Zero-field Muon Spin Relaxation Research Articles

Novel approach to explore hydrogen trapping sites in aluminum: Integrating Muon spin relaxation with first-principles calculations

This paper provides a novel technique to explore hydrogen trapping in aluminum alloys by combining muon spin relaxation and first-principles calculations. Zero-field muon spin relaxation experiments were conducted on Al–Mn, Al–Cr, Al–Fe, and Al–Ni alloys, resulting in temperature-dependent variations of the dipole field widths (Δ) that elucidated four distinct peaks for the prepared alloys. Our first-principles calculations have clarified that atomic configurations of the muon trapping, which correspond to the Δ peaks below 200 K, are consistent with hydrogen trapping sites in proximity to a solute and solute-vacancy pair. However, significant deviations from this linear relationship were observed for the fourth Δ peaks above 200 K in Al–Mn, Al–Cr, Al–Fe, and Al–Ni alloys. This discrepancy can be interpreted by considering the disparate distribution functions of muon and hydrogen within the tetrahedral site, wherein two of the four Al atoms are substituted by the solute element and vacancy (solute-vacancy pair).

Static magnetic order with strong quantum fluctuations in spin-1/2 honeycomb magnet Na2Co2TeO6

Kitaev interactions, arising from the interplay of frustration and bond anisotropy, can lead to strong quantum fluctuations and, in an ideal case, to a quantum-spin-liquid state. However, in many nonideal materials, spurious non-Kitaev interactions typically promote a zigzag antiferromagnetic order in the d-orbital transition-metal compounds. Here, by combining neutron scattering with muon-spin rotation and relaxation techniques, we provide mechanism insights into the exotic properties of Na2Co2TeO6, a candidate material of the Kitaev model. Below TN, the zero-field muon-spin relaxation rate becomes almost constant (~0.45 μs−1). We attribute this temperature-independent relaxation rate to the strong quantum fluctuations, as well as to the frustrated Kitaev interactions. As the magnetic field increases, neutron scattering data indicate a broader spin-wave excitation at the K-point. Therefore, quantum fluctuations seem not only robust but are even enhanced by the applied magnetic field. Our findings provide valuable hints for understanding the onset of the quantum-spin-liquid state in Kitaev materials.

Magnetic skin effect in Pb(Fe _{1/2}$ Nb _{1/2}$ )O3

Relaxor-ferroelectrics display exceptional dielectric properties resulting from the underlying random dipolar fields induced by strong chemical inhomogeneity. An unusual structural aspect of relaxors is a skin-effect where the near-surface region in single crystals exhibit structures and critical phenomena that differ from the bulk. Relaxors are unique in that this skin effect extends over a macroscopic lengthscale of ∼100 μm whereas usual surface layers only extend over a few unit cells (or ∼nm). We present a muon spectroscopy study of Pb(Fe _{1/2} Nb _{1/2} )O3 (PFN) which displays ferroelectric order, including many relaxor-like dielectric properties such as a frequency broadened dielectric response, and antiferromagnetism with spatially short-range polar correlations and hence can be termed a multiferroic. In terms of the magnetic behavior determined by the Fe3+ ( S=5/2 , L ≈ 0) ions, PFN has been characterized as a unique example of a ‘cluster spin-glass’. We use variable momentum muon spectroscopy to study the depth dependence of the slow magnetic relaxations in a large 1 cm3 crystal of PFN. Zero-field positive muon spin relaxation is parameterized using a stretched exponential, indicative of a distribution of relaxation rates of the Fe3+ spins. This bandwidth of frequencies changes as a function of muon momentum, indicative of a change in the Fe3+ relaxation rates as a function of muon implantation depth in our single crystal. Using negative muon elemental analysis, we find small-to-no measurable change in the Fe3+/Nb5+ concentration with depth implying that chemical concentration alone cannot account for the change in the relaxational dynamics. PFN displays an analogous magnetic skin effect reported to exist in the structural properties of relaxor-ferroelectrics.

Muon spin relaxation and emergence of disorder-induced unconventional dynamic magnetic fluctuations in Dy2Zr2O7

The disordered pyrochlore oxide Dy2Zr2O7 shows the signatures of field-induced spin freezing with remnant zero-point spin-ice entropy at 5 kOe magnetic field. We have performed zero-field and longitudinal field Muon spin relaxation (µSR) studies on Dy2Zr2O7. Our zero field studies reveal the absence of both long-range ordering and spin freezing down to 62 mK. The µSR relaxation rate exhibits a temperature-independent plateau below 4 K, indicating a dynamic ground state of fluctuating spins similar to the well-known spin ice system Dy2Ti2O7. The low-temperature spin fluctuations persist in the longitudinal field of 20 kOe as well and show unusual field dependence of the relaxation rate, which is uncommon for a spin-liquid system. Our results, combined with the previous studies do not show any evidence of spin ice or spin glass ground state, rather point to a disorder-induced dynamic magnetic ground state in the Dy2Zr2O7 material.

