Introduction

The newly discovered heavy fermion superconductor UTe2 with Tsc = 1.6–2 K1,2 has led to a large amount of experimental and theoretical works as this compound appears to be a candidate for spin-triplet and topological superconductivity (see Ref. 3. and references therein). It shows some unusual phenomena quite similar to other uranium-based ferromagnetic superconductors UGe2, URhGe or UCoGe4, like metamagnetism, field induced reentrance or reinforcement of superconductivity5,6. However, unlike these systems, UTe2 does not order magnetically down to 25 mK under ambient pressure7. The extremely large upper critical fields along different crystallographic directions, far above the Pauli limit, suggest a spin-triplet pairing of the Cooper pairs. The observations of an almost temperature independent nuclear magnetic resonance (NMR) Knight shift in the superconducting phase8,9 and a gradual slowing down of “ferromagnetic” fluctuations by muon spectroscopy (μSR)7 support a spin-triplet pairing mechanism.

UTe2 crystallizes with a body-centered orthorhombic structure (space group Immm)10. This crystal structure is unique and presents some peculiarities, which appear to have some interplay with its electronic properties. The U atoms form a ladder-like structure along, the a axis with the leg along the c axis. These are surrounded by trigonal prism of Te. The Te atoms occupy two different positions; 4j for Te(1) and 4 h for Te(2). The latter ones form chains along the b axis with interatomic distances (3.035 Å) far below that of the non-bonding Te2- ions (4.42 Å). Another unusual feature of the UTe2 structure is the existence of a single short U–U distance (3.72 Å) at 2.7 K10. In view of possible 5f-5f interaction and together with the presence of polyanionic structure fragments the question of the uranium valence in this compound is especially interesting. Within the Zintl–Klemm concept, UTe2 could be described by the formula U3+δTe(1)2-Te(2) (1+δ) - which suggests a non-integer 5 f occupancy in UTe211.

The paramagnetic Curie temperature obtained from Curie-Weiss law fits of M(H) is negative, indicating antiferromagnetic interactions at high temperatures. UTe2 presents moderate Ising magnetic behavior with a being the easy axis1,2. The most spectacular is the observation of multi-superconducting phases under pressure. The superconductivity in these phases disappears at a critical pressure Pc ≈ 1.5 GPa12,13,14 where a long-range magnetic order is developed. From thermodynamic measurements, the magnetic order is most probably antiferromagnetic. The antiferromagnetic fluctuations were experimentally observed by inelastic neutron scattering in15,16, and the presence of a resonance in the SC phase even suggests them as the pairing glue17,18. Recent magnetic susceptibility and magnetization measurements under pressure up to 1.7 GPa pointed out a change of the magnetic anisotropy from a to b axis19.

Not only magnetic and superconducting properties are strongly affected by pressure but the structure as well. Firstly, at the magnetic ordering critical pressure there is a volume reduction of about 3%20. At higher pressures, a structural transition to a body-centered tetragonal phase (I4/mmm) has been recently observed at 4–5 GPa21,22 with an unexpected appearance of a new superconducting phase21.

Although there is a general agreement to consider that the U 5 f electrons in UTe2 have a non-integer occupancy between three and two (“intermediate valence”), the actual 5 f count is still under debate23,24,25,26,27,28,29,30. In addition, X-ray absorption experiments at the Uranium L3-edge suggested that the 5 f count is slightly changing towards two (U4+) under pressure at the transition to a magnetically ordered phase26. Note that the shift of the U L3 white line (2p3/2 → 6d transition) to higher energy is due either to the decrease of the 5 f count or to the delocalization of the 5 f electrons (less screening of the core hole). The actual value of the shift of the 5 f count under pressure depends critically on the white line energy of the reference compounds corresponding to the 5 f 2 (U4+) and 5 f 3 (U3+) electronic configurations and to the strength of the 5 f delocalization. The knowledge of the 5 f count in different phases is absolutely essential for any faithful understanding of the electronic structure of UTe2 where the magnetic and charge instabilities strongly coupled to the occupancy of the 5 f levels play important roles.

