Muon Spin Depolarization Research Articles

Experimental evidence for a valence-bond glass in the 5d1 double perovskite Ba2YWO6

We report the magnetic susceptibility, specific heat, and muon spin relaxation results of the $5{d}^{1}$ double perovskite ${\mathrm{Ba}}_{2}{\mathrm{YWO}}_{6}$. The dc magnetic susceptibility shows two distinct Curie-Weiss regimes and a sub-Curie-Weiss increase ${T}^{\ensuremath{-}n}$ with $n=0.75(1)$ for $T=3\text{--}100$ K, alluding to the presence of random magnetism. The ac magnetic susceptibility reveals a spin freezing at ${T}_{f}\ensuremath{\sim}0.3$ K with the activation energy of $\mathrm{\ensuremath{\Delta}}/{k}_{B}=27.6$ K. The specific heat data exhibit the pseudogap behavior at 25 K and the subsequent power-law dependence with decreasing temperature, indicating the gradual spin freezing with the quenching of orbital fluctuations. However, the muon spin relaxation data display only a weak muon spin depolarization with lacking long-range magnetic ordering down to 26 mK. Taken together, our results suggest that ${\mathrm{Ba}}_{2}{\mathrm{YWO}}_{6}$ is the proximate realization of a random spin-orbit dimer state.

Self-Consistent Two-Gap Approach in Studying Multi-Band Superconductivity of NdFeAsO0.65F0.35

High-quality single crystals of NdFeAsO$_{0.65}$F$_{0.35}$ (the transition temperature $T_{\rm c} \simeq 30.6$~K) were studied in zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation ($\mu$SR) experiments. An upturn in muon-spin depolarization rate at $T\lesssim 3$~K was observed in ZF-$\mu$SR measurements and it was associated with the onset of ordering of Nd electronic moments. Measurements of the magnetic field penetration depth ($\lambda$) were performed in the TF geometry. By applying the external magnetic field $B_{\rm ex}$ parallel to the crystallographic $c$-axis ($B_{\rm ex}\| c$) and parallel to the $ab$-plane ($B_{\rm ex}\| ab$), the temperature dependencies of the in-plane component ($\lambda_{ab}^{-2}$) and the combination of the in-plane and the out of plane components ($\lambda_{ab,c}^{-2}$) of the superfluid density were determined, respectively. The out-of-plane superfluid density component ($\lambda_{c}^{-2}$) was further obtained by combining the results of $B_{\rm ex} \| c$ and $B_{\rm ex} \| {ab}$ set of experiments. The temperature dependencies of $\lambda_{ab}^{-2}$, $\lambda_{ab,c}^{-2}$, and $\lambda_{c}^{-2}$ were analyzed within the framework of a self-consistent two-gap model despite of using the traditional $\alpha$-model. Interband coupling was taken into account, instead of assuming it to be zero as it stated in the $\alpha$-model. A relatively small value of the interband coupling constant $\Lambda_{12} \simeq 0.01$ was obtained, thus indicating that the energy bands in NdFeAsO$_{0.65}$F$_{0.35}$ are only weakly coupled. In spite of their small magnitude, the coupling between the bands leads to the single value of the superconducting transition temperature $T_{\rm c}$.

An Approach to the Intermediate State of the Distributed Internal Fields on Muon Site

We show a new approach to provide anaysis functions of the muon-spin depolarization in order to describe the intermediate state between Gaussian and Lorentzian behavior. The Kubo Golden Rule (KGR) formula was used to mix the Gaussian and Lorentzian probability density functions. The result confirmed that the KGR formula can analytically explain the intermediate states. The current study suggests a new approach to investigate the so-called pseudogap state of high-Tc superconducting oxides.

Multigap superconductivity in the charge density wave superconductor LaPt2Si2

The superconducting gap structure of a charge density wave (CDW) superconductor LaPt$_2$Si$_2$ ($T_c$ = 1.6~K) having a quasi two dimensional crystal structure has been investigated using muon spin rotation/relaxation ($\mu$SR) measurements carried out in transverse field (TF), zero field (ZF) and longitudinal field (LF) geometries. Rigorous analysis of TF-$\mu$SR spectra in the superconducting state corroborates that the temperature dependence of the effective penetration depth, $\lambda_L$, derived from muon spin depolarization, fits to an isotropic $s+s-$wave model suggesting that the Fermi surface contains two gaps of different magnitude rather than an isotropic gap expected for a conventional $s-$wave superconductor. On the other hand, ZF $\mu$SR data do not show any significant change in muon spin relaxation rate above and below the superconducting transition indicating the fact that time-reversal symmetry is preserved in the system.

Low-temperature breakdown of antiferromagnetic quantum critical behavior in FeSe

A nematic transition preceding a long-range spin density wave antiferromagnetic phase is a common feature of many Fe based superconductors. However, in the FeSe system with a nematic transition at $T_{\rm s} \approx$ 90 K no evidence for long-range static magnetism down to very low temperature was found. The lack of magnetism is a challenge for the theoretical description of FeSe. Here, we investigated high-quality single crystals of FeSe using high-field (up to 9.5 Tesla) muon spin rotation ($\mu$SR) measurements. The $\mu$SR Knight shift and the bulk susceptibility linearly scale at high temperatures but deviate from this behavior around $T^{*} \sim 10$ K, where the Knight shift exhibits a kink. This behavior hints to an essential change of the electronic and/or magnetic properties crossing the region near $T^{*}$. In the temperature range $T_{\rm s} \gtrsim T \gtrsim T^{*}$ the muon spin depolarization rate follows a critical behavior $\Lambda \propto T^{-0.4}$. The observed non-Fermi liquid behavior with a cutoff at $T^{*}$ indicates that FeSe is in the vicinity to a antiferromagnetic quantum critical point. Our analysis is suggestive for $T^{*}$ triggered by the Lifshitz transition.

Robustness of dynamic magnetism in the triangle-based antiferromagnets Ba3Ru1−xIrxTi2O9 (x = 0.5 and 0.8)

We report on the spin dynamics of the strong spin-orbit coupled antiferromagnets Ba3Ru1−xIr x Ti2O9 (x = 0.5 and 0.8), which comprise a mixture of edge- and corner-sharing triangles. Muon spin-relaxation measurements give no hints of long-range magnetic order down to 25 mK. Rather, the muon spin-relaxation rates λ(T) show persistent spin dynamics below 1 K, indicating that fast fluctuations are dominant in spite of Ir4+(Jeff = 1/2)/Ru4+(S = 1) randomness. The muon spin depolarization of both compounds is well described by a stretched exponential function with the stretching exponent β = 0.4 (0.6) for x = 0.5 (0.8) at low temperatures, which is larger than β = 1/3 expected for a spin glass. Our results suggest that randomness in the spin number and the exchange interaction induces a partial spin freezing, but the majority of spins remain dynamically fluctuating.

Evidence for spin liquid ground state in SrDy2O4 frustrated magnet probed by μSR

Muon spin relaxation (μSR) measurements were carried out on SrDy2O4, a frustrated magnet featuring short range magnetic correlations at low temperatures. Zero-field muon spin depolarization measurements demonstrate that fast magnetic fluctuations are present from T = 300 K down to 20 mK. The coexistence of short range magnetic correlations and fluctuations at T = 20 mK indicates that SrDy2O4 features a spin liquid ground state. Large longitudinal fields affect weakly the muon spin depolarization, also suggesting the presence of fast fluctuations. For a longitudinal field of μ0H = 2 T, a non-relaxing asymmetry contribution appears below T = 6 K, indicating considerable slowing down of the magnetic fluctuations as field-induced magnetically-ordered phases are approached.

Successive Magnetic Transitions Relating to Itinerant Spins and Localized Cu Spins in La2−xSrxCu1−yFeyO4: Possible Existence of Stripe Correlations in the Overdoped Regime

In order to investigate the relationship between the so-called stripe correlations and the high-Tc superconductivity, we have carried out magnetic susceptibility and zero-field muon-spin-relaxation measurements in partially Fe-substituted La2-xSrxCu1-yFeyO4 (LSCFO). It has been found that the Fe substitution induces successive magnetic transitions in the overdoped regime, namely, a spin-glass transition of Fe3+ spins due to the RKKY interaction based on itinerant spins at higher temperatures and a stripe-order transition of localized Cu2+ spins at lower temperatures. The stripe-order transition disappears at the hole concentration of ~0.28 per Cu which coincides with the endpoint of the superconductivity in pristine La2-xSrxCuO4, suggesting that the stripe correlations are closely related to the high-Tc superconductivity in the overdoped regime as well as in the underdoped regime. As for the spin-glass state, it has been found that the contribution of polarized itinerant spins to the muon-spin depolarization is not negligible. Taking into account neutron-scattering results by R.-H. He et al. [Phys. Rev. Lett. 107, 127002 (2011)] that a spin-density-wave (SDW) order has been observed in overdoped LSCFO, the present results demonstrate the presence of a novel coexistent state of a SDW order and a spin-glass state.

Low-energy μSR Study on the Tetradymite Topological Insulator Bi1.5Sb0.5TeSe2

A new method utilizing the low energy muon spin rotation (μSR) technique to investigate the spin structure within the surface layer of topological insulator has been proposed. In order to detect the spin polarization parallel with the surface, one applies a weak field Bpar, which, by breaking the time reversal symmetry, is expected to induce a net magnetization perpendicular the surface. This will affect the profile of muon spin depolarization spectra. Preliminary measurements on the topological insulator Bi1.5Sb0.5TeSe2 with tetradymite structure are also shown.

Evolution of spin relaxation processes in LiY1−xHoxF4studied via ac-susceptibility and muon spin relaxation

We present measurements of magnetic field and frequency dependence of the low-temperature ($T$ = 1.8 K) ac-susceptibility and temperature and field dependence of the longitudinal field positive muon spin relaxation (\ensuremath{\mu}SR) for LiY${}_{1\ensuremath{-}x}$Ho${}_{x}$F${}_{4}$ with $x$ = 0.0017, 0.0085, 0.0408, and 0.0855. The fits of numerical simulations to the susceptibility data for the $x$ = 0.0017, 0.0085, and 0.0408 show that Ho-Ho cross-relaxation processes become more important at higher concentrations, signaling the crossover from single-ion to correlated behavior. We simulate the muon spin depolarization using the parameters extracted from the susceptibility, and the simulations agree well with our data for samples with $x$ = 0.0017 and 0.0085. The \ensuremath{\mu}SR data for samples with $x$ = 0.0408 and 0.0855 at low temperatures ($T$ 10 K) cannot be described within a single-ion picture of magnetic field fluctuations and give evidence for additional mechanisms of depolarization due to Ho${}^{3+}$ correlations. We also observe an unusual peak in the magnetic field dependence of the muon relaxation rate in the temperature interval 10--20 K that we ascribe to a modification of the Ho${}^{3+}$ fluctuation rate due to a field induced shift of the energy gap between the ground and the first excited doublet crystal field states relative to a peak in the phonon density of states centered near 63 cm${}^{\ensuremath{-}1}$.

Motion of Mu+ inTransparent Conducting Oxides

We have been investigating diamagnetic muonium centers in several optically transparent conducting oxides by zero field (ZF) muon spin depolarization. In this report we present our findings on single crystal β -Ga2O3. ZF data from Ga2O3 are represented with a single static Kubo Toyabe (sKT) function over the whole scanned temperature range. Below room temperature we confirm shallow donor ionization. Between 400 and 500 K, sKT relaxation rates indicate local motion for Mu + among a set of similar sites. Above 500K the relaxation rate decreases and reachesa plateau staying roughly constant up to 650 K. This behaviour is consistent with Mu + finding an energetically more favorable site with a smaller local dipolar field. Above 650K the depolarization rate starts to decrease again. We attribute this behavior to the onset of global Mu + diffusion. We have performed transverse field muon spin rotation experiments at low temperatures to investigate Mu 0 ionization. We will discuss the general trend of Mu + behavior and possibility of a second shallow Mu donor.

Longitudinal Muon Spin Depolarization in Ge-Rich SiGe Alloys

Abstract We report preliminary results of our most recent LF-μSR investigations of Mu site-and charge-state transitions in the Czochralski-grown Si 0.09 Ge 0.91 alloy. The experiments reported here constitute the latest component of a large-scale project examining energy levels and electronic structure of Mu defect centers across the full alloy range for bulk Si 1-x Ge x Prior MuSR observations in Ge-rich alloys have indicated that states originating as Mu 0 T undergo a cyclic process. The present LF muon spin depolarization measurements examining the associated dynamics show slow and fast cyclic processes at high and low fields, respectively. The transition from the fast to slow charge-exchange regime occurs near B = 70mT for this sample. A temperature scan at this specific applied LF produced some compelling results. Trends in relaxation rates and transition energies that are strongly dependent on Ge content suggest a model for the various components of the observed cyclic dynamics. We discuss the processes that may be responsible for this observed behavior. Combined with the previous μSR data on the same sample, current results more clearly identifies the involved Mu species and transition dynamics among them. We will discuss Mu states and the picture of the dynamics for transitions among these states emerging from our most recent LF-μSR measurements.

Initial Study of Positively Charged Muonium Motion in ZnO, CdO, TiO2, and SnO2

Abstract Transparent conducting oxide materials ZnO, CdO, TiO2 and SnO2 are being studied to determine the motional characteristics of diamagnetic muonium. These materials are being studied with an eye for future applications in solar cells, LEDs, and other transparent electrode applications. Theoretical studies show that H+ is the only stable form of hydrogen seen in these materials; therefore we expect to only observe a Mu+ state except at the very lowest temperatures. Zero field muon spin depolarization measurements have been performed to determine Mu+ motional characteristics in these samples; with the aim of addressing a controversy regarding the diffusion barrier for hydrogen in ZnO. The results of initial data fits are discussed and interpreted in light of the data on H diffusion. We observe ionization of shallow donor Mu states at low temperatures, confirming earlier observations that are consistent with hydrogen as an n-type dopant in these compounds.

Zero-field Spin Depolarization of Low-Energy Muons in Ferromagnetic Nickel and Silver Metal

We present zero-field muon-spin depolarization measurements in nickel and silver performed using low-energy muon-spin relaxation technique.Ni or Ag are usually used in this depth-resolved technique as a backing material to enable background subtraction when studying small crystals or materials with weak magnetism. The depolarization rate of the asymmetry in silver and that of the slow relaxing part of the asymmetry in nickel are small(≤ 0.05 μ s −1 ), and weakly temperature and energy-dependent.

Lithium Diffusion in Lithium-Transition-Metal Oxides Detected by μ+SR

Abstract Diffusion of Li+ ionsin solidsisa basic principle behindthe operationof Li-ion batteries. Suchdiffusive behavior is represented by the diffusion equation (Fick's law), J = − D × δ ϕ/ δ x , where J is the diffusion flux, D is the self diffusion coeffcient, ϕ is the concentration, and x is the position. Although D of Li + ions( D Li)in solids is usually evaluatedby 7 Li-NMR, diffculties arise for materials that contain magnetic ions. This is because the magnetic ions contribute additional spin-lattice relaxation processes thatis considerably larger than the1/ T 1 expected from only Li diffusion [1] , [2] , [3] . This implies that 7Li-NMRprovidesa rough estimateof D Li for the positive electrode materials of Li-ion batteries, which include transition metal ions in order to compensate charge neutrality during a Li + intercala-tion/deintercalation reaction. This is an unsatisfactory situation since D Li is one of the primary parameters that govern the charge/discharge rate of a Li-ion battery. We have, therefore, attempted to measure D Li for lithium-transition-metal-oxides with muon-spin relaxation (μ + SR) since 2005 [4] , [5] , [6] . Muons do not feel fluctuating magnetic moments at high T, but instead sense the change in nuclear dipole field due to Li diffusion. Even if magnetic moments still affect the muon-spin depolarization rate, such aneffectis, in principle, distinguishablefromthatof nucleardipole fields.In particular,aweak longitudinal field can be applied that decouples the magnetic and nuclear dipole interactions [7] , [8] . Here, we wish to summarize our μ + SR study on the lithium-transition-metal-oxides, LixCoO2, LiNiO2, and LiCrO2.

