Frequency shift and relaxation of muon-spin-precession in Cd1−xMnxTe

Transverse-field muon spin roation (μSR) is studied in Cd_1−xMn_xTe, x=0.4 and 0.6 mixed crystals. A large temperature dependent frequency shift and a strong relaxation of the μSR-signal are observed. In the vicinity of the spinglass transition, the relaxation rate becomes so large that the signal disappears. The rate of Mn spin fluctuations causing the μ⁺-line narrowing at high temperatures is estimated to be of the order of 10⁹ S⁻¹.     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

A μSR and neutron polarisation analysis study of Mn moment delocalisation in Fe substituted YMn2

Neutron polarisation analysis measurements reveal antiferromagnetic spin correlations persisting to temperatures of 120 K in Pauli paramagnetic Y(Mn_1−x Fe _x )₂, 0.03≤x≤0.05. The mean moment at the Mn(Fe) site is found to be 0.2μ _B. Transverse field μSR is characterised by weak exponential damping with a rate of 0.02 μs⁻¹ at 300 K increasing according to the power lawT ^−0.75 to only 0.16μ _S ⁻¹ at 12 K. It is suggested that these results are consistent with a slowing down of longitudinal spin fluctuations at the Mn site as temperature decreases.     

Addition and spin exchange rate constants by longitudinal field μSR: The Mu+NO reaction

The addition reaction Mu+NO+M→MuNO+M and the spin exchange reaction Mu(↑) +MO(↓)→Mu(↓)+NO(↑) have been measured by longitudinal field μSR at room temperature in the presence of up to 58 atm of N₂ as inert collider. The pressure dependence of the longitudinal relaxation rate due to the addition reaction (λ_c) demostrates that the system is still in the low pressure regime in this pressure range. The corresponding termolecular rate constant has been determined ask _0,Mu =(1.10±0.25)×10⁻³² cm⁶ molecules⁻² s⁻¹, almost 4 times smaller than the corresponding H atom reactionk _0,H=3.90×10⁻³² cm⁶ molecules⁻² s⁻¹ [I.M. Campbell et al., J. Chem. Soc. Faraday Trans. 1.71 (1975) 2097]. The average value of the spin exchange rate constants in the 2.5–58 atm pressure range,k _SE=(3.16±0.06)×10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, is in good agreement with previous values obtained by transverse field μSR [D.G. Fleming et al., J. Chem. Phys. 73 (1980) 2751].     

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.     

The superconducting properties of YBa2(Cu1−xMx)3O7 for M=Zn and Ni

Transverse and zero-field μSR measurements were made on YBa₂(Cu_1−xNi_x)₃O_7−y withx=0.1 and 0.2, and YBa₂(Cu_1−x Zn _x )₃O_7−y withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained, and the low temperature values of these are σ=3.2 μs⁻¹.1.6μs⁻¹, and 1 μs⁻¹ forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs⁻¹, 0.75 μs⁻¹, 0.65 μs⁻¹, and 0.4 μs⁻¹ forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made, but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect of scattering.     

Spin dynamics in Cd1−xMnx Te studied by muon spin rotation

Spin fluctuations in Cd_1−xMn_xTe (x=0.05, 0.10, 0.20, 0.30, 0.40, 0.54, 0.60, 0.68) were studied by the muon spin rotation (μSR) technique. Correlation times of the Mn-spins are deduced from the muon depolarization rates. A strong increase of the depolarization rate near the Mn-spin freezing temperature is observed. At 88 K, larger depolization rates are found forx=0.10 andx=0.20 than for higher Mn-concentrations, indicating that the exchange narrowing is considerably reduced (spin fluctuations slow down) for lower Mn-concentrations.     

Muons in type-II superconductors: μ+ diffusion in ultra-pure niobiumdiffusion in ultra-pure niobium

The diffusivityD _μ of positive muons (μ⁺) in the mixed state of superconducting high-purity, high-perfection niobium single crystals is investigated by measurements of the relaxation of the transverse muon spin polarization (μ⁺SR). The method makes use of the strong magnetic field gradients existing in the mixed state of Type-II superconductors and monitorsD _μ through the variation of the magnetic field felt by the μ⁺ during their diffusion through the crystals. For μ⁺ near the centres of the flux lines inNb it givesD _μ(4.6 K)=(8±2)·10⁻¹¹m²S⁻¹. The positive temperature coefficient ofD _μ indicates that at liquid-helium temperatures the diffusivity of μ⁺ inNb is mainly due to phonon-assisted tunnelling processes.     

