Time Reversal Symmetry Breaking and {\it Fragile Magnetic Superconductors}

TL;DR

This paper reviews evidence for time-reversal symmetry breaking in low-Tc superconductors, discusses the fragile nature of these magnetic states, and examines the role of muon spin relaxation measurements, highlighting potential measurement artifacts and alternative interpretations.

Contribution

It introduces the concept of fragile magnetic superconductors with TRSB, critiques the muon-based detection method, and offers alternative explanations for observed phenomena in LaNiGa$_2$.

Findings

TRSB states are detected in low-Tc superconductors via $$SR.

Detected magnetic fields are extremely small, around 10$^{-3}$ $$/atom.

Measurement process may influence the system, affecting the interpretation of TRSB evidence.

Abstract

Roughly twenty reports (as of 2025) of time-reversal-symmetry breaking (TRSB) states in low critical temperature (T$_c$) superconducting (SC), otherwise conventional Fermi liquid, metals have emerged primarily from muon spin relaxation ($\mu$SR) data. The detected fields, inferred from the current interpretation of depolarization data, are similar in magnitude and not far above the lower limit of detection, corresponding to magnetizations of no more than 10$^{-3}$ $\mu_B$/atom. These materials comprise a new class of {\it fragile magnetic superconductors} modeled as triplet pairing. The measured SC state properties, excepting only the fields detected below T$_c$, are representative of low T$_c$ singlet BCS SCs, not showing unusual coherence lengths or critical fields. While it is recognized that the muon does affect the sample by displacing nearby atoms and impacting magnetic interaction parameters, the measurement process, changing the system from sample $\rightarrow$ sample+$\mu^+$ thereby breaking TRS, may deserve further scrutiny. This overview provides a survey of the environment of the muon, from the normal state to the superfluid state, where the induced supercurrent and Yu-Shiba-Rusinov gap states provide coupling of the muon moment to the superfluid. The unusual topological superconductor LaNiGa$_2$, currently modeled as non-unitary triplet, is used as a case study. Supposing that the prevailing $\mu$SR inference of a small spontaneous field within the bulk of theSC obtains, the current picture of (possibly non-unitary) triplet pairing is discussed and an attractive alternative for LaNiGa$_2$ is noted.