Muon Spin Rotation Experiments Research Articles

Evidence for an antiferromagnetic component in the magnetic structure of ZrZn 2

Zero-field muon spin rotation experiments provide evidence for an antiferromagnetic component in the magnetic structure of the intermetallic ZrZn 2.

Coexistence of Long-Range Order and Spin Fluctuation in Geometrically Frustrated ClinoatacamiteCu2Cl(OH)3

Muon spin rotation experiments are carried out on clinoatacamite, Cu2Cl(OH)3, which is a new geometrically frustrated system featuring a three-dimensional network of corner-sharing tetrahedral 3d Cu2+ spins. A long-range antiferromagnetic order occurs below 18.1 K with a surprisingly small entropy release of about 0.05Rln2/Cu. Below 6.5 K, the static long-range order transforms abruptly into a metastable state with nearly complete depolarization of muon spins which suggests strong fluctuation. The system then enters a state in which partial long-range order and spin fluctuation coexist down to the lowest experimentally attainable temperature of 20 mK. This work presents a novel system for studying geometric frustration.

Disorder, inhomogeneity and spin dynamics in f-electron non-Fermi liquid systems

Muon spin rotation and relaxation(μSR) experiments have yielded evidence that structural disorder is an important factor in manyf-electron-based non-Fermi-liquid (NFL) systems. Disorder-driven mechanisms for NFLbehaviour are suggested by the observed broad and strongly temperature-dependentμSR (and NMR) linewidths in several NFL compounds and alloys. Local disorder-driventheories (Kondo disorder, Griffiths–McCoy singularity) are, however, not capable ofdescribing the time-field scaling seen in muon spin relaxation experiments, which suggestcooperative and critical spin fluctuations rather than a distribution of local fluctuationrates. A strong empirical correlation is established between electronic disorder and slowspin fluctuations in NFL materials.

Coexistence of magnetism and superconductivity inEu1.4Ce0.6RuSr2Cu2O10:A muon spin rotation and magnetization study

We performed zero-field muon spin rotation (ZF-μSR) and dc magnetization experiments in the ruthenate-cuprate Eu 1 . 4 Ce 0 . 6 RuSr 2 Cu 2 O 1 0 . It was found that this compound becomes weakly ferromagnetic at T m = 77.6 K and superconducting below T c =40 K. ZF-μSR experiments indicate that the magnetic order accounts for most of the sample volume and magnetism is not significantly affected in the superconducting state. The present investigation provides evidence for the coexistence of magnetism and superconductivity in Eu 1 . 4 Ce 0 . 6 RuSr 2 Cu 2 O 1 0 .

A common behaviour of thermoelectric layered cobaltites: incommensurate spin density wave statesin [Ca2Co4/3Cu2/3O4]0.62[CoO2] and [Ca2CoO3]0.62[CoO2

Magnetism of a misfit layered cobaltite[Ca2Co4/3Cu2/3O4]xRS[CoO2] (, RS denotes a rocksalt-type block) was investigated by a positive muon spin rotation and relaxation(μ+SR)experiment. A transition to an incommensurate (IC) spin density wave (SDW) state was found below180 K (= TCon); and a clear oscillation due to a static internal magnetic field was observed below140 K (= TC). Furthermore, an anisotropic behaviour of the zero-fieldμ+SR experiment indicated that the IC-SDW lies in thea–b plane, with oscillating moments directed along thec axis. These results were quite similar to those for the related compound[Ca2CoO3]0.62RS[CoO2], i.e.,Ca3Co4O9. Since theIC-SDW field in [Ca2Co4/3Cu2/3O4]0.62RS[CoO2] was approximately the same as those in pure and doped[Ca2CoO3]0.62RS[CoO2], it was concluded that the IC-SDW exists in the[CoO2 ] planes.

