Chapter 206 μSR studies of rare-earth and actinide magnetic materials

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

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.

Structural Transition with a Sharp Change in the Electrical Resistivity and Spin-Orbit Mott Insulating State in a Rhenium Oxide, Sr3Re2O9

We report the successful synthesis, crystal structure, and electrical properties of Sr₃Re₂O₉, which contains Re⁶⁺ with the 5d¹ configuration. This compound is isostructural with Ba₃Re₂O₉ and shows a first-order structural phase transition at ∼370 K. The low-temperature (LT) phase crystallizes in a hettotype structure of Ba₃Re₂O₉, which is different from that of the LT phase of Sr₃W₂O₉, suggesting that the electronic state of Re⁶⁺ plays an important role in determining the crystal structure of the LT phase. The structural transition is accompanied by a sharp change in the electrical resistivity. This is likely a metal-insulator transition, as suggested by the electronic band calculation and magnetic susceptibility. In the LT phase, the ReO₆ octahedra are rotated in a pseudo-a⁰a⁰a⁺ manner in Glazer notation, which corresponds to C-type orbital ordering. Paramagnetic dipole moments were confirmed to exist in the LT phase by muon spin rotation and relaxation measurements. However, the dipole moments shrink greatly because of the strong spin-orbit coupling in the Re ions. Thus, the electronic state of the LT phase corresponds to a Mott insulating state with strong spin-orbit interactions at the Re sites.

On the Robustness of the MnSi Magnetic Structure Determined by Muon Spin Rotation

Muon spin rotation ( μ SR) spectra recorded for manganese silicide MnSi and interpreted in terms of a quantitative analysis constrained by symmetry arguments were recently published. The magnetic structures of MnSi in zero-field at low temperature and in the conical phase near the magnetic phase transition were shown to substantially deviate from the expected helical and conical structures. Here, we present material backing the previous results obtained in zero-field. First, from simulations of the field distributions experienced by the muons as a function of relevant parameters, we confirm the uniqueness of the initial interpretation and illustrate the remarkable complementarity of neutron scattering and μ SR for the MnSi magnetic structure determination. Second, we present the result of a μ SR experiment performed on MnSi crystallites grown in a Zn-flux and compare it with the previous data recorded with a crystal obtained from Czochralski pulling. We find the magnetic structure for the two types of crystals to be identical within experimental uncertainties. We finally address the question of a possible muon-induced effect by presenting transverse field μ SR spectra recorded in a wide range of temperature and field intensity. The field distribution parameters perfectly scale with the macroscopic magnetization, ruling out a muon-induced effect.

Magnetism of the chromium thio-spinels Fe1-xCuxCr2S4 studied using muon spin rotation and relaxation

Powder samples of Fe1-xCuxCr2S4 with x = 0,0.2,0.5,0.8 were studied, between 5 and 300 K. The results reveal that for x < 1, the magnetic order in the series is more varied than the simple collinear ferrimagnetic structure traditionally assumed to exist everywhere from the Curie point to T → 0. In FeCr2S4 several ordered magnetic phases are present, with the ground state likely to have an incommensurate cone-like helical structure. Fe0.8Cu0.2Cr2S4 is the compound for which simple collinear ferrimagnetism is best developed. In Fe0.5Cu0.5Cr2S4 the ferrimagnetic spin structure is not stable, causing spin reorientation around 90 K. In Fe0.2Cu0.8Cr2S4 the ferrimagnetic structure is at low temperatures considerably distorted locally, but with rising temperature this disorder shows a rapid reduction, coupled to increased spin fluctuation rates. In summary, the present data show that the changes induced by the replacement of Fe by Cu have more profound influences on the magnetic properties of the Fe1-xCuxCr2S4 compounds than merely a shift of Curie temperature, saturation magnetization and internal field magnitude.

Low temperature incommensurately modulated and noncollinear spin structure in FeCr2S4

FeCr(2)S(4) orders magnetically at T(N)≈ 170 K. According to neutron diffraction, the ordered state down to 4.2 K is a simple collinear ferrimagnet maintaining the cubic spinel structure. Later studies, however, claimed trigonal distortions below ∼ 60 K coupled to the formation of a spin glass type ground state. To obtain further insight, muon spin rotation/relaxation (μSR) spectroscopy was carried out between 5 and 200 K together with new (57)Fe Mössbauer measurements. Below ∼ 50 K, our data point to the formation of an incommensurately modulated noncollinear spin arrangement like a helical spin structure. Above 50 K, the spectra are compatible with collinear ferrimagnetism, albeit with a substantial spin disorder on the scale of a few lattice constants. These spin lattice distortions become very large at 150 K and the magnetic state is now better characterized as consisting of rapidly fluctuating short-range ordered spins. The Néel transition is of second order, but ill defined, extending over a range of ∼ 10 K. The Mössbauer data around 10 K confirm the onset of orbital freezing and are also compatible with the noncollinear order of iron. The absence of a major change in the quadrupole interaction around 50 K renders the distortion of crystal symmetry to be small.

A New Basic Motif in Cyanometallate Coordination Polymers: Structure and Magnetic Behavior of M(μ-OH2)2[Au(CN)2]2 (M=Cu, Ni)

The structures of two cyanoaurate-based coordination polymers, M(mu-OH(2))(2)[Au(CN)(2)](2) (M=Cu, Ni), were determined by using a combination of powder and single-crystal X-ray diffraction techniques. The basic structural motif for both polymers contains rarely observed M(mu-OH(2))(2)M double aqua-bridges, which generate an infinite chain; two trans [Au(CN)(2)](-) units also dangle from each metal center. The chains form ribbons that interact three dimensionally through CNH hydrogen bonding. The magnetic properties of both compounds and of the dehydrated analogue Cu[Au(CN)(2)](2) were investigated by direct current (dc) and alternating current (ac) magnetometry; muon spin-relaxation data was also obtained to probe their magnetic properties in zero-field. In M(mu-OH(2))(2)[Au(CN)(2)](2), ferromagnetic chains of M(mu-OH(2))(2)M are present below 20 K. Interchain magnetic interactions mediated through hydrogen bonding, involving water and cyanoaurate units, yield a long-range magnetically ordered system in Cu(mu-OH(2))(2)[Au(CN)(2)](2) below 0.20 K, as indicated by precession in the muon spin polarization decay. Ni(mu-OH(2))(2)[Au(CN)(2)](2) undergoes a transition to a spin-glass state in zero-field at 3.6 K, as indicated by a combination of muon spin-relaxation and ac-susceptibility data. This transition is probably due to competing interactions that lead to spin frustration. A phase transition to a paramagnetic state is possible for Ni(mu-OH(2))(2)[Au(CN)(2)](2) upon application of an external field; the critical field was determined to be 700 Oe at 1.8 K. The dehydrated compound Cu[Au(CN)(2)](2) shows weak antiferromagnetic interactions at low temperatures.