Magnetic dynamics of dilute iron nano-clusters in silver films from Mössbauer spectroscopy and muon spin rotation

A silver film containing nanometer size clusters of iron (nominal conc. 1 at%) has been studied by Mossbauer spectroscopy and Low-Energy Muon Spin Rotation. Below about 20 K spin glass freezing due to interparticle interactions is found from both methods. Whereas Mossbauer spectra are insensitive to the fast fluctuations of cluster moments above spin glass freezing temperature, muon spin rotation in magnetic fields applied perpendicular to the polarized muon spins allows tracing the fluctuations of superparamagnetic moments. The temperature dependence of the damping of the muon spin rotation signal shows Arrhenius behavior between 10 to 100 K. Depending on the assumed shape of damping the activation energy of superparamagnetic fluctuations of cluster moments ranges between about 20 K ·kB and 40 K ·kB. Above about 120 K muon spin depolarization indicates diffusion and trapping of muons.

Motion of positively charged muonium in ZnO

We report on a study of the motional characteristics of positively charged muonium defect centers in ZnO as an analog for H+ behavior. Muon spin depolarization measurements at zero applied magnetic field were completed from 20K to 400K, with preliminary results to 750K. Results at the lower temperatures imply that Mu+ occupied two sites, and indicate local motion as thermally assisted tunneling with a characteristic energy of ∼60meV, as well as a site change transition above 200K with barrier energy ∼440meV. Based on theoretical results, we have tentatively assigned these features to tunneling among three equivalent oxygen anti-bonding sites (AB⊥) and a transition to a lower-energy bond-centered site (BC‖) oriented along the c-axis. Preliminary fits suggest that global diffusion of muonium occurs above 400K, with a diffusion barrier energy of ∼0.7eV.

Magnetic Ordering and Spin Dynamics of Ba1–xEuxSi Phases

AbstractWe have investigated the magnetic ordering and spin dynamics of the solid solution series Ba1–xEuxSi with 0 < x ≤ 1 applying X‐ray diffraction, electric conductivity measurements, Mössbauer spectroscopy, muon spin depolarization, and neutron diffraction. Our results suggest a spin glass‐like behavior of Ba1–xEuxSi for concentrations close to x = 0.3 exist. Different spin ordering phenomena are found, which are dependent on the relative europium concentrations.

μSR Investigation of magnetic phases in R 1− xSr xCoO 3 oxides (R=Pr, Nd)

We report results of our muon spin relaxation measurements in the series of polycrystalline compounds Pr 1− x Sr x CoO 3 ( x=0.3, 0.4 and 0.5) and Nd 1− x Sr x CoO 3 ( x=0.3 and 0.5). For the Pr-based samples our data clearly indicate the existence of two magnetic transitions, as also inferred from macroscopic measurements. While the high temperature transition is typical for cobaltites (∼200 K), the low temperature one is unusual. In our experiments it occurs below about 120 K and it manifests itself as a change in the slope of the temperature variation of the muon spin depolarization rate λ( T). For the Nd-based samples we found an increase of the muon spin depolarization rate below 45 K, temperature at which the sample is ferrimagnetic, when the Nd sublattice coupled antiparallel to the Co lattice. No phase separation could be evidenced in our samples by μSR experiments.

Superconductivity of the Filled Skutterudite ThPt4Ge12Investigated by Muon Spin Rotation

The superconducting state of the filled skutterudite ThPt 4 Ge 12 has been investigated by the zero-field longitudinal and transverse-field muon spin rotation technique. The deduced temperature dependence of the muon spin depolarization rate, σ s , at 0.04 T has been analyzed in terms of a phenomenological power-law behavior and a model appropriate for clean limit superconductors. The estimated effective Fermi temperature T F = 87 K has been compared by means of the Uemura plot with those derived for other superconducting systems. The gap parameter Δ(0)/ k B = 7.7(1) and the magnetic penetration depth λ= 156(5) nm, obtained from the muon data, confirm the specific heat results reported before.