Low-temperature magnetic order and spin dynamics inYbRh2Si2

Muon spin rotation and relaxation experiments have been carried out in single crystals of ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2},$ a compound that exhibits non-Fermi-liquid (NFL) behavior associated with a quantum critical point (QCP) at $T=0.$ The zero-field muon relaxation rate is found to be independent of temperature down to 100 mK but to increase below $\ensuremath{\sim}70\mathrm{mK},$ which suggests magnetic order at low temperatures. From the relation between the internal field at the ${\ensuremath{\mu}}^{+}$ stopping site and the hyperfine coupling constant the ordered ${\mathrm{Yb}}^{3+}$ moment is very small, $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{\ensuremath{\mu}}_{B}.$ Muon spin rotation linewidths in a transverse field of 6 kOe indicate a homogeneous susceptibility down to 2 K, which is an order of magnitude lower than the characteristic (Kondo) temperature ${T}_{K}\ensuremath{\approx}25\mathrm{K}.$ This is evidence against the importance of disorder-driven NFL mechanisms in ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}.$ In longitudinal magnetic fields the muon spin-lattice relaxation function $G(t)$ is exponential, again indicative of a homogeneous system. The relaxation obeys the time-field scaling relation $G(t,H)=G(t/H),$ which suggests long-lived spin correlations at low temperatures. The ${\mathrm{Yb}}^{3+}$ spin dynamics derived from muon spin relaxation appear to be intimately related to critical magnetic fluctuations near the QCP.

μSR studies of organic and molecular magnets

Muon-spin rotation and relaxation (μSR) experiments have been performed on a variety of novel organic and molecular magnetic systems. In these experiments, implanted muons are used to study the magnitude, distribution and dynamics of the local field at the muon site. Calculations of the spatial dependence of the dipole-field inside the unit cell are used to interpret the data and determine the muon site in certain cases. We describe and review muon experiments on nitronyl nitroxide organic ferromagnets and antiferromagnets. We discuss a muon study of the spin crossover phenomenon which has been studied in Fe(PM-PEA)2(NCS)2, and which shows Gaussian and root-exponential muon relaxation in the high-spin and low-spin phases, respectively. The effects of high temperature annealing on TDAE-C60 have also been studied with μSR. Experiments on a disc-shaped molecular complex containing Fe19 (with spin 31/2) reveal the effects of fluctuations of magnetization and allow an estimate of the fluctuation rate. These experiments demonstrate the wide range of problems which can be tackled using the μSR technique.

Anisotropic magnetic properties ofCa3Co4O9:Evidence for a spin-density-wave transition at 27 K

The dc susceptibility $\ensuremath{\chi}$ of single crystal platelets of ${\mathrm{Ca}}_{3}{\mathrm{Co}}_{4}{\mathrm{O}}_{9}$ was measured in applied magnetic fields H below 55 kOe. At temperatures below 400 K, the crystals exhibited three magnetic transitions successively at ${T}_{\mathrm{SS}}\ensuremath{\sim}380\mathrm{K},$ ${T}_{\mathrm{SDW}}=27\mathrm{K},$ and ${T}_{\mathrm{ferri}}=19\mathrm{K}.$ The highest spin state (SS) transition was found to be discontinuous with the appearance of a thermal hysteresis loop about 20 K wide. At 27 K, a small shoulder in the $\ensuremath{\chi}(T)$ curve was observed only for $H\ensuremath{\perp}ab,$ indicating the formation of an incommensurate spin-density-wave (SDW) state, which was also confirmed by independent muon spin rotation and relaxation experiments. The lowest of ${T}_{\mathrm{ferri}}$ is a transition to a ferrimagnetic state, for which also a ferrimagnetic hysteresis loop was observed for $H\ensuremath{\perp}ab,$ but not for $H\ensuremath{\Vert}\mathrm{ab}.$ This anisotropic behavior indicated that the ferrimagnetic interaction is parallel to the c axis. Considering the alternating stacking structure of ${\mathrm{Ca}}_{3}{\mathrm{Co}}_{4}{\mathrm{O}}_{9}$ along the c axis, the ferrimagnetism is most likely caused by interlayer coupling between the $[{\mathrm{Ca}}_{2}{\mathrm{CoO}}_{3}]$ and $[{\mathrm{CoO}}_{2}]$ subsystems.

