
==== Front
Nat Commun
Nat Commun
Nature Communications
2041-1723
Nature Publishing Group UK London

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51569
10.1038/s41467-024-51569-2
Article
Mixed-valence state in the dilute-impurity regime of La-substituted SmB6
http://orcid.org/0000-0003-0668-5146
Zonno M. marta.zonno@synchrotron-soleil.fr

12310
http://orcid.org/0000-0001-9640-5093
Michiardi M. 124
http://orcid.org/0000-0003-3503-9389
Boschini F. 25
http://orcid.org/0000-0003-2980-0805
Levy G. 12
Volckaert K. 6
Curcio D. 6
http://orcid.org/0000-0002-0122-9443
Bianchi M. 6
http://orcid.org/0000-0002-3437-548X
Rosa P. F. S. 7
Fisk Z. 8
http://orcid.org/0000-0002-7367-5821
Hofmann Ph. 6
Elfimov I. S. 12
Green R. J. 29
http://orcid.org/0000-0003-1265-2770
Sawatzky G. A. 12
http://orcid.org/0000-0001-9895-2226
Damascelli A. damascelli@physics.ubc.ca

12
1 https://ror.org/03rmrcq20 grid.17091.3e 0000 0001 2288 9830 Department of Physics & Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1 Canada
2 https://ror.org/03rmrcq20 grid.17091.3e 0000 0001 2288 9830 Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z1 Canada
3 https://ror.org/001bvc968 grid.423571.6 0000 0004 0443 7584 Canadian Light Source Inc., Saskatoon, SK S7N 2V3 Canada
4 https://ror.org/01c997669 grid.419507.e 0000 0004 0491 351X Max Planck Institute for Chemical Physics of Solids, Dresden, 01187 Germany
5 Centre Énergie Matériaux Télécommunications Institut National de la Recherche Scientifique, Varennes, QC J3X 1S2 Canada
6 https://ror.org/01aj84f44 grid.7048.b 0000 0001 1956 2722 Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University, 8000 Aarhus C, Denmark
7 https://ror.org/01e41cf67 grid.148313.c 0000 0004 0428 3079 Los Alamos National Laboratory, Los Alamos, NM 87545 USA
8 grid.266093.8 0000 0001 0668 7243 Department of Physics and Astronomy, University of California, Irvine, CA 92697 USA
9 https://ror.org/010x8gc63 grid.25152.31 0000 0001 2154 235X Department of Physics & Engineering Physics, University of Saskatchewan, Saskatoon, SK S7N 5E2 Canada
10 https://ror.org/01ydb3330 grid.426328.9 Present Address: Synchrotron SOLEIL, Saint-Aubin, 91192 France
2 9 2024
2 9 2024
2024
15 762117 10 2023
7 8 2024
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Homogeneous mixed-valence (MV) behaviour is one of the most intriguing phenomena of f-electron systems. Despite extensive efforts, a fundamental aspect which remains unsettled is the experimental determination of the limiting cases for which MV emerges. Here we address this question for SmB6, a prototypical MV system characterized by two nearly-degenerate Sm2+ and Sm3+ configurations. By combining angle-resolved photoemission spectroscopy (ARPES) and x-ray absorption spectroscopy (XAS), we track the evolution of the mean Sm valence, vSm, in the SmxLa1−xB6 series. Upon substitution of Sm ions with trivalent La, we observe a linear decrease of valence fluctuations to an almost complete suppression at x = 0.2, with vSm ~ 2; surprisingly, by further reducing x, a re-entrant increase of vSm develops, approaching the value of vimp ~ 2.35 in the dilute-impurity limit. Such behaviour departs from a monotonic evolution of vSm across the whole series, as well as from the expectation of its convergence to an integer value for x → 0. Our ARPES and XAS results, complemented by a phenomenological model, demonstrate an unconventional evolution of the MV character in the SmxLa1−xB6 series, paving the way to further theoretical and experimental considerations on the concept of MV itself, and its influence on the macroscopic properties of rare-earth compounds in the dilute-to-intermediate impurity regime.

