Muon Stopping Research Articles

Muon-spin relaxation investigation of magnetic bistability in a crystalline organic radical compound

We present the results of a muon-spin relaxation (μ+SR) investigation of the crystalline organic radical compound 4-(2-benzimidazolyl)-1,2,3,5-dithiadiazolyl (HbimDTDA), in which we demonstrate the hysteretic magnetic switching of the system that takes place at T=(274 ± 11)K caused by a structural phase transition. Muon-site analysis using electronic structure calculations suggests a range of candidate muon stopping sites. The sites are numerous and similar in energy but, significantly, differ between the two structural phases of the material. Despite the difference in the sites, the muon remains a faithful probe of the transition, revealing a dynamically-fluctuating magnetically disordered state in the low-temperature structural phase. In contrast, in the high temperature phase the relaxation is caused by static nuclear moments, with rapid electronic dynamics being motionally narrowed from the muon spectra.

Magnetic structure and crystal field states ofPr2Pd3Ge5:μSRand neutron scattering investigations

We present the results of muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), neutron powder diffration (NPD), and inelastic neutron scattering (INS) investigations on polycrystalline ${\mathrm{Pr}}_{2}{\mathrm{Pd}}_{3}{\mathrm{Ge}}_{5}$. The polycrystalline ${\mathrm{Pr}}_{2}{\mathrm{Pd}}_{3}{\mathrm{Ge}}_{5}$ is known to exhibit two antiferromagnetic transitions near ${T}_{\mathrm{N}1}=8.3$ K and ${T}_{\mathrm{N}2}=7.5$ K which is confirmed by the heat capacity measurements on the present sample. In the magnetically ordered state the NPD data show clear evidence for magnetic Bragg peaks, which for $T<{T}_{\mathrm{N}2}$ could be indexed with a propagation vector k = (1, 0, 0), and with k = (1, 0, 0.07) for ${T}_{\mathrm{N}2}<T<{T}_{\mathrm{N}1}$. We have determined the magnetic structure and found a canted antiferromagnetic structure of ordered ${\mathrm{Pr}}^{3+}$ moments. At 7.6 K we find an amplitude modulated incommensurate antiferromagnetic arrangement of ordered moments with a maximum ordered moment of 1.64(3) ${\ensuremath{\mu}}_{\mathrm{B}}$/Pr lying in the $ab$ plane tilted at about ${26}^{\ensuremath{\circ}}$ from the $b$ axis. At 1.8 K the antiferromagnetic structure is found to be commensurate with an ordered moment of 2.80(6) ${\ensuremath{\mu}}_{\mathrm{B}}$/Pr lying in the $ab$ plane tilted at about ${28}^{\ensuremath{\circ}}$ from the $b$ axis. Our zero-field $\ensuremath{\mu}\mathrm{SR}$ spectra at 1.5 K and at shorter time scale (below 0.5 $\ensuremath{\mu}\mathrm{s}$) reveal two oscillatory frequencies further supporting a long-range-ordered magnetic ground state. We have calculated the muon sites using the density functional theory calculation and present the results of internal field calculations at the muon stopping sites, which are in good agreement with the experimental observations. In the paramagnetic state, the INS data show three well defined CEF excitations near 8.0, 12.3, and 18.1 meV arising from the crystal electric field (CEF) split $J=4$ ground state of ${\mathrm{Pr}}^{3+}$. The CEF level scheme is deduced by analyzing the INS data by a model based on the CEF model.

TRIM Simulations Tool for µ + Stopping Fraction in Hydrostatic Pressure Cells

For quantum systems or materials, a common procedure for probing their behaviour is to tune electronic/magnetic properties using external parameters, e.g. temperature, magnetic field or pressure. Pressure application as an external stimuli is a widely used tool, where the sample in question is inserted into a pressure cell providing a hydrostatic pressure condition. Such device causes some practical problems when using in Muon Spin Rotation/Relaxation (µ +SR) experiments as a large proportion of the muons will be implanted in the pressure cell rather than in the sample, resulting in a higher background signal. This issue gets further amplified when the temperature dependent response from the sample is much smaller than that of the pressure cell,which may cause the sample response to be lost in the background and cause difficulties in aligning the sample within the beam. To tackle this issue, we have used pySRIM [1] to construct a practical and helpful simulation tool for calculating muon stopping fractions, specifically for the pressure cell setup at the µE1 beamline using the GPD spectrometer at the Paul Scherrer Institute, with the use of TRIM simulations. The program is used to estimate the number of muon stopping in both the sample and the pressure cell at a given momentum. The simultion tool is programmed into a GUI, making it accessible to user to approximate prior to their experiments at GPD what fractions will belong to the sample and the pressure cell in their fitting procedure.