Combining muon spin relaxation and DFT simulations of hydrogen trapping in Al6Mn

Hydrogen at the mass ppm level causes hydrogen embrittlement in metallic materials, but experimentally elucidating the hydrogen trapping sites is extremely difficult. We exploit the fact that positive muons can act as light isotopes of hydrogen to study the trapping state of hydrogen in matter. Zero-field muon spin relaxation experiments and density functional theory (DFT) calculations of the hydrogen trapping energy are carried out for Al6Mn. The DFT calculations reveal four possible trapping sites for hydrogen in Al6Mn, at which the hydrogen trapping energies are 0.168 (site 1), 0.312 (site 2), 0.364 (site 3), and 0.495 (site 4) in units of eV/atom. The variations in the deduced dipole field width (Δ) with temperature indicate noticeable changes at 94, 193, and 236 K. Considering the site densities, the observed Δ change temperatures are interpreted as muon trapping at sites 1, 3, and 4.

Nodeless time-reversal symmetry breaking in the centrosymmetric superconductor Sc5Co4Si10 probed by muon-spin spectroscopy

We investigate the superconducting properties of Sc$_{5}$Co$_{4}$Si$_{10}$ using low-temperature resistivity, magnetization, heat capacity, and muon-spin rotation and relaxation ($\mu$SR) measurements. We find that Sc$_{5}$Co$_{4}$Si$_{10}$ {exhibits type-II} superconductivity with a superconducting transition temperature $T_\mathrm{C}= 3.5 (1)$\,K. The temperature dependence of the superfluid density obtained from transverse-field $\mu$SR spectra is best modeled using an isotropic Bardeen-Cooper-Schrieffer type $s$-wave gap symmetry with $2\Delta/k_\mathrm{B}T_\mathrm{C} = 2.84(2)$. However, the zero-field muon-spin relaxation asymmetry reveals the appearance of a spontaneous magnetic field below $T_\mathrm{C}$, indicating that time-reversal symmetry (TRS) is broken in the superconducting state. Although this behavior is commonly associated with non-unitary or mixed singlet-triplet pairing, our group-theoretical analysis of the Ginzburg-Landau free energy alongside density functional theory calculations indicates that unconventional mechanisms are pretty unlikely. Therefore, we have hypothesized that TRS breaking may occur via a conventional electron-phonon process.

Quantum muon diffusion and the preservation of time-reversal symmetry in the superconducting state of type-I rhenium

Elemental rhenium exhibiting type-II superconductivity has been previously reported to break time-reversal symmetry in the superconducting state. We have investigated an arc-melted sample of rhenium exhibiting type-I superconductivity. Low-temperature zero-field muon-spin relaxation measurements indicate that time-reversal symmetry is preserved in the superconducting state. Muon diffusion is observed, which is due to quantum mechanical tunneling between interstitial sites. The normal state behavior is characterized by the conduction electrons screening the muons and thermal broadening, and is typical for a metal. Energy asymmetries between muon trapping sites and the superconducting energy gap also characterize the superconducting state behavior.

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.

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.

Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress

Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-$\mu$SR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking, consistent with qualitative expectations for chiral superconductivity. We also report the appearance of unexpected bulk magnetic order under a uniaxial stress of ~ 1.0 GPa in clean Sr$_2$RuO$_4$.

Temporal and field evolution of spin excitations in the disorder-free triangular antiferromagnet Na2BaCo(PO4)2

The realization of quantum spin liquids on a triangular lattice magnet remains challenging due to quenched disorders present in real materials. Here, we report local-probe signatures of spin-liquid-like excitations in the structurally perfect triangular antiferromagnet ${\mathrm{Na}}_{2}\mathrm{BaCo}{({\mathrm{PO}}_{4})}_{2}$. Our zero-field and longitudinal-field muon spin relaxation measurements reveal both spatially and temporally correlated spins with no hint of static magnetism down to 80 mK, consistent with a quantum spin liquid. Comprehensive $^{23}\mathrm{Na}$ nuclear magnetic resonance experiments enable us to identify a field-induced crossover of magnetic excitations from a spinonlike to a gapped magnon at the critical field ${\ensuremath{\mu}}_{0}{H}_{C}=1.65$ T. Our findings uncover the temporal, thermal, and magnetic-field characteristics of the magnetic excitations in the triangular-lattice quantum spin liquid candidate ${\mathrm{Na}}_{2}\mathrm{BaCo}{({\mathrm{PO}}_{4})}_{2}$.