This study reveals a non-monotonic evolution of the mixed-valence character in the SmxLa1−xB6 series, with near-complete suppression of valence fluctuations in the intermediate substitution regime, followed by a re-emergent mixed-valence behavior in the dilute-impurity limit.

Subject terms

Electronic properties and materials
Condensed-matter physics
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Strong many-body interactions play a critical role in shaping the electronic, magnetic, and even mechanical properties of quantum materials. In compounds containing rare-earth or actinide elements, electron correlations originate from the localized and partially filled f-electron shells. The resulting entanglement of the relevant degrees of freedom—orbital, spin, charge, and lattice—gives rise to a plethora of novel phenomena in such materials, including spin and charge order1, superconductivity2,3, quantum criticality4, heavy fermion behavior5,6, Kondo physics7, and mixed-valence behavior8,9.

In particular, mixed valence (MV) is a fascinating phenomenon observed in a wide range of rare-earth compounds8,10–13, yet a full microscopic understanding of its nature and limits remains elusive. MV is defined by the presence of a given rare-earth element in the system exhibiting more than one electronic occupation for the f shell14. Within the whole class of MV compounds, an important distinction arises between inhomogeneous and homogeneous MV scenarios. While in the former case ions with differing f occupation values reside on inequivalent crystallographic sites, in the latter all rare-earth ions retain the same non-integer f valence at each site15,16. Here, we focus on the case of homogeneous MV—also referred to as intermediate valence in the literature15—to explore experimentally the parameter space in which such MV behavior emerges. Various theoretical works have discussed the phenomenon of MV in the dilute- to single-impurity limit17,18, from mean-field theories19,20 to exact solutions by Wilson’s renormalization group method or bosonization21,22. However, an experimental study tracking the crossover of the MV character going from a periodic f-electron lattice to a dilute f-impurity system is still lacking.

In this work, we address this question by focusing on the prototypical homogeneous mixed-valence system SmB6, wherein the interplay between two nearly degenerate f-shell valence configurations of the Sm ions profoundly shapes its electronic structure and macroscopic properties. While it has been shown that temperature and pressure may be exploited as external perturbations to tune the intermediate valence of the Sm ions23–29, we base our experimental strategy on elemental substitution on the rare-earth site. This approach provides a powerful chemical control parameter acting directly on the occupation of the f-states, allowing the precise tracking of the mean Sm valence across different concentration regimes.

To this end, we employ trivalent La ions as substituents in the SmxLa1−xB6 hexaboride series. Although all the compounds of the series share the same CsCl-type crystal structure, the two end members exhibit very different physics. LaB6 (x = 0) is metallic owing to the partially occupied La-5d band and the lack of 4f electrons (see Supplementary Information I and Fig. S1). In contrast, the precise nature of the ground state of SmB6 (x = 1) still remains an open question. Exhibiting a resistivity plateau at low temperature30, it has been theoretically proposed as realization of a topological Kondo insulator31,32, and various experimental studies have later discussed the possible presence and nature of in-gap electronic states33–42, as well as controversial reports of quantum oscillations43–45. Even though a clear answer has yet to emerge, a fundamental aspect characterizing the physics of SmB6 is undoubtedly the nearly-complete admixture of the two possible Sm ions valence configurations 4f 6 5d0 and 4f 5 5d1, which in terms of the f-level occupation are generally referred to as Sm2+ and Sm3+, respectively. This leads to a mean Sm valence for the f shell of  +2.505 in SmB6 at low temperature23,24,46, while the single d band is characterized by a strongly mixed B-Sm character.