Identifying muon sites “by eye” in KPF6 and KBF4

Molecular magnets are one of the key research themes of µSR, but locating the muon stopping site in these compounds using density functional theory is often very challenging as their unit cells tend to contain a very large number of atoms. Nevertheless, many molecular magnets contain the [PF6]− and [BF4]− molecular ions, which, due to their fluorine nuclei, produce a distinctive µSR spectrum, which can give information about the muon stopping site. This paper details the calculation of the muon sites in the much simpler materials KPF6 and KBF4, providing insights which can be applied to situations where these molecular ions are found in complicated molecular magnets.

Development of apparatus for mean-lifetime measurement of cosmic-ray muons using plastic scintillation detectors and FLASH-ADC/FPGA-based readout electronics

Introduction: This paper presents the development and results of an apparatus for measuring the mean lifetime of cosmic-ray muons. Methods: The apparatus uses three plastic scintillation detectors and a readout electronics system based on Flash Analog Digital Converter (Flash-ADC) and Embedded Field Programmable Gate Array (FPGA). The readout system has 8-bit resolution and a 125 Msample/sec sampling rate. The system's trigger and data collection are controlled through a computer interface based on LabVIEWTM. The readout electronics are calibrated with an accuracy of 8 nsec/TDC channel. Results: Over 6000 events were recorded during the measurements performed at ground level using aluminum as the muon stopping material, and the muon decay time spectrum was obtained and fit with a combination of two exponential components and a constant background. The mean lifetimes of negative and positive muons were determined. Conclusion: Our results indicate that the mean lifetimes of negative and positive muons in aluminum are 0.70 ± 0.24 µsec and 2.05 ± 0.16 µsec, respectively.

Muon spin rotation study of the layered oxyselenide Sr2CoO2Ag2Se2

The results of a muon spin rotation experiment on the layered oxyselenide ${\mathrm{Sr}}_{2}{\mathrm{CoO}}_{2}{\mathrm{Ag}}_{2}{\mathrm{Se}}_{2}$ are presented. The compound contains square-planar ${\mathrm{CoO}}_{2}$ layers and is found to exhibit a phase transition at 160.4(1) K to an antiferromagnetic configuration of the ${\mathrm{Co}}^{2+}$ ions. Density functional theory calculations were performed in order to determine the stopping site of the muon within the unit cell. The calculated magnetic dipole field at the muon stopping site was shown to be consistent with the proposed magnetic structure.

Muon spin rotation and relaxation study on Nb1−yFe2+y

We present a detailed study of the magnetic properties of weakly ferromagnetic/quantum critical Nb$_{1-y}$Fe$_{2+y}$ using muon spin rotation and relaxation ($\mu$SR). By means of an angular dependent study of the muon spin rotation signal in applied magnetic fields on a single crystal in the paramagnetic state we establish the muon stopping site in the crystallographic lattice of NbFe$_2$. With this knowledge we develop models to describe the muon spin rotation and relaxation signals in the weakly ferromagnetic, spin density wave and quantum critical phases of Nb$_{1-y}$Fe$_{2+y}$ and fit the corresponding experimental data. In particular, we quantify the $\mu$SR response for quantum critical behavior in Nb$_{1.0117}$Fe$_{1.9883}$ and extract the influence of residual weak structural disorder. From our analysis, Nb$_{1-y}$Fe$_{2+y}$ emerges to be uniquely suited to study quantum criticality close to weak itinerant ferromagnetic order.

MuFinder: A program to determine and analyse muon stopping sites

Significant progress has recently been made in calculating muon stopping sites using density functional theory. The technique aims to address two of the most common criticisms of the muon-spin spectroscopy (μ+SR) technique, namely, where in the sample does the muon stop, and what is its effect on its local environment. We have designed and developed a program called MuFinder that enables users to carry out these calculations through a simple graphical user interface (GUI). The procedure for calculating muon sites by generating initial muon positions, relaxing the structures, and then clustering and analysing the resulting candidate sites, can be done entirely within the GUI. The local magnetic field at the muon site can also be computed, allowing the connection between the muon sites obtained and experiment to be made. MuFinder will make these computations significantly more accessible to non-experts and help to establish muon site calculations as a routine part of μ+SR experiments. Program summaryProgram Title: MuFinderCPC Library link to program files:https://doi.org/10.17632/pwwt7p9hv8.1Developer's repository link:https://gitlab.com/BenHuddart/mufinderLicensing provisions: GPLv3Programming language: PythonNature of problem: To automate the process of calculating muon stopping sites using density functional theory, thereby making these calculations accessible to non-experts.Solution method: A Python-based graphical user interface (GUI) through which users can calculate muon stopping sites using the structural relaxation method. The program makes use of newly-developed algorithms for generating candidate initial muon positions and for clustering muon positions obtained from the structural relaxations. Analysis of the muon sites, including calculation of the local dipolar magnetic field, is also possible within the GUI.

