Positive Muon Spin Relaxation Research Articles

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.

Evidence of Spin Density Waves in La_{3}Ni_{2}O_{7-δ}.

The recently discovered superconductivity with critical temperature T_{c} up to 80K in the double-layer Nickelate La_{3}Ni_{2}O_{7-δ} under pressure has drawn great attention. Here, we report the positive muon spin relaxation (μ^{+}SR) study of polycrystalline La_{3}Ni_{2}O_{6.92} under ambient pressure. Zero-field μ^{+}SR experiments reveal the existence of magnetic order in La_{3}Ni_{2}O_{6.92} with T_{N}=154 K. The weak transverse field μ^{+}SR measurements reveal the bulk nature of magnetism. In addition, a small quantity of oxygen deficiencies can greatly broaden the internal magnetic field distribution sensed by muons.

Operando Muon Spin Rotation and Relaxation Measurement on LiCoO2 Half-Cell

The self-diffusion coefficient of Li+ ions (DLiJ) in LixCoO2 has been determined during charge and discharge reactions of a LiCoO2 half-cell using a positive muon spin rotation and relaxation (μ+SR) technique through the observation of the fluctuating nuclear magnetic field at room temperature: specifically, with an operando μ+SR technique in the half-cell potential range between 3.0 and 4.7 V. The estimated DLiJ was found to range between 10–12 and 10–11 cm2/s and increase as Li content (x) decreased. Although the slope (dDLiJ/dx) was relatively steep below the vicinity of x = 1, DLiJ slowly increases with decreasing x at x < 0.8 with two small minima at x ∼ 2/3 and x ∼ 1/2. The obtained result in the initial charging process agreed with that obtained in the second charging process. Furthermore, it was discovered that the change in DLiJ with x is similar to that of the reported self-diffusion coefficient estimated using an electrochemical technique for a film sample. By combining with the electrochemical measurement, the x dependence of the reactive surface area of the LixCoO2 electrode was first determined, while it was assumed to be independent of x.

Co-existence of short- and long-range magnetic order in LaCo2P2

The ferromagnetic (FM) nature of the metallic LaCo2P2 was investigated with the positive muon spin rotation, relaxation and resonance (μ +SR) technique. Transverse and zero field μ + SR measurements revealed that the compound enters a long range FM ground state at K, consistent with previous studies. Based on the reported FM structure, the internal magnetic field was computed at the muon sites, which were predicted with first principles calculations. The computed result agree well with the experimental data. Moreover, although LaCo2P2 is a paramagnet at higher temperatures T > 160 K, it enters a short range ordered (SRO) magnetic phase for K. Measurements below the vicinity of revealed that the SRO phase co-exists with the long range FM order at temperatures 124 K . Such co-existence is an intrinsic property and may be explained by an interplay between spin and lattice degree of freedoms.

Na Diffusion in Hard Carbon Studied with Positive Muon Spin Rotation and Relaxation.

The diffusive nature of Na+ in Na-inserted hard carbon (C x Na), which is the most common anode material for a Na-ion battery, was studied with a positive muon spin rotation and relaxation (μ+SR) technique in transverse, zero, and longitudinal magnetic fields (TF, ZF, and LF) at temperatures between 50 and 375 K, where TF (LF) denotes the applied magnetic field perpendicular (parallel) to the initial muon spin polarization. At temperatures above 150 K, TF-μ+SR measurements showed a distinct motional narrowing behavior, implying that Na+ begins to diffuse above 150 K. The presence of two different muon sites in C x Na was confirmed with ZF- and LF-μ+SR measurements; one is in the Na-inserted graphene layer, and the other is in the Na-vacant graphene layer adjacent to the Na-inserted graphene layer. A systematic increase in the field fluctuation rate (ν) with increasing temperature also evidenced a thermally activated Na diffusion, particularly above 150 K. Assuming the two-dimensional diffusion of Na+ in the graphene layers, the self-diffusion coefficient of Na+ (D Na J) at 300 K was estimated to be 2.5 × 10-11 cm2/s with a thermal activation energy of 39(7) meV.

