Transverse Field Muon Spin Rotation Research Articles

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.

µSR studies for radical reactions of unsaturated organophosphorus compounds

In this paper, the µSR studies of some unsaturated organophosphorus compounds containing heavier congeners of cyclobutane-1,3-diyl and anthracene are reviewed by discussing the usefulness of µSR for main group chemistry. The regioselective addition of muonium (Mu = [µ+e–]) to one of the skeletal phosphorus atoms in an electron-donating air-stable crystalline 1,3-diphosphacyclobutane-2,4-diyl leading to the paramagnetic 4-membered P-heterocycle was characterized by the Δ1 (ΔM = ± 1) resonance signal observed by muon (avoided) level-crossing resonance (µLCR). Meanwhile, a crystalline 1,3-diphosphacyclobutane-2,4-diyl bearing an electron-deficient nitrogen heterocyclic unit was analyzed by transverse-field muon spin rotation (TF-µSR) to characterize predominant muoniation at the skeletal radical carbon centre. A 9-phosphaanthracene bearing the trifluoromethyl (CF3) stabilizing groups at the peri positions was also investigated from the views of radical reactivity, and the regioselective addition of muonium to the skeletal sp2-type phosphorus atom was characterized by the muon hyperfine coupling (hfc) constant observed by TF-µSR and the Δ0 (ΔM = 0) signal of µLCR. The light mass of muon (Mass = 0.1134 amu) causes the larger zero-point energy and promotes the high-energy molecular structure in which the fused aromatic rings are almost flat, although the CF3 groups would prefer the non-planar saddle-like 9-phosphaanthracene skeleton.

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.

Muon Spin Rotation (μSR) for Characterizing Radical Addition to C=S in Xanthene-9-thione and Thioxanthene-9-thione

Abstract Muonium (μ+e−) can be produced by capture of an electron by a spin-polarized muon (μ+) and has been utilized as a light isotope of hydrogen. In this paper, we demonstrate muon spin rotation (μSR) experiments and preliminary computational analyses of the regioselective muonium addition to xanthene-9-thione and thioxanthene-9-thione providing the C-centered radicals. The transverse-field muon spin rotation (TF-μSR) experiments of the cyclic thioketones revealed considerable increase of muon hyperfine coupling constants (muon hfc, Aμ) compared with the muoniated thiobenzophenone, indicating crucial roles of the bridging chalcogen atom promoting the overlap between the S–Mu bond orbital and the radical p orbital.

Structure of muoniated trimethylsilylvinyl radicals

Muoniated vinyl radicals can be produced by muonium (Mu) addition to triple bonds. Rhodes et al. observed a muoniated radical formed by Mu addition to trimethylsilylacetylene but were unable to determine the structure (J. Chem. Soc., Chem. Commun. 1987, 447). We have performed transverse field muon spin rotation measurements on trimethylsilylacetylene at 298 K and two different applied magnetic fields and observed that two types of muoniated radical were formed: a major product with muon hyperfine coupling constant (A µ ) of 587.3(1) MHz and a minor product with A µ of 570.9(5) MHz. DFT calculations show that Mu addition is preferred to the terminal carbon of the triple bond and that the two resulting radicals are isomers of the Me3SiĊ =CH(Mu) radical. Calculated muon hyperfine coupling constants were used to assign the observed radicals, which have Mu cis and trans to the trimethylsilyl substituent, respectively.

Impact of Mn-Pn intermixing on magnetic properties of an intrinsic magnetic topological insulator: the µSR perspective

We investigated the magnetic properties of polycrystalline samples of the intrinsic magnetic topological insulators MnPn2Te4, with pnictogen Pn = Sb, Bi, by bulk magnetization and µSR. DC susceptibility detects the onset of magnetic ordering at TN = 27 K and 24 K and a field dependence of the macroscopic magnetization compatible with ferri- (or ferro-) and atiferro- magnetic ordering, respectively. Weak transverse field (wTF) Muon Spin Rotation (µSR) confirms the homogeneous bulk nature of magnetic ordering at the same two distinct transition temperatures. Zero Field (ZF) µSR shows that the Sb based material displays a broader distribution of internal field at the muon, in accordance with a larger deviation from the stoichiomectric composition and a higher degree of positional disorder (Mn at the Pn(6c) site), which however does not affect significantly the sharpness of the thermodynamic transition, as detected by the muon magnetic volume fraction and the observability of a critical divergence in the longitudinal and transverse muon relaxation rates.

