AVS 70 Session AC+MI-ThM: Superconductivity, Electron Correlation, Magnetism and Complex Behavior

The unconventional superconductors in f-based materials attract much attention in recent years. In the present talk the electronic structures of f-electron superconductors UTe₂ and CeIr₃ will be presented.

Recently, it was discovered that UTe₂ has relatively high transition temperature (T_C=2.1 K), and it is classified into one of such class of materials [1,2]. The electronic structure of UTe₂ was studied by resonant photoelectron spectroscopy (RPES) and angle-resolved photoelectron spectroscopy (ARPES) with soft X-ray synchrotron radiation [3]. The partial U 5f density of states of UTe₂ were imaged by the U 4d-5f RPES and it was found that the U 5f state has an itinerant character, but there exists an incoherent peak due to the strong electron correlation effects. The band structure of UTe₂ was obtained by ARPES and its overall band structure was mostly explained by band structure calculations, except for the incoherent band at E_B~0.5 eV. These results suggest that the U 5f states of UTe₂ have itinerant but strongly-correlated nature.

The electronic structure of the f-based superconductor CeIr₃ (T_SC=3.1 K) was also studied by photoelectron spectroscopy [4]. The energy distribution of the Ce 4f states were revealed by the Ce 3d-4f RPES. The contribution of the Ce 4f states to the density of states (DOS) at the Fermi energy was estimated to be nearly half of that of the Ir 5d states, implying that the Ce 4f states have a considerable contribution to the DOS at the Fermi energy. These results suggest that CeIr₃ is an s-wave-type superconductor with a considerable contribution from the Ce 4f states.

Work performed in collaboration with Ikuto Kawasaki, Yukiharu Takeda, Hiroshi Yamagami, Norimasa Sasabe, Yoshiki J Sato, Ai Nakamura, Yusei Shimizu, Arvind Maurya, Yoshiya Homma, Dexin Li, Fuminori Honda, and Dai Aoki.

References

[1] S. Ran et al., Science 365, 684 (2019).

[2] D. Aoki et al.,J. Phys. Soc. 88, 043702 (2019).

[3] S. Fujimori, et al., J. Phys. Soc. Jpn. 88, 103701 (2019).

[4] S. Fujimori et al., Electron. Struct. 5, 045009 (2023).

UTe₂ is a recently discovered odd-parity superconductor, emerging as a promising candidate for topological superconductivity [1-3]. A key challenge in understanding its anisotropic properties and their dependence on tuning parameters is finding the appropriate Ansatz for describing such a complex electronic system, situated at the border between localization and itinerancy. It is essential to determine the extent to which local physics persists and to identify the governing electronic fⁿ configuration. Although the latter has been addressed using various methods, a fierce debate remains about whether the main configuration is f² or f³.

Discrepancies in determining the dominant fⁿ configuration are common in uranium-based intermetallics. We argue that this apparent contradiction arises from the challenge of accurately analyzing the spectra, given the complexity associated with the underlying many-body problem and uncertainties in the input model parameters.

In our study, we opt for a newly developed spectroscopic method for U materials, namely resonant inelastic x-ray scattering (RIXS) in the tender x-ray range [4]. Applying this method to UTe₂, we can unambiguously detect the presence of atomic-like U 5f-5f low-energy excitations. This establishes the correlated nature of UTe₂ despite the presence of strong covalence and band formation. Moreover, we can also fingerprint the U 5f² as the main configuration without the need to rely on accurate calculations, thus settling the debate about the 5f valence state [5].

The short Te2-Te2 distances, however, seem incompatible with a formal U⁴⁺ valence. We resolve this puzzle by utilizing band structure calculations and photon energy-dependent photoemission. We found that the charge transfer from the 5p_y||b band of the Te2 chain is directed not to the U 5f but to the bonding state of the U 6d_3z2-r2 orbitals of the U dimer. Notably, these two band states are non-bonding to each other or to other non-5f states in the material. Yet, both bands hybridize with the U 5f, emphasizing that the description of the physical properties of UTe₂ must include the Te2 5p_y||b and U 6d_3z2-r2 bands plus the 5f²Ansatz [5] These are all very peculiar findings, making UTe₂ a very special material indeed.

[1] S. Ran et al., Science, 365(6454), 684–687 (2019).

[2] D. Aoki et al., J. Phys. Soc. Jpn. 88(4), 043702 (2019)

[3] for recent review: S.K. Lewin et al., Rep. Prog. Phys. 86(11):114501, 2023.