Absence of μSR evidence for magnetic order in the pseudogap phase of Bi2+xSr2−xCaCu2O8+δ

We present an extended zero-field muon spin relaxation (ZF-$\mu$SR) study of overdoped Bi$_{2+x}$Sr$_{2-x}$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystals, intended to elucidate the origin of weak quasistatic magnetism previously detected by $\mu$SR in the superconducting and normal states of optimally-doped and overdoped samples. New results on heavily-overdoped single crystals show a similar monotonically decreasing ZF-$\mu$SR relaxation rate with increasing temperature that persists above the pseudogap (PG) temperature $T^*$ and does not evolve with hole doping ($p$). Additional measurements using an ultra-low background apparatus confirm that this behavior is an intrinsic property of Bi2212, which cannot be due to magnetic order associated with the PG phase. Instead we show that the temperature-dependent relaxation rate is most likely caused by structural changes that modify the contribution of the nuclear dipole fields to the ZF-$\mu$SR signal. Our results for Bi2212 emphasize the importance of not assuming the nuclear-dipole field contribution is independent of temperature in ZF-$\mu$SR studies of high-temperature (high-$T_c$) cuprate superconductors, and do not support a recent $\mu$SR study of YBa$_2$Cu$_3$O$_{6+x}$ that claims to detect magnetic order in the PG phase.

Time Dependence of Muon Spin Relaxation Rate in Aluminum and Al-1.6%Mg<sub>2</sub>Si Alloy

Zero-field muon spin relaxation experiments were carried out for Al-1.6%Mg2Si and a pure aluminum in isothermal conditions between 260 and 300 K. Observed relaxation spectra were analyzed to extract the dipole width (D) values which were found to decrease with time after solution heat treatment and quenching. Time variations of D appeared to take place two stages in both samples. The stage transition times (tII) deduced for Al-1.6%Mg2Si were comparable to those for the Si-rich clustering stage reported for Al-Mg-Si alloys. The estimated activation energy of Si-rich clustering was 0.62 (±0.04) eV. The stage transition times (tM) for the pure aluminum were 255, 110 and 82 min after quenching at the measuring temperatures of 260, 280 and 300 K, respectively. An Arrhenius plot of logarithmic tM against reciprocal temperature resulted in an activation energy of 0.19 (±0.06) eV.

Quantitative theory of triplet pairing in the unconventional superconductor LaNiGa2

The exceptionally low-symmetry crystal structures of the time-reversal symmetry breaking superconductors LaNiC$_2$ and LaNiGa$_2$ lead to an internally-antisymmetric non-unitary triplet (INT) state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the Density of States (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of LaNiGa$_2$ capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter. The latter is fixed by the critical temperature $T_c$ allowing parameter-free predictions. We compute the electronic specific heat and find excellent agreement with experiment. The size of the ordered moment in the superconducting state is compatible with zero-field muon spin relaxation experiments and the predicted spin-resolved DOS suggests the spin-splitting is within the reach of present experimental technology.

Ir 5d-band derived superconductivity in LaIr3

The superconducting properties of rhombohedral LaIr3 were examined using susceptibility, resistivity, heat capacity, and zero-field (ZF) and transverse-field (TF) muon spin relaxation and rotation (SR) measurements. The susceptibility and resistivity measurements confirm a superconducting transition below K. Two successive transitions are observed in the heat capacity data, one at K and a second at 1.2 K below . The heat capacity jump is , which is lower than 1.43 expected for Bardeen–Cooper–Schrieffer (BCS) weak-coupling limit. TF-SR measurements reveal a fully gapped s-wave superconductivity with , which is small compared to the BCS value of 3.56, suggesting weak-coupling superconductivity. The magnetic penetration depth, , estimated from TF-SR gives nm, a superconducting carrier density carriers m−3 and a carrier effective-mass enhancement factor . ZF-SR data show no evidence for any spontaneous magnetic fields below , which demonstrates that time-reversal symmetry is preserved in the superconducting state of LaIr3.

Broken time-reversal symmetry in superconducting Pr1−xLaxPt4Ge12

The superconducting state of the filled skutterudite alloy series Pr$_{1-x}$La$_{x}$Pt$_{4}$Ge$_{12}$ has been systematically studied by specific heat, zero-field muon spin relaxation ($\mu$SR), and superconducting critical field measurements. An additional inhomogeneous local magnetic field, indicative of broken time-reversal symmetry (TRS), is observed in the superconducting states of the alloys. For $x \lesssim 0.5$ the broken-TRS phase sets in below a temperature $T_m$ distinctly lower than the superconducting transition temperature $T_c$. For $x \gtrsim 0.5$ $T_m \approx T_c$. The local field strength decreases as $x \to 1$, where LaPt$_{4}$Ge$_{12}$ is characterized by conventional pairing. The lower critical field $H_{c1}(T)$ of PrPt$_{4}$Ge$_{12}$ shows the onset of a second quadratic temperature region below $T_q \sim T_m$. Upper critical field $H_{c2}(T)$ measurements suggest multiband superconductivity, and point gap nodes are consistent with the specific heat data. In Pr$_{1-x}$La$_{x}$Pt$_{4}$Ge$_{12}$ only a single specific heat discontinuity is observed at $T_c$, in contrast to the second jump seen in PrOs$_{4}$Sb$_{12}$ below $T_c$. These results suggest that superconductivity in PrPt$_{4}$Ge$_{12}$ is characterized by a complex order parameter.

