🔬 materials science

Drastic field-induced resistivity upturns as signatures of unconventional magnetism in superconducting iron chalcogenides

This study reveals that high magnetic fields induce significant resistivity upturns in FeSe $_{0.96}$ S $_{0.04}$ under pressure, serving as signatures of field-stabilized unconventional magnetic orders that compete with or coexist alongside superconductivity depending on the pressure regime.

Original authors: Z. Zajicek, I. Paulescu, P. Reiss, R. M. Abedin, K. Sun, S. J. Singh, A. A. Haghighirad, A. I. Coldea

Published 2026-09-09

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Original authors: Z. Zajicek, I. Paulescu, P. Reiss, R. M. Abedin, K. Sun, S. J. Singh, A. A. Haghighirad, A. I. Coldea

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of materials science, some substances hold a secret that defies simple explanation: they can conduct electricity with zero resistance, a state known as superconductivity, but only when cooled to extremely low temperatures. Among the most intriguing of these materials are iron-based compounds, which behave like a crowded dance floor where electrons must navigate a complex landscape of magnetic forces and structural shifts. A key feature of these materials is a phenomenon called nematicity, where the electrons spontaneously break the symmetry of the crystal, choosing a preferred direction much like a crowd of people turning to face the same way in a room that was previously uniform. Often, this electronic preference is tightly woven together with magnetic order, creating a tangled relationship where the material's ability to superconduct competes with its tendency to organize magnetically. Understanding how these forces interact is crucial because it may reveal the rules that govern how superconductivity works, potentially leading to materials that can carry electricity without loss at more practical temperatures.

Researchers at the University of Oxford and the Karlsruhe Institute of Technology have taken a closer look at a specific version of an iron-based material called iron selenide, where a small amount of the selenium atoms has been swapped with sulfur atoms. By squeezing this material with immense pressure and subjecting it to powerful magnetic fields, they uncovered a hidden layer of behavior that changes depending on how hard the material is pushed. The team, led by Z. Zajicek and colleagues, studied crystals of this iron-sulfur-selenium mix under pressures reaching up to 20,000 times the atmospheric pressure at sea level. They measured how easily electricity flowed through the material as they cooled it down, first in a quiet environment with no magnetic field, and then again while applying magnetic fields as strong as 15 Tesla, which is roughly 300,000 times stronger than the Earth's magnetic field.

At moderate levels of pressure, while the material was still in its nematic state, the researchers observed a surprising behavior. As the temperature dropped, the electrical resistance did not simply decrease smoothly; instead, it began to rise sharply, a sign that the electrons were encountering a new kind of obstacle. This resistance spike grew even larger when a magnetic field was applied, suggesting that the field was stabilizing a specific type of magnetic order, known as a spin-density wave, where the spins of the electrons align in a repeating pattern. This magnetic state appears to compete directly with the material's ability to superconduct, making it harder for the electricity to flow without resistance. The study suggests that this magnetic order is a distinct phase that emerges inside the nematic region, acting as a rival to the superconducting state.

When the researchers increased the pressure even further, pushing the material beyond the nematic phase and into a different structural state, the behavior changed again. In this high-pressure zone, the sharp rise in resistance disappeared when no magnetic field was present, and the material returned to a more standard, smooth flow of electricity. However, the moment a strong magnetic field was introduced, the resistance shot up dramatically once more. This indicated that while the magnetic order was not naturally present in this high-pressure state, the external magnetic field could force it to appear. The researchers found that this field-induced state was more fragile and sensitive than the one seen at lower pressures, yet it still coexisted with superconductivity, suggesting a complex balance where both phenomena could exist side by side.

The team mapped out these changes to create a detailed picture of how the material's phases evolve. They identified two distinct regions where superconductivity thrives, separated by a zone where magnetic order is strongest. In the first region, at intermediate pressures, the superconductivity weakens as the magnetic order strengthens, confirming a direct competition between the two. In the second region, at the highest pressures, the superconductivity remains robust even as the magnetic order is induced by the field, hinting that the mechanism holding the superconducting electrons together might be different here. The study highlights that the way electrons scatter and move through the material is deeply tied to these magnetic fluctuations, and that high magnetic fields are essential tools for revealing these hidden electronic phases.

Ultimately, this work provides a clearer view of the delicate tug-of-war between magnetism and superconductivity in iron-based materials. By using pressure to tune the material and magnetic fields to probe its inner workings, the researchers showed that the nature of the magnetic order changes significantly as the material is squeezed. The findings suggest that the magnetic interactions driving superconductivity are not static but evolve with the material's structure, offering new clues about how these exotic states of matter are stabilized. The research underscores the importance of looking beyond zero-field conditions, as the application of a magnetic field can unlock a different electronic reality, revealing a complex interplay that would otherwise remain hidden.

Technical Summary: Drastic Field-Induced Resistivity Upturns in FeSe $_{0.96}$ S $_{0.04}$

Problem Statement
The electronic phase diagrams of unconventional high- $T_c$ superconductors, particularly iron chalcogenides like FeSe, are characterized by complex interplays between nematic order, magnetism, and superconductivity. In FeSe, these phases are strongly intertwined under applied pressure, making it difficult to isolate their individual contributions to the electronic behavior. While isoelectronic substitution (e.g., substituting Selenium with Sulfur) offers a pathway to decouple these phases, the specific evolution of electronic scattering and the nature of competing orders under the combined influence of pressure and high magnetic fields remain to be fully elucidated. Specifically, the mechanisms behind resistivity upturns—often signatures of competing orders like spin-density waves (SDW)—require detailed investigation to distinguish between intrinsic magnetic instabilities and disorder-induced effects.