How Li diffusion in spinel Li[Ni1/2Mn3/2]O4 is seen with μ ±SR

Abstract The diffusive behavior in a spinel-type Li+ ion battery material, Li[Ni1/2Mn3/2]O4, has been studied with positive and negative muon spin rotation and relaxation (μ ±SR) measurements in the temperature range between 200 and 400 K using a powder sample. The implanted μ + locates at an interstitial site near O2− ion so as to form a O–H like bond, while the implanted μ − is mainly captured by an oxygen nucleus, resulting in the formation of muonic oxygen. This means that local magnetic environments in Li[Ni1/2Mn3/2]O4 were investigated from the two different sites in the lattice, i.e., one is an interstitial site for μ +SR and the other is an oxygen site for μ −SR. Since both μ +SR and μ −SR detected an increase in the fluctuation rate of a nuclear magnetic field for temperatures above 200 K, the origin of this increase is clearly confirmed as Li diffusion. Assuming a random walk process with the hopping of thermally activated Li+ between a regular Li site and the nearest neighboring vacant octahedral sites, a self-diffusion coefficient of Li+ was found to range above 10−11 cm2/s at temperatures above 250 K with an activation energy of about 0.06 eV.

Positive and Negative Muon Spin Rotation and Relaxation

Although a positive muon spin rotation and relaxation (μ+SR) technique is commonly used for materials science, its counterpart technique, μ-SR, has been less common due to its very limited availability and a very slow counting rate. However, a combination between an intense pulsed muon beam, such as, J-PARC and ISIS, and the development of a multi-channel counter system enables us to utilize μ-SR for studying a small nuclear magnetic field in solids. Here, we summarize the advantage and disadvantage of the two μSR techniques and propose μ±SR as a novel tool to identify diffusing species and clarify the ion diffusive nature in battery materials.

Pressure dependence of ferromagnetic phase boundary in BaVSe3 studied with high-pressure μ+SR

The magnetic nature of a quasi-one-dimensional compound, ${\mathrm{BaVSe}}_{3}$, has been investigated with positive muon spin rotation and relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) measurements at ambient and high pressures. At ambient pressure, the ${\ensuremath{\mu}}^{+}\mathrm{SR}$ spectrum recorded under zero external magnetic field exhibited a clear oscillation below the Curie temperature (${T}_{C}\ensuremath{\sim}41\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) due to the formation of quasistatic ferromagnetic order. The oscillation consisted of two different muon spin precession signals, indicating the presence of two magnetically different muon sites in the lattice. However, the two precession frequencies, which correspond to the internal magnetic fields at the two muon sites, could not be adequately explained with relatively simple ferromagnetic structures using the muon sites predicted by density functional theory calculations. The detailed analysis of the internal magnetic field suggested that the V moments align ferromagnetically along the $c$ axis but slightly canted toward the $a$ axis by ${28}^{\ensuremath{\circ}}$ that is coupled antiferromagnetically. The ordered V moment (${\mathbit{M}}_{\mathrm{V}}$) is estimated as (0.59, 0, 1.11) ${\ensuremath{\mu}}_{\mathrm{B}}$. As pressure increased from ambient pressure, ${T}_{C}$ was found to decrease slightly up to about 1.5 GPa, at which point ${T}_{C}$ started to increase rapidly with the further increase of the pressure. Based on a strong ferromagnetic interaction along the $c$ axis, the high-pressure ${\ensuremath{\mu}}^{+}\mathrm{SR}$ result revealed that there are two magnetic interactions in the $ab$ plane; one is an antiferromagnetic interaction that is enhanced with pressure, mainly at pressures below 1.5 GPa, while the other is a ferromagnetic interaction that becomes predominant at pressures above 1.5 GPa.

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.

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.

Muon Spectroscopy for Investigating Diffusion in Energy Storage Materials

We review recent applications of positive muon spin relaxation (μSR) spectroscopy as an active probe of ion diffusion in energy storage materials. μSR spectroscopy allows the study of ionic diffusion in solid-state materials on a time scale between 10−5 and 10−8 s where most long-range and consecutive short-range jumps of ions between interstitial sites occur. μSR also allows one to probe and model ionic diffusion in materials that contain magnetic ions, since both electronic and nuclear contributions to the muon depolarization can be separated, making μSR an excellent technique for the microscopic study of the ionic motions in crystalline materials. We highlight a series of battery materials for which μSR has provided insight into intrinsic ionic conduction and magnetic properties without interference of external factors, such as the presence of magnetic ions, macroscopic particle morphologies, or elaborate measurement setups.