μSR Study of Unconventional Pairing Symmetry in the Quasi-1D Na2Cr3As3 Superconductor

We report the finding of a novel pairing state in a newly discovered superconductor Na2Cr3As3. This material has a non-centrosymmetric quasi-one-dimensional crystal structure and is superconducting at TC∼ 8.0 K. We find that the magnetic penetration depth data suggests the presence of a nodal line pz-wave pairing state with zero magnetic moment using transverse-field muon-spin rotation (TF-μSR) measurements. The nodal gap observed in Na2Cr3As3 compound is consistent with that observed in isostructural (K,Cs)2Cr3As3 compounds using TF-μSR measurements. The observed pairing state is consistent with a three-band model spin-fluctuation calculation, which reveals the Sz=0 spin-triplet pairing state with the sinkz pairing symmetry. The long-sought search for chiral superconductivity with topological applications could be aided by such a novel triplet Sz=0p-wave pairing state.

Paramagnetic probes in an organic semiconductor: μSR and DFT calculations of the Mu adducts of Alq3 and 8-hydroxyquinoline.

It has been claimed that longitudinal field muon spin relaxation (LF-μSR) experiments on the organic semiconductor (OSC) tris-(8-hydroxyquinoline)aluminum(III) (Alq3) have measured electron hopping rates of ∼1012s-1, while density functional theory (DFT) calculations suggest that electron hopping between a muoniated radical and a neighboring molecule is energetically unfavorable and that the LF-μSR experiments were probing muoniated radicals with localized spin density. We have performed avoided level crossing muon spin resonance (ALC-μSR) and transverse field muon spin rotation (TF-μSR) measurements on Alq3 and 8-hydroxyquinoline (8hq), which is meant to model the muoniated radicals present in Alq3 when they are not in an OSC. These are supplemented by benchmarked DFT calculations. The ALC-μSR and TF-μSR spectra of 8hq and Alq3 are best explained by Mu adding to all six secondary carbons of the quinolate rings with roughly equal yields and localized spin density. There is no evidence in the TF-μSR spectrum of Alq3 for the formation of radicals with muon hyperfine coupling constants of 23 or 91MHz as reported earlier by others. Our measurements support the view that there is localized spin density on the molecule to which Mu is covalently bound and the muon is not a passive probe in organic systems as it can be incorporated into radicals that have different electronic structures to the parent compounds. The muoniated radicals in Alq3 are more short-lived than in 8hq, which could be due to interactions with mobile electrons in the OSC, but with electron spin flip rates on the order of ∼107s-1.

Probing spin fluctuations of the quantum phase transition in Ce3Al by muon spin rotation

We report on the dynamics of a magnetic-field-driven antiferromagnetic-to-paramagnetic quantum phase transition in monocrystalline Ce3Al via transverse-field muon spin rotation (TF-µSR) experiments down to low temperature of sim 80 mK. The quantum phase transition is of a spin-flip type and takes place on the Ce–Al magnetic chains as a result of competition between the indirect exchange and the Zeeman interaction of the Ce moments with the external field, applied along the chain direction (also the direction of the antiferromagnetic axis). The Ce moments are not static at T to 0, but fluctuate in their direction due to the Heisenberg uncertainty principle. Upon applying the magnetic field sweep, the fluctuations exhibit the largest amplitude at the quantum critical point, manifested in a maximum of the muon transverse relaxation rate at the critical field. The quantum nature of fluctuations observed in the TF-µSR experiments is reflected in the temperature independence of the average local magnetic field component along the external magnetic field at the muon stopping site(s) and the muon transverse relaxation rate within the investigated temperature range 1.5 K–80 mK. Quantum fluctuations are fast on the muon Larmor frequency scale, tau_{0} < 10–10 s.

Microscopic evidence for anisotropic multigap superconductivity in the CsV3Sb5 kagome superconductor

The recently discovered kagome superconductor CsV3Sb5 (Tc ≃ 2.5 K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report anisotropic superconducting properties of CsV3Sb5 by means of transverse-field muon spin rotation (μSR) experiments. The fits of temperature dependences of in-plane and out-of-plane components of the magnetic penetration depth suggest that the superconducting order parameter may have a two-gap (s + s)-wave symmetry. The multiband nature of superconductivity could be further supported by the different temperature dependences of the anisotropic magnetic penetration depth γλ(T) and upper critical field {gamma }_{{{{{rm{B}}}}}_{{{{rm{c}}}}2}}(T). The relaxation rates obtained from zero field μSR experiments do not show noticeable change across the superconducting transition, indicating that superconductivity does not break time reversal symmetry.