Here we present x-ray absorption near edge structure (XANES) and x-ray magnetic circular dichroism (XMCD) at the U M4,5 edges and at the Te L1 edge that probe directly the 5f- and 5p- states, respectively. The Uranium 5 f spin and orbital moments in the paramagnetic phase were determined using high field XMCD and sum rules. Their ratio suggests that the 5 f electrons are rather delocalized in UTe2. We also performed XANES measurements under pressure at the U M4,5 edges with the aim to follow accurately the pressure dependence of the occupancy of the U 5f levels. These experiments allowed to conclude that UTe2 is indeed an “intermediate valence compound” and that the 5f count is close to 3 (U3+) at ambient pressure and changes towards 2 (U4+) up to the critical pressure of 1.5 GPa. Surprisingly, the 5 f count is increased towards U3+ configuration above 4 GPa following the transition to the tetragonal structure. The interplay between the crystal structure and 5 f counts in UTe2 is discussed.

Results

Determination of the uranium 5 f count

It is now well documented that XANES and XMCD at the M4,5 edges of actinides are the most suitable techniques to provide direct information on the 5 f states31. The strong resonance at these absorption edges, usually called white lines, are due to the dipole allowed transitions 3d3/2 → 5 f5/2 (M4 edge) and 3d5/2 → 5 f5/2,7/2 (M5 edge). The M4,5 XANES spectra are, thus, a sensitive probe of the occupancy of the 5 f levels whereas the corresponding XMCD spectra are unique tool to disentangle orbital (μL) and spin (μS) magnetic moments carried by the 5 f electrons. These offer two different ways to estimate the 5 f count of Uranium: (i) based on the branching ratio which is defined as B = IM5/ (IM5 + IM4), where IM5 and IM4 are the integrated intensities of the white lines at the M5 and M4 edges, respectively and (ii) based on the value of the orbital to spin moment ratio as well as the difference of the total 5f magnetic moment and the macroscopically measured magnetization. Even though both approaches are using results of X-ray absorption spectroscopy, the underlying mechanisms are quite different and the obtained 5f count by two methods could also be different.

The XANES and XMCD spectra of UTe2 recorded at the U M4,5 edges at ambient pressure, at 2.7 K under a magnetic field of 17 T applied along the easy-axis a are shown in Fig. 1. Firstly we apply the branching ratio approach to isotropic M4,5 XANES spectra. The experimental spectra were corrected for re-absorption effect and normalized using the procedure described in31 and Methods section. We estimate that the relative experimental error should be of the order of two percent. For UTe2 the branching ratio is 0.706(15) which falls in between values 0.729 and 0.686 calculated within intermediate coupling scheme for pure ionic configurations 5 f 3(U3+) and 5 f 2 (U4+), respectively32. Our experimental value of the branching ration is pointing out to a non-integer 5 f occupancy. Note that this value is slightly >0.701 observed in UCoGe33 and 0.698 in UCoAl34 but significantly <0.723 in URu2Si2 or 0.74 in UTe35. The XANES branching ratio at the spin-orbit split edges was shown by van der Laan et al.36 to be proportional to the ground-state expectation value of the angular part of the spin-orbit interaction \( < \vec{l}.\vec{s} > \) in the valence band. In the case of the M4,5 edges this so-called spin-orbit sum rule reads:

$$\frac{2 < \vec{l}.\vec{s} > }{3{n}_{h}^{5f}}-\Delta =-\frac{5}{2}\left(B-\frac{3}{5}\right)$$
(1)

