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Time-reversal symmetry breaking (TRSB) in magnetic topological insulators induces a Dirac gap in the topological surface state (TSS), leading to exotic phenomena such as the quantum anomalous Hall effect. Yet, the interplay between TRSB and topology in superconductors remains underexplored due to limited suitable materials. Here we employ zero-fieldmuon spin relaxation (μSR) as a sensitive probe of TRSB to map out the electronic phase diagrams of iron-chalcogenide superconductors FeSe1−xTex. For the Te composition x = 0.64 with the highest superconducting transition temperature Tc = 14.5K, which is known to host a TSS and Majorana zero modes within vortices, we detect spontaneous magnetic fields below Tc distinct from a magnetic order. This signifies a TRSB superconducting state in the bulk, revealing the convergence of unconventional TRSB superconductivity with topologically nontrivial electronic structures in FeSe1−xTex. Given the relatively high Tc and the tunability of the Fermi level through chemical substitution, iron-chalcogenide superconductors offer an intriguing platform for investigating the synergy between topological superconductivity and TRSB. 

The investigation of novel diluted magnetic semiconductors (DMSs) provides a promising platform for studying magnetism and transport characteristics, with significant implications for spintronics. DMSs based on BaZn2As2 are particularly noteworthy due to their high Curie temperature (TC) of 260 K, diverse magnetic states, and potential for multilayer heterojunctions. This study investigates the magnetic evolution of carrier doping and spin dynamics in the asperomagnet (Ba,Na)(Zn,Mn)2As2, utilizing a combination of magnetization measurements, ac susceptibility, and muon spin rotation (µSR). Key findings include the following: (1) lower transition temperatures and coercive forces in (Ba,Na)(Zn,Mn)2As2 compared to the ferromagnet (Ba,K)(Zn,Mn)2As2; (2) a dynamic fluctuation peak around the transition temperature observed in both the ac susceptibility and longitudinal field (LF) µSR; and (3) the coexistence of static and dynamic states at low temperatures, exhibiting spin-glass-like characteristics. This study, to the best of our knowledge, may represent the first investigation of asperomagnetic order utilizing µSR techniques. It enhances the understanding of magnetic interactions in BaZn2As2-based systems and provides valuable insights into the exploration of high TC DMSs. 

Dirac material LaCuSb2 shows anisotropic superconducting response to applied magnetic fields. 

We study the magnetic properties of the metallic kagome system (Fe1−xCox )Sn by a combination of muon spin relaxation (μSR), magnetic susceptibility, and scanning tunneling microscopy (STM) measurements in single crystal specimens with Co concentrations x = 0, 0.11, 0.8. In the undoped antiferromagnetic compound FeSn, we find possible signatures for a previously unidentified phase that sets in at T ∗ ∼ 50K, well beneath the Neel temperature TN ∼ 376K, as indicated by a peak in the relaxation rate 1/T1 observed in zero field (ZF) and longitudinal field (LF) μSR measurements, with a corresponding anomaly in the ac and dc susceptibility, and an increase in the static width 1/T2 in ZF-μSR measurements. No signatures of spatial symmetry breaking are found in STM down to 7 K. Related to the location and motion of muons in FeSn, we confirm a previous report that about 40% of the implanted muons reside at a field-cancelling high symmetry site at T < 250K, while an onset of thermal hopping changes the site occupancy at higher temperatures. In Fe0.89Co0.11Sn, where disorder eliminates the field-cancellation effect, all the implanted muons exhibit precession and/or relaxation in the ordered state. In Fe0.2Co0.8Sn, we find canonical spin glass behavior with freezing temperature Tg ∼ 3.5K; the ZF- and LF-μSR time spectra exhibit results similar to those observed in dilute alloy spin glasses CuMn and AuFe, with a critical behavior of 1/T1 at Tg and 1/T1 → 0 as T → 0. The absence of spin dynamics at low temperatures makes a clear contrast to the spin dynamics observed by μSR in many geometrically frustrated spin systems on insulating kagome, pyrochlore, and triangular lattices. The spin glass behavior of CoSn doped with dilute Fe moments is shown to originate primarily from the randomness of doped Fe moments rather than due to geometrical frustration of the underlying lattice. 

Iron-chalcogenide superconductors FeSe_1−xS_xpossess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe_1−xS_xsuperconductors for0≤x≤0.22covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperatureT_cfor all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-fieldμSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x>0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe_1−xS_x, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.