[4] A. Marino et al., Phys. Rev. B 108, 045142 (2023)

[5] D. S. Christovam et al.,arXiv 2402.03852 [https://arxiv.org/abs/2402.03852] (2024)

The discovery of multiple superconducting phases in UTe₂ boosted research on correlated-electron physics [1,2,3,4]. The proximity to a ferromagnetic quantum phase transition was initially proposed as a driving force to triplet-pairing superconductivity [1], and this heavy-fermion paramagnet was rapidly identified as a reference compound to study the interplay between magnetism and unconventional superconductivity with multiple degrees of freedom.

Here, we present neutron diffraction experiments showing that long-range incommensurate antiferromagnetic order is established in UTe₂ under pressure [5]. The propagation vector k_m = (0.07,0.33,1) of the observed antiferromagnetic phase is close to a wavevector where antiferromagnetic fluctuations have previously been observed at ambient pressure [6,7]. Our work shows that superconductivity in UTe₂ develops in the vicinity of a long-range antiferromagnetic phase, which differs from the initial proposition of a nearby ferromagnetic phase. The nearly-antiferromagnetic nature of UTe₂ at ambient pressure and its relationship with superconductivity will be discussed.

This work was done in collaboration with T. Thebault, P. Manuel, D. Khalyavin, F. Orlandi, E. Ressouche, K. Beauvois, G. Lapertot, K. Kaneko, D. Aoki, D. Braithwaite, G. Knebel, and S. Raymond.

[1] Ran et al., Science 365, 684 (2019).
[2] Knebel et al, J. Phys. Soc. Jpn. 88, 063707 (2019).
[3] Braithwaite et al., Commun. Phys. 2, 147 (2019).
[4] Ran et al., Nat. Phys. 15, 1250–1254 (2019).
[5] Knafo et al., arXiv:2311.05455.
[6] Duan et al., Phys. Rev. Lett. 125, 237003 (2020).
[7] Knafo et al., Phys. Rev. B 104, L100409 (2021).

Uranium intermetallic compounds exhibit a wide range of fascinating physical phenomena that arise from the intricate interplay between atomic-like correlations and band formation of the U 5f electrons. Describing their electronic structure is a challenge, particularly as atomic-like states have remained experimentally inaccessible. Ongoing disputes revolve around the existence of atomic-like states and, if present, around determining which configuration—U 5f³ or U 5f²—provides the Ansatz or starting point for describing the low-energy properties. Furthermore, these correlated compounds exhibit strong intermediate valency, fuelling intense debates about the actual filling of the 5f shell and the degree of covalency.

This presentation introduces two novel and complementary methods: (1) valence band resonant inelastic x-ray scattering (RIXS) using tender x-rays and (2) photon energy-dependent photoelectron spectroscopy (PES & HAXPES) in combination with DFT+DMFT calculations.

(1) Valence Band RIXS: Using high-resolution RIXS at the U M-edges (3.5-3.7 keV), we observe low-energy excitations originating from atomic-like multiplet interactions [1]. The excellent signal-to-background ratio and the multiplet structure serve as a unique fingerprint for the U 5fⁿ configuration involved, offering clear evidence of the presence of local correlation physics. This method unambiguously determines the dominating configuration [1].

(2) Combination of DFT+DMFT calculations with soft and hard x-ray photoemission (PES & HAXPES): The energy dependencies of the photoionization cross-sections allow for the disentanglement of correlated 5f from band-like non-5f spectral contributions, enabling reliable tuning of parameters such as Hund’s-J, Hubbard-U_ff, and, most importantly, the double counting correction (m_dc) to reproduce valence band spectra. We applied this method to UGa₂ and UB₂, two model materials representing the extreme ends of the localization-delocalization range. Despite their vastly different properties, we found the mean 5f shell filling to be almost the same. However, crucially, the distribution of uranium 5f configurations contributing to the ground state differs significantly: narrow in 'localized' UGa₂ and almost statistically broad in 'itinerant' UB₂. This method also reproduces the satellites in the 4f core-level spectra and explains the presence/absence of 5f-5f-multiplet excitations in the RIXS spectra [2].

[1] A. Marino et al. Phys. Rev. B, 108 (2023) 045142
[2] A. Marino, A. Hariki et al., to be published

The heavy-fermion compound CeRh2As₂ exhibits a complex phase diagram with rather unusual states at low temperatures. A prominent example is multi-phase superconductivity[1] which seems to develop inside a normal state characterized by itinerant multi-polar order. The present talk focusses on the instabilities of the strongly renormalized Fermi liquid state in the heavy-fermion compound CeRh2As2. The central focus is the role played by the non-symmorphic lattice structure and the consequences of the Crystalline Electric Field (CEF) which removes the orbital degeneracy of the Ce 4f states. The narrow quasiparticle bands which arise from the Ce-4f degrees of freedom via the Kondo effect are calculated by means of the Renormalized Band (RB) method. We conjecture that the quasi-quartet CEF ground state in combination with pronounced nesting features of the Fermi surface may give rise to ordered states involving multipolar degrees of freedom [2].