A recent de Haas-van Alphen (dHvA) investigation of dilute Sm-doped LaB6 (x = 0.05 and x = 0.1) reported only a small reduction of the FS volume upon Sm substitution47. Interestingly, such reduction rate would not be compatible with having Sm ions either purely divalent or trivalent in this concentration regime. Here, we track the electronic structure of the SmxLa1−xB6 series over the entire doping range, by means of angle-resolved photoemission (ARPES) and x-ray absorption spectroscopy (XAS), and observe a non-monotonic evolution of the mean Sm valence. While the strong Sm2+/Sm3+ admixture is quenched in the intermediate substitution regime, it resurges for low Sm concentrations, with a persisting MV behavior all the way into the dilute-impurity limit. These results provide experimental evidence of the emergence of the MV phenomenon even in this dilute limit, and establish the key role of unconventional behavior of f-electrons in defining the properties of rare-earth compounds also in such extreme regimes.

Results

We begin by showcasing the evolution of the electronic structure of SmxLa1−xB6, upon La-Sm chemical substitution, as measured by ARPES. Figure 1a summarizes the ARPES spectra acquired along the XM¯ direction (black dashed line in Fig. 1b, left) for x = [0, 0.2, 0.55, 0.7, 0.8, 1]. Common to all compounds, bulk electron-like pockets are centered at the X high-symmetry points of the Brillouin zone (BZ), forming elliptic iso-energy contours (see Fig. 1b). Being primarily associated with B-2p and rare-earth 5d electrons, their size is directly related to the valence of the rare-earth element in the material: for a full 3+ configuration the d-pocket is half filled and at its largest, while in a 2+ state the valence electrons only fall in the f-states and the d-pocket lays in the unoccupied part of the spectrum. This observation makes the study of the evolution of the bulk 5d pockets centered at X instrumental to track the possible valence fluctuations of the Sm ions in the SmxLa1−xB6 series.Fig. 1 ARPES spectra of SmxLa1−xB6.

a ARPES spectra along the XM¯ high-symmetry direction of the Brillouin zone (black dashed line in b, left) for x = [0, 0.2, 0.55, 0.7, 0.8, 1]. b ARPES iso-energy contours close to EF for the same samples shown in a; the integration window in energy is 15 meV about EF. All data were acquired at 10 K with hν = 21.2 eV.

Note that as Sm is introduced into the system, three non-dispersing 4f-states emerge in the ARPES spectra within the first 1 eV of the Fermi level. Starting very weak and broad for small x values, these states become gradually sharper and shift to slightly lower binding energies as x increases, finally settling at 15 meV, 150 meV, and 1 eV for pristine SmB6, consistent with the values reported in the literature36,38,48. Concurrently, the size of the X-pockets progressively decreases upon increasing x. While the interplay between localized 4f-electrons and itinerant 5d electrons is undoubtedly an important defining aspect of the electronic structure of these materials, in this work, we focus our analysis on the evolution of the bulk X-pockets’ dispersion as a function of x, which can be directly linked to changes in the concentration of trivalent ions in the system.

While a decrease in the size of the X-pockets is expected throughout the series due to the removal of trivalent La ions contributing to the occupation of the 5d-band, by visual inspection of Fig. 1, we note that the observed behavior departs from a constant-rate reduction. In fact, the change in the ARPES dispersion is more pronounced for x ≤ 0.55 than for higher Sm concentrations. This progression is showcased by the evolution of the 5d-band dispersion extracted as a function of x along the ΓX¯ and XM¯ high-symmetry directions shown in Fig. 2a. In order to quantitatively assess this variation and thus establish a direct relation between the ARPES dispersion and the fractional percentage of Sm2+ and Sm3+ present in the system, we must convert the size of the X-pocket contours as extracted from the ARPES data into the pocket’s occupation n5d. This is done via application of the Luttinger’s theorem, which directly relates the volume enclosed by a material’s Fermi surface to the electron density49,50. Here we emphasize that the bare X-pocket dispersion in the SmxLa1−xB6 series can be described to a first approximation by the same effective mass as observed for LaB6, with the only Fermi momentum kF5d changing to accommodate for the varying electronic occupation. This assumption is supported by the ARPES dispersions shown in Fig. 2a, and facilitates a direct comparison among different compounds in the series.Fig. 2 Extracting the Sm valence from the ARPES dispersion.

