Exchange field enhanced upper critical field of the superconductivity in compressed antiferromagnetic EuTe₂

The study addresses how superconductivity interplays with magnetism, a central open problem in condensed matter physics. Conventional Bardeen–Cooper–Schrieffer (BCS) superconductors form spin-singlet Cooper pairs mediated by electron–phonon coupling and are Pauli limited. In contrast, unconventional superconductors often occur near magnetic order, with magnetism believed to contribute to pairing; some still obey Pauli-limited Hc₂ while others (e.g., UTe₂) exceed it, implying spin-triplet pairing. Magnetic fluctuations are known to couple to superconductivity in many systems. EuTe₂ is an antiferromagnetic (AFM) semiconductor hosting localized Eu²⁺ 4f moments (S = 7/2) that can interact with itinerant electrons in Te-derived bands. Prior work established EuTe₂ as an antiferromagnetic semiconductor with large negative and angular magnetoresistance at ambient pressure, with a small thermal activation gap. Pressure can tune electronic structure and magnetism and has induced superconductivity in related tellurides and Eu-based compounds, sometimes accompanied by Eu valence changes. A recent high-pressure study up to 12 GPa reported superconductivity in EuTe₂ and suggested an exotic pairing mechanism. This work investigates EuTe₂ under pressure up to 36 GPa to determine its structural transitions, magnetic state evolution, emergence of superconductivity, and the origin of unusually high upper critical fields, testing whether exchange-field effects from Eu moments can enhance Hc₂ beyond the Pauli limit.

- High-Tc cuprates and iron-based superconductors exhibit strong interplay between magnetism and superconductivity, often with spin-singlet pairing and Pauli-limited Hc₂ in some cases (refs. 2–6). - Systems with Hc₂ beyond the Pauli limit (e.g., UTe₂) suggest spin-triplet pairing with heavy-fermion behavior where f-electrons cross the Fermi level (refs. 7, 8, 33–35). - Rare-earth magnetic layers can coexist with superconductivity in some BCS materials (e.g., RNi₂B₂C) and Eu-containing iron pnictides, influencing physical properties including Hc₂ (refs. 9–11). - EuTe₂ at ambient pressure is a small-gap AFM semiconductor with large negative and colossal angular magnetoresistance; magnetic fields polarize Eu²⁺ moments and reconstruct Te 5p orbitals (refs. 12, 13). - Pressure-induced superconductivity has been observed in Te-based and related compounds (CrSiTe₃, WTe₂, HfTe₅, Bi₂Te₃) (refs. 14, 15, 30–32), and in EuIn₂As₂ and EuSn₂As₂ pressure enhances magnetic exchange and can affect Eu valence (refs. 16, 17). - Prior high-pressure EuTe₂ study up to 12 GPa reported superconductivity with large Hc₂ and proposed exotic pairing (ref. 18). - The Jaccarino–Peter mechanism predicts exchange-field compensation by localized magnetic moments can enhance effective critical fields in superconductors (ref. 19), offering a possible explanation for elevated Hc₂ without invoking triplet pairing.

