Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess 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 FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field µSR 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 FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Producing Conventional and Transient Amino(mercapto)methyl Radicals by Addition of Muonium to a Crystalline Thioformamide (Mes*NHCH=S).

Muonium (Mu=µ+e-) is composed of a muon of light isotope of proton (µ+) and electron (e-) and can be used as a light surrogate for a hydrogen atom. In this paper, we investigated addition of muonium to a newly synthesized Mes*-substituted thioformamide (Mes*NHCH=S, Mes*=2,4,6-tBu3C6H2). Transverse-field muon spin rotation (TF-µSR) of a solution sample of the thioformamide confirmed addition of muonium to the sulfur atom leading to the corresponding C-centered radical [Mes*NHC(H)⋅-SMu]. Density functional theory (DFT) calculations assigned a conventional amino(mercapto)methyl radical, in which both nitrogen and carbon were slightly pyramidalized, and the calculated muon hyperfine coupling constant (hfcc) including the muon isotope effect was compatible with the experimentally determined parameter. However, the muon level-crossing resonance (µLCR) spectrum of an anisotropic crystalline sample indicated two paramagnetic species, and the major product showed the considerably larger muon hfcc compared with the conventional structure of the amino(mercapto)methyl radical. The unusual transient muoniated thioformamide with the larger muon hfcc that showed rapid relaxation could be only explained by a transient structure including planarization of the nitrogen and carbon atoms in Mes*NHC(H)⋅-SMu.

Difluoromethylborates and Muonium for the Study of Isonitrile Insertion Affording Phenanthridines via Imidoyl Radicals.

The 6-(difluoromethyl)phenanthridine unit is a highly attractive fluoroalkyl-substituted planar nitrogen heterocycle in pharmaceutical and agrochemical research. In this paper, we report that difluoromethylborates can be used as a source of difluoromethyl radicals for isonitrile insertion, leading to 6-(difluoromethyl)phenanthridines. Tuning the aryl substituents in the difluoromethylborates and oxidizing reagents enabled the synthesis of 6-(difluoromethyl)phenanthridines through the generation of difluoromethyl radical and spontaneous intramolecular cyclization of the CF2H-imidoyl radical intermediates. The presence of difluoromethyl radicals was experimentally confirmed, and the reaction mechanisms including imidoyl radical and prompt cyclization reactions could be supported theoretically. Furthermore, we obtained valuable information about the imidoyl radical intermediate by performing transverse-field muon spin rotation (TF-µSR) measurements of 2-isocyano-4'-methoxy-1,1'-biphenyl and using density functional theory (DFT) calculations to interpret the spectra. Muonium, a simple free radical, preferentially adds to the carbon atom of the isonitrile unit, yielding the corresponding imidoyl radical. The temperature dependence of the muon hyperfine coupling constant and the spin relaxation of the muoniated radical signal are compatible with the intramolecular cyclization of biaryl-substituted imidoyl radicals on the µs time scale.

Muonium Addition to a peri-Trifluoromethylated 9-Phosphaanthracene Producing a High-Energy Paramagnetic π-Conjugated Fused Heterocycle.

In this communication, we report muon spin rotation/resonance (µSR) studies for understanding radical reactivity of 10-mesityl-1,8-bis(trifluoromethyl)-9-phosphaanthracene. Transverse-field muon spin rotation (TF-µSR) and muon avoided level-crossing resonance (µLCR) measurements successfully visualized a paramagnetic species produced by regioselective addition of muonium (Mu) to the skeletal phosphorus atom. Density functional theory (DFT) calculations for the P-muoniation product suggested two possible isomers. Whereas the most stable isomer including the envelope-type phosphorus heterocycle shows considerably different hyperfine coupling constants (hfcs) from those of the TF-µSR and µLCR, the metastable structure accompanying the almost planar tricyclic π-conjugated skeleton could simulate the experimentally determined hfcs. The metastable planar π-conjugated paramagnetic tricyclic-fused skeleton is promoted by the larger zero-point energy due to the light muon (µ+ ), one ninth of the proton mass.

Observation of a Metastable P-Heterocyclic Radical by Muonium Addition to a 1,3-Diphosphacyclobutane-2,4-diyl.

A 1,3-diphosphacyclobutane-2,4-diyl contains a unique unsaturated cyclic unit, and the presence of radical-type centers have been expected as a source of functionality. This study demonstrates that the P-heterocyclic singlet biradical captures muonium (Mu=[µ+ e- ]), the light isotope of a hydrogen radical, to generate an observable P-heterocyclic paramagnetic species. Investigation of a powder sample of 2,4-bis(2,4,6-tri-t-butylphenyl)-1-t-butyl-3-benzyl-1,3-diphosphacyclobutane-2,4-diyl using muon (avoided) level-crossing resonance (µLCR) spectroscopy revealed that muonium adds to the cyclic P2 C2 unit. The muon hyperfine coupling constant (Aµ ) indicated that the phosphorus atom bearing the t-butyl group trapped muonium to provide a metastable P-heterocyclic radical involving the ylidic MuP(<)=C moiety. The observed regioselective muonium addition correlates the canonical formula of 1,3-diphosphacyclobutane-2,4-diyl.

Dimensional reduction by geometrical frustration in a cubic antiferromagnet composed of tetrahedral clusters.

Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here, we study the spin dynamics of the tetrahedral cluster antiferromagnet, pharmacosiderite, via muon spin resonance and neutron scattering. We find that the spin correlation exhibits a two-dimensional characteristic despite the isotropic connectivity of tetrahedral clusters made of spin 5/2 Fe3+ ions in the three-dimensional cubic crystal, which we ascribe to two-dimensionalisation by geometrical frustration based on spin wave calculations. Moreover, we suggest that even one-dimensionalisation occurs in the decoupled layers, generating low-energy and one-dimensional excitation modes, causing large spin fluctuation in the classical spin system. Pharmacosiderite facilitates studying the emergence of low-dimensionality and manipulating anisotropic responses arising from the dimensionality using an external magnetic field.

Muonium in stishovite: implications for the possible existence of neutral atomic hydrogen in the earth's deep mantle.

Hydrogen in the Earth's deep interior has been thought to exist as a hydroxyl group in high-pressure minerals. We present Muon Spin Rotation experiments on SiO2 stishovite, which is an archetypal high-pressure mineral. Positive muon (which can be considered as a light isotope of proton) implanted in stishovite was found to capture electron to form muonium (corresponding to neutral hydrogen). The hyperfine-coupling parameter and the relaxation rate of spin polarization of muonium in stishovite were measured to be very large, suggesting that muonium is squeezed in small and anisotropic interstitial voids without binding to silicon or oxygen. These results imply that hydrogen may also exist in the form of neutral atomic hydrogen in the deep mantle.