a Evolution of the X-pocket dispersion along ΓX¯ and XM¯ directions for x = [0, 0.2, 0.55, 0.7, 0.8, 1], as extracted from the ARPES spectra in Fig. 1. b Electronic occupation number of the X-pocket, n5d(x), for different SmxLa1−xB6 compounds. Data points were obtained from ARPES spectra acquired with 21.2 eV and 67 eV. The dashed black line illustrates the case of a constant 1:1 ratio of Sm2+:Sm3+ across the series; this is computed from the general expression n5d(x) = [1−x*a/(a + b)], where a and b are the fractional percentage of Sm2+ and Sm3+, which reduces to n1:15d = 1−x/2 in the case of a = b. c Calculated fractional percentage of Sm2+ (top) and Sm3+ (bottom) by using Eq. (1) for the different compounds measured by ARPES. Error bars in b, c are determined as follow: on the x axis are based on energy dispersive x-ray (EDX) measurements; on n5d(x) are derived from the fitting of the ARPES data; on the fractions of Sm2+/Sm3+ are calculated by combining the uncertainties on x and n5d(x) via error propagation rules.

Figure 2b displays the values of n5d(x) as extracted via Luttinger’s theorem from the ARPES spectra acquired with 21.2 eV and 67 eV probe energy (the latter associated with the bulk Γ high-symmetry point; see Supplementary Information I, in particular Figs. S2, S3). The values were obtained by calculating the total enclosed volume of the X-pockets based on the collected ARPES while relying on the cubic crystal sysmmetry, and by taking into account the reported variation of the lattice parameter in the SmxLa1−xB6 series51,52. For LaB6 (x = 0), the pockets enclose  ~50% of the bulk cubic BZ, corresponding to having 1 electron n5d = 1. At the other end of the series, in SmB6 (x = 1) only a quarter of the cubic BZ is filled by the X-pockets, yielding n5d = 0.5. These results are fully consistent with the metallic ground state observed in LaB6 and the reported valence of +2.505 of Sm ions in SmB6, thus validating our analysis. By applying the same approach to the intermediate compounds of the series, we find that n5d(x) clearly deviates from the linear reduction expected in the case of a constant 1:1 ratio of Sm2+:Sm3+, represented in Fig. 2b by the black dashed line. To better quantify the evolution, we compute the fractional percentage of Sm2+ and Sm3+ from n5d(x), as follows (normalized over the total amount of Sm in the system, x):1 FractionSm2+(%)=1−n5d(x)xFractionSm3+(%)=1+n5d(x)−1x.

The resulting values are presented in Fig. 2c. As x decreases from 1, the amount of Sm2+ gradually increases upon reaching a maximum of  ~85% at x = 0.2, followed by a re-entrant reduction at even lower Sm concentrations. Despite the uncertainties associated with probing minimal modifications of the X-pocket ARPES dispersion for concentrations smaller than 0.1 (as reflected in the large error bars in Fig. 2c), our ARPES results suggest a clear distinction between the low (x ≤ 0.2) and high (x ≥ 0.55) Sm concentration regimes, along with a substantial variation of the Sm2+:Sm3+ ratio across the SmxLa1−xB6 series.

