Muon Relaxation Rate Research Articles

μSR and low-temperature antiferromagnetism in the ordered non-Fermi-liquid compound YbRh 2Si 2

Muon spin relaxation experiments have been carried out at low temperatures in the non-Fermi-liquid heavy-fermion compound YbRh 2Si 2, to study antiferromagnetism in the vicinity of the quantum critical point T=0, H≈600 Oe . The zero-field muon relaxation rate is found to be independent of temperature down to 100 mK , but increases substantially below ∼70 mK , indicative of the onset of static magnetism. The estimated internal field at a muon stopping site is ∼2 Oe , which suggests a very small ordered moment ( μ ord≈10 −3–10 −2 μ B).

μSR and NMR in f-electron non-Fermi liquid materials

Magnetic resonance (μSR and NMR) studies of f-electron non-Fermi-liquid (NFL) materials give clear evidence that structural disorder is a major factor in NFL behavior. Longitudinal-field μSR relaxation measurements at low fields reveal a wide distribution of muon relaxation rates and divergences in the frequency dependence of spin correlation functions in the NFL systems UCu 5− x Pd x and CePtSi 1− x Ge x . These divergences seem to be due to slow dynamics associated with quantum spin-glass behavior, rather than quantum criticality as in a uniform system, for two reasons: the observed strong inhomogeneity in the muon relaxation rate, and the strong and frequency-dependent low-frequency fluctuation observed in U(Cu,Pd) 5 and CePt(Si,Ge). In the NFL materials CeCu 5.9Au 0.1, Ce(Ru 0.5Rh 0.5) 2Si 2, CeNi 2Ge 2, and YbRh 2Si 2 the low-frequency weight of the spin fluctuation spectrum is much weaker than in the disordered NFL systems.

High frequency measurements at a pulsed muon source: beating the pulse width!

The pulsed nature of the ISIS beam is advantageous for many types of experiments. Limitations arise, however, because the finite width of the muon pulse restricts the maximum muon precession frequency and relaxation rate that can be measured. This paper considers two methods currently under development at ISIS that can be used to extend the upper frequency limit at a pulsed muon source. Firstly, a technique using a fast switching electrostatic kicker to time slice the incoming muon pulse is described. Data is presented that demonstrates the effective manner in which the μSR usable frequency response at ISIS is increased in inverse proportion to the pulse width. The second technique uses a 90° radio-frequency (RF) pulse to remove the time structure of the pulsed beam; this method is demonstrated by studying the flux penetration in the mixed state in the type II superconductor YNi 2B 2C. The merits of both techniques are considered and contrasted.

Quasicritical behaviour of the nuclear magnetic resonance and muon spin-rotationrelaxation in cubic ferromagnets and antiferromagnets

A theoretical model describing quasicritical behaviour ofthe nuclear magnetic resonance (NMR) relaxation rates1/T1,1/T2 and muonrelaxation rate λfor cubic ferromagnets and antiferromagnets with spin fluctuations is presented.The model extends and generalizes the model of Moriya and explains why theobserved experimental values of the critical exponents are different from thevalues predicted by the theory of critical phenomena. The formulae for therelaxation rates obtained from this model are used for fitting to the experimentalNMR data for YMn2Dx, TbMn2D2 and the muon spin-rotation (μ SR)data for YMn2, YMn2Dx, GdMn2 and Y(Co1−xAlx)2 (ferromagnetic). It is shownthat the dependence of the exchange coupling constant on the wavevector k isimportant for understanding the observed quasicritical effects.

μSR studies on the charge density waves in RE 5Ir 4Si 10

The series of intermetallic compounds RE 5Ir 4Si 10 (RE=rare-earth) shows unusual charge density wave (CDW) order for temperatures lower than 160 K . This work presents a muon spin rotation (μSR) study, in zero external field, on single crystalline samples of the magnetic Er 5Ir 4Si 10 ( T CDW=155 and 55 K ) and polycrystalline samples of Er 5Ir 4Ge 10 (no CDW). The muon relaxation rate λ is strongly temperature dependent in both compounds. Furthermore, upon cooling below the CDW transition temperatures, a kink is seen in λ in Er 5Ir 4Si 10. We interpret this result as a signature of the change in the density of states due to the establishment of the CDW.

Non-Fermi-liquid spin dynamics in CeCoGe3-xSi(x) for x = 1.2 and 1.5.

