Reports Reveal Fragile Magnetism Breaks Symmetry in Roughly Twenty Superconductors

Researchers are increasingly observing instances of time-reversal symmetry breaking (TRSB) within low critical temperature superconductors, challenging conventional understandings of these materials. Warren E. Pickett from the Department of Physics and Astronomy, University of California Davis, and colleagues present a comprehensive survey of this phenomenon, focusing on the potential influence of measurement techniques on observed results. Their work examines roughly twenty recent reports of TRSB states detected via muon spin relaxation, and proposes that the interaction between the muon probe and the sample itself may contribute to the detected magnetic fields. This research is significant because it questions the interpretation of current data, potentially offering an alternative explanation for the emergence of fragile magnetic superconductivity and prompting a re-evaluation of triplet pairing models, using LaNiGa as a key case study.

Researchers are re-examining the established understanding of superconductivity in materials exhibiting fragile magnetism. Recent data from muon spin relaxation (μSR) experiments suggest that approximately twenty low critical temperature superconducting metals display evidence of time-reversal symmetry breaking (TRSB), a phenomenon where fundamental physical symmetries appear to be violated within the superconducting state.

These detected magnetic fields, though subtle, challenge conventional models of superconductivity and point towards a more complex interplay between magnetism and the superconducting condensate. This study delves into the environment surrounding muons, subatomic particles used in μSR, as they interact with both the normal and superconducting states of these materials.

The induced supercurrents and the formation of Yu-Shiba-Rusinov gap states, localized energy levels arising from impurities in a superconductor, provide a crucial coupling mechanism between the muon’s moment and the superfluid electrons. LaNiGa₂, an unusual topological superconductor, serves as a detailed case study to explore these interactions and the implications for unconventional pairing mechanisms.

However, this research proposes an alternative perspective, questioning whether the observed TRSB genuinely originates within the superconducting material itself or is an artifact of the measurement process. Introducing muons into the sample disrupts the atomic structure and potentially induces magnetic interactions, thereby breaking time-reversal symmetry.

By carefully surveying the muon’s environment and the intricacies of the μSR technique, this work aims to refine the interpretation of experimental data and provide a more accurate understanding of the order parameters governing these fragile magnetic superconductors. Understanding these subtle effects could unlock new avenues for designing and controlling superconducting materials with tailored properties and functionalities.

Muon spin relaxation (μSR) techniques underpin this work, providing a sensitive probe of internal magnetic fields within materials. This method exploits the sensitivity of muon spin to magnetic fields, functioning as a local probe of magnetic induction at the nuclear timescale. Positively charged muons, created at particle accelerators, are implanted into the sample where they act as sensitive magnetic dipoles, and the evolution of the muon spin polarization is monitored using detectors surrounding the sample, revealing information about the local magnetic environment.

To accurately model muon behaviour within the lattice, density functional theory (DFT) calculations, specifically a ‘DFT+μ’ method, are employed to determine the muon’s stopping position(s) within the crystal structure. This approach accounts for the muon’s interaction with the host lattice, providing a more realistic representation of its environment.

Researchers utilise the ‘MuFinder’ interface to facilitate these calculations, streamlining the process of locating muon sites. Furthermore, the anharmonicity and zero-point positional uncertainty of muons are calculated, as demonstrated by work on solid N₂, to refine the precision of hyperfine constant determinations. Application of quantum muon position uncertainty methods has extended to elemental and binary metals, yielding improved values for hyperfine constants.

Measurements from μSR studies reveal subtle magnetic signatures within low critical temperature superconductors, specifically fields detected at magnitudes no more than 10⁻³/atom. These detected fields, interpreted as evidence of time-reversal-symmetry breaking, are consistently found just above the lower limit of detection for the instrumentation. The research focuses on materials exhibiting ‘fragile magnetism’ and modelled as triplet pairing, yet their superconducting properties, excluding the detected fields below the critical temperature, closely resemble conventional low-temperature BCS superconductors.

Analysis of the immediate environment surrounding the muon indicates an induced electron density, approximated as a 1s orbital centred on the muon’s location, arising from the attraction of electrons from the valence band. Hybridization of this muon 1s orbital with itinerant electronic states in densely packed intermetallic superconductors prevents spin polarization due to electron gas exchange effects, a phenomenon potentially complicated by the muon’s light mass and resulting quantum uncertainty in its spatial position.

The induced magnetization at a given position is calculated using linear response, expressed as M ind(r) = χsp[n(r)] Bμ(r), where χsp represents the Pauli spin susceptibility and Bμ(r) is the muon’s magnetic field. Calculations demonstrate that in a homogeneous electron gas, the induced field at the muon, Bind, aligns with the muon moment, rendering it undetectable by depolarization studies due to the absence of torque.

Consideration of orbital polarization reveals a Landau diamagnetic susceptibility, χorb = −(1/3)χsp, contributing to a net paramagnetic susceptibility, χp = χsp + χorb, typically ranging from 10⁻³ to 10⁻⁴ in cgs-gaussian units for normal density Fermi liquid metals. This small polarization may be relevant given the unusually small spontaneous fields reported in these materials.

The total magnetic flux density is then described by Btot(r) = 1 + 4πχp(r) Bμ(r), a result consistent with textbook linear response theory, except within a small volume immediately surrounding the muon. Scientists are increasingly scrutinising the subtle magnetic signatures within unconventional superconductors, and a growing body of evidence suggests that time-reversal symmetry may be broken in some of these materials.

The challenge lies in disentangling genuine intrinsic magnetism from artefacts introduced by the tools used to detect it. Muon spin relaxation, a sensitive technique for probing magnetic fields, is at the heart of these investigations, but the muon itself is not a passive observer. The possibility that the measurement process itself induces the observed magnetic fields, rather than revealing a pre-existing state, is a crucial point of debate.

If confirmed, this would necessitate a re-evaluation of numerous recent findings and a more nuanced understanding of the interplay between the probe and the probed. Alternative models, and a deeper consideration of the experimental setup, are essential. Future work must prioritise refining the theoretical framework for muon interactions within superconductors, and developing independent methods to verify the existence of intrinsic magnetism.