- Single-crystal growth: EuTe₂ single crystals grown by Te self-flux (Eu:Te = 1:10). Heat to 850 °C (100 h), dwell 75 h, slow cool to 450 °C over 300 h; crystals separated from flux at 450 °C. Structure verified by single-crystal XRD. - Neutron diffraction: Powdered crystals measured on the Xingzhi cold-neutron triple-axis spectrometer at the China Advanced Research Reactor. Samples mounted on Al foil with hydrogen-free glue, sealed in vanadium can; temperature 3.5–300 K; incident neutron energy 16 meV with velocity selector to remove higher orders. Used to determine magnetic structure (distinguish C-type vs A-type AFM) and track AFM order. - High-pressure synchrotron XRD: Room-temperature in situ powder XRD at Beijing Synchrotron Radiation Facility, λ = 0.6199 Å. Symmetric diamond anvil cell (300 μm culets), steel gasket pre-indented; 120 μm hole; EuTe₂ powders compressed into an 80 μm × 20 μm pellet; silicone oil as pressure medium; ruby fluorescence for pressure calibration. Data processed with Dioptas (CeO₂ calibration) and refined by Rietveld method using TOPAS-Academic. Structure search using CALYPSO informed phase identification. - Electrical transport and magnetotransport under pressure: Four-probe measurements in a PPMS using a miniature Be–Cu diamond anvil cell (400 μm culets), insulating cBN–epoxy gasket with 150 μm chamber; NaCl powder as quasi-hydrostatic medium; pressure calibrated by ruby fluorescence. Temperature- and field-dependent resistance measured up to 27.7 GPa and fields up to ±14 T. Hall effect measured at 10 K to determine carrier type and density. Magnetoresistance integrated over −10 to 10 T used to assess magnetic order as a function of pressure and temperature. - Data analysis: Thermal activation gap Ea extracted by fitting ρ(T) = ρ₀ exp(Ea/kBT) at 60–300 K. Néel temperature TN and superconducting Tc determined from resistive anomalies (tangent intersection method). Upper critical fields Hc₂(T) analyzed using segmented Ginzburg–Landau fits in different magnetic states and Werthamer–Helfand–Hohenberg (WHH) slopes. - Structure prediction and electronic/magnetic modeling: CALYPSO swarm-intelligence structural searches at 5, 15, 25 GPa (1–4 f.u.). First-principles relaxations using VASP with GGA-PBE, PAW potentials, 500 eV cutoff; atomic positions fully relaxed to forces <0.01 eV Å⁻¹; Eu 4f treated with U = 4.4 eV. Exchange couplings up to six nearest neighbors extracted; single-ion anisotropy included. TN under pressure obtained via parallel tempering Monte Carlo simulations. Electronic structure used to assess Eu 4f level position and Te 5p conduction character.

- Structural transition: EuTe₂ undergoes a pressure-induced structural phase transition near 16 GPa from tetragonal I4/mcm (No. 140) to monoclinic C2/m (No. 12). Rietveld refinement at 17.9 GPa matches C2/m. The unit cell volume drops sharply from 317.157(9) ų at 15.9 GPa to 262.524(3) ų at 17.9 GPa. Eu remains eightfold coordinated with significant octagon deformation and interlayer slip. The transition may be accompanied by a Eu²⁺→Eu³⁺ valence change. - Electronic transport and gap evolution: At ambient pressure EuTe₂ is a semiconductor with a thermal activation gap Ea ≈ 16.24 meV; Ea progressively closes with pressure. Resistance decreases with pressure and shows an abrupt drop between 14.7–16.2 GPa consistent with the structural transition. Hall coefficient stays positive; hole density increases abruptly across the transition. - Magnetism under pressure: Low-pressure (LP) phase exhibits C-type AFM order. TN increases from 11.4 K (0 GPa) to 16.7 K (8.0 GPa) due to enhanced exchange couplings from lattice compression. Integrated magnetoresistance decreases with pressure/temperature and is strongly suppressed above ~16.2 GPa, indicating the high-pressure (HP) phase is nonmagnetic. Neutron diffraction confirms C-type AFM at ambient pressure; DFT+MC modeling reproduces and explains TN trends. - Emergence of superconductivity (SC): SC appears at ~4.9–5.0 GPa with Tc ≈ 3.2 K. Tc reaches a maximum of 6.1 K at 7.0 GPa and then decreases smoothly, persisting across the structural transition up to at least 27 GPa. SC exists in both LP (magnetic) and HP (nonmagnetic) phases, indicating SC is largely insensitive to magnetic order and structural change in terms of Tc. - Upper critical field Hc₂ and spin-state dependence (7.0 GPa case): Field-induced spin transitions in the LP AFM state shift to higher fields under pressure (spin flop ≈ 5.5 T, spin flip ≈ 12.5 T at 5 K). Tc(H) separates into three regimes aligned with AFM, spin-flop, and spin-flipped states. GL fits yield μ₀Hc₂(0) ≈ 10.1 T (AFM, Tc = 6.1 K), 16.2 T (spin flop, Tc = 5.2 K), and 21.6 T (spin flipped, Tc = 4.3 K). WHH estimates are 10.7 T, 15.9–15.8 T, and 20.8 T, respectively. The Pauli limit for Tc = 6.1 K is ≈11.2 T; thus, spin-flop and spin-flipped Hc₂ exceed the Pauli limit markedly. - HP phase superconductivity (18.0 GPa): Nonmagnetic HP phase shows GL behavior with Tc ≈ 5.5 K and μ₀Hc₂(0) ≈ 6.15 T, below the Pauli limit (~10.12 T), in contrast to the LP phase. - Mechanism: The enhanced Hc₂ in the LP phase is attributed to the Jaccarino–Peter exchange-field compensation from polarized Eu²⁺ moments acting on Te 5p conduction electrons; the exchange field opposes the applied field in the spin-flipped state, reducing the net Zeeman effect and enabling Hc₂ > Pauli limit. Calculations indicate Eu 4f states are localized ~1.25 eV below the Fermi level, while Te 5p states form the conduction bands, consistent with BCS-like pairing augmented by exchange-field effects.