where \({n}_{h}^{5f}\) = (14 -\({n}_{e}^{5f}\)) is the number of holes in the 5 f shell and ∆ is a small correction dependent on the electronic configuration (for U3+, e.g., \(\Delta\) \(=\) −0.010)36. Using atomic model, the ground-state 5 f spin-orbit interaction per hole (left hand side of Eq. 1) has been calculated as a function of the 5 f counts (\({n}_{e}^{5f}\)) for the three angular momentum coupling schemes (LS, intermediate and jj) by Jeffries et al. (see Fig. 2 in ref. 35.). In the intermediate coupling scheme this value is either −0.2017 or −0.3138 for the 5 f 2 (U4+) and 5 f 3 (U3+) ionic configurations, respectively. Note that the same values in the LS coupling are −0.1807 and −0.222132,36. The experimentally deduced value for UTe2 is found to be −0.265(5) and this confirms the intermediate coupling scheme. Assuming linear dependence of the ground-state 5 f spin-orbit interaction per hole on the 5 f count we deduce from the experimental value that the occupancy of the 5 f levels is about 2.57(5) in UTe2. Note that this approach relies on ionic calculations and therefore, the delocalization of the 5 f electrons could result in underestimation the 5 f count37.

Fig. 1: X-ray absorption and magnetic circular dichroism spectra at the U M4,5 edges.
figure 1

X-ray absorption near edge structure (left axis, red curves,) and x-ray magnetic circular dichroism (right axis blue curves) spectra recorded at the U M4,5 edges for a UTe2 single crystal in a magnetic field of 17 T applied along the a easy axis at 2.7 K as a function of the incident photon energy.

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Fig. 2: Pressure dependence of the U M4,5 white lines.
figure 2

Shape of the M5 (full lines) and M4 white lines for some selected pressures at 2.7 K. The inset shows the enlarged part of the top of the M5 white line. E0, the energy of the maximum of the M5 white line at 0.75 GPa, was set to zero.

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The XMCD spectra at the U M4, 5 absorption edges have a typical shape for Uranium based intermetallics. The signal at the M4 edge is large and consists of a negative slightly asymmetric peak. The dichroic signal at the M5 edge is nearly ten times smaller than at the M4 edge and its dispersive like shape has been interpreted based on band structure theory31. The integrated values of XMCD signals at the M4,5 edges (∆IM4,5) allows one to deduce the orbital (\({\mu }_{L}^{U}\)(5 f ) = −<Lz > μB) and spin (\({\mu }_{S}^{U}\) (5 f) = −2 < Sz > μB) moments carried by the U 5f-electrons using the so-called magneto-optical sum rules38,39:

$$ < {{{{{\rm{L}}}}}}{{{{{\rm{z}}}}}} > =\frac{{n}_{h}^{5f}}{{I}_{M5}+{I}_{M4}}\left(\Delta {I}_{M5}+\Delta {I}_{M4}\right)$$
(2)
$$ < {{{{{\rm{S}}}}}}{{{{{\rm{z}}}}}} > =\frac{{n}_{h}^{5f}}{{2}(I_{M5}+{I}_{M4})}\left(\Delta {I}_{M5}-\frac{3}{2}\Delta {I}_{M4}\right)-3 < {{{{{\rm{T}}}}}}{{{{{\rm{z}}}}}} > $$
(3)

The total U moment \({\mu }_{{tot}}^{U}\) (5 f)= −(<Lz> + 2 <Sz>) µB can be obtained from XMCD spectra if reasonable estimates of the number of holes in the 5 f shell and the expectation value of the magnetic dipole operator <Tz> can be provided. Unfortunately, the <Tz> term cannot be measured experimentally but it may be estimated either by using first principle calculations or by combination of XMCD results with polarized neutron diffraction or magnetic Compton scattering and macroscopic magnetization results40.

The results of application of these sum rules to the M4,5 XMCD spectra of UTe2 are summarized in Table 1 for four different occupancies of the 5 f levels: \({n}_{e}^{5f}\) = 3, 2.8, 2.6 and 2 i.e., \({n}_{h}^{5f}\) = 11, 11.2, 11.4 and 12. In all cases, the 5 f orbital magnetic moment is parallel to the applied field as found for nearly all uranium compounds. To evaluate the spin component, the ratio <Tz > /<Sz> was estimated using linear interpolation of ionic values in the intermediate spin coupling scheme, between 0.62 for U3+ (\({n}_{h}^{5f}\) = 11) and 1.16 for U4+ (\({n}_{h}^{5f}\) = 12) configurations32. Table 1 shows that the magnetism of U is dominated by the orbital moment, whereas the spin moment is aligned antiparallel. Note that the U 5 f moments for \({n}_{e}^{5f}\,=\,3\) and \({n}_{e}^{5f}\,=\,2.8\) configurations are very close to the macroscopic magnetic moment as observed in other U intermetallic compounds when the U ions are bound to non-magnetic ligands31. The total 5 f U moment as well the orbital-to spin moment ratio for 5 f 2 and 5 f 2.6 configurations are too high and can be disregarded (the orbital to spin moment ratio in the intermediate coupling scheme amounts to –3.36 and to −2.60 for U4+ and U3+ free ions, respectively). The orbital to spin moment ratio for 5 f 3 and 5 f 2.8 configurations is found to be lower than what is expected for free ion U3+ value indicating a delocalization of the 5 f electrons due to hybridization with the Te spd electrons (as confirmed by the observation by 125Te NMR of large transferred hyperfine coupling constants at the Te nuclei41 and the presence of a finite orbital magnetic moment at the Te atoms as shown by our XMCD measurements at the Te L1 edge (see Supplementary Note. 1)). Comparison of XMCD findings with macroscopic measurements suggests that the 5 f electron count is about 2.8(1), i.e., higher than the one, possibly underestimated, deduced from the branching ratio analysis. We could therefore conclude that the 5 f occupation value in UTe2 is in-between 2.6 and 2.8. This result confirms a non-integer 5f count with electronic configurations closer to U3+ 5f 3 than U4+ 5f 2. Our finding agrees well with core level photoelectron spectroscopy data29 and more recent band structure calculations by Shick et al.28. However, their earlier results27 gave the same 5f occupation number, but the calculated Fermi surfaces (FS) were in contradiction with recent de Haas van Alphen (dHvA) experiments42. The cylindrical FS calculated by Ishizuka et al.25 succeed in reproducing the experimental observed dHvA oscillations but affords the lower 5f count of 2.5. We should note that there are some results pointing to a dominant 5f 2 configuration in UTe223,24,25. This view is supported by X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS)30 as well as by angle resolved photoelectron spectroscopy (ARPES)23 at O edges of Uranium which are extremely surface sensitive techniques. Moreover, a possible contribution of the 5f 3 state may be underrepresented in the O edge XAS spectrum if they are relatively itinerant43. Assignment of U4+ valence in UTe2 from U L3 XANES measurements26 seems to be ambiguous because if one uses the energy position of the inflection point instead of the maximum signal of the U L3 XANES, one would find a 5f count slightly below 3. This would be in good agreement with our conclusion. The observed discrepancies between different spectroscopy techniques (XAS, RIXS, ARPES) appear to be recurrent for uranium intermetallics (see, for example, extensive literature on URu2Si244). A way to reconciliate these seemingly contradicting results would be to invoke the dual nature of the 5f-electron system. The observation of multiplet structure in XAS, RIXS or ARPES spectra reproduced by atomic like calculations is due to the localized 5f orbitals whereas both delocalized and localized 5f states are probed by XANES-XMCD and core level photoelectron spectroscopy45.

Table. 1 interplay 5f count and magnetic moments.
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Finally, we have also recorded Uranium 5f magnetization curve by monitoring intensity of the XMCD signal at the M4 edge as a function of the applied magnetic field and compared it with the macroscopic pulsed high-field magnetization curve46 when H applied along the a easy axis (see Supplementary Note. 2). Taking the 5f 2.8 electronic configuration of uranium we can deduce that the contribution arising from the polarization of the Te 5p states (μTe) and the U 6d7s electrons (μcond) is much weaker and amounts to −0.05 μB at 17 T.

Evolution of the 5 f count under high pressure

To study the evolution of the 5 f count in UTe2 as a function of applied pressure we have used XANES measurements at the M4,5 edges. This approach is routinely used to follow the pressure dependence of the valence of Ce or Yb compounds47,48 but using x-ray absorption spectra at the L3 edge. Use of the L3 XANES (2p3/2 → 6d transition) in the case of actinides is more intricate because of the larger intrinsic broadening of the spectra (~7.5 eV) owing to the shorter core hole life time, and the tendency of the 5 f electrons to be more hybridized with 6d states and having less overlap with the 2p hole created in the absorption process49. Moreover, presence of strong quadrupolar 2p → 5 f transitions50 could lead to misinterpretation of the absorption spectra. Nevertheless the shift of the energy of the L3 white line could provide helpful, but indirect, information on the 5 f count26,49. On the contrary, X-ray absorption spectra at the M4,5 edges of actinides provide direct information on the 5 f states but they are technically more difficult due to relatively low binding energies of the 3d core electrons. Moreover, high pressure experiments at these energies (3.5–3.7 keV) in diamond anvil cells requires a dedicated instrumentation described in the Methods section.

The major advantage of the XANES at the M4,5 edges is a possibility to quantify relative changes in the 5 f count using what is called the first x-ray sum rule derived by Starace51. Adopted to the case of actinides it states that the integrated intensities of the white lines at the M4,5 edges, is proportional to the number of holes, \({n}_{h}^{5f},\) in the 5 f shell ({IM5 + IM4} \(\propto {n}_{h}^{5f}\)). These transitions are typically very strong and can be easily separated from the transitions into continuum. Moreover, dipolar transitions to a very broad 6p band and quadrupolar transitions to 6d states can be safely neglected at these low photon energies. A nice illustration of the validity of this analysis is given in52, where the evolution of the number of 5 f holes across the actinide series AnFe2 was determined by comparing white lines intensities at the M4,5 edges.

In Fig. 2, the XANES M5 and M4 at three selected pressure points (0.75, 1.85 and 4.72 GPa) are shown on the same energy scale. All spectra were normalized following the same procedure as described in section Methods and the energy of the maximum of the M5 white line at 0.75 GPa was set to zero and the M4 spectrum was shifted in energy in such a way that the first EXAFS oscillations above both M4 and M5 edges31 overlaps. The difference in energy between the absorption maxima of the M5 and M4 white lines of about 0.8 eV is proportional to ζ(5 f), the spin-orbit parameter for the 5 f electrons. The most remarkable is the observation, that the white line intensities measured at 1.85 GPa are significantly higher at both M5 and M4 edges than those recorded at lower and higher pressures. However, the white lines in the spectra measured at 4.7 GPa is slightly less intense.

These data together with the spectra recorded at 0.28, 1.31, 23.1, and 3.85 GPa have been used to measure quantitatively the change of the 5 f occupation using the first x-ray sum rule. The integrated intensities of the white lines at the M4,5 edges, or the 5f-count, show a gradual decrease from 0.28 GPa to 1.3 GPa followed by a drop at the pressure about 1.85 GPa, which is slightly above the critical pressure for the appearance of magnetic order12,14. These results are at variance with the conclusions drawn from the energy shift of the U L3 edge26. The changes that we see are as large as 7% variations of the 5 f count, independent of its exact value between 2.6 and 2.8 electrons. For the sake of definitude we can set the 5 f count at 0.28 GPa to 2.8, i.e., to the value obtained from band structure calculations at ambient pressure27,28 and our XMCD analysis, the 5 f count at 1.85 GPa would be smaller by 0.2 electrons. The overall results of the changes in the 5 f count as a function of pressure are summarized in Fig. 3. Knowing the pressure dependence of the 5 f count and of the branching ratio, we may estimate the change of the number of electrons in the individual spin-orbit electron shells corresponding to j = 7/2 and j = 5/2, i.e., \({n}_{e}^{5f7/2}\) and \({n}_{e}^{5f5/2}\), respectively (see Supplementary Note. 3).

Fig. 3: Variation of the 5 f electron count versus pressure.
figure 3

Pc represents the critical pressure of the transition from the paramagnetic state (PM) towards a magnetically ordered (MO) state. The blue dashed curve is a guide to the eyes. The size of the square represents the experimental error\(.\) The shaded part indicates the pressure region where the crystal structure changes from orthorhombic to tetragonal21,22.

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The observed changes of about 0.2 electrons in the 5 f count towards 5f 2 (U4+) configuration is not unexpected if one considers the values of the ionic radii of U3+ and U4+ and the observed large volume shrinking close to 3% at 1.7 GPa with respect to ambient pressure20. Note, the rather low bulk modulus of UTe2 (57 GPa) is typical for highly compressible materials which are generally prone to “valence instability”20,53. The observed substantial decrease of the 5 f occupation is much larger than the values reported for other uranium intermetallics under pressure54,55,56. Our result is reminiscent of the one observed in the pressure induced metallic ferromagnetic phase of TmTe, where the 4f electron count changes by >0.5 e− between 2 and 6 GPa57. The described change of the electronic properties with pressure shows also up in macroscopic measurements. As shown in Supplementary Note. 4 the anisotropy of magnetic susceptibility χa/χb inverses at Pc. It is accompanied with the collapse of metamagnetism along b53,58 and possibly occurring along the c axis59, the collapse of the Kondo temperature13,60, and a significant increase of the residual resistivity ρ0 as a function of pressure (see Supplementary Note. 4 and ref. 60). All these changes appear to be directly associated with the drop of the 5 f occupation at Pc.

Surprisingly, we have observed that \({n}_{e}^{5f}\) increases towards U3+ at pressures above 4 GPa and reaching the value at ambient pressure and even higher at 4.75 GPa. It is certainly associated with a change of the electronic structure induced by the structural transition (orthorhombic to tetragonal) observed by Honda et al.21 and Huston et al.22 at pressures above 3.5 GPa. These authors have shown that the shortest U–U distance increases by about 8% in the tetragonal phase. We can assume that a direct overlap between 5 f orbitals of neighboring uranium atoms is absent in tetragonal phase and this leads to an increase of the localization of the 5 f electrons and consequently to a change of the 5 f count towards U3+ as we observed. Furthermore, the low temperature resistivity measurements in the high pressure tetragonal phase also suggests an electronic configuration close to U3 + 21.

Conclusions

The XANES spectra measured at the U M4,5 edges in a UTe2 single crystal confirms that the U ions have a non-integer occupancy between three (U3+) and two (U4+). The use of the M4,5 branching ratio and the XMCD data combined with macroscopic magnetization allows one to conclude that the 5 f electron count is in between 2.6 and 2.8, i.e., close to U3+. The reduction of the uranium orbital to spin magnetic moment ratio, compared to the free ion U3+ value, is a fingerprint of the 5 f electron delocalization (hybridization). These findings agree with other measurements (soft x-ray ARPES, core level photo- electron spectroscopy) as well as with some band structure calculations. A description of Uranium electronic state in UTe2 as being dominated by the 5 f 2 configuration can be unambiguously ruled out.

