cooled Si(111) double crystal monochromator and focused onto the sample by a toroidal mirror in a 30 µm × 80 µm spot. The Fe Kβ spectra were measured on the beamline XES spectrometer in transmission geometry through the DAC at a scattering angle of 15 • . The spectrometer was equipped with a Si(531) 1m spherically bent crystal analyzer operated around the Bragg angle of 73.1 • and a silicon drift diode (SDD) as detector. The XES spectra were acquired in a continuous scanning mode by sweeping the emission energy from 7020 to 7080 eV at fixed incident photon energy of 9000 eV. This energy was found to yield the the strongest emission intensity in the DAC. At some selected pressure, we also acquired high-resolution XAS spectra in the partial fluorescence yield (PFY) mode by setting the spectrometer emission energy at the maximum of the Kβ emission line while sweeping the incident photon energy through the Fe K-edge. This method -also known as high energy resolution fluorescence detected (HERFD) XAS -yields the absorption spectrum with improved intrinsic resolution with respect to conventional XAS as the core-hole lifetime broadening has been partly removed owing to the second order scattering process [START_REF] Hämäläinen | Elimination of the inner-shell lifetime broadening in x-ray absorption spectroscopy[END_REF].

B. Results

XES

The Fe Kβ XES spectra are shown in Fig. 2 as a function of pressure P . To emphasize the spectral changes in the figure, the spectra were normalized to the maximum intensity and aligned in energy. The spectra are composed of a large intensity peak and a weaker, low energy satellite respectively referred to as Kβ 1,3 and Kβ . As it is now well established, the Kβ spectral shape and specially the satellite region is sensitive to the magnitude S of the local spin state of the 3d ion [START_REF] Rueff | Pressure induced high-spin to low-spin transition in FeS evidenced by x-ray emission spectroscopy[END_REF][START_REF] De Groot | High resolution x-ray emission and x-ray absorption spectroscopy[END_REF]. To first assess the nature of the high pressure phase, we compare in Fig. 2 the emission spectra in SrFeO 2 with spectra measured in reference compounds borrowed from Ref. [START_REF] Carlantuono | X-ray Emission Spectroscopy to retrieve the local spin moment in 3d transition metal compounds[END_REF], the Fe(II) compounds FeS and FeS 2 with nominal spin states S = 2 and S = 0 and Fe metal with nominal S = 1. While FeS 2 XES spectrum shows no distinct Kβ feature, Fe metal exhibits is weak satellite which seems very comparable to SrFeO 2 high pressure spectra. This qualitatively confirms the intermediate spin state (S = 1) assignment of the high pressure phase of SrFeO 2 . The low pressure spectra compares well with that of the S = 2 compound FeS although the satellite intensity is somewhat higher in SrFeO 2 , likely due to the different Fe environment and degree of covalency.

The pressure dependence of the local spin moment S can be more quantitatively estimated by means of the Integral Absolute Difference (IAD) method which has been developed earlier [START_REF] Vankó | Probing the 3d Spin Momentum with X-ray Emission Spectroscopy: The Case of Molecular-Spin Transitions[END_REF][START_REF] Rueff | Magnetism and structural α-phase transition in Fe monitored by x-ray emission spectroscopy[END_REF]. Following Vankó et al. [START_REF] Vankó | Probing the 3d Spin Momentum with X-ray Emission Spectroscopy: The Case of Molecular-Spin Transitions[END_REF], the IAD values were computed by integrating the spectral difference |XES(P ) -XES(P = 0)| after normalizing the spectral intensity to the total area and align- ing the spectra to the center of gravity. Figure 3 shows the IAD change (here expressed as max(IAD) -IAD(P )) as a function of pressure. This pressure dependence is very comparable to the one obtained by other methods of evaluating S, including first moment analysis or satellite intensity, demonstrating its robustness. Using the reference spectra of Figure 3, we have the converted the IAD values onto an indicative spin scale represented by the right axis in Figure 3. The IAD analysis confirms the pressure-induced transition form HS to IS states. We can obtain a rough estimate of the transition pressure P c by fitting the IAD dependence with an arctan function :

H/π(π -arctan(2/w(P -P c ) + π/2))

with H the step height and w the distribution width. The fit shown in Fig. 3 with solid line yields P c = 42 GPa, a value somewhat higher than value of 33 GPa reported by Kawakami et al. [START_REF] Kawakami | Spin transition in a four-coordinate iron oxide[END_REF]. The width w is estimated at 14 GPa, which could be due to pressure gradient and phase mixing.