Exotic Low-Energy Excitations Emergent in the Random Kitaev Magnet Cu_{2}IrO_{3}.

We report on magnetization M(H), dc and ac magnetic susceptibility χ(T), specific heat C_{m}(T) and muon spin relaxation (μSR) measurements of the Kitaev honeycomb iridate Cu_{2}IrO_{3} with quenched disorder. In spite of the chemical disorders, we find no indication of spin glass down to 260mK from the C_{m}(T) and μSR data. Furthermore, a persistent spin dynamics observed by the zero-field muon spin relaxation evidences an absence of static magnetism. The remarkable observation is a scaling relation of χ[H,T] and M[H,T] in H/T with the scaling exponent α=0.26-0.28, expected from bond randomness. However, C_{m}[H,T]/T disobeys the predicted universal scaling law, pointing towards the presence of additional low-lying excitations on the background of bond-disordered spin liquid. Our results signify a many-faceted impact of quenched disorder in a Kitaev spin system due to its peculiar bond character.

Spin dynamics and field-induced magnetic phase transition in the honeycomb Kitaev magnet α−Li2IrO3

The layered honeycomb iridate $\alpha$-Li$_2$IrO$_3$ displays an incommensurate magnetic structure with counterrotating moments on nearest-neighbor sites, proposed to be stabilized by strongly-frustrated anisotropic Kitaev interactions between spin-orbit entangled Ir$^{4+}$ magnetic moments. Here we report powder inelastic neutron scattering measurements that observe sharply dispersive low-energy magnetic excitations centered at the magnetic ordering wavevector, attributed to Goldstone excitations of the incommensurate order, as well as an additional intense mode above a gap $\Delta\simeq2.3$ meV. Zero-field muon-spin relaxation measurements show clear oscillations in the muon polarization below the N\'{e}el temperature $T_{\rm N}\simeq15$ K with a time-dependent profile consistent with bulk incommensurate long-range magnetism. Pulsed field magnetization measurements observe that only about half the saturation magnetization value is reached at the maximum field of 64 T. A clear anomaly near 25 T indicates a transition to a phase with reduced susceptibility. The transition field has a Zeeman energy comparable to the zero-field gapped mode, suggesting gap suppression as a possible mechanism for the field-induced transition.

Unveiling spin-glass transition and antiferromagnetic order by μSR studies in spin-chain Sm2BaNiO5

We report the zero-field and longitudinal field muon spin relaxation studies in a spin-chain compound Sm2BaNiO5. Two magnetic transitions, that have not been previously detected by the heat capacity and magnetization measurements, are confirmed at 46 and 9 K. The antiferromagnetic order is suggested at 46 K. Analysis of the muon spin polarization unveils the spin-glass transition at 9 K. Time-field scaling relation of the muon spin polarization verifies the spin–spin autocorrelation function following the cut-off power law, which is approximated by the Ogielski form, as employed numerically for characterizing the spin-glasses.

Dipolar-octupolar Ising antiferromagnetism in Sm2Ti2O7 : A moment fragmentation candidate

Over the past two decades, the magnetic ground states of all rare-earth titanate pyrochlores have been extensively studied, with the exception of ${\mathrm{Sm}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. This is, in large part, due to the very high absorption cross section of naturally occurring samarium, which renders neutron scattering infeasible. To combat this, we have grown a large, isotopically enriched single crystal of ${\mathrm{Sm}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. Using inelastic neutron scattering, we determine that the crystal field ground state for ${\mathrm{Sm}}^{3+}$ is a dipolar-octupolar doublet with Ising anisotropy. Neutron diffraction experiments reveal that ${\mathrm{Sm}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ orders into the all-in, all-out magnetic structure with an ordered moment of $0.44(7){\ensuremath{\mu}}_{B}$ below ${T}_{N}=0.35$ K, consistent with expectations for antiferromagnetically coupled Ising spins on the pyrochlore lattice. Zero-field muon spin relaxation measurements reveal an absence of spontaneous oscillations and persistent spin fluctuations down to 0.03 K. The combination of the dipolar-octupolar nature of the ${\mathrm{Sm}}^{3+}$ moment, the all-in, all-out ordered state, and the low-temperature persistent spin dynamics make this material an intriguing candidate for moment fragmentation physics.