🔬 materials science

Field-induced incipient spin-density phase stabilized inside the nematic phase of FeSe $_{1-x}$ S $_x$

This study demonstrates that applying high magnetic fields to FeSe $_{1-x}$ S $_x$ stabilizes an incipient spin-density wave phase within the nematic state, evidenced by resistivity upturns and quantum oscillations, revealing that weakening nematicity promotes the emergence of SDW order and the dominant superconducting pairing mechanism in iron chalcogenides.

Original authors: I. Paulescu, R. M. Abedin, J. S. Pearce, W. H. Fong, Z. Zajicek, A. Morfoot, W. Knafo, O. Squire, D. Graf, A. A. Haghighirad, A. I. Coldea

Published 2026-09-24

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Original authors: I. Paulescu, R. M. Abedin, J. S. Pearce, W. H. Fong, Z. Zajicek, A. Morfoot, W. Knafo, O. Squire, D. Graf, 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 tension between two different ways of organizing their atoms and electrons. One way is a magnetic order, where tiny atomic magnets line up in a rigid, repeating pattern. The other is a superconducting state, where electricity flows with zero resistance, a phenomenon that usually requires these magnetic tendencies to be quieted down. For decades, scientists have studied iron-based superconductors to understand how these two states compete and sometimes coexist. A key concept in this field is "nematicity," a state where the electrons behave differently depending on the direction they move, breaking the symmetry of the material's structure without necessarily forming a magnetic pattern. In many of these materials, applying pressure or changing the chemical makeup can push the system from a nematic state into a magnetic one, or vice versa. Understanding exactly how and when these transitions happen is crucial because the fluctuations between these states are believed to be the very glue that holds the superconducting pairs together, allowing electricity to flow without loss.

A team of researchers has now uncovered a delicate, hidden phase within one of these iron-based materials, a compound made of iron, selenium, and sulfur. By subjecting crystals of this material to incredibly strong magnetic fields, they were able to suppress the superconductivity that usually hides the underlying electronic behavior. What they found was surprising: even inside the nematic state, where no magnetic order was expected, a faint, emerging magnetic pattern appeared. This pattern, known as a spin-density wave, is a state where the electron spins arrange themselves in a wave-like structure. The researchers discovered that this magnetic order is fragile; it only becomes visible when the superconducting state is knocked out by a magnetic field of up to 68 tesla, a strength roughly a million times that of a typical refrigerator magnet.

The material they studied, FeSe1−xSx, is a solid solution where some selenium atoms are replaced by sulfur. The amount of sulfur acts as a tuning knob, changing the material's properties. The team focused on samples with different sulfur levels, specifically those near the boundary where the nematic phase ends. In the absence of a magnetic field, these samples are superconductors at low temperatures. However, as the researchers increased the magnetic field, the superconductivity vanished, and something else took its place. The electrical resistance of the material, which usually drops as it gets colder, suddenly began to rise sharply at a specific temperature. This upturn in resistance is a classic signature of a material transitioning into an insulating or magnetic state, suggesting that the electrons were organizing themselves into a new, ordered pattern.

To confirm that this was indeed a magnetic order and not just a random glitch, the team used several different measurement techniques. They monitored the frequency of a tiny electronic oscillator, which is sensitive to changes in how electricity flows through the material, and they measured the torque, or twisting force, exerted on the crystal by the magnetic field. All these different methods pointed to the same conclusion: at a specific temperature, the material underwent a transition. The electrons were rearranging themselves, creating a new structure that altered how the material conducted electricity. Furthermore, the researchers observed quantum oscillations, which are ripples in the electrical resistance that occur when electrons move in circular paths within a magnetic field. The frequency of these ripples revealed that the electrons were confined to very small pockets, a sign that the original, larger electron structure had been reconstructed by the new magnetic order.

To ensure this wasn't just a quirk of the specific sulfur-doped samples, the team compared their findings with a different version of the same material. They took a sample with very little sulfur and squeezed it with high pressure, which mimics the effect of adding sulfur but does so by physically compressing the crystal lattice. Under this pressure, the same magnetic order appeared, but this time it was stable and visible even without a magnetic field. This direct comparison confirmed that the magnetic order observed in the sulfur-doped samples was a real, intrinsic property of the material, one that was simply being masked by superconductivity under normal conditions. The researchers found that the magnetic order in the sulfur-doped samples was much weaker and more sensitive to the magnetic field than in the pressurized sample, describing it as an "incipient" or emerging phase.

The implications of this discovery are significant for understanding how these materials work. The study shows that the magnetic order and the nematic state can coexist, with the magnetic order hiding just beneath the surface of the superconducting state. By weakening the nematic state through chemical substitution or pressure, the magnetic order becomes more stable. This suggests that the competition between these different electronic phases is a delicate balance. The fact that the magnetic order can be revealed by a magnetic field implies that it is always present but suppressed by the superconductivity. This finding helps scientists map out the complex phase diagram of iron-based superconductors, showing that the path to understanding high-temperature superconductivity involves navigating a landscape where magnetism and superconductivity are constantly vying for dominance. The work provides a clearer picture of how these materials behave under extreme conditions, offering new clues about the fundamental mechanisms that allow electricity to flow without resistance.