In an effort to verify this scenario and gain more insights on the low concentration regime also in connection to the previous dHvA work on dilute Sm-doped LaB647, we complemented the ARPES data with a XAS study of the same SmxLa1−xB6 series. In particular, to achieve a higher bulk sensitivity and thus establish our results as an intrinsic bulk property, we exploited partial and inverse partial fluorescence yield (PFY and IPFY). Both of these techniques are characterized by a probing depth of tens of nm (thus excluding significant surface-related contributions to the XAS signal; see Supplementary Information II for details, in particular, Fig. S5), allowing one to circumvent some of the challenges characteristic of ARPES on SmxLa1−xB6, such as cleaving and surface degradation. Furthermore, XAS has already been shown to be a powerful technique to explore the physics of MV systems, such as SmB6: the absorption spectrum can be described as the first approximation by the sum of two independent components, corresponding to Sm2+ and Sm3+ ions. By tuning the incident energy across the Sm M4 and M5 edges (i.e., exciting 3d core electrons into 4f orbitals), each XAS spectrum can be mapped into a specific Sm2+:Sm3+ ratio, providing us with a tool to directly determine the mean Sm valence in the SmxLa1−xB6 series.

In Fig. 3a, we present the evolution of the XAS intensity at the Sm M5 edge for x = [0.07, 0.13, 0.2, 0.3, 0.7, 0.9, 0.975, 1], along with a weighted sum fit of the Sm2+ and Sm3+ components (red and orange, respectively). While for high x the Sm3+ component dominates, its contribution dramatically reduces at x = 0.2. However, upon further decrease of x, a clear inversion in the progression of the XAS spectra is observed, as the Sm3+ component strengthens again for x ≤ 0.2.Fig. 3 XAS study of the SmxLa1−xB6 series.

a Evolution of the XAS intensity at the Sm M5 edge for x = [0.07, 0.13, 0.2, 0.3, 0.7, 0.9, 0.975, 1]. The absorption profiles (gray dots) have been extracted at 640 eV (La fluorescence line) of IPFY spectra for x ≤ 0.3, and at 850 eV (Sm fluorescence line) of PFY spectra for x > 0.3. The total XAS spectral weight is fit (black lines) by the sum of two independent components associated to Sm2+ (red lines and shaded regions) and Sm3+ ions (orange lines and shaded regions). b Intensity evolution of the Sm2+ (top) and Sm3+ (bottom) components normalized to the x = 1 case. All data were taken at a base temperature of 20 K. Error bars in b are determined as follow: on the x axis are based on EDX measurements; on ΔISm2+/Sm3+ are derived from the fitting of the XAS data.

Such behavior is highlighted by the intensity variation of the two components displayed in Fig. 3b (normalized to the x = 1 values) and is fully consistent with the evolution of the fractional percentages of Sm2+ and Sm3+ obtained from ARPES, thus confirming the two-regime scenario already suggested in Fig. 2. In particular, the Sm2+ contribution peaks nearly doubling at x = 0.2, corresponding to an increment of Sm2+ ions in the system as large as  ~90% with respect to the pure SmB6 case. We remark that such significant increase of Sm2+ sets apart from what reported on pure SmB6 by employing high-temperature and high pressure, with both perturbations causing an increase of the mean Sm valence towards +323–29. Also note that the deviation from an almost 1:1 ratio of the Sm2+:Sm3+ peaks expected at x = 1 may reflect a difference in the relative cross-sections of the two Sm components at the energies the XAS measurements were performed: while not affecting the qualitative evolution of the intensities shown in Fig. 3b, it is taken into account for computing the mean Sm valence (see Supplementary Information II and Fig. S4 for details on the XAS analysis and normalization).

In Figs. 2 and 3, we showed that both ARPES and XAS measurements of the SmxLa1−xB6 series display a progression from an evenly Sm2+/Sm3+ regime into a predominant presence of Sm2+ as x decreases. This result is consistent with the observation of the average Sm valence tending towards +2 upon trivalent ion substitution (such as La3+ or Y3+) reported in early works51,52. Furthermore, recent transport studies on La-substituted SmB6 have reported the complete closure of the d-f hybridization gap, and the consequent emergence of a metallic-like behavior, for La concentrations higher than 25% (here x ≤ 0.75)53,54, corroborating the substantial increase of Sm2+ in the system observed in this work. However, according to these arguments one may expect the valence fluctuations to be quenched at zero doping, i.e., vSm→+2 for x→0, in stark contrast with the clear suppression detected at x = 0.2, followed by the sudden overturn for even lower x. Nevertheless, a scenario in which the Sm ions are neither purely divalent nor trivalent even in the dilute-impurity regime is in agreement with the evolution of the FS volume reported by dHvA, which exhibits a reduction rate smaller than the amount of Sm introduced in the system47.