Superconductivity in noncentrosymmetric NbReSi investigated by muon spin rotation and relaxation

Noncentrosymmetric materials are promising paradigm to explore unconventional superconductivity. In particular, several Re containing noncentrosymmetric materials have attracted considerable attention due to a superconducting state with a broken time reversal symmetry. A comprehensive study on the superconducting ground state of NbReSi was investigated using magnetization, resistivity, and muon spin rotation/relaxation measurements. Zero field muon spectroscopy results showed the absence of any spontaneous magnetic field below the superconducting transition temperature, T$ _{c} $ = 6.29 K, indicating the preserved time-reversal symmetry. Transverse field muon spin rotation measurements confirms a s-wave nature of the sample with $\Delta(0)/k_{B}T_{c} $ = 1.726. This study urges further investigation on more noncentrosymmetric materials to elucidate the selective appearance of unconventional nature and unveil its dependence on antisymmetric spin-orbit coupling strength.

Time-reversal symmetry breaking in frustrated superconductor Re2Hf

Geometrical frustration leads to novel quantum phenomena such as the spin-liquid phase in triangular and kagome lattices. Intraband and interband Fermi surface (FS) nesting can drive unique superconducting (SC) ground states with $d$-wave and ${s}^{\ifmmode\pm\else\textpm\fi{}}$-pairing symmetries, respectively, according to the criterion that the SC gap changes sign across the nesting wave vector. For an odd number of FSs, when multiple interband nesting is of comparable strength, the sign-reversal criterion between different FS sheets can lead to frustration, which promotes novel SC order parameters. Here, we report the experimental observation of a time-reversal symmetry breaking pairing state in ${\mathrm{Re}}_{2}\mathrm{Hf}$ resulting from FS nesting frustration. Furthermore, our electronic specific heat and transverse-field muon spin rotation experiments suggest a fully gapped pairing symmetry. The first-principles electronic structure calculation reveals multiple Fermi surface sheets with comparable interband nesting strength. Implementing the ab initio band structure, we compute spin-fluctuation mediated SC pairing symmetry which reveals an $s+i{s}^{\ensuremath{'}}$-pairing state---consistent with experimental observations. Our investigation demonstrates an alternative SC state which provides a putative setting for both applied and fundamental study.

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.

Probing the superconducting ground state of noncentrosymmetric high-entropy alloys using muon-spin rotation and relaxation

Recently, high entropy alloys (HEAs) have emerged as a new platform for discovering superconducting materials and offer avenues to explore exotic superconductivity. The highly disordered nature of HEA suggests regular phonon required for BCS superconductivity may be unlikely to occur. Therefore understanding the microscopic properties of these superconducting HEA is important. We report the first detailed characterization of the superconducting properties of the noncentrosymmetric ($\alpha$-Mn structure) HEA {(HfNb)}$_{0.10}${(MoReRu)}$_{0.90}$, and {(ZrNb)}$_{0.10}${(MoReRu)}$_{0.90}$ by using magnetization, specific heat, AC transport, and muon-spin relaxation/rotation ($\mu$SR). Despite the disordered nature, low temperature specific heat and transverse-field muon spin rotation measurements suggest nodeless isotropic superconducting gap and Zero-field $\mu$SR measurements confirm that time reversal symmetry is preserved in the superconducting ground state.

Superconducting ground state of the nonsymmorphic superconducting compound Zr2Ir

The nonsymmorphic Zr$_{2}$Ir alloy is a possible topological semimetal candidate material and as such may be part of an exotic class of superconductors. Zr$_{2}$Ir is a superconductor with a transition temperature of 7.4 K with critical fields of 19.6(3) mT and 3.79(3) T, as determined by heat capacity and magnetisation. Zero field muon spin relaxation measurements show that time-reversal symmetry is preserved in these materials. The specific heat and transverse field muon spin rotation measurements rule out any possibility to have a nodal or anisotropic superconducting gap, revealing a conventional s-wave nature in the superconducting ground state. Therefore, this system is found to be conventional nonsymmorphic superconductor, with time-reversal symmetry being preserved and an isotropic superconducting gap.

Superconductivity in Ti67Zr19Nb11.5Sn2.5 shape memory alloy

Shape memory alloys (SMAs) exhibit unique functionalities due to their superelastic and shape memory properties. The ability to program and alter their shapes following a thermomechanical stimulus makes them highly important materials for a vast number of applications in the aerospace, automotive, biomedical, and robotic sectors. Research on SMAs has largely focused on metallurgical, mechanical, structural, or phase transformation properties. Here, we investigate the electrical, magnetic, and thermodynamic properties of the biocompatible SMA, ${\mathrm{Ti}}_{67}{\mathrm{Zr}}_{19}{\mathrm{Nb}}_{11.5}{\mathrm{Sn}}_{2.5}$ (at. %). In particular, we report the discovery of a superconducting phase transition with a critical temperature of 4.65 K with 0 K critical magnetic fields of ${H}_{\mathrm{c}1}=13.7\phantom{\rule{0.16em}{0ex}}\mathrm{mT}$ and ${H}_{\mathrm{c}2}=9.2\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. From the temperature dependence of the specific heat and local magnetic field measurements using transverse field muon spin rotation, we also determine a superconducting coherence of 6 nm and a London penetration depth of 776 nm. The results are key towards the development of cryogenic electrical device applications of SMA materials.