The results directly address how localized Eu²⁺ magnetism influences superconductivity in EuTe₂ under pressure. In the LP, magnetically ordered phase, the field-tuned spin texture (AFM → spin flop → spin flip) correlates with progressive enhancement of Hc₂, culminating in Hc₂ well above the Pauli limit in the spin-flipped state. This behavior is consistent with the Jaccarino–Peter mechanism, where the exchange field from fully polarized Eu²⁺ moments compensates the external field at the Te sites, reducing the effective Zeeman pair-breaking on spin-singlet Cooper pairs. Consequently, large Hc₂ does not require spin-triplet pairing or heavy-fermion behavior, aligning with the observation that Eu 4f levels lie far below EF. In the HP phase, the absence of magnetic order removes the exchange-field compensation; superconductivity persists with similar Tc but Hc₂ falls below the Pauli limit and follows single-regime GL behavior. The persistence of Tc across the structural and magnetic transitions suggests that the pairing is predominantly governed by Te 5p-derived itinerant electrons and conventional interactions, while Eu magnetism primarily modulates Hc₂ via exchange fields rather than providing the pairing glue. The pressure-enhanced TN in the LP phase is captured by strengthened nearest-neighbor exchange couplings from lattice compression, whereas the structural transition likely alters Eu valence and quenches magnetism, consistent with transport and MR data.

EuTe₂ exhibits pressure-induced superconductivity above ~5 GPa with Tc peaking at 6.1 K near 7 GPa and persisting across a structural transition from I4/mcm to C2/m at ~16 GPa. The LP phase hosts C-type AFM order with increasing TN under pressure; in this phase, field-driven spin transitions strongly enhance Hc₂, reaching up to ~21.6 T in the spin-flipped state—well above the Pauli limit—due to exchange-field compensation from Eu²⁺ local moments (Jaccarino–Peter mechanism). In the nonmagnetic HP phase, Hc₂ follows GL behavior and remains below the Pauli limit. Electronic structure indicates Eu 4f states are localized well below EF, and Te 5p states form the conduction bands, supporting a BCS-like pairing framework where Eu magnetism modulates critical fields. Future work could include direct spectroscopic determination of Eu valence under pressure, anisotropic single-crystal Hc₂ studies to quantify exchange-field directions, high-field thermodynamic probes to corroborate the exchange-compensation scenario, and microscopic measurements (e.g., μSR, NMR, inelastic neutron scattering under pressure) to track magnetic fluctuations and their coupling to superconductivity.

- The Eu valence change across the structural transition is inferred from structural collapse and loss of magnetism but not directly measured (e.g., by XAS/Mössbauer). - Upper critical fields are extracted from resistive criteria, which can overestimate Hc₂ relative to thermodynamic determinations; anisotropy of Hc₂ in single crystals under pressure is not resolved. - Magnetism in the HP phase is concluded to be absent based on transport/MR; direct magnetic probes under pressure (e.g., neutron, μSR) are lacking. - DFT calculations employ a chosen U = 4.4 eV for Eu 4f and use experimental lattice parameters; uncertainties in U and pressure-induced structural details may affect exchange coupling estimates. - Transport measurements were performed up to 27.7 GPa, while structural data extend to 36 GPa; full correlation beyond ~28 GPa is limited.