μ− SR studies of oxide-superconductorsSR studies of oxide-superconductors

The negative muon spin rotation method (μ⁻ SR) has been applied to studies of electronic states at oxygen sites of oxide superconductors YBa₂Cu₃O₇, Nd_2−x Ce _x CuO_4−δ (x=0.15, oxygen reduced), LiTi₂O₄ and related oxide-insulators La₂CuO_4−δ, CuO, Cu₂O. The paramagnetic shifts of μ⁻ trapped at oxygen nuclei in these polycrystalline powder samples have been measured at 300 K. All the measured shifts are positive. In copper-oxides the paramagnetic shifts are of the order 10⁻³, while in LiTi₂O₄ is very small (8.4±3.34×10⁻⁵). In YBa₂Cu₃O₇, a fast μ⁻ spin relaxation timeT ₂ ^* (∼ 200 ns) has been observed; the reason for this is unknown and further studies are now in progress.     

μSR Study of the Unusual Magnetic Ordering in the Frustrated Antiferromagnet Zn(Cr x Ga1−x )2O4

μSR spectra on the spin frustrating spinel antiferromagnet Zn(Cr _x Ga_1−x )₂O₄ (x=0.9,1.0) have been measured. For x=1.0 compound, both the relaxation rate and the initial asymmetry showed distinct anomalies at the Néel temperature. The magnetic susceptibility for the x=0.9 compound was known to have a faint peak at around 12 K, whose origin was not clear so far. Our μSR study revealed that this temperature is the onset temperature of development of the magnetic correlation accompanied by appreciable spin fluctuations. This revised version was published online in September 2006 with corrections to the Cover Date.     

NMR and other magnetic resonance techniques in unstable magnets

This paper reviews and compares the use of nuclear magnetic resonance (NMR) and related hyperfine techniques [muon spin rotation (μSR) and, to a lesser extent, other methods] in the study of 4f and 5f magnetism in “unstable magnets”, i.e., intermediate-valent and heavy-fermion materials. In both NMR and μSR the features of interest are the spectral shape, the frequency shiftK (Knight shift in metals) and the spin-lattice relaxation rate 1/T ₁. For temperatures below the characteristic or “Kondo” temperatureT ₀ these experiments given evidence for (1) modification of the transferred hyperfine field [nonlinearK(χ)]. (2) spin fluctuations with a characteristic fluctuation rate ∼k _B T ₀/h, (3) strong energy-gap anisotropy (zeros of the gap along lines on the Fermi surface) in heavy-fermion superconductors, (4) spin-singlet Cooper pairing from the change in muon Knight shift in superconducting UBe₁₃, and (5) very weak static magnetism (10⁻¹–10⁻³ μ_B/f atom) in CeAl₃, CeCu₂Si₂, U_1−x Th _x Be₁₃ (x=0.033), and UPt₃. There is some controversy concerning the interpretation of 1/T ₁ well aboveT ₀ in UBe₁₃; the situation is reviewed.     

μSR on an induced‐moment spin glass system: Hg1-xFexSe

Zero and longitudinal field μSR have been used to examine the singlet ground state magnetism of the diluted magnetic semiconductor Hg_1-xFe_xSe. For x\geq 0.05\ μSR experiments indicate spin glass behaviour which is limited to sample regions with locally enhanced Fe²⁺ content. Longitudinal field spectra in the glassy state reveal a static local field \sim 50 mT due to induced moments of Fe²⁺. These are proposed to originate from a distribution of bound magnetic polaron energies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Negative muon spin precession in ferromagnetic iron and the hyperfine anomaly

The hyperfine field (B _μ ^hf ) at the negative muon μ⁻ in ferromagnetic iron was investigated by means of the zero-field μ⁻ spin precession technique. In the temperature range 320–690 K,B _μ ^hf for μ⁻ Fe departs from the magnetization curve of pure iron in the same way as the hyperfine field seen by a⁵⁵Mn impurity in dilute MnFe measured by NMR. The hyperfine anomaly for μ⁻ Fe relative to dilute (1.5 at.%)⁵⁵Mn in iron is found to be −0.9(3)% and temperature independent over the temperature range investigated.     