Fully gapped superconductivity with preserved time-reversal symmetry in noncentrosymmetric LaPdIn

We report an investigation of the superconducting properties of the hexagonal noncentrosymmetric compound LaPdIn. Electrical resistivity, specific heat and ac susceptibility measurements demonstrate the presence of bulk superconductivity below $T_c$ = 1.6 K. The specific heat, together with the penetration depth measured using transverse-field muon spin rotation and the tunnel diode oscillator based method, are well described by single gap $s$-wave superconductivity, with a gap magnitude of 1.8$k_BT_c$. From zero-field muon spin relaxation results no evidence is found for the spontaneous emergence of magnetic fields in the superconducting state, indicating that time-reversal symmetry is preserved. Band structure calculations reveal that there is a relatively weak effect of antisymmetric spin-orbit coupling on the electronic bands near the Fermi level, which is consistent with there being negligible singlet-triplet mixing due to broken inversion symmetry. On the other hand, isostructural LuPdIn and LaPtIn do not exhibit superconductivity down to 0.4 K, which may be due to these systems having a smaller density of states at the Fermi level.

Type-I superconductivity in single-crystal Pb2Pd

We have investigated the superconducting properties in a single crystal of a new superconductor Pb$_{2}$Pd via various techniques including magnetization, AC transport, transverse field muon spin rotation and relaxation (TF-$\mu$SR), and heat capacity. Pb$_{2}$Pd crystallizes in a body-centred tetragonal structure with space group I4/$mcm$. All measurements confirm the superconducting transition temperature, T$_{C}$ = 3.0 $\pm$ 0.1 K. Electronic specific heat data are well described by the BCS fitting, suggesting that Pb$_{2}$Pd opens an isotropic gap on entering the superconducting state. The specific heat jump and $\lambda_{e-ph}$ value categorize Pb$_{2}$Pd as a moderately coupled superconductor. Magnetization and transverse field muon spin rotation measurements along with Ginzburg-Landau parameter, $\kappa$ < 1/$\sqrt{2}$ strongly infers that Pb$_{2}$Pd is a type I superconductor.

Unconventional superconducting properties of noncentrosymmetric Re5.5Ta

Rhenium based noncentrosymmetric superconductors crystallizing in $\alpha$-Mn structure have become potential candidates to exhibit an unconventional superconducting ground-state. Here we report a detailed investigation on the superconducting and normal state properties of Re$_{5.5}$Ta, that also has the $\alpha$-Mn structure. Magnetization, specific heat, and transport measurements confirm the bulk superconducting transition \textit{T}$_{C}$ at 8.0 K. Upper critical field value (H$_{C2}$(0)) calculated from magnetization, specific heat and AC transport measurements exceed the Pauli paramagnetic limit (14.7 T), indicating that the superconducting properties of Re$_{5.5}$Ta are probably unconventional in nature. However, low-temperature specific heat and transverse-field muon spin rotation measurements suggest a surprising nodeless isotropic superconducting gap, although with strong electron-phonon coupling.

Two-band superconductivity with unconventional pairing symmetry in HfV2Ga4

In this letter, we have examined the superconducting ground state of the HfV$_2$Ga$_4$ compound using resistivity, magnetization, zero-field (ZF) and transverse-field (TF) muon-spin relaxation and rotation ($\mu$SR) measurements. Resistivity and magnetization unveil the onset of bulk superconductivity with $T_{\bf c}\sim$ 3.9~K, while TF-$\mu$SR measurements show that the temperature dependence of the superfluid density is well described by a nodal two-gap $s$+$d$-wave order parameter model. In addition, ZF muon relaxation rate increases with decreasing temperature below 4.6 K, indicating the presence of weak spin fluctuations. These observations suggest an unconventional multiband nature of the superconductivity possibly arising from the distinct $d$-bands of V and Hf ions with spin fluctuations playing an important role. To better understand these findings, we carry out first-principles electronic-structure calculations, further highlighting that the Fermi surface consists of multiple disconnected sheets with very different orbital weights and spin-orbit coupling, bridging the way for a nodal multiband superconductivity scenario. In this vein, therefore, HfV$_2$Ga$_4$-family stands out as an open avenue to novel unexplored unconventional superconducting compounds, such as ScV$_2$Ga$_4$ and ZrV$_2$Ga$_4$, and other many rare earths based materials.