On the effect of heterovalent substitutions in ruthenocuprates

We discuss the properties of superconducting derivatives of the RuSr 2GdCu 2O 8 (1212-type) ruthenocuprate, for which heterovalent doping has been achieved through partial substitution of Cu ions into the RuO 2 planes (Ru 1− x Sr 2GdCu 2+ x O 8− δ , 0⩽ x⩽0.75, T c max=72 K for x=0.3–0.4) and Ce ions into the Gd sites (RuSr 2Gd 1− y Ce y Cu 2O 8, 0⩽ y⩽0.1). The measurements of XANES, thermopower, and magnetization under external pressure reveal an underdoped character of all compounds. Muon spin rotation experiments indicate the presence of magnetic order at low temperatures ( T m=14–2 K for x=0.1–0.4). Properties of these two series lead us to the qualitative phase diagram for differently doped 1212-type ruthenocuprates. The difference in temperature of magnetic ordering found for superconducting and non-superconducting RuSr 2GdCu 2O 8 is discussed in the context of the properties of substituted compounds. The high pressure oxygen conditions required for synthesis of Ru 1− x Sr 2RECu 2+ x O 8− δ , have been extended to synthesis of a Ru 1− x Sr 2Eu 2− y Ce y Cu 2+ x O 10− δ series. The Cu → Ru doping achieved in these phases is found to decrease the temperature for magnetic ordering as well the volume fraction of the magnetic phase.

Molecular dynamics simulation of norbornene plastic crystal

Molecular dynamics simulations have been performed on the norbornene plastic crystal in the temperature range 125–320 K. This investigation shows the existence of a remarkable dynamical crossover in the pico–nanosecond regime at the temperature T A≃200 K consistent with previous NMR and muon spin rotation experiments performed on the same compound. This temperature corresponds to the onset of non-exponential relaxation and non-Arrhenius behavior very much in keeping with recent views proposed for supercooled liquids.

Muon study of molecular magnets, spin crossover and magnetic nanodiscs

We present the results of recent muon-spin rotation ( μSR) experiments on a variety of novel molecular magnetic systems. Muons are sensitive to local static fields and magnetic fluctuations, but can probe much more than just the onset of long-range magnetic order. The spin-crossover phenomenon has been studied in Fe(PM-PEA) 2(NCS) 2, which shows Gaussian and root-exponential muon relaxation in the high-spin and low-spin phases, respectively. Dy spin fluctuations have been studied with μSR in the ferrimagnetic chain Dy(hfac) 3(NITEt). Experiments on a disc-shaped molecular complex containing Fe 19 (with spin 31 2 ) reveal the effects of quantum tunneling of magnetization and allow an estimate of the quantum tunneling rate.

Susceptibility inhomogeneity and non-Fermi-liquid behavior inCe(Ru0.5Rh0.5)2Si2

Magnetic susceptibility and muon spin rotation (\muSR) experiments have been carried out to study the effect of structural disorder on the non-Fermi-liquid (NFL) behavior of the heavy-fermion alloy Ce(Ru_{0.5}Rh_{0.5})_2Si_2. Analysis of the bulk susceptibility in the framework of disorder-driven Griffiths-phase and Kondo-disorder models for NFL behavior yields relatively narrow distributions of characteristic spin fluctuation energies, in agreement with \muSR linewidths that give the inhomogeneous spread in susceptibility. \muSR and NMR data both indicate that disorder explains the "nearly NFL" behavior observed above \sim2 K, but does not dominate the NFL physics found at low temperatures and low magnetic fields.

Magnetic properties of RuSr 2RECu 2O 8 (RE=Gd, Eu) and Ru 1− xSr 2GdCu 2+ xO 8− y superