Muon Spin Relaxation Research Articles

Gapless Quantum Spin Liquid in the Triangular System Sr_{3}CuSb_{2}O_{9}.

We report gapless quantum spin liquid behavior in the layered triangular Sr_{3}CuSb_{2}O_{9} system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well separated by Sb planes. Muon spin relaxation measurements show that the S=1/2 moments at the magnetically active Cu sites remain dynamic down to 65mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature θ_{CW}≃-143 K as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35K. The magnetic specific heat (C_{m}) below 5K reveals a C_{m}=γT+αT^{2} behavior. The significant T^{2} contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-T specific heat data, we estimate the dominant exchange scale to be ∼36 K using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations (∼45 K) as well as high-temperature susceptibility analysis (∼70 K). The linear specific heat coefficient is about 18 mJ/mol K^{2} which is somewhat larger than for typical Fermi liquids.

UNDI: An open-source library to simulate muon-nuclear interactions in solids

We present UNDI, an open-source program to analyze the time dependent spin polarization of an isolated muon interacting with the surrounding nuclear magnetic dipoles in the context of standard muon spin rotation and relaxation spectroscopy experiments.The code can perform both exact and approximated estimates of the muon polarization function in presence of external fields and electric field gradients on the nuclei surrounding the muon.We show that this tool, combined to ab initio estimations of the electric field gradient at the nuclei interacting with the muon, can become a valuable complement to supercell based identifications of muon sites in crystals when large nuclear magnetic moments are present in the sample. In addition, it allows to properly investigate physical properties influenced by the presence of a non-negligible electric field gradient such as avoided level crossing resonance, nature of the ground state, disentanglement of electronic and nuclear magnetic moments or charge ordered states.The efficiency and effectiveness of this method is shown along the lines of three realistic examples. Program summaryProgram Title: UNDICPC Library link to program files:http://dx.doi.org/10.17632/grp8njy6gz.1Developer’s repository link:https://github.com/bonfus/undiCode Ocean capsule:https://codeocean.com/capsule/8365303Licensing provisions: GPLv3Programming language: PythonNature of problem: To simplify and potentially automate the analysis of the nuclear contribution to muon polarization functions in crystalline materials.Solution method: A python library that provides a set of tools to efficiently solve the spin Hamiltonian describing the interaction between the muon and its neighboring nuclei. The code provides the time development of the spin polarization of the muon subject to external fields and accounts for quadrupolar interactions at the nuclear sites. The solution is sought at quantum level accuracy and Hilbert spaces with dimension up to one million can be handled, thus providing accurate results for all standard experimental conditions.

Low-temperature anomalies in muon spin relaxation of solid and hollowγ−Fe2O3nanoparticles: A pathway to detect unusual local spin dynamics

By means of muon spin relaxation measurements we unraveled the temperature spin dynamics in monodisperse maghemite spherical nanoparticles with different surface to volume ratio, in two samples wit ...

Magnetic order and disorder in a quasi-two-dimensional quantum Heisenberg antiferromagnet with randomized exchange

We present an investigation of the effect of randomizing exchange strengths in the $S=1/2$ square lattice quasi-two-dimensional quantum Heisenberg antiferromagnet (QuinH)$_2$Cu(Cl$_{x}$Br$_{1-x}$)$_{4}\cdot$2H$_2$O (QuinH$=$Quinolinium, C$_9$H$_8$N$^+$), with $0\leq x \leq 1$. Pulsed-field magnetization measurements allow us to estimate an effective in-plane exchange strength $J$ in a regime where exchange fosters short-range order, while the temperature $T_{\mathrm{N}}$ at which long range order (LRO) occurs is found using muon-spin relaxation, allowing us to construct a phase diagram for the series. We evaluate the effectiveness of disorder in suppressing $T_{\mathrm{N}}$ and the ordered moment size and find an extended disordered phase in the region $0.4 \lesssim x \lesssim 0.8$ where no magnetic order occurs, driven by quantum effects of the exchange randomness.

Revisiting the A -type antiferromagnet NaNiO2 with muon spin rotation measurements and density functional theory calculations

An $A$-type antiferromagnet, ${\mathrm{NaNiO}}_{2}$, was examined by means of positive muon spin rotation and relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) measurements and first-principles calculations based on a density functional theory (DFT). Below ${T}_{\mathrm{N}}=20$ K, a clear muon spin precession signal was observed in the ${\ensuremath{\mu}}^{+}\mathrm{SR}$ time spectrum recorded under zero field, due to the formation of a static internal magnetic field. The microscopic origin of such an internal field was computed as a sum of dipolar and hyperfine contact fields at the site (0.624, 0, 0.854), where both the muon site and the local spin density at such a site were predicted with DFT calculations. While the computed values were consistent with experimentally obtained ones, in both the antiferromagnetic and the paramagnetic states, the contribution of the hyperfine contact field was shown to be insignificant even below ${T}_{\mathrm{N}}$. Finally, measurements at higher temperatures signified thermally activated Na-ion diffusion with ${E}_{\mathrm{a}}=50(20)$ meV and ${D}_{\mathrm{Na}}(300\phantom{\rule{0.16em}{0ex}}\mathrm{K})=8.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}$/s, commonly observed in layered-type compounds.

Re1\u2212xMox as an ideal test case of time-reversal symmetry breaking in unconventional superconductors

Non-centrosymmetric superconductors (NCSCs) are promising candidates in the search for unconventional and topological superconductivity. The α-Mn-type rhenium-based alloys represent excellent examples of NCSCs, where spontaneous magnetic fields, peculiar to time-reversal symmetry (TRS) breaking, have been shown to develop in the superconducting phase. By converse, TRS is preserved in many other isostructural NCSCs, thus leaving the key question about its origin fully open. Here, we consider the superconducting Re1−xMox (0 ≤ x ≤ 1) family, which comprises both centro- and non-centrosymmetric structures and includes also two extra superconducting phases, β-CrFe and bcc-W. Muon-spin relaxation and rotation (μSR) measurements show a gradual increase of the relaxation rate below Tc, yet its independence of the crystal structure, suggesting that rhenium presence and its amount are among the key factors for the appearance and the extent of TRS breaking in the α-Mn-type NCSCs. The reported results propose Re1−xMox as an ideal test case for investigating TRS breaking in unconventional superconductors.

Magnetism and ion diffusion in honeycomb layered oxide {hbox {K}_2hbox {Ni}_2hbox {TeO}_6}

In the quest for developing novel and efficient batteries, a great interest has been raised for sustainable K-based honeycomb layer oxide materials, both for their application in energy devices as well as for their fundamental material properties. A key issue in the realization of efficient batteries based on such compounds, is to understand the K-ion diffusion mechanism. However, investigation of potassium-ion (K^+) dynamics in materials using e.g. NMR and related techniques has so far been very challenging, due to its inherently weak nuclear magnetic moment, in contrast to other alkali ions such as lithium and sodium. Spin-polarised muons, having a high gyromagnetic ratio, make the muon spin rotation and relaxation (mu ^+SR) technique ideal for probing ions dynamics in these types of energy materials. Here we present a study of the low-temperature magnetic properties as well as K^+ dynamics in honeycomb layered oxide material {hbox {K}_2hbox {Ni}_2hbox {TeO}_6} using mainly the mu ^+SR technique. Our low-temperature mu ^+SR results together with complementary magnetic susceptibility measurements find an antiferromagnetic transition at T_{mathrm{N}}approx 27 K. Further {mu}^{+}SR studies performed at higher temperatures reveal that potassium ions (K^+) become mobile above 200 K and the activation energy for the diffusion process is obtained as E_{mathrm{a}}=121 (13) meV. This is the first time that K^+ dynamics in potassium-based battery materials has been measured using mu ^+SR. Assisted by high-resolution neutron diffraction, the temperature dependence of the K-ion self diffusion constant is also extracted. Finally our results also reveal that K-ion diffusion occurs predominantly at the surface of the powder particles. This opens future possibilities for potentially improving ion diffusion as well as K-ion battery device performance using nano-structuring and surface coatings of the particles.

Time-reversal-symmetry breaking and unconventional pairing in the noncentrosymmetric superconductor La7Rh3

Noncentrosymmetric superconductors have sparked significant research interests due to their exciting properties, such as the admixture of spin-singlet and spin-triplet pairing. Here we report on the muon spin rotation and relaxation and thermodynamic measurements on the noncentrosymmetric superconductor ${\mathrm{La}}_{7}{\mathrm{Rh}}_{3}$, which show an isotropic superconducting gap but also spontaneous time-reversal-symmetry breaking occurring at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in this system. A symmetry analysis identifies ground states compatible with time-reversal-symmetry breaking, and the resulting gap functions are discussed. Furthermore, general energetic considerations indicate the relevance of electron-electron interactions for the pairing mechanism, in accordance with hints of spin fluctuations revealed in susceptibility measurements.

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.

Nuclear magnetic field in Na0.7CoO2 detected with μ−SR

The internal magnetic field in a sodium battery compound, i.e., the paramagnet ${\mathrm{Na}}_{0.7}{\mathrm{CoO}}_{2}$, was investigated with negative muon spin rotation and relaxation (${\ensuremath{\mu}}^{\ensuremath{-}}\mathrm{SR}$), and the result was compared with the results previously obtained with ${\ensuremath{\mu}}^{+}\mathrm{SR}$. The majority of implanted ${\ensuremath{\mu}}^{\ensuremath{-}}$ is captured on an oxygen nucleus, while ${\ensuremath{\mu}}^{+}$ locates an interstitial site. Therefore, a ${\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}\mathrm{SR}$ work provides information on the internal magnetic field, which is formed by nuclear magnetic moments of $^{23}\mathrm{Na}$ and $^{59}\mathrm{Co}$, from the two different viewpoints. Besides a slight decrease in the field distribution width ($\mathrm{\ensuremath{\Delta}}$) around 300 K, the nuclear magnetic field detected with ${\ensuremath{\mu}}^{\ensuremath{-}}\mathrm{SR}$ was found to be almost static and temperature independent up to 400 K, even though Na ions are known to start to diffuse above 290 K based on ${\ensuremath{\mu}}^{+}\mathrm{SR}$, Na-NMR, neutron scattering, and electrochemical measurements. Such a discrepancy is caused by the fact that the Na contribution to $\mathrm{\ensuremath{\Delta}}$ is only about 3% at the O site whereas it is about 13% at the interstitial site, where the ${\ensuremath{\mu}}^{+}$ is presumably located.

Isotropic s -wave superconductivity in the noncentrosymmetric charge density wave superconductor SrPt2As2

${\mathrm{SrPt}}_{2}{\mathrm{As}}_{2}$ undergoes a structural transition around 470 K (from a high-temperature tetragonal to a low-temperature orthorhombic phase) accompanied by a charge density wave transition and followed by a superconducting transition at much lower temperature (5 K). The superconducting gap symmetry of this noncentrosymmetric compound was investigated in detail by means of muon-spin rotation or relaxation $(\ensuremath{\mu}\mathrm{SR})$ experiments in transverse-field (TF) configuration. The temperature-dependent magnetic penetration depth obtained from the $\mathrm{TF}\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{SR}$ spectra suggests an isotropic $s$-wave-type superconducting gap. No observable differences are seen in the asymmetry time spectra collected in zero field above and below the superconducting transition temperature ${T}_{c}$. This strongly suggests the absence of spontaneous magnetic fields in the superconducting state, hence pointing to a preserved time-reversal symmetry below ${T}_{c}$.

Piezoelectric-driven uniaxial pressure cell for muon spin relaxation and neutron scattering experiments.

We present a piezoelectric-driven uniaxial pressure cell that is optimized for muon spin relaxation and neutron scattering experiments and that is operable over a wide temperature range including cryogenic temperatures. To accommodate the large samples required for these measurement techniques, the cell is designed to generate forces up to ∼1000 N. To minimize the background signal, the space around the sample is kept as open as possible. We demonstrate here that by mounting plate-like samples with epoxy, a uniaxial stress exceeding 1 GPa can be achieved in an active volume of at least 5 mm3. We show that for practical operation, it is important to monitor both the force and displacement applied to the sample. In addition, because time is critical during facility experiments, samples are mounted in detachable holders that can be rapidly exchanged. The piezoelectric actuators are likewise contained in an exchangeable cartridge.

Magnetic Phase Diagram of Cu4–xZnx(OH)6FBr Studied by Neutron-Diffraction and μSR Techniques*Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302900, 2016YFA0300500, 2018YFA0704200, 2017YFA0303100, and 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 11874401, 11674406, 11674372, 11961160699, 11774399, 12061130200, 11974392, and 11822411), the Strategic Priority Research Program(B) of the Chinese Academy of Sciences (Grant Nos.

We systematically investigate the magnetic properties of Cu4 – xZnx(OH)6FBr using the neutron diffraction and muon spin rotation and relaxation (μSR) techniques. Neutron-diffraction measurements suggest that the long-range magnetic order and the orthorhombic nuclear structure in the x = 0 sample can persist up to x = 0.23 and 0.43, respectively. The temperature dependence of the zero-field μSR spectra provides two characteristic temperatures, TA0 and Tλ, which are associated with the initial drop close to zero time and the long-time exponential decay of the muon relaxation, respectively. Comparison between TA0 and TM from previously reported magnetic-susceptibility measurements suggest that the former comes from the short-range interlayer-spin clusters that persist up to x = 0.82. On the other hand, the doping level where Tλ becomes zero is about 0.66, which is much higher than threshold of the long-range order, i.e., ∼0.4. Our results suggest that the change in the nuclear structure may alter the spin dynamics of the kagome layers and a gapped quantum-spin-liquid state may exist above x = 0.66 with the perfect kagome planes.

Probing nodeless superconductivity in LaMSi ( M=Ni , Pt) using muon-spin rotation and relaxation

Systems with strong spin-orbit coupling have been a topic of fundamental interest in condensed matter physics due to the exotic topological phases and the unconventional phenomenon they exhibit. In this particular study, we have investigated the superconductivity in the transition-metal ternary noncentrosymmetric compounds $\mathrm{La}M\mathrm{Si}$ ($M=\mathrm{Ni}$, Pt) with different spin-orbit coupling strength, using muon-spin rotation and relaxation measurements. Transverse-field measurements made in the vortex state indicate that the superconductivity in both materials is fully gapped, with a conventional $s$-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. Zero-field measurements suggest a time-reversal symmetry preserved superconductivity in both the systems, though a small increase in muon depolarization is observed upon decreasing temperature. However, this has been attributed to quasistatic electronic fluctuations.

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.

Multigap superconductivity in the Mo5PB2 boron–phosphorus compound

The tetragonal Mo5PB2 compound was recently reported to show superconductivity with a critical temperature up to 9.2 K. In search of evidence for multiple superconducting gaps in Mo5PB2, comprehensive measurements, including magnetic susceptibility, electrical resistivity, heat capacity, and muon-spin rotation and relaxation measurements were carried out. Data from both low-temperature superfluid density and electronic specific heat suggest a nodeless superconducting ground state in Mo5PB2. Two superconducting energy gaps Δ0 = 1.02 meV (25%) and 1.49 meV (75%) are required to describe the low-T electronic specific-heat data. The multigap features are clearly evidenced by the field dependence of the electronic specific-heat coefficient and the Gaussian relaxation rate in the superconducting state (i.e., superfluid density), as well as by the temperature dependence of the upper critical field. By combining our extensive experimental results with numerical band-structure calculations, we provide compelling evidence of multigap superconductivity in Mo5PB2.

Information and Decoherence in a Muon-Fluorine Coupled System.

The unitary evolution of a quantum system preserves its coherence, but interactions between the system and its environment result in decoherence, a process in which the quantum information stored in the system becomes degraded. A spin-polarized positively charged muon implanted in a fluoride crystal realizes such a coherent quantum system, and the entanglement of muon and nearest-neighbor fluorine nuclear spins gives rise to an oscillatory time dependence of the muon polarization that can be detected and measured. Here we show that the decohering effect of more distant nuclear spins can be modelled quantitatively, allowing a very detailed description of the decoherence processes coupling the muon-fluorine "system" with its "environment," and allowing us to track the system entropy as the quantum information degrades. These results show how to precisely quantify the spin relaxation of muons implanted into quantum entangled states in fluoride crystals.

Theory of strain-induced magnetic order and splitting of Tc and TTRSB in Sr2RuO4

The internal structure of the superconducting state in Sr$_2$RuO$_4$ remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\rm TRSB}$ with applied strain [Grinenko et al., arXiv:2001.08152]. In addition, static magnetic order is induced by the uniaxial strain beyond $\sim$1 GPa, indicating that unstrained Sr$_2$RuO$_4$ is close to a magnetic quantum critical point. Here, we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. It is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain-dependence of accidentally degenerate pair states in unstrained Sr$_2$RuO$_4$. In addition, while unstrained Sr$_2$RuO$_4$ features mainly $(2\pi/3,2\pi/3)$ magnetic fluctuations, uniaxial strain promotes $(\pi,\pm\pi/2)$ magnetism.

Magnetic Properties of Pyrochlore Ruthenate Nd<sub>2</sub>Ru<sub>2</sub>O<sub>7</sub> Studied by μSr

We investigated the magnetic properties of pyrochlore ruthenates, R2Ru2O7, by using the muon spin relaxation (μSR) method. The appearance of a magnetically ordered state was confirmed below 145 K by observing the decrease in the initial asymmetry of the muon-spin polarization. This was due to a long-range ordering of Ru4+ spins. An additional anomaly in the μSR time spectrum was observed around 30 K. A part of the lost initial asymmetry was recovered and gradually decreases again with decreasing temperature below 30 K. This anomaly was supposed to be due to a magnetic ordering of Nd3+ spins which was coupled with ordered Ir moment via the 3d-4f exchange interaction.

Lithium diffusion in LiMnPO4 detected with μ±SR

The authors use a combination of positive and negative muon spin rotation and relaxation to investigate fluctuations of nuclear magnetic fields in an olivinetype Li-ion battery material.