Zero-field muon spin relaxation reflecting dynamics of spin glass

The muon spin relaxation function is calculated in a fluctuating random dilute spin system, and the effect of Edwards—Anderson's order parameter is considered in a time-dependent treatment. The results demonstrate the unique capability of zero-field μSR probing spin glasses.     

Zero-field muon spin rotation in monocrystalline chromium

Spin precession of positive muons in chromium in zero applied magnetic field is reported for the first time. The observations cover the temperature range from about 2.5 K to 10 K and thus pertain to the so-called longitudinal spin-density wave (LSDW) state of antiferromagnetic Cr. The conclusions that may be drawn from the existence of one rather sharp spin precession line are discussed, among them the estimateD _μ=2.4·10⁻¹⁴ m² s⁻¹ for the muon diffusivity at 4 K. Considerable evidence exists for a strong interactions of μ⁺ with the charge-density waves that are likely to accompany the LSDWs in Cr.     

Zero field spin relaxation studies as a probe of positive muon diffusion mechanisms

A theory of spin relaxation in zero external field is developed for a nonstationary distribution of diffusing particles. Application to μSR experiments in Nb and Bi is made to distinguish between models of muon diffusion in the presence of traps.     

Longitudinal muon spin relaxation in muonium-like systems

Nuclear spin-lattice relaxation in paramagnetic systems is treated using the classic expression for transition probability between the coupled electron and nuclear spin states. The rate equations governing the incoherent occupancies of these states are solved analytically (where possible) and numerically (where not) to construct the relaxation function for the nuclear spin. The method is illustrated for muonium, and the muonium-substituted molecular radicals, for the case of perturbation due to fluctuation of the local field,i.e. modulation of the interaction with a third spin. A slight departure from single exponential behaviour is demonstrated for slow fluctuations.     

Non-secular part of nuclear dipolar broadening detected by zero-field spin relaxation of positive muon

The zero-field spin relaxation function of μ⁺ observed in ZrH₂ has revealed that the second moment of the nuclear dipolar broadening is five times larger than the high-field value. This experiment clearly demonstrates the recovery of the non-secular part of dipolar interaction between unlike spins. A general expression of zero-field relaxation function is presented to account for a slow modulation of random fields on μ⁺ found at room temperature.     

Lattice relaxation around positive muon in copper

A model to study the local structure and geometry of condensed matter was applied to the lattice dilatation of Cu if a ⁺ is implanted interstitially. The model system consists of a finite cluster of atoms embedded in the spherically symmetric part of the potential of the rest of the material.The calculations were calibrated with crystalline Cu using a cluster of 6 atoms and 0, 6 or a practical infinite number of layers around this central cluster. It is found that 6 layers are enough to deseribe the boundary conditions that the material imposes to the selected central cluster.Afterwards it was applied to a cluster of a central ⁺ and 6 octahedrally disposed Cu. The equilibrium geometries, electronic configurations, electronic densities of states are presented and compared with SR.     

Zero field muon spin relaxation in simple magnets and spin glasses

A theory is developed for the calculation of zero field muon spin relaxation function for classical simple magnets (Ising, XY, and Heisenberg) in D(=1,2,3) dimensions. The results are different from the Kubo-Toyabe theory, except for Heisenberg system in three dimension. Relation between the relaxation function and random field distribution is dicussed and a new method of analysing experimental data is suggested and discussed in the context of spin glasses.     

Longitudinal muon spin relaxation in the organic metal polypyrrole

Longitudinal and zero field measurements of the muon spin relaxation function are reported for muons implanted in the conducting polymer polypyrrole. The observed muon relaxation can be accounted for by interaction with polaron excitations in the conducting polymer. Evidence is found for polaron localisation at temperatures below ∼ 50 K. The temperature dependence of the polaron mobility derived from the muon data is consistent with direct electrical conductivity measurements.     

Fast dynamization routine for muon spin relaxation functions

The calculation of dynamic relaxation functions is an essential ingredient for the analysis ofSR, spectra. So far no fastand memory efficient algorithm has been presented to cure this problem. The traditional method is the calculation of large, memory inefficient tables by means of either Monte Carlo simulation or numerical Laplace inversion. An alternate treatment within the strong collision model is presented making use of a Fourier transform.This work was supported by the German Federal Minister for Research and Technology (Bundesminister für Forschung und Technologie [BMFT]) under Contract Nr. 03KA2-TUM-4.     

Field dependence of the muon spin relaxation rate in MnSi

Muon spin rotation/relaxation measurements have been performed in the itinerant helical magnet MnSi at ambient pressure and at 8.3 kbar. We have found the following: (a) the spin-lattice relaxation rate 1/T(1) shows divergence as T1T proportional, variant (T-T(c))(beta) with the power beta larger than 1 near T(c); (b) 1/T(1) is strongly reduced in an applied external field B(L) and the divergent behavior near T(c) is completely suppressed at B(L)> or =4000 G. We discuss that (a) is consistent with the self-consistent renormalization theory and reflects a departure from "mean-field" behavior, while (b) indicates selective suppression of spin fluctuations of the q=0 component by B(L).     