The most striking result is the peculiar pressure dependence of the 5 f electron count. We observe a significant decrease of about 7 percent of the 5 f count at the transition towards a magnetically ordered state. This drastic change of the 5 f count is accompanied by a modification of the electronic structure, a decrease and change of the magnetic anisotropy. Worth to mention that this transition is accompanied by the disappearance of superconductivity at lower temperatures. The sudden increase of the 5f count above 4 GPa is due to a further change of the electronic structure associated with the structural transition observed by x-ray diffraction at about 4–5 GPa. To conclude, the element specific and orbital selective studies revealed that the magnetic and charge instabilities in UTe2 are strongly coupled to the occupancy of the 5 f levels. This coupling could play an important role in mechanism of superconductivity of UTe2. To get a deeper insight, more sophisticated experiments like XMCD or neutron diffraction under high pressure, as well as the new theoretical models are needed.

Methods

Sample preparation and characterization

High quality single crystals of UTe2 were grown by chemical vapor transport with iodine as transport agent. Details of the crystal growth and their characterization were published elsewhere60.

X- ray absorption and magnetic circular dichroism

The XANES and XMCD experiments were carried out at the ID12 beamline of the European Synchrotron Radiation Facility (ESRF Grenoble)52. For the experiments at the U M4,5 (3.728 and 3.552 keV, respectively) edges and at the Te L1 edge (4.939 keV) the source was the helical undulator of Helios II type. After monochromatization with a double crystal Si (111), the circular polarization rate of the x-rays was reduced to about 77% at Te L1 edge, to 45% and 35%, at the U M4 and M5 edges, respectively. The monochromatic X-rays were focused using a parabolic Be refractive lens with apex curvature radius of 100 μm61. The focal spot at the sample location was about 10 μm diameter.

The bar shaped crystal aligned by Laue diffraction and glued on an aluminium support, was mounted on a cold finger of the constant flow cryostat (T ≈ 2.7 K) and inserted in the bore of a superconducting solenoid (H ≤ 17 T) for the XMCD experiments. The magnetic field was applied parallel to the easy magnetization direction—a axis of the crystal.

The pressure dependent XANES measurements carried out at temperature 2.7 K were limited to 4.72 GPa. Pressure was applied via a diamond anvil cell (DAC) driven with a helium gas membrane for pressure generation. To minimize the absorption of X-rays by the diamonds we used a combination of a fully perforated anvil (cullet size 600 μm) combined with a thin diamond disc (30 μm thick). The pressure cell was mounted in a dedicated cryostat. The pressure was recorded in situ via the ruby luminescence. Each pressure point at 2.7 K was obtained after heating up the pressure cell to about 200 K where it is slowly pressurized and then cooled down to 2.7 K.

The XANES spectra at ambient pressure were recorded using the total fluorescence yield detection mode in backscattering geometry for parallel \(\sigma\)+(E) and antiparallel \(\sigma\)-(E) alignment of the photon helicity with respect to direction of applied magnetic field. The partial fluorescence yield method was used for high pressure XANES measurements by using two energy resolved detectors—Si drift diodes with active area of 100 mm2. The spectra were corrected by standard procedure for the self-absorption and by taking into account the incomplete polarization rates of the incident X-rays in the XMCD analysis.

Due to the large difference in the binding energies of the core 3d states of Uranium (∼176 eV), the M4 and M5 spectra are measured separately and therefore a proper normalization procedure has been applied. To avoid an arbitress choice in spectra normalization and energy position of step function simulating transition into continuum we have adopted a method described in31. This method is based on the idea that the EXAFS oscillations are identical above the two spin-orbit split edges, e.g. M5 and M4, for the isotropic XAS spectra recorded under the same experimental conditions. Therefore, the spectra recorded at the M4 and M5 edges are shifted to a common energy scale and normalized in such a way that the corresponding first EXAFS wiggles at each edge are superimposed. The both edge jumps are taken equal to unity. The same normalization procedure was used for other spectra but exploiting the EXAFS wiggles above M4 and M5 edges taken at every pressure point which are obviously slightly different for various pressures.

Residual resistivity and magnetic susceptibility

The pressure dependence of the residual resistivity has been determined from resistivity measurements under pressure already presented in ref. 60, Supplementary Note. 4. The pressure dependence of χa / χb has been adapted from ref. 19.