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.

Measurement of proton, deuteron, triton, and α particle emission after nuclear muon capture on Al, Si, and Ti with the AlCap experiment

Background: Heavy charged particles after nuclear muon capture are an important nuclear physics background to the muon-to-electron conversion experiments Mu2e and COMET, which will search for charged lepton flavor violation at an unprecedented level of sensitivity. Purpose: The AlCap experiment aimed to measure the yield and energy spectra of protons, deuterons, tritons, and α particles emitted after the nuclear capture of muons stopped in Al, Si, and Ti in the low-energy range relevant for the muon-to-electron conversion experiments. Methods: Individual charged particle types were identified in layered silicon detector packages and their initial energy distributions were unfolded from the observed energy spectra. Results: The proton yields per muon capture were determined as Yp(Al)=26.64(28stat.)(77syst.)×10−3 and Yp(Ti)=26.48(35)(80)×10−3 in the energy range 3.5–20.0 MeV, and as Yp(Si)=52.5(6)(18)×10−3 in the energy range 4.0–20.0 MeV. Detailed information on yields and energy spectra for all observed nuclei are presented in the paper. Conclusions: The yields in the candidate muon stopping targets, Al and Ti, are approximately half of that in Si, which was used in the past to estimate this background. The reduced background allows for less shielding and a better energy resolution in these experiments. It is anticipated that the comprehensive information presented in this paper will stimulate modern theoretical calculations of the rare process of muon capture with charged particle emission and inform the design of future muon-to-electron conversion experiments.12 MoreReceived 23 October 2021Accepted 4 March 2022DOI:https://doi.org/10.1103/PhysRevC.105.035501©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectron & muon captureLepton induced nuclear reactionsPhysical SystemsMuonic atoms & moleculesParticles & FieldsNuclear Physics

Formula omitted]SR investigation of the Fe-doped Ca3Ru2O7 polar metal

Ca3Ru2O7 is a polar metal that belongs to the class of multiferroic magnetic materials. Here, tiny amounts of Fe doping in the Ru sites bring about dramatic changes in the electronic and magnetic properties and generate a complex H–T phase diagram. To date, not much is known about the ground state of such a system in the absence of magnetic field. By performing muon-spin spectroscopy (μSR) measurements in 5% Fe-doped Ca3Ru2O7 single crystals, we investigate its electronic properties at a local level. Transverse-field μSR results indicate a very sharp normal-to-antiferromagnetic transition at TN=79.7(1)K, with a width of only 1K. Zero-field μSR measurements in the magnetically ordered state allow us to determine the local fields Bi at the muon implantation sites. By symmetry, muons stopping close to the RuO2 planes detect only the weak nuclear dipolar fields, while those stopping next to apical oxygens sense magnetic fields as high as 150mT. In remarkable agreement with the nominal Fe-doping, a ∼6% minority of the these muons feel slightly lower fields, reflecting a local magnetic frustration induced by iron ions. Finally, Bi shows no significant changes across the metal-to-insulator transition, close to 40K. We ascribe this surprising lack of sensitivity to the presence of crystal twinning.

Looking forward to lepton-flavor-violating ALPs

We assess the status of past and future experiments on lepton flavor violating (LFV) muon and tau decays into a light, invisible, axion-like particle (ALP), a. We propose a new experimental setup for MEG II, the MEGII-fwd, with a forward calorimeter placed downstream from the muon stopping target. Searching for μ → ea decays MEGII-fwd is maximally sensitive to LFV ALPs, if these have nonzero couplings to right-handed leptons. The experimental set-up suppresses the (left-handed) Standard Model background in the forward direction by controlling the polarization purity of the muon beam. The reach of MEGII-fwd is compared with the present constraints, the reach of Mu3e and the Belle-II reach from τ → ℓa decays. We show that a dedicated experimental campaign for LFV muon decays into ALPs at MEG II and Mu3e will be able to probe the ALP parameter space in an unexplored region well beyond the existing astrophysical constraints. We study the implications of these searches for representative LFV ALP models, where the presence of a light ALP is motivated by neutrino masses, the strong CP problem and/or the SM flavor puzzle. To this extent we discuss the majoron in low-scale seesaw setups and introduce the LFV QCD axion, the LFV axiflavon and the leptonic familon, paying particular attention to the cases where the LFV ALPs constitute cold dark matter.