Spin dynamics of geometrically frustrated spin systems observed by muon spin relaxation

μSR is shown to be a sensitive probe of fluctuating internal magnetic fields in geometrically frustrated magnets. The usefulness of μSR in these systems is illustrated in the case of pyrochlores, in which the antiferromagnetically coupled ions occupy a lattice of corner sharing tetrahedra. Remarkably, one observes a type of spin freezing in Y₂Mo₂O₇ and Tb₂Mo₂O₇ which is similar to that seen in conventional spin glasses, even though there is no detectable structural disorder. Unlike ordinary spin glasses these geometrically frustrated antiferromagnets display unusual low temperature spin dynamics which persist down to the lowest accessible temperatures.     

Spin dynamics in magnetic materials investigated by muon spin relaxation

We present a quantitative analysis of the temperature dependence of the muon spin relaxation rate measured in simple magnets. We consider the low temperature, critical and high temperature regimes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spin-glass dynamics determined from muon spin relaxation and neutron spin echo measurements

Muon spin relaxation (SR) and neutron spin echo (NSE) measurements of magnetic ion correlation times and correlation functions in the spin glass systemsCuMn,AgMn, andAuFe are compared. It is found that theSR and NSE measurements are in excellent agreement both above and below the spin-glass freezing temperatures. The experimental results are compared to recent theories of spin-glass dynamics.We are grateful to D.L. Huber and R.E. Walstedt for stimulating discussions. This work was performed under the auspices of the U.S. Department of Energy, and was also supported by the U.S. National Science Foundation, Grant No. DMR-8115543.     

Theory of muon spin relaxation by critical fluctuations in antiferromagnetic salts

Relaxation rates for positive muons implanted in antiferromagnetic salts are predicted on the basis of calculations performed with a coupled-mode theory of critical fluctuations in isotropic and uniaxial magnets. Anisotropy suppresses fluctuations transmitted by the isotropic (hyperfine) relaxation mechanism. The dipolar mechanism leads to a relaxation rate which increases on lowering the temperature to the critical point; the predicted form, proportional to the critical correlation length, yields the same temperature dependence as for the NMR linewidth. For a magnet with isotropic spin interactions, both contributions (hyperfine and dipolar) to the relaxation rate diverge with a temperature dependence given by the square-root of the correlation length.     

The effect of traps on the muon spin relaxation function

Summary In summary it is clear that SR in the presence of traps has led to a significant generalization of prior NMR theories of spin relaxation to include the effects of a non-stationary distribution of diffusing particles. In both the high field transverse geometry and in zero field it is possible to extract significant information regarding the concentrations and binding energies of traps, and, in the latter case, to unambiguously measure the temperature dependence of the relaxation rate to traps.At the same time it is also clear that significant problems still remain to be solved. Many of these are concerned with our present inadequate knowledge regarding the diffusion of muons in even pure materials, let alone the disordered systems upon which we have concentrated here. However, given the growth in our understanding of trapping phenomena over the past several years, it is probably not too much to hope that in another few years many of these present questions will also be answered.     

MuSR技术在凝聚态物理中的应用

缪子自旋弛豫/旋转(MuSR)实验技术利用缪子的自旋,在原子尺度上研究样品内部磁场的静态分布和动态涨落。文章介绍MuSR实验技术在凝聚态物理中的应用,阐述了MuSR在磁性、超导材料中发现的独特信息,包括磁有序、内部磁场分布、具有特定频率范围的自旋涨落,以及在半导体材料中获得杂质的电子状态和位置。这些应用表明 MuSR 对于理解关联电子材料复杂的物理现象及其物理机制具有重要意义。     

Longitudinal muon spin relaxation in organic radicals in the vapour phase

The aim of this work is the study of longitudinal field relaxation for organic radicals in the gas or vapour phase, for which the technique of Muon Spin Relaxation proves to be uniquely suitable. Following on from the first such study of the muonium substituted ethyl radical in gaseous ethene [1], the present work represents the beginning of a systematic study of species of various molecular symmetries and still higher molecular weight, with a view to investigating their collisional dynamics. Preliminary data for the muonium substituted cyclohexadienyl radical in benzene vapour, and the results of tests for radical formation in acetylene and carbon monoxide, are presented.     

Combination of muon spin relaxation and neutron scattering studies on magnetism

We combine the results from muon spin relaxation (μSR) and neutron scattering measurements performed on the same specimen (or system) of magnetic materials. The example on a spin glassCuMn (5%) shows that the two techniques have complementary time windows for studying dynamic spin fluctuations. In combining the results, one should note that muons and neutrons probe dynamic phenomena with different wavevectors. The results on antiferromagnetic La₂CuO_4−y illustrate the difference in the spatial range of static spin correlations reflected in the μSR precession frequency and the neutron Bragg peak intensity. With the examples of CeCu_2.1Si₂, YBa₂Cu₃O_x and Bi₂Sr₂YCu₂O_8+y , we point out that μSR is a superb tool for discovering static magnetic order while neutron scattering is the unique method to determine the spin structure. We emphasize that it is very fruitful to perform μSR and neutron experiments on the same specimen and to compare and combine the results for the better understanding of magnetism of various system.