XAS

We now turn to the XAS results which provides a local view of structural change across the pressure induced spin transition. The Fe K-ege X-ray absorption spectra were measured at two pressures across P c in the low pressure (LP) phase at 0 GPa and high pressure (HP) phase at 45 GPa. Figure 4 (top panel) displays the two spectra on a relative energy scale E -E 0 with E 0 = 7115.5 eV. The spectra were corrected for self-absorption. For the sake of comparison, the XAS spectra were normalized in intensity to an edge jump of unity and align in energy so that the flex point falls at E 0 . The spectra are composed of an intense pre-edge feature (0-5 eV) of mixed p-d char-acter (as explained bellow) followed by an intense edge jump (5-20 eV) related to the p states due to dipolar transitions. The spectra undergo a drastic change with pressure marked by a shift of the pre-edge and post-edge features toward high energy along with a sizable broadening. (bottom panel) Computed spectra using FDMNES in both LP and HP phases (solid lines) ; D and Q refer to the dipolar and quadrupolar contributions. For the sake of clarity, the latter (dashed lines) has been multiplied by 10.

To get deeper insight in the spectral changes, the experimental spectra are compared to the first-principle calculations (Fig. 4, bottom panel). The calculations were performed using the FDMNES code [START_REF] Bunȃu | Self-consistent aspects of x-ray absorption calculations[END_REF] on a 7 Å radius atomic cluster within the LDA+U approximation. The Hubbard parameter was set to U = 5 eV for the LP phase in agreement with the previous works [START_REF] Rahman | Electronic structures and magnetism of srfeo2 under pressure: A firstprinciples study[END_REF][START_REF] Xiang | Origin of the structural and magnetic anomalies of the layered compound srfeo2: A density functional investigation[END_REF][START_REF] Pruneda | Structural and electronic properties of SrFeO2 from first principles[END_REF] and U = 0 eV for the HP phase following the vanishing U value predicted at high pressure in Rahman et al. [START_REF] Rahman | Electronic structures and magnetism of srfeo2 under pressure: A firstprinciples study[END_REF] and the observation of the gap closing around 50 GPa [START_REF] Kawakami | Spin transition in a four-coordinate iron oxide[END_REF]. We used the structural parameters obtained at 0 GPa (a = 3.991 Å, c = 3.474 Å) and 45 GPa (a = 3.744 Å, c = 3.002 Å) obtained from Refs. [START_REF] Kawakami | Spin transition in a four-coordinate iron oxide[END_REF][START_REF] Tsujimoto | Infinite-layer iron oxide with a square-planar coordination[END_REF] within the same space group P 4/mmm as illustrated in 1. We forced Fe to adopt a 3d 6 electronic configuration with a high-spin (respectively intermediate spin) state at 0 (resp. 45) GPa. The computation was conducted using self-consistent, non muffin tin potentials and including spin-orbit effect and both dipolar (D) and quadrupolar (Q) contributions. To take into account the sharpening effect due to the PFY approach, the computed spectra were convolved by a Lorentzian with FWHM of 0.5 eV (below the 1s lifetime estimated at 1.3 eV).