Megahertz dynamics in skyrmion systems probed with muon-spin relaxation

We present longitudinal-field muon-spin relaxation (LF $\mu$SR) measurements on two systems that stabilize a skyrmion lattice (SkL): Cu$_2$OSeO$_3$, and Co$_x$Zn$_y$Mn$_{20-x-y}$ for $(x,y)~=~(10,10)$, $(8,9)$ and $(8,8)$. We find that the SkL phase of Cu$_2$OSeO$_3$ exhibits emergent dynamic behavior at megahertz frequencies, likely due to collective excitations, allowing the SkL to be identified from the $\mu$SR response. From measurements following different cooling protocols and calculations of the muon stopping site, we suggest that the metastable SkL is not the majority phase throughout the bulk of this material at the fields and temperatures where it is often observed. The dynamics of bulk Co$_8$Zn$_9$Mn$_3$ are well described by $\simeq~2$ GHz excitations that reduce in frequency near the critical temperature, while in Co$_8$Zn$_8$Mn$_4$ we observe similar behavior over a wide range of temperatures, implying that dynamics of this kind persist beyond the SkL phase.

From magnetic order to quantum disorder in the Zn-barlowite series of S\u2009=\u20091/2 kagom\xe9 antiferromagnets

We report a comprehensive muon spectroscopy study of the Zn-barlowite series of S=frac{1}{2} kagomé antiferromagnets, ZnxCu4−x(OH)6FBr, for x = 0.00 to 0.99(1). By combining muon spin relaxation and rotation measurements with state-of-the-art density-functional theory muon-site calculations, we observe the formation of both μ–F and μ–OH complexes in Zn-barlowite. From these stopping sites, implanted muon spins reveal the suppression of long-range magnetic order into a possible quantum spin liquid state upon the increasing concentration of Zn-substitution. In the parent compound (x = 0), static long-range magnetic order below TN = 15 K manifests itself in the form of spontaneous oscillations in the time-dependent muon asymmetry signal consistent with the dipolar fields expected from the calculated muon stopping sites and the previously determined magnetic structure of barlowite. Meanwhile, in the x = 1.0 end-member of the series—in which antiferromagnetic kagomé layers of Cu2+S=frac{1}{2} moments are decoupled by diamagnetic Zn2+ ions—we observe that dynamic magnetic moment fluctuations persist down to at least 50 mK, indicative of a quantum disordered ground state. We demonstrate that this crossover from a static to dynamic magnetic ground state occurs for compositions of Zn-barlowite with x > 0.5, which bears resemblance to the dynamical behaviour of the widely studied Zn-paratacamite series that contains the quantum spin liquid candidate herbertsmithite.

Demonstration of Muon-Beam Transverse Phase-Space Compression.

We demonstrate efficient transverse compression of a 12.5 MeV/c muon beam stopped in a helium gas target featuring a vertical density gradient and crossed electric and magnetic fields. The muon stop distribution extending vertically over 14mm was reduced to a 0.25mm size (rms) within 3.5 μs. The simulation including cross sections for low-energy μ^{+}-He elastic and charge exchange (μ^{+}↔ muonium) collisions describes the measurements well. By combining the transverse compression stage with a previously demonstrated longitudinal compression stage, we can improve the phase space density of a μ^{+} beam by a factor of 10^{10} with 10^{-3} efficiency.

Magnetism and its coexistence with superconductivity in CaK(Fe0.949Ni0.051)4As4 : Muon spin rotation/relaxation studies

The magnetic response of CaK(Fe$_{0.949}$Ni$_{0.051}$)$_4$As$_4$ was investigated by means of the muon-spin rotation/relaxation. The long-range commensurate magnetic order sets in below the N\'{e}el temperature $T_{\rm N}= 50.0(5)$~K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the $ab-$plane and the antiferromagnetic stacking along the $c-$direction. The value of the ordered magnetic moment at $T\approx3$ K was estimated to be $m_{\rm Fe}=0.38(11)$ $\mu_{\rm B}$ ($\mu_{\rm B}$ is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature $T_{\rm c}\simeq 9$ K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at $T\rightarrow 0$ and the ratio of the transition temperatures $T_{\rm c}/T_{\rm N}$. Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density wave magnetism and superconductivity [Machida, J. Phys. Soc. Jpn. 50, 2195 (1981) and Bud'ko et al., Phys. Rev. B 98, 144520 (2018)].