Interaction of Muons with H2/H3-Centres in Diamond

We report on transverse field muon spin rotation measurements on a nitrogen-rich type Ia diamond, both before and after the conversion of some of the aggregated nitrogen centres to nitrogen-vacancy complexes known as H2/H3-centres. The prompt fractions f and the spin relaxation rates λ were determined for the diamagnetic (μ_d) and the paramagnetic (Mu_T) states in the temperature range 10–300 K. The production of the nitrogen-vacancy complexes had little effect on the parameters of the Mu_T state for which f and λ remained unchanged at approximately 30% and 4 μs⁻¹, respectively. For the μ_d state, on the other hand, the formation of the H2/H3-centres resulted in an increase of the prompt fraction from 10(2)% to 20(3)%, and (for the first time) the spin relaxation rate showed a non-zero value of 0.020(3) μs⁻¹. These results show evidence of strong μ_d interactions with the nitrogen-vacancy complexes in diamond, and suggest a more complex structure for this state than a bare μ⁺. This revised version was published online in September 2006 with corrections to the Cover Date.     

μ + Knight shift and spin relaxation in indium single crystalKnight shift and spin relaxation in indium single crystal

μ ⁺ SR measurements have been performed in a single crystal indium sample between 12 K and 300 K with a stroboscopic μSR spectrometer. The muonic Knight shiftK _μ and the muonic depolarization rate σ were obtained for various angles θ between the tetragonal crystallinec-axis and the direction of the external field. The isotropic part ofK _μ is only weakly temperature dependent and is consistent with the estimated Pauli spin susceptibility value. At a temperature of 12 K the angular dependence ofM ₂ (the second moment of the field distribution at the muon, obtained from the measured σ(θ) values) allows a clear determination of the muon location — the symmetric tetrahedral site. The observed anisotropicK _μ cannot be explained by the dipoles at the In atoms responsible for the bulk magnetic susceptibility but probably originates from an anisotropic Pauli spin susceptibility.     

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu_2.1Si₂, the relaxation rate of muon spins increases rapidly with decreasing temperature below T_C. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5T_C, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift K_μ in the normal (or paramagnetic) state of various heavy-fermion systems. K_μ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu₂Si₂, UPt₃ and CeAl₃, while more complicated signals are measured in CePb₃ and CeB₆. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.     

A muon spin relaxation study of the magnetic ordering of (NH4)2FeCl5·H2O

We report muon spin relaxation (μSR) spectra from the antiferromagnetic salt (NH₄)₂FeCl₅· H₂O at various temperatures in the region of magnetic ordering (≈ 7 K). The μSR response includes an oscillatory time dependence of the forward-backward asymmetry over a small (≈ 0.4 K) but well-defined temperature interval. Analysis shows this to be consistent with the existence of two ordering temperatures. This confirms that a two-staged ordering is responsible for the two close-lying heat capacity cusps for this compound. It is further suggested that the two Fe spin systems associated with each of the ordering temperatures are closely intermingled rather than well separated in, for example, different domains. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spatial correlation study of internal magnetic fields in magnets by μSR2-technique

It is shown that using position-sensitive detectors in μSR experiments to determine the muon stopping site in a target permits one to study correlation effects in μSR time histograms produced by the decay of muons stopping in the same domain, i.e. to obtain time correlators of μSR histograms of decays from a small region. These correlators contain information on the spatial correlation of magnetic fields in the sample under study. The proposed method (μSR²-technique) allows measuring correlation radii (r _c ) down to 10⁻⁵ cm in a bulk sample. Among interesting physical phenomena occuring overr _c≥3×10⁻⁶ cm are, for instance, long wavelength fluctuations of the order parameter near the phase transition point in ferromagnets and antiferromagnets and magnetic field correlations in magnet domains and spin glasses. One may use this method also on heavy-current accelerators producing pulsed muon beams to investigate the variation in time of spatial correlations in magnets, spin glasses and superconductors.     

Spin-cluster effects and frustration in the uniaxial spin glass Fe2−xTi1+xO5

Transverse-field (TF) muon-spin-relaxation (μSR) and Mössbauer experiments on the uniaxial insulating spin glass Fe_2?xTi_1+xO₅ (x=0.25) have been performed near and below the spin-glass temperature (T _g). The effect of a transverse field on the spin-freezing process and spin-glass state has been investigated by measuring the field-and temperature-dependencies of the μSR parameters. Spin-cluster effects signaled by anomalous μ-spin relaxation have been observed in a temperature region just aboveT _g. An interpretation supported by recently developed theoretical models addressing non-linear relaxation in an intermediate Griffiths phase is offered.     

μ− SR in semiconductorsSR in semiconductors

μ⁻ SR experiments have been performed on Si between room temperature and 6 K. The amplitude of the muon spin precession signal in an applied magnetic field of 0.04 T decreased below 30 K. A zero-field measurement at 6 K revealed a μ⁻ spin precession frequency of 650 MHz. The muonic atom represents an aluminium acceptor in the silicon matrix, its electronic state is responsible for the μSR signal. A possible influence of the γ recoil produced by the X-ray cascade is discussed.