XANES and XMCD at the U M 4,5 edges at ambient pressure — It is now well documented that X-ray absorption near-edge spectroscopy and XMCD at the M4,5-edges of actinides are the most suitable techniques to provide direct information on the 5f states [31]. The strong resonance at these absorption edges, usually called white lines, are due to the dipole allowed transitions 3d3/2→ 5f5/2 (M4-edge) and 3d5/2→5f5/2,7/2 (M5-edge). The M4,5 XANES spectra are, thus, a sensitive probe of the occupancy of the 5f levels, whereas the corresponding XMCD spectra are unique tool to disentangle spin and orbital magnetic moments carried by the 5f electrons. 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. To get a deeper insight into the nature of the 5f electronic states, on can use the so-called branching ratio which is defined as B = IM5/ (IM5 + IM4), where IM5 and IM4 are the integrated areas of the white lines at the M5 and M4 edges, respectively. For UTe2 we obtain 0.706(2) which is in between values 0.729 and 0.686 for pure ionic configurations 5f3(U3+) and 5f2 (U4+), respectively, calculated within intermediate coupling scheme [32]. This observation places UTe2 as an intermediate valence compound. Note that similar values have been observed for other uranium intermetallics: 0.701 in UCoGe [33] and 0.698 in UCoAl [34]. The experimentally determined branching ratio was shown by van der Laan et al. [35] to be proportional to the expectation value of the angular part of the spin-orbit interaction of the 5f states:
$$\frac{2<\overrightarrow{l }.\overrightarrow{s}> }{3 {n}_{h}^{5f}}- \varDelta = -\frac{5}{2 } \left(B- \frac{3}{5}\right) \left(1\right)$$
where \({n}_{h}^{5f}\)= (14 - \({n}_{e}^{5f}\)) is the number of holes in the 5f shell and ∆ is a small correction dependent on the strength of the core-valence interaction [35]. Using atomic model, it has been calculated as a function of the 5f counts (\({n}_{e}^{5f}\)) for the three angular momentum coupling schemes (LS, intermediate and jj) by Jeffries et al (see Fig. 2 in Ref. [36]). The deduced value of − 0.265 seems to favor the intermediate coupling scheme and allows us to conclude that the occupancy of the 5f levels is about 2.6 in UTe2. Note however that this estimate relies on the assumption of a linear interpolation between the 5f2 and 5f3 electronic configurations. In conclusion, XANES results at ambient pressure confirm the intermediate valence state of UTe2.
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 theory [31]. The integrated values of XMCD signals at the M4,5 edges (∆IM4,5) allows one to deduce the orbital (\({\mu }_{L}^{U}\)(5f) = -<Lz > µB ) and spin (\({\mu }_{S}^{U}\) (5f) = -2 < Sz > µB) moments carried by the U 5f-electrons using the so-called magneto-optical sum rules [37, 38]:
<Lz> \(=\frac{{n}_{h}^{5f}}{{I}_{M5}+ {I}_{M4}} \left(\varDelta {I}_{M5}+ \varDelta {I}_{M4}\right)\) (2)
<Sz>\(= \frac{{n}_{h}^{5f}}{{2 (I}_{M5}+ {I}_{M4})} \left(\varDelta {I}_{M5}- \frac{3}{2} \varDelta {I}_{M4}\right)-3\)<Tz> (3)
The total U moment \({\mu }_{tot}^{U}\) (5f) = - (< Lz > + 2 < Sz>) µB can be obtained from XMCD spectra if reasonable estimates of the number of holes in the 5f 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 results.
The results of application of these sum rules to the M4,5 XMCD spectra of UTe2 are summarized in Table I for four different occupancies of the 5f 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 5f 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) configurations [32]. Table I shows that the magnetism of U is dominated by the orbital moment, whereas the spin moment is aligned antiparallel. Note that the U 5f 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 ligands [31]. The total 5f U moment as well the orbital-to spin moment ratio for 5f2 and 5f2.6 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 5f3 and 5f2.8 configurations is found to be lower than what is expected for free ion U3+ value indicating a delocalization of the 5f electrons due to hybridization with the Te spd electrons (as confirmed by the observation by 125 Te NMR of large transferred hyperfine coupling constants at the Te nuclei [39] and the presence of an orbital magnetic moment at the Te atoms as shown by our XMCD measurements at the Te L1 edge (see supplementary information Figure S1.) The XMCD results suggest that the 5f electron count is close to 2.8 and are in contrast to the results of band structure calculations, predicting a dominant 5f2 configuration [23–25]. On the other hand, our findings agree well with core level photoelectron spectroscopy data [30] and more recent band structure calculations by Shick et al. [29]. However, their earlier results [28] gave the same 5f occupation number, but the calculated Fermi surfaces (FS) were in contradiction with recent de Haas van Alphen (dHvA) experiments [40]. The cylindrical FS calculated by Ishizuka et al [25] succeed in reproducing the experimental observed dHvA oscillations but affords the low 5f count of 2.5.
Monitoring intensity of the XMCD signal at the M4 edge as a function of the applied magnetic field we were able to record magnetization curve that matches rather well with the macroscopic pulsed high-field magnetization curve [41] when H applied along the a easy axis (see Supplementary information Figure S2). Taking the 5f2.8 electronic configuration of uranium we can deduce that the contribution arising from the polarization of the Te valence band (µTe) and the U 6d7s conduction bands (µcond) is much weaker and amounts to − 0.05 µB at 17 T.
High pressure XANES at the U M 4,5 edges — The x-ray absorption under pressure at the L3 edge of lanthanides is routinely used to follow the pressure dependence of the valence of Ce or Yb compounds [42, 43]. In the case of actinides its use is more intricate because of the larger intrinsic broadening of the spectra owing to the shorter core hole life time, and the tendency of the 5f electrons to be more hybridized with 6d states and therefore having less overlap with the 2p hole created in the absorption process. Nevertheless the shift of the energy of the white line (2p3/2→ 6d transition) could provide helpful, but indirect, information on the U valence [26, 44]. Moreover, presence of quadrupolar 2p→5f transitions could lead to misinterpretation of the absorption spectra. On the contrary, X- ray absorption spectra at the M4,5 edges of actinides provide direct information on the 5f states but they are technically more difficult owing to relatively low binding energy 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 changes in the 5f count using what is called the first x-ray sum rule derived by Starace [45]. 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 5f 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 in [46], where the evolution of the number of 5f 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 to unity 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 to obtain a perfect overlap of the first EXAFS oscillation (at ca. 37 eV. The same energy scale is used to plot the spectra at higher pressures. The difference in energy between the absorption maxima of the M5 and M4 white lines of about 8 eV is proportional to ζ(5f), the spin-orbit parameter for the 5f 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 5f occupation using the first x-ray rule. For the sake of definitude we set the 5f count at 0.28 GPa to 2.8, i.e., to the value obtained from band structure calculations at ambient pressure [28, 29] and our XMCD analysis. The results of the changes in the 5f count are summarized in Fig. 3.
At variance with the results obtained from the energy shift of the U- L3 edge [26], we observe a gradual decrease of the U 5f count from 0.28 GPa to 1.3 GPa followed by a drop by increasing the pressure up to 1.85 GPa, slightly above the critical pressure for the appearance of magnetic order [10, 12]. The observed changes of about 0.2 electrons in the 5f count towards 5f2 (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 pressure [20]. Note, the rather low bulk modulus of UTe2 (57 GPa) is typical for highly compressible materials which are generally prone to valence instability [10, 47]. The observed substantial decrease of the 5f occupation is much larger than the values reported for other uranium intermetallics under pressure
[48–50]. Our result is reminiscent of the one observed in the pressure induced metallic ferromagnetic phase of TmTe, where the 4f- electron count changes by more than 0.5 e− between 2 and 6 GPa [51]. The described change of the electronic properties with pressure shows also up in macroscopic measurements. As shown in Fig. S3 (supplementary information) the anisotropy of magnetic susceptibility χa/χb inverses at Pc. It is accompanied with the collapse of metamagnetism along b [52, 47] and possibly occurring along the c axis [53], the collapse of the Kondo temperature [11, 53], and a significant increase of the residual resistivity ρ0 as a function of pressure (see Fig. S4 supplementary information and Ref [54]). All these changes appear to be directly associated with the drop of the 5f 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 5f orbitals of neighbouring uranium atoms is absent in tetragonal phase and this leads to an increase of the localization of the 5f electrons and consequently to a change of the 5f 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].