AVS 71 Session AC+MI-ThM: Superconductivity, Magnetism, Electron Correlation and Complex Behavior

Exotic magnetism and superconductivity have been observed in uranium-based compounds, including spin-triplet superconductivity in UTe₂ and a hidden order(likely a high-rank multipole ordering never been observed before) in URu₂Si₂. These phenomena may arise from the strong correlations and the unique characteristics at the boundary between itinerant and localized states of U 5f electrons. Recent advancements in the physics of strongly correlated materials in uranium-based compounds will be discussed.

There is a growing interest in high entropy alloys (HEAs), which are solid solutions of five or more elements, at least 5 at.% each, that crystallize in simple structures and are characterized by high configurational entropy during solidification [1]. Known for their exceptional mechanical properties, thermal stability, and corrosion resistance [2–4], they are considered materials with high potential for applications such as durable mechanical devices, magnets, or, more recently, superconductors [5].

Currently, the study of HEA with uranium or thorium is mainly focused on the development of advanced high-strength materials. However, a superconducting state has also been discovered in one of the alloys, namely (TaNb)_0.31(TiUHf)_0.69 [6]. Here we present the crystal structure and physical properties of two other high-entropy alloys, namely (NbTa)_0.67(MoWTh)_0.33 [7] and UNbTiVZr [8], which exhibit BCS superconductivity with the critical temperature of about 5.6-7.5 K in the case of the thorium-based alloy and 2.1 K in the case of uranium-based system. Their upper critical magnetic field is of about 0.7 T and 5 T, respectively. In addition, we present the results of a numerical study of the electron structure of the alloy using the DFT formalism.

This research was funded in whole by National Centre of Science (Poland) Grant number 2020/39/B/ST5/01782. R.T. acknowledges the support of Dioscuri program initiated by the Max Planck Society, jointly managed with the National Centre of Science (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research.

References

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[8] W. Nowak et al., unpublished.

The uranium-based superconductors have attracted considerable interest because of their unusual superconducting (SC) and normal-state properties. Among them, UBe₁₃ (cubic O_h⁶, space group #226) has attracted much attention as a promising candidate for spin triplet superconductivity since the early stage [1]. The strong sample dependence of this superconductivity [2,3] and the lack of understanding of its 5f electronic state make the unraveling of superconductivity in UBe₁₃ even more difficult. In particular, the non-monotonic Th concentration dependence of T_sc in U_1-xTh_xBe₁₃ and occurrence of SC double transition of heat capacity with a small amount of thorium (0.019 < x < 0.045) [4-8] are quite anomalous properties, and understanding this multiple SC phase diagram is important for elucidating the true nature of uranium spin triplet superconductors.

In this study, we focus on the low-temperature physics on thorium-doped UBe₁₃ and we revisit their unusual SC and normal-state properties. We have fabricated polycrystals of U_1-xTh_xBe₁₃ (x = 0.01, 0.015, 0.02, 0.03, 0.04, 0.05, 0.07) in an arc furnace. We determined their lattice constants from x-ray powder diffraction. Previous studies have found double transition of superconductivity at 0.019 < x < 0.045 in heat capacity [5-8]. In order to clarify whether this double SC transition is intrinsic, we have performed detailed EDS (Energy Dispersive X-ray Spectroscopy), low-temperature heat-capacity and electrical resistivity measurements for U_1-xTh_xBe₁₃. The EDS results show that the distribution of Th is uniform within the crystals and that there is no heterogeneous U_1-xTh_xBe₁₃ composition within the experimental accuracy. Furthermore, the low-temperature heat capacity results for U_1-xTh_xBe₁₃ show that for x = 0.02, 0.03, 0.04 a second transition occurs in the SC state, while for x = 0.015, 0.05 only one SC transition is observed, which is consistent with previous studies. In our presentation, we will discuss the detail of SC H-T-x phase diagram and non-Fermi-liquid behavior in U_1-xTh_xBe₁₃.