Muon spin relaxation has been measured in CeCoGe3-xSi(x) at the magnetic/nonmagnetic boundary compositions of x = 1.2 and x = 1.5. Both the alloys are found to exhibit an ordered region and a disordered region. At x = 1.2, short-range magnetic ordering is observed below 0.86 K in the ordered region. The disordered region is paramagnetic and the muon spin-lattice relaxation rate lambda2 in this region displays non-Fermi-liquid (NFL) spin dynamics, i.e., the power law lambda2 proportional to T0.72 which shows the formation of Griffiths phase. lambda2 in the x = 1.5 alloy displays logarithmic (NFL) scaling below 1 K, in agreement with the theory of a T = 0 K magnetic transition.

Staggered magnetization, critical behavior, and weak ferromagnetic properties ofLaMnO3by muon spin rotation

We present a study of a microtwinned single crystal of ${\mathrm{LaMnO}}_{3}$ by means of implanted muons. Two muon stopping sites are identified from the symmetry of the internal field in the ordered phase. The temperature dependence of these fields yields the behavior of the staggered magnetization, from which a static critical exponent $[\ensuremath{\beta}=0.36(2)]$ is extracted and discussed. The muon spin-spin relaxation rate shows a critical slowing down (contrary to preliminary findings), with a critical exponent $n=0.7(1),$ demonstrating the Ising nature of the dynamic fluctuations. The muon precession frequencies vs the applied magnetic field reveal the saturation of the weak ferromagnetic domain structure originated by the Dzialoshinski-Moriya antisymmetric exchange.

Muon spin rotation and non-Fermi liquid behavior in UCu 4Pd

Muon spin rotation and relaxation (μSR) experiments have been carrried out on the non-Fermi liquid (NFL) heavy-fermion compound UCu 4Pd. Transverse-field μSR line widths indicate that the U-ion susceptibility is inhomogeneous and in good agreement with predictions of disorder-driven NFL mechanisms. The inhomogeneity seems to be remarkably independent of the exact amount of structural disorder. Longitudinal-field experiments yield muon spin-lattice relaxation rates which are two orders of magnitude faster than estimates from a single-ion ‘Kondo disorder’ model. This suggests a cooperative rather than a single-ion NFL mechanism. No evidence is found for freezing of more than a few percent of U-ion moments in UCu 4Pd above 100 mK.

A μSR study of the magnetic properties of CeAgSb 2

Zero and longitudinal field muon spin relaxation measurements have been performed on the Kondo lattice system CeAgSb 2 in the magnetically ordered ( T<10 K) and paramagnetic ( T>10 K) states. The resulting spectra are consistent with a single muon site which senses a unique coherent internal field of 53 mT at low temperatures and dynamic atomic fields, arising from extremely rapid RKKY-dominated paramagnetic fluctuations of the Ce 3+ spins, at higher temperatures. Small stepwise increases in the temperature dependence of the muon relaxation rate at 60 and 17 K appear to be coincident with the Kondo temperature and the onset of coherence, respectively.

Muon sites and diffusion in doped lithium oxide

We present muon-spin relaxation results for pure and doped lithium oxide, and deduce the muon site and the diffusion rates. Samples were doped with fluoride and hydroxide ions both of which carry a nuclear moment. These ions with charge −e substitute in place of an oxide ion with charge −2e, so must be accompanied by a corresponding vacancy on the Li + sublattice. The static muon relaxation rate is the same in all samples, showing that the muons are not trapped at or near the anion impurity sites. Muons occupy Li + vacancy sites at around 150 K and this suggests that the vacancies and anion impurities are well separated. The variation of hop rate with temperature is also almost identical for all the samples. This suggests that the impurities do not play any role in the hopping mechanism at this length scale. The doped samples show a significantly larger diamagnetic muon fraction than the pure material, probably a result of differences in electron mobility.