Estimation of Muon Stopping Site in CoCr2O4 Using Density Functional Theory

Spinel material Cobalt Chromite (CoCr2O4) is a ferrimagnetic material with TC of about 93 K. This compound has attracted much attention due to the presence of electrical polarization which related to spiral magnetic transition at TS = 26 K. [Physical Review B, 70, 214434, 2004]. This spiral magnetic transition phenomena could be explored by experiment using Muon Spin Rotation, Relaxation, and Resonance (liSR) . Positive muon in liSR plays a role as a local magnetic probethus, we need to determine the muon stopping site information. In this study, we investigate the muon stopping site of CoCr2O4 with ferrimagnetic ground state using spin polarized Density Functional Theory implemented in Full-potential Linearized Augmented Plane Wave (FLAPW) method. The exchange-correlation effect was considered in the scheme of GGA+Ueff approximation. Based on the minimum energy of electrostatic potential, we obtain the muon stopping site around the three Oxygen ions in the tetrahedral site of Cobalt.

Stopping muon effect and estimation of intracloud electric field

Employing large thunderstorm ground enhancements (TGEs) as a manifestation of the strong electric field in thundercloud we measure fluxes of almost all species of secondary cosmic rays to estimate the strength of the intracloud electric field. The modulation that electric field poses on charged particle flux gives a sizable change in count rate of detectors measuring high energy muon flux and inclined muon flux in the presence of a TGE. The muon stopping effect, observed by the particle detectors located at 3200 m altitude at Aragats Space Environmental Center (ASEC) implicates the abrupt decline of count rate of high energy muons (at vertical incidence with energies above 250 MeV and at inclined incidence with azimuth angle θ> 22° for lower energies). For the large TGE events (relative enhancement > 10% in SEVAN detector upper layer, registering low energy charged particles and electrons) muon count rate decreases down to 2-5% from the mean count rate measured before the TGE event. A simple model of shifting of the energy spectrum of particles entering the electric field was applied for the analysis of several events where the muon stopping (deceleration) effect has been observed. For the large TGE events that occurred during last decade the maximal potential drop of 350 MV was estimated. The most probable electric field strength for this event was found to be ∼2 kV/cm.

Computational prediction of muon stopping sites: A novel take on the unperturbed electrostatic potential method.

Finding the stopping site of the muon in a muon-spin relaxation experiment is one of the main problems of muon spectroscopy, and computational techniques that make use of quantum chemistry simulations can be of great help when looking for this stopping site. The most thorough approach would require the use of simulations, such as Density Functional Theory (DFT), to test and optimize multiple possible sites, accounting for the effect that the added muon has on its surroundings. However, this can be computationally expensive and sometimes unnecessary. Hence, in this work, we present a software implementation of the Unperturbed Electrostatic Potential (UEP) Method: an approach used for finding the muon stopping site in crystalline materials. The UEP method requires only one DFT calculation, necessary to compute the electronic density. This, in turn, is used to calculate the minima of the crystalline material's electrostatic potential and the estimates of the muon stopping site, relying on the approximation that the muon's presence does not significantly affect its surroundings. One of the main UEP's assumptions is that the muon stopping site will be one of the crystalline material's electrostatic potential minima. In this regard, we also propose some symmetry-based considerations about the properties of this crystalline material's electrostatic potential, in particular, which sites are more likely to be its minima and why the unperturbed approximation may be sufficiently robust for them. We introduce the Python software package pymuon-suite and the various utilities it provides to facilitate these calculations, and finally, we demonstrate the effectiveness of the method with some chosen example systems.

Benchmarking Full-Potential Linearized Augmented Plane Wave (FLAPW) Method for Determination of Muon Stopping Sites in LiF

Muon stopping sites in Lithium Fluoride have been determined based on the minimum electrostatic potential calculation using density functional theory implemented in the full-potential linearized augmented planewave method. The isosurface of the electrostatic potential obtained in our calculation is similar to the calculation obtained by using pseudopotential-based plane wave (PPPW) method reported by Bernadini et al. [Physical Review B, 87 (2013) 115148]. This yields to the two possible muon sites inside the cage structure of Li-F forming tetrahedral coordination. One of the muon sites is located at the center of the tetrahedral while the other is at the equivalent site of the tetrahedral. In spite of the similar isosurface results, our global minimum is found at the center of the tetrahedral in contrast to the previous result obtained at the tetrahedral sites. The strategy to determine the muon possible sites based on the minimum of the total energy of the system will also be considered including the muon sites position between the two fluorine ions (F-).