Technical Summary: Field-Induced Incipient Spin-Density Phase in FeSe $_{1-x}$ S $_x$

Problem Statement
In iron-based superconductors, spin-density wave (SDW) order and superconductivity frequently compete and coexist. While iron pnictides typically exhibit stripe-type SDW order connected to Fermi surface nesting, iron chalcogenides like FeSe present a more frustrated magnetic landscape. At ambient pressure, FeSe displays a nematic electronic state without long-range static magnetic order, yet several magnetic configurations remain close in energy. Previous studies have shown that applying hydrostatic pressure to FeSe can suppress the nematic phase and stabilize an SDW phase, which subsequently allows superconductivity to re-emerge at higher temperatures. However, the interplay between nematicity, magnetic order, and superconductivity in the FeSe $_{1-x}$ S $_x$ system, particularly near the nematic endpoint ( $x \approx 0.175$ ), remains complex. Specifically, it is unclear whether an SDW phase can be stabilized within the nematic phase of FeSe $_{1-x}$ S $_x$ via chemical substitution alone, or if such an order is only accessible under high pressure. Furthermore, the nature of this magnetic order—whether it is a robust ground state or a fragile, "incipient" phase sensitive to external perturbations—requires clarification.

Methodology
The study employs a multi-faceted experimental approach to probe the electronic ground state of FeSe $_{1-x}$ S $_x$ single crystals under varying conditions:

Sample Tuning: The researchers utilized chemical substitution (varying sulfur content $x$ from $\sim0.13$ to $\sim0.17$ ) and applied hydrostatic pressure (up to $\sim12$ kbar) to tune the nematic transition temperature ( $T_s$ ) and suppress the nematic phase. A direct comparison was made between chemically substituted samples at ambient pressure and a pressure-tuned analogue (FeSe $_{0.96}$ S $_{0.04}$ ).
High-Field Magnetotransport: Longitudinal resistivity ( $\rho_{xx}$ ) was measured in magnetic fields up to 68 T (pulsed field) and 41 T (resistive magnet) to suppress superconductivity and reveal underlying electronic orders.
Tunnel Diode Oscillator (TDO): Contactless TDO measurements were performed to monitor changes in in-plane resistivity and magnetic susceptibility, providing a sensitive probe for phase transitions.
Magnetic Torque: Torque anisotropy measurements were conducted to detect changes in magnetic susceptibility ( $\chi_a - \chi_c$ ) and identify magnetic ordering.
Quantum Oscillations: High-field measurements were analyzed to extract Fermi surface topology, effective masses, and oscillation frequencies, serving as a direct probe of Fermi surface reconstruction.

Key Results

Field-Induced Resistivity Upturns: In the nematic B phase of FeSe $_{1-x}$ S $_x$ (specifically samples with $x \sim 0.13$ and $x \sim 0.17$ ), superconductivity is suppressed at fields above 5 T. Upon further increasing the field, a pronounced upturn in resistivity emerges at a characteristic temperature $T_{MI}$ . This upturn signifies a crossover from metallic-like to insulating-like behavior, shifting to lower temperatures as the magnetic field increases.
Correlated Anomalies: The resistivity upturns are accompanied by distinct anomalies in the TDO resonant frequency and magnetic torque anisotropy. These features appear at similar temperatures ( $T_p$ and $T_\tau$ ), indicating a field-induced intrinsic electronic order that affects both transport and magnetic properties.
Quantum Oscillations and Fermi Surface Reconstruction: Dominant low-frequency quantum oscillations were observed in the high-field normal state. For the chemically substituted samples, a frequency of $F \sim 83$ T was detected with a light effective mass ( $m^* \approx 1.53 m_e$ ). This corresponds to a small, reconstructed Fermi surface pocket, consistent with the formation of an SDW order that gaps portions of the Fermi surface.
Comparison with Pressure-Tuned Analogue: Direct comparison with FeSe $_{0.96}$ S $_{0.04}$ under hydrostatic pressure ( $p \sim 10.5$ kbar) revealed similar signatures: a resistivity upturn defining an SDW phase, TDO anomalies, and low-frequency quantum oscillations ( $F \sim 70$ T). However, the pressure-tuned sample exhibited a more robust SDW phase that is stable at zero magnetic field, whereas the chemically substituted samples required high magnetic fields to reveal the order.
Energy Scales: The activation energy ( $\Delta_m$ ) derived from the resistivity upturn in the chemically substituted samples is approximately an order of magnitude smaller ( $\sim 0.2 - 0.5$ meV) than in the pressure-tuned sample. This suggests the SDW order in the chemically substituted samples is "incipient" and highly sensitive to magnetic fields.

Significance and Claims
The paper claims to provide evidence for a field-induced incipient SDW phase stabilized within the nematic state of FeSe $_{1-x}$ S $_x$ . The authors demonstrate that by weakening nematicity through either chemical substitution or applied pressure, the system becomes susceptible to SDW ordering.

Mechanism: The findings suggest that the SDW order is not a competing instability that completely destroys superconductivity but rather a fragile state that can coexist with or emerge from the nematic phase when superconductivity is suppressed by magnetic fields.
Electronic Reconstruction: The observation of small Fermi surface pockets via quantum oscillations confirms that the field-induced order reconstructs the electronic structure, consistent with SDW formation driven by Fermi surface nesting.
Implications for Pairing: The authors posit that the stabilization of SDW orders (and the associated spin fluctuations) by weakening nematicity may promote the dominant superconducting pairing mechanism in iron chalcogenides. The coexistence of incipient SDW and superconductivity could influence the nature of the superconducting gap and potentially support scenarios involving Bogoliubov Fermi surfaces or toroidal magnetic order.
Generalizability: The study highlights that the boundaries of the phase diagram in FeSe $_{1-x}$ S $_x$ are tunable, and that the "incipient" nature of the SDW order makes it a sensitive probe for understanding the competition between nematicity, magnetism, and superconductivity in unconventional superconductors.

Technical Summary: Field-Induced Incipient Spin-Density Phase in FeSe1−x_{1-x}1−x​Sx_xx​

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Technical Summary: Field-Induced Incipient Spin-Density Phase in FeSe $_{1-x}$ S $_x$