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The search for new types of exotic topological orders has recently rekindled the interest in Fermi surface reconstructions. Of particular interest are Electronic Topological (Lifshitz) transitions where the number of Fermi surface sheets changes abruptly under the influence of external parameters like chemical doping, pressure, or magnetic field.Lifshitz transitions are generally associated with the presence of critical points in the electronic band structure, i. e., maxima, minima, or saddle points whose presence follows directly from lattice periodicity. As their separation from the chemical potential is of the order of the bandwidth, the critical points hardly affect the low temperature behavior of “conventional” metals. In heavy-fermion materials, however, the widths of the quasi-particle bands are strongly reduced by electronic correlations and, consequently, magnetic fields can drive Lifshitz transitions. The characteristic anomalies in the equilibrium and transport properties provide a method to test the quasi-particle dispersion away from the Fermi surface. The values of the field at which the transitions occur reflects the microscopic mechanism leading to the formation of the heavy quasi-particles.

Here we demonstrate that the magnetic field-dependent anomalies in the Seebeck coefficient provide detailed information not only on the critical points, i. e., their character and position relative to the chemical potential but also on the effective mass tensor, i. e.,the quasi-particle dispersion in the vicinity of the critical points. For lanthanide-based HFS, the theoretical analysis is based on Renormalized Band (RB) structure calculations assuming that the heavy quasi-particles result from a Kondo effect. For U-based HFS, on the other hand, we adopt the fully microscopic model which emphasizes the role of intra-atomic Hund's rule-type correlations for appearance of heavy quasi-particle masses. The calculations reproduce the observed positions of the anomalies very well.

For the magnetic properties of UTe₂ the correlated band theory implemented as a combination of the relativistic density functional theory with exact diagonalization [DFT+U(ED)] of the Anderson impurity term with Coulomb repulsion U in the 5f shell needs to be applied. This allows us to determine the orbital to spin ration as well as number of the uranium valence states in close correspondance with recent experiment (XANES, XMCD). The uranium atom 5f -shell ground state with 33% of f² and 58% of f³ configurations is determined[1]. In contrast to the above, for the bonding in UTe₂ it is satisfactory to be modelled by DFT+U methodology. We theoretically determined the lattice contribution to the specific heat of UTe₂ over the measured temperatures ranging from 30 to 400 K as well as the the orthorhombic-to-tetragonal phase transition pressure of 3.8 GPa at room temperature in very good agreement with the recent experimental studies. Last, but not least we determined the Raman spectra that were compared with recent Raman scattering experiments as well.

[1] A. B. Shick, U. D. Wdovik, I. Halevy, and D. Legut, Spin and Orbital Magnetic Moments of UTe₂ induced by the external magnetic field, Scientific Reports 14, 25337 (2024), https://doi.org/10.1038/s41598-024-75321-4.

5f states in light actinides adopt either an itinerant, i.e. bonding, nature, or they preserve their localized atomic character similar to free ions and they stand aside from bonding. The large pool of known U intermetallics comprises mainly compounds with itinerant 5f states. One of exceptions is arguably UPt₂Si₂, at which some features of 5f localization were identified [1,2]. One of its interesting features is the Charge Density Wave (CDW) with a propagation vector (0.42,0,0), developing below T = 320 K [3]. Importantly, practically identical CDW appears also in multiple rare-earth isotypes REPt₂Si₂ with localized (or empty) 4f states, all crystallizing in the tetragonal structure type CaBe₂Ge₂[4]. While the CDW phenomenon is very interesting per se (one can discuss whether it is primarily due to phonon softening of Fermi surface nesting), one can also assume it as a sensitive indicator of the 5f localization. The only U-based sibling, UIr₂Si₂, is undoubtedly an itinerant antiferromagnet and no CDW has been reported.

Here we describe results of the study of the pseudo-ternary system U(Pt_1-xIr_x)₂Si₂. The γ coefficient of 32 mJ/mol K² of UPt₂Si₂ starts to increase for x > 0.05, reaching 100 mJ/mol K² for 20% Ir, which indicates that the localization with 5f states out of the Fermi level is suppressed already for low Ir concentrations. Variations of lattice parameters a,c are non-monotonous, but the unit cell volume tends to decrease, which is compatible with the progress in 5f bonding. The Néel temperature T_N of the AF order decreases towards 6 K in UIr₂Si₂. The diffuse X-ray scattering experiment at ESRF, ID28 beamline, reveals that the CDW state, developing gradually below 400 K, is still present for x = 0.05, where γ is still rather low, 33 mJ/mol K². Further CDW development will be revealed at a forthcoming experiment.

This work was supported by the Czech Science Foundation under the grant # 25-16339S.

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