Methodology
The study focuses on single crystals of FeSe $_{0.96}$ S $_{0.04}$ , prepared via chemical vapor transport. The authors employed longitudinal magnetoresistance measurements on two high-quality samples (S1 and S2) under hydrostatic pressure (up to ~20 kbar) using a Daphne 7373 pressure medium. Experiments were conducted in a 16 T Physical Property Measurement System (PPMS) at temperatures down to 2 K. Key experimental parameters included:

Pressure Control: Pressure was tuned in situ, calibrated using the superconducting transition of tin.
Magnetic Field: Longitudinal resistivity ( $\rho_{xx}$ ) was measured in magnetic fields up to 15 T to suppress superconductivity and reveal underlying electronic states.
Analysis: The study analyzed the temperature dependence of resistivity, the first derivatives of resistivity to identify transition points ( $T_s$ , $T_m$ , $T_{MI}$ ), and the evolution of the superconducting transition width ( $\Delta T_c$ ). Activation energies ( $\Delta_m$ ) were extracted from the slope of $\ln(\rho)$ versus $1/T$ in the low-temperature, high-field regime.

Key Results
The investigation reveals a complex evolution of electronic phases in FeSe $_{0.96}$ S $_{0.04}$ as a function of pressure and magnetic field, characterized by two distinct pressure regimes separated by critical pressures $p_1$ (~~7.5 kbar) and $p_2$ (~~12.5 kbar):

Intermediate Pressure Regime ( $p_1 < p < p_2$ ):
- Inside the nematic phase, zero-field resistivity exhibits a sharp upturn at a temperature $T_{MI}$ , accompanied by a local maximum at $T_p$ .
- Application of a magnetic field significantly enhances this upturn, suggesting the stabilization of a Spin-Density Wave (SDW) phase that competes with superconductivity.
- The superconducting transition broadens significantly in this regime, indicating strong competition between the SDW order and superconductivity.
- The magnetic transition temperature ( $T_m$ ) and the effective activation energy ( $\Delta_m$ ) show a field dependence scaling as $H^{0.5}$ .
High-Pressure Regime ( $p > p_2$ ):
- Beyond the nematic phase boundary, the zero-field resistivity no longer displays clear anomalies; the upturn disappears, and the resistivity becomes linear in temperature.
- However, the application of an external magnetic field induces significant resistivity upturns across the entire pressure range. This indicates the formation of a field-induced order (labeled M2) distinct from the zero-field state.
- In this regime, the high-pressure superconductivity (SC2) remains robust, whereas the magnetic phase is more fragile, with the magnetic transition temperature ( $T_m$ ) decreasing by approximately 10 K compared to lower pressures.
- The magnetic transition temperature ( $T_m$ ) and activation energy ( $\Delta_m$ ) in this regime are highly sensitive to magnetic fields, varying faster toward saturation compared to the intermediate pressure regime.
Phase Diagram Structure:
- The pressure-temperature phase diagram reveals a "two-dome" structure for superconductivity (SC1 and SC2).
- The first superconducting dome (SC1) coincides with the nematic phase and shows a minimum in $T_c$ where the magnetic phase (M1) is maximal, implying competition.
- The second superconducting dome (SC2) emerges at high pressures, coexisting with a fragile magnetic phase (M2).
- Comparisons with Cu-doped FeSe suggest that impurity scattering in the Fe plane can obscure zero-field resistivity upturns, whereas S-substitution allows for their observation.

Significance and Claims
The authors claim that this study highlights the essential role of high magnetic fields in stabilizing and revealing distinct electronic phases that are otherwise hidden or suppressed in zero field. The primary findings include:

Distinction of Magnetic Orders: The work differentiates between a robust SDW order (M1) coupled with orthorhombic distortion inside the nematic phase and a more fragile, field-induced magnetic order (M2) outside the nematic phase.
Mechanism of Resistivity Upturns: The drastic resistivity upturns are attributed to Fermi surface reconstruction and the opening of an SDW energy gap, leading to activated transport behavior. The field-induced nature of the upturns at high pressures suggests that magnetic fields can stabilize magnetic order even when it is absent in zero field.
Pairing Symmetry: The robustness of the high-pressure superconducting phase (SC2) against different chemical substitutions (S vs. Cu) supports the possibility of a sign-preserving $s_{++}$ pairing symmetry, or a complex phase where superconductivity coexists with fragile magnetism.
Role of Fluctuations: The differentiation in magnetic behavior across pressure regimes is linked to variations in the size and length scale of spin fluctuations, consistent with NMR studies showing longer antiferromagnetic correlation lengths inside the nematic phase.

The paper concludes that the interplay between magnetism and superconductivity in FeSe $_{1-x}$ S $_x$ is tuned by applied pressure, with magnetic fields serving as a critical tool to probe the underlying electronic instabilities and the nature of the competing orders.

Technical Summary: Drastic Field-Induced Resistivity Upturns in FeSe0.96_{0.96}0.96​S0.04_{0.04}0.04​

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Technical Summary: Drastic Field-Induced Resistivity Upturns in FeSe $_{0.96}$ S $_{0.04}$