Magnetic phase boundary of BaVS3 clarified with high-pressure μ+SR

The magnetic nature of the quasi-one-dimensional BaVS3 has been studied as a function of temperature down to 0.25 K and pressure up to 1.97 GPa on a powder sample using the positive muon spin rotation and relaxation (mu(+) SR) technique. At ambient pressure, BaVS3 enters an incommensurate antiferromagnetic ordered state below the Neel temperature (T-N)31 K. T-N is almost constant as the pressure (p) increases from ambient pressure to 1.4 GPa, then T-N decreases rapidly for p > 1.4 GPa, and finally disappears at p similar to 1.8 GPa, above which a metallic phase is stabilized. Hence, T-N is found to be equivalent to the pressure-induced metal-insulator transition temperature (T-MI) at p > 1.4 GPa.

Spin polarized beam for battery materials research: µ±SR and ß-NMR

Spin polarized particles exhibiting beta decay, such as, muon and 8Li are very useful for detecting internal magnetic fields in solids. Here, I review our attempts to use these spin polarized beams for battery materials research. Due to a unique lifetime and gyromagnetic ratio of muon, a positive muon spin rotation and relaxation (µ+SR) technique is very popular for studying microscopic internal magnetic fields in condensed matters caused by electron and nuclear magnetism. Particularly in 2009, it was found that Li+ ion diffusion in LixCoO2, which is the most common cathode material in a Li-ion battery, is detectable with µ+SR even under the presence of paramagnetic Co ions (Sugiyama et al., Phys. Rev. Lett. 103, 147601, 2009), while NMR is unable to do so due to the effect of localized magnetic moments on a spin-lattice relaxation rate. Such finding opened the door for µ+SR on energy materials research. Since then, many battery materials have been investigated with µ+SR in order to determine their intrinsic diffusion coefficient (D) of Li+ and Na+ ions. Furthermore, using such intrinsic D, the other important parameters are successfully derived, such as, the reactive surface area, diffusion pathway, and density of mobile ions. In 2018, we have initiated to measure internal magnetic fields in solids with a negative muon, i.e. a µ-SR technique, in J-PARC (Sugiyama et al., Phys. Rev. Lett. 121, 087202, 2018). This will provide a new insight for microscopic internal magnetic fields from lattice sites, while µ+SR does so from interstitial sites. On the contrary, a long lifetime of 8Li (1.21 s) makes a 8Li s-NMR technique suitable for detecting both concentration and diffusion of Li in solids. Particularly in TRIUMF, since the implantation energy of 8Li is tunable from almost 0 to about 28 keV, we can measure both spin-lattice relaxation rate and spin-spin relaxation rate as a function of depth up to about 200 nm, as well as µ+SR using a low energy muon beam in PSI. These will clarify whether the space charge layer of Li+ exists at the interface between electrode and electrolyte material.

Muon contact hyperfine field in metals: A DFT calculation

In positive muon spin rotation and relaxation spectroscopy it is becoming nowadays customary to take advantage of Density Functional Theory (DFT) based computational methods to aid the experimental data analysis. DFT aided muon site determination is especially useful for measurements performed in magnetic materials, where large contact hyperfine interactions may arise. Here we present a systematic analysis of the accuracy of the ab initio estimation of muon's hyperfine contact field on elemental transition metals, performing state of the art spin-polarized plane wave DFT and using the projector augmented pseudopotential approach, which allows to include the core state effects due to the spin ordering. We further validate this method in not-so-simple, non-centrosymmetric metallic compounds, presently of topical interest for their spiral magnetic structure giving rise to skyrmion phases, such as MnSi and MnGe. The calculated hyperfine fields agree with experimental values in all cases, provided the spontaneous spin magnetization of the metal is well reproduced within the approach. To overcome the known limits of the conventional mean field approximation of DFT on itinerant magnets, we adopt the so-called reduced Stoner theory [L. Ortenzi et al.,Phys. Rev. B 86, 064437 (2012)]. We establish the accuracy of the estimated muon contact field in metallic compounds with DFT and our results show improved agreement with experiments compared to those of earlier publications.

Excited configurations of hydrogen in the BaTiO3−xHx perovskite lattice associated with hydrogen exchange and transport

Excited configurations of hydrogen in the oxyhydride BaTiO$_{3-x}$H$_x$ ($x=0.1-0.5$), which are considered to be involved in its hydrogen transport and exchange processes, were investigated by positive muon spin relaxation ($\mu^+$SR) spectroscopy using muonium (Mu) as a pseudoisotope of hydrogen. Muons implanted into the BaTiO$_{3-x}$H$_x$ perovskite lattice were mainly found in two qualitatively different metastable states. One was assigned to a highly mobile interstitial protonic state, which is commonly observed in perovskite oxides. The other was found to form an entangled two spin-$\frac{1}{2}$ system with the nuclear spin of an H$^-$ ion at the anion site. The structure of the (H,Mu) complex agrees well with that of a neutralized center containing two H$^-$ ions at a doubly charged oxygen vacancy, which was predicted to form in the SrTiO$_{3-\delta}$ perovskite lattice by a computational study [Y. Iwazaki $et$ $al$., APL Materials 2, 012103 (2014)]. Above 100 K, interstitial Mu$^+$ diffusion and retrapping to a deep defect were observed, which could be a rate-limiting step of macroscopic Mu/H transport in the BaTiO$_{3-x}$H$_x$ lattice.

Anomalously slow spin dynamics and short-range correlations in the quantum spin ice systemsYb2Ti2O7andYb2Sn2O7

We report a positive muon spin relaxation and rotation (\muSR) study of the quantum spin ice materials Yb2Ti2O7 and Yb2Sn2O7 focusing on the low field response. In agreement with earlier reports, data recorded in small longitudinal fields evidence anomalously slow spin dynamics in the microsecond range below the temperature T_c at which the specific heat displays an intense peak, namely T_c = 0.24 K and 0.15 K, respectively, for the two systems. We found that slow dynamics extends above T_c up to at least 0.7 K for both compounds. The conventional dynamical Gaussian Kubo-Toyabe model describes the \muSR spectra recorded above T_c. At lower temperatures a published analytical extension of the Gaussian Kubo-Toyabe model provides a good description, consistent with the existence of short-range magnetic correlations. While the physical response of the two systems is qualitatively the same, Yb2Ti2O7 exhibits a much larger local magnetic susceptibility than Yb2Sn2O7 below T_c. Considering previously reported ac susceptibility, neutron scattering and \muSR results, we suggest the existence of anomalously slow spin dynamics to be a common physical property of pyrochlore magnetic materials. The possibility of molecular spin substructures to be associated to the slow dynamics and therefore the short-range correlations is mentioned. The slow spin dynamics observed under field does not exclude the presence of much faster dynamics detected in extremely low or zero field.

Core-shell nanostructure in aGe0.9Mn0.1film observed via structural and magnetic measurements

We have characterized a film of Ge_0.9Mn_0.1 forming self-organized nanocolumns perpendicular to the Ge substrate with high resolution scanning transmission electron microscopy combined with electron energy loss spectroscopy, and bulk magnetization and positive muon spin rotation and relaxation (muSR) measurements. The Mn-rich nanocolumns form a triangular lattice with no detectable Mn atoms in the matrix. They consist of cores surrounded by shells. The combined analysis of bulk magnetization and muSR data enables us to characterize the electronic and magnetic properties of both the cores and shells. The discovered phase separation of the columns between a core and a shell is probably relevant for other transition-metal doped semiconductors.

Magnetic order in the 2D Heavy-Fermion system CePt2In7 studied by μ+SR

The low-temperature microscopic magnetic properties of the quasi-2D heavy- fermion compound, CePt2In7 are investigated by using a positive muon-spin rotation and relaxation (μ+SR) technique. Clear evidence for the formation of a commensurate antiferromagnetic order below TN ≈ 5.40 K is presented. The magnetic order parameter is shown to fit well to a modified BCS gap-energy function in a strong-coupling scenario.

Li diffusive behavior of garnet-type oxides studied by muon-spin relaxation and QENS

A diffusive behavior of Li+ ion in a garnet-type oxide, Li5 + xLa3ZrxNb2 − x012 with x = 0–2, has been investigated by both a positive muon-spin relaxation (μ+SR) and quasi-elastic neutron scattering (QENS) technique using powder samples. The μ+SR results revealed that Li+ ions start to diffuse above ~ 150 K for the whole samples measured. The activation energy of Li diffusion (Ea) estimated from the μ+SR data was in good agreement with Ea obtained by the QENS measurements. However, both Eas were about a half of Ea of ionic conductivity of Li+ (σLi), which was evaluated by AC-impedance measurements on sintered pellets. This indicated the serious effect of grain boundary and/or surface on Ea. Furthermore, since the diffusion coefficient of Li+ estimated by μ+SR is roughly independent of x, the number of mobile Li+ in the garnet lattice was found to be the predominant parameter to determine σLi.

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${}^{\ensuremath{-}1}$.