References

1. S. Khim et al., Science 373, 1012 (2021)
2. RevX 12, 011023 (2022)

Crystallographic features play an important role in the physical and chemical properties of a given solid-state material. In particular, actinide-based systems exhibit a wide range of properties – from unconventional superconductivity to peculiar magnetic orders. In this talk, I will highlight some of the old and new actinide-based superconductors, in which a delicate interplay between chemistry and physics is observed. A comprehensive characterization of properties of UBe₁₃ has revealed a deep interrelation between the physical and chemical features. Notably, single crystals of this material tend of include many defects which have a dramatic effect on superconducting state [1]. Motivated by this issue, an alternative method of studying intrinsic properties is investigated [2-4]. By creating a micro-scale device, it is possible to measure intrinsic superconductivity of UBe₁₃, whichhas so far remained out of reach [4]. The properties of UBe₁₃ are compare to those of other actinide-based superconductors – UTe₂ [5] and Th₄Be₃₃Pt₁₆ [6] – in which a strong coupling of lattice and superconducting properties is observed. By studying these systems, it is possible to expand the understanding of crystal chemistry of solid-state materials, while simultaneously providing an insight into which crystallographic parameters impact the physical properties of a given solid-state material.

[1] A. Amon et al., “Tracking aluminium impurities in single crystals of the heavy-fermion superconductor UBe₁₃,” Sci. Rep. 8, 10654 (2018)

[2] E. Svanidze et al., “Revealing intrinsic properties of UBe₁₃”, in preparation (2024)

[3] A. Amon et al., "Interplay of atomic interactions in the intermetallic semiconductor Be₅Pt", Angew. Chem. Int. Ed. 58, 2 (2019).

[4] I. Antonyshyn et al., "Micro-scale device - an alternative route for studying the intrinsic properties of solid-state materials: case of semiconducting TaGeIr", Angew. Chem. Int. Ed. 59, 2 (2020)

[5] E. Svanidze et al., “Intrinsic crystal structure of UTe₂”, in preparation (2024)

[6] P. Kozelj et al., “A noncentrosymmetric cage superconductor Th₄Be₃₃Pt₁₆”, Sci. Rep. 11, 22352 (2021)

Motivated by a recent experimental study [1], we model the valence-to-core resonant inelastic x-ray scattering (RIXS) measured at the uranium M₅ edge in insulating compounds UO₂ and UF₄. We employ the Kramers–Heisenberg formula in conjunction with the Anderson impurity model extracted from the corresponding LDA+DMFT electronic-structure calculations [2], in which the double-counting correction is adjusted to best reproduce the experimental valence-band XPS [3,4]. In our simulations, we find two sets of excited states. One group is formed by excitations of the 5f² shell that appear at energy losses ≲ 4 eV. These excitations are not well resolved in the experimental data [1] as they are largely obscured by the elastic peak. The other group of excited states is formed by the charge-transfer excitations corresponding to a transfer of an electron from the oxygen/fluor 2p states to the uranium 5f shell. We identify these excitations with the spectral feature experimentally observed at an energy loss of roughly 8–10 eV, in agreement with other closely related investigations [5,6]. Our model estimates the intensity, with which the charge-transfer excitations appear in the RIXS spectra, to be larger in UO₂ that in UF₄, just like it is observed in the experiment [1]. We analyze in some detail how this intensity depends on the strength of the metal-ligand hybridization and on other parameters of the model, such as the magnitude of the core-valence interaction acting in the intermediate state of the RIXS process.

1. J. G. Tobin et al., J. Phys.: Condens. Matter 34, 505601 (2022).
   [https://doi.org/10.1088/1361-648X/ac9bbd]

2. J. Kolorenč, A. Shick, A. Lichtenstein, Phys. Rev. B 92, 085125 (2015).
   [https://doi.org/10.1103/PhysRevB.92.085125]

3. Y. Baer, J. Schoenes, Solid State Comm. 33, 885 (1980).
   [https://doi.org/10.1016/0038-1098(80)91210-7]

4. A. Yu. Teterin et al., Phys. Rev B 74, 045101 (2006).
   [https://doi.org/10.1103/PhysRevB.74.045101]
   

5. K. Kvashnina et al., Phys. Rev. B 95, 245103 (2017).
   [https://doi.org/10.1039/c8cc05464a]

6. K. Kvashnina et al., Chem. Commun. 54, 9757 (2018).
   [https://doi.org/10.1039/c8cc05464a]