Muon spin relaxation and nonmagnetic Kondo state inPrInAg2

Muon spin relaxation experiments have been carried out in the Kondo compound ${\mathrm{PrInAg}}_{2}.$ The zero-field muon relaxation rate is found to be independent of temperature between 0.1 and 10 K, which rules out a magnetic origin (spin freezing or a conventional Kondo effect) for the previously observed specific-heat anomaly at $\ensuremath{\sim}0.5 \mathrm{K}.$ At low temperatures the muon relaxation can be quantitatively understood in terms of the muon's interaction with nuclear magnetism, including hyperfine enhancement of the ${}^{141}\mathrm{Pr}$ nuclear moment at low temperatures. This argues against a ${\mathrm{Pr}}^{3+}$ ground-state electronic magnetic moment, and is strong evidence for the doublet ${\ensuremath{\Gamma}}_{3}$ crystalline-electric-field-split ground state required for a nonmagnetic route to heavy-electron behavior. The data imply the existence of an exchange interaction between neighboring ${\mathrm{Pr}}^{3+}$ ions of the order of 0.2 K in temperature units, which should be taken into account in a complete theory of a nonmagnetic Kondo effect in ${\mathrm{PrInAg}}_{2}.$

Muon spin relaxation in Re-substitutedHgA2Can−1CunO2n+2+x(A=Sr,Ba;n=2,3)superconductors

The muon relaxation rate \ensuremath{\sigma} for the Re-substituted ${\mathrm{HgSr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{6+y}$ and ${\mathrm{HgBa}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{8+y}$ superconductors has been measured as a function of temperature. The low-temperature values of \ensuremath{\sigma} fall close to the universal Uemura line ${T}_{c}(\ensuremath{\sigma}),$ as observed for other layered superconductors; therefore our data show no evidence of a reduced anisotropy, i.e., interlayer metallization, induced by Re. The in-plane penetration depth values obtained for these 1212 and 1223 compounds are found to be significantly different $(\ensuremath{\lambda}=1665\AA{}$ and $\ensuremath{\lambda}=1310\AA{},$ respectively). The roles of the inserted ${\mathrm{CuO}}_{2}$ planes, the Ba/Sr substitution and the character of the spacing layers are considered to discuss the observed features.

Charge localization and magnetic dynamics in ferromagnetic and charge-ordered manganites

The local spin dynamics in the paramagnetic phase of ferromagnetic and charge-ordered Mn perovskites has been investigated by muon spin relaxation. Significant differences are observed in the muon relaxation in ferromagnetic (F) and antiferromagnetic (AF) Ln1−xCaxMnO3 samples with x=1/3 and 1/2. A glassy like spin dynamics is found close to TC in the former which is completely suppressed in samples with dominant AF exchange interactions. The observation of a falloff in the muon relaxation rate at TCO in Ln1/2Ca1/2MnO3 is also discussed.

Proton NMR and μSR inMn12O12acetate: A mesoscopic magnetic molecular cluster

The spin dynamics of Mn spins in the dodecanuclear manganese cluster of formula [Mn{sub 12}O{sub 12}(CH{sub 3}COO){sub 16}(H{sub 2}O){sub 4}]{center_dot}2CH{sub 3}-COOH{center_dot}4H{sub 2}O(Mn{sub 12}) has been investigated by {sup 1}HNMR and muon spin-lattice relaxation rate 1/T{sub 1} as a function of temperature (10{endash}400 K) and external magnetic field (0{endash}9.4 T). At room temperature, the proton 1/T{sub 1} depends on the measuring frequency. The results can be interpreted in terms of a slow decay of the Mn electronic-spin autocorrelation function, a feature characteristic of the almost zero dimensionality of the system. As the temperature is lowered, 1/T{sub 1} displays a critical enhancement that can be related to the slowing down of the local spin fluctuations as the cluster approaches the condensation into the total spin S=10 ground-state configuration. It is found that the application of an external magnetic field greatly depresses the enhancement of 1/T{sub 1} an effect that could be related to the superparamagnetic behavior of the Mn{sub 12} molecule. {copyright} {ital 1998} {ital The American Physical Society}

μSR on the novel heavy‐fermion system Nd 2-y Ce y CuO 4

The magnetic correlations in Nd2-yCeyCuO4 have been studied by zero and longitudinal field μSR. Nd1.8Ce0.2CuO4 reveals a saturation of the muon relaxation rate below 0.5 K. Even down to 70 mK LF spectra evidence spin fluctuations in the dynamic regime with a rate of \sim 109 s-1 excluding long range magnetic order or spin glass freezing. The average Nd moment is estimated to be \approx 0.2\muB, i.e., strongly reduced from the value determined for the ground state Kramers doublet of Nd2CuO4. Extending former μSR measurements on Nd2CuO4, a gradual enhancement of the internal field has been detected below 10 K which is accompanied by an increase of the relaxation rate. These results are attributed to the development of ordered Nd moments.