The pressure induced experimental changes are well reproduced by the calculations confirming that the observed spectral difference are driven by changes in the Fe electronic structure upon lattice compression. The quadrupolar contribution shown as dashed line in Figure 5 appears to be of minute intensity and located in a narrow energy window around E 0 . This demonstrates that the overall spectrum including the pre-edge region is dominated by the dipolar component related to the Fe p states. To evaluate the change of the electronic structure, we show in Fig. 6 the projected density of states (pDOS) of the absorbing Fe atom at low and high pressures. Our computed pDOS differ from previously reported works [START_REF] Kawakami | Spin transition in a four-coordinate iron oxide[END_REF][START_REF] Rahman | Electronic structures and magnetism of srfeo2 under pressure: A firstprinciples study[END_REF][START_REF] Xiang | Origin of the structural and magnetic anomalies of the layered compound srfeo2: A density functional investigation[END_REF][START_REF] Pruneda | Structural and electronic properties of SrFeO2 from first principles[END_REF] as it takes into account the 1s core-hole present in the XAS final state. Our purpose moreover is to focus on the changes observed in the empty d and p states which are probed by XAS. A comparison with Fig. 5 confirms that the XAS spectra mainly reflects the Fe unoccupied p-pDOS with some admixture of d character in the pre-edge region near E 0 . The pDOS further highlight the strong hybridization between the Fe p and d states. We notice that while the AFM state in the LP phase is well established, the FM nature of HP phase is still debated. Because XES is a local probe, it cannot discriminate between FM or other magnetic structures. But other probes of the long range order such as X-ray magnetic dichroism at the Fe K-edge could be tempted in the future.

III. CONCLUSIONS

We have studied the pressure-induced spin transition in SrFeO 2 by x-ray spectroscopy by combining Fe Kβ XES and XAS at the Fe K-edge up to 60 GPa. The results provide a detailed picture of the Fe electronic changes across the magnetic transition from a local point of view. While Fe remains magnetic at 60 GPa, we can expect a second transition to another IS state or even a complete loss of magnetic moment at even higher pressure when the d-electrons become fully delocalized. This should motivate a continuation of this work towards the 100 GPa range.

FIG. 1 .

 1 FIG. 1. SrFeO2 structure in the P 4/mmm space group highlighting the square planar environment of Fe (yellow balls) surrounding by four O atoms (red balls). The Sr atom (green ball) lies in the interplanes region. The local x and z axes are aligned with the a and c directions.

FIG. 2 .

 2 FIG.2. Fe Kβ XES spectra as a function pressure; the inset shows a zoom of the satelite (Kβ ) region. References spectra representative of S = 0, 1, 2 spin state and measured in FeS2, Fe metal and FeS are shows with black solid, dashed and dotted lines from[START_REF] Carlantuono | X-ray Emission Spectroscopy to retrieve the local spin moment in 3d transition metal compounds[END_REF]

FIG. 3 .

 3 FIG. 3. Computed IAD as a function of pressure (circles) and arctan fit (solid line); the IAD is converted onto a indicative spin scale (right axis)

FIG. 4 .

 4 FIG. 4. (top panel) Experimental Fe K-edge XAS spectra in the low pressure (LP) and high pressure (HP) phases ;(bottom panel) Computed spectra using FDMNES in both LP and HP phases (solid lines) ; D and Q refer to the dipolar and quadrupolar contributions. For the sake of clarity, the latter (dashed lines) has been multiplied by 10.

FIG. 5 .

 5 FIG. 5. (top panel) Computed Fe p-pDOS (top panel) and Fe d-pDOS (bottom panel) in the low pressure (thick line) and high pressure (thin filled line) phase

FIG. 6 .

 6 FIG. 6. Details of the Fe d-pDOS (two top panels) and O p-pDOS (bottom panel) in the low pressure (tick lines) and high pressure phase (thin lines)

ACKNOWLEDGMENTS

We wish to acknowledge the SOLEIL Synchrotron for provision of beamtime (proposal 20181616). This work was supported by JSPS Core-to-Core Program (grant number: JPJSCCA20200004).


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Nathalie Pansu

Clément Le Bihan

Guillaume Cartron

Emmanuelle Tchernonog

Camille Roubille

David Morquin

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