Here we present a basic phenomenological model for vSm in the SmxLa1−xB6 series based on the two distinct regimes observed experimentally. On one hand, for high x we mimic the convergence towards +2 upon La-substitution (i.e., upon reducing x) by fitting the experimental data for 0.2 ≤ x ≤ 1 with a linear fit, V0(x) [orange line in Fig. 4a]. On the other hand, to provide a phenomenological description of the increase of vSm detected at low x (i.e., x < 0.2), in connection to the literature discussing the MV behavior in the extreme dilute limit of a single magnetic impurity in a non-magnetic band metal, we consider here the possibility of additional contributions to vSm stemming from Sm ions acting as single impurities with a specific fixed fractional valence, vimp. In this regard, we compute the probability as a function of x for a Sm ion to have no other Sm in the next-nearest-neighbor sites, P0(x) [light blue line in Fig. 4a]. This function is used to define in first approximation the fraction of Sm ions that exhibit a dilute-impurity valence vimp = +2.35, as extrapolated from the experimental results in Figs. 2c, 3b, at any given concentration x. We can then express the evolution of the Sm valence in the SmxLa1−xB6 series as:2 vmodel=P0(x)⋅vimp+[1−P0(x)]⋅V0(x).

Figure 4b compares the model of Eq. (2) with the experimental values of the mean Sm valence obtained from ARPES (light and dark blue circles) and XAS (red diamonds), showing an overall good agreement. In particular, the inclusion of the emerging Sm dilute-impurity regime with fixed fractional valence is proven pivotal to capture the steep increase of vSm experimentally observed for low x; however, its contribution becomes negligible at high x, owing to the rapid decay of P0(x) below 0.1 for x ≥ 0.3.Fig. 4 Simplified model for the description of vSm in the two different x regimes.

a Light blue line: calculated probability for a Sm ions to have no other Sm as next-nearest-neighbors, P0(x). This function is used to define the fraction of Sm ions which acquires the impurity valence vimp = 2.35 at each x. Orange line: linear fit to the experimental vSm values for x ≥ 0.2 (gray data points), V0(x), capturing the decrease in the valence due to formation of Sm2+ upon La-substitution. Light blue and yellow shadowed regions indicate the Sm concentrations regimes at which P0(x) and V0(x) dominates, respectively. b Comparison between the model of Eq. (2) [solid line; light blue/yellow color indicates the two different contributions to our model shown in a] and the experimental values of vSm obtained from ARPES (light and dark blue circles, acquired with 21 eV and 67 eV, respectively) and XAS (red diamonds). Error bars in b are determined as follow: on the x axis are based on EDX measurements; on vSm are derived from the uncertainties on the fractions of Sm2+/Sm3+ and on ΔISm2+/Sm3+ for ARPES and XAS data, respectively.

As a final note, we emphasize that the model of Eq. (2) does not fully describe the nearly complete suppression of Sm2+/Sm3+ admixture detected at x = 0.2. When performing density functional theory calculations of the doping dependence on the Fermi energy using virtual crystal approximation, no anomalous behavior was found which could explain this observation; indeed, additional investigations are needed to specifically address the sharp crossover observed around x = 0.2 with the development of more refined theories. Nevertheless, our combined ARPES and XAS study provides evidence of the realization of a dilute-impurity MV state in the SmxLa1−xB6 series. Our results may stimulate further theoretical and experimental considerations on the concept of MV and its influence on the macroscopic electronic and transport properties of rare-earth compounds in the dilute-to-intermediate impurity regime.