μSR study of intermediate heavy fermion system CeRuSi2

ZF, LF and TF μSR measurements have been carried out with a polycrystalline CeRuSi2 sample. ZF data show a sharp increase of the muon relaxation rate below the temperature T=12 K (0.42 μ s-1 at T=4.2 K) justifying the phase transition to the magnetically ordered state. The results of LF measurements at T=4.2 K show that the magnetic fields on the muon Bμ, produced by the cerium magnetic moments, are mainly static – external longitudinal field of 150 Oe practically recovers the muon spin polarization. In the paramagnetic phase the polarization decay has an exponential form at all measured temperatures 20 K < T < K, though LF experiment at T=20 K clearly shows a significant static contribution (\sim 75%). This situation is discussed in frames of double relaxation model. The ferromagnetic type of magnetic ordering was proved by hysteresis behavior of (B–H) observed in TF‐experiment.

Spin dynamics in the reentrant spin glass (Fe 0:65 Ni 0:35 ) 1 x Mn x

The spin dynamics in the reentrant spin glass ( Fe0.65 Ni0.35)1-x Mn_x has been studied by zero, longitudinal and transverse field μSR. In the ferromagnetic reentrant and pure spin glass regimes (x\leqslant 0.175), zero field experiments reveal a stretched exponential muon relaxation with a universal behaviour of the dynamic exponent \beta above the spin glass transition. There are no qualitative differences between the ferromagnetic and paramagnetic phases. In transversal field μSR experiments the divergence of the relaxation rate close to the spin glass transition is suppressed for manganese doping up to x=0.113 but enhanced for slightly higher doping (x\geqslant 0.12). We understand this behaviour as a crossover from an itinerant to a more localized state of the 3d electron system. This is also supported by the fact that in the highly doped regime with dominant antiferromagnetic interactions the muon relaxation rate diverges above the antiferromagnetic transition temperature.

μSR investigations of gadolinium in the paramagnetic regime near the ferromagnetic transition

We report on the measurements of the muon relaxation rate in gadolinium (Gd) in the critical regime down to T-TC=0.1 K. The results are compared to the predictions of mode‐coupling calculations for a uniaxial and dipolar ferromagnet. One observes that even if the uniaxiality in Gd is quite small, it should not be neglected in order to get a consistent description of our data. Most striking is the fact that these investigations support the assumption that above TC the muon resides on the tetrahedral interstitial sites and not on the octahedral sites which are chosen in the low temperature phase.

Muon spin relaxation and hydrogen diffusion in the HfV2 Laves phase

Muon spin relaxation has been measured using the zero-magnetic-field technique in the HfV2 Laves compound containing interstitial hydrogen. At low temperatures the relaxation profiles have the characteristic form associated with fluctuating local fields. The correlation time is almost independent of temperature. As the temperature is raised above about 100 K, motional narrowing takes place in which the correlation time of the local field decreases rapidly. Comparison with the hopping rate of the hydrogen atoms, as measured by means of nuclear magnetic relaxation, shows that the change in the correlation time is consistent with an increasingly rapid motion of the hydrogen atoms. If the sample is then cooled, hysteresis occurs, in which the motional narrowing is retained to lower temperatures. The hysteresis in the muon relaxation rate together with parallel effects present in the nuclear magnetic relaxation are discussed in relation to the phase changes that are known to occur in this alloy.

Muon spin relaxation in antiferromagnets: a study of RbMnF3 based on the coupled mode theory of paramagnetic and critical spin fluctuations

The relaxation rate for the depolarization of a positive muon implanted in an antiferromagnetically coupled Heisenberg magnet is studied on the basis of a coupled mode theory of critical and paramagnetic spin fluctuations, which gives overall an unrivalled account of spin fluctuations. The paper includes the first comprehensive treatment of the dipole field that couples the muon and atomic (spin) magnetic moments. An analytical calculation of the relaxation rate is feasible in the vicinity of the critical temperature, because of the dominant role of the critical fluctuations, whereas in general numerical methods are required to calculate the spin response function and the dipole field. In the approach to the critical temperature, the muon relaxation rate increases as the square root of the correlation length. Results for the isotropic antiferromagnet RbMnF3 demonstrate that the relaxation rate is not a monotonic function of the temperature, and the magnitude and temperature variation of the relaxation rate depend to a significant degree on the site of the implanted muon. A theoretical framework for the interpretation of the muon relaxation rate is reviewed in a set of appendices.