Methods

High-quality single crystals of SmxLa1−xB6 were grown by the aluminum flux method in a continuous Ar-purged vertical high-temperature tube furnace33. Post-growth characterization by scanning electron microscope and energy dispersive x-ray measurements for the actual Sm concentration was performed at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated by the U.S. Department of Energy Office of Science. ARPES experiments were performed at the Stewart Blusson Quantum Matter Institute at UBC employing a photon energy of hν = 21.2 eV, at a base pressure  < 3 × 10−11 Torr and base temperature of 10 K. The electrons were collected using a SPECS Phoibos 150 hemisperical analyzer, with energy and momentum resolution of 25 meV and 0.02 Å, respectively. Additional ARPES measurements were carried out at the SGM3 endstation at the ASTRID2 synchrotron radiation facility55, using a photon energy of hν = 67 eV, with base temperature 35 K and energy resolution 35 meV. All samples were cleaved in situ and measured along the (001) surface. XAS measurements were performed using the four-circle UHV diffractometer at the REIXS 10ID-2 beamline at the Canadian Light Source in Saskatoon56, with base pressure and temperature of 5 × 10−10 Torr and 22 K, respectively.

Supplementary information

Supplementary Information

Peer Review File

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-51569-2.

Acknowledgements

We thank E.H. da Silva Neto, R.P. Day, A.M. Hallas, N. Harrison, H.-H. Kung, E. Razzoli, H.L. Tjeng, C.M. Varma, and B. Zwartsenberg for fruitful discussions. This research was undertaken thanks in part to funding from the Max Planck-UBC-UTokyo Centre for Quantum Materials and the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program. This project is also funded by the Killam, Alfred P. Sloan, and Natural Sciences and Engineering Research Council of Canada’s (NSERC’s) Steacie Memorial Fellowships (A.D.); the Alexander von Humboldt Fellowship (A.D.); the Canada Research Chairs Program (A.D.); NSERC, Canada Foundation for Innovation (CFI); the Department of National Defence (DND); British Columbia Knowledge Development Fund (BCKDF); and the CIFAR Quantum Materials Program. Part of the research described in this work was performed at the Canadian Light Source, a national research facility of the University of Saskatchewan, which is supported by CFI, NSERC, the National Research Council (NRC), the Canadian Institutes of Health Research (CIHR), the Government of Saskatchewan, and the University of Saskatchewan. The research carried out in Aarhus was supported by the Independent Research Fund Denmark (Grant no. 1026-00089B) and the VILLUM FONDEN via the Centre of Excellence for Dirac Materials (Grant no. 11744). Work at Los Alamos was performed under the auspices of the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering.

Author contributions

M.Z., I.S.E, G.A.S., and A.D. conceived the project and M.Z. and A.D. designed the experiment. P.F.S.R. and Z.F. grew the single crystals and P.F.S.R. characterized them. M.Z. and M.M. performed the ARPES experiments, with assistance from F.B., G.L., K.V., D.C., M.B., and Ph.H. XAS measurements were carried out by M.Z. and R.J.G. M.Z. analyzed the ARPES data with input from M.M., F.B. and A.D.; R.J.G. analyzed the XAS data; M.Z. and R.J.G. developed the phenomenological model. M.Z. and A.D. wrote the manuscript with input from all authors. A.D. was responsible for the overall direction, planning, and management of the project.

Peer review

Peer review information

Nature Communications thanks Chandra Varma and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The authors declare that the main data supporting the findings of this study are available within the paper and its Supplementary Information files. Source ARPES and XAS waves used in this study have been deposited in the Zenodo database under the digital object identifier 10.5281/zenodo.12759092. Additional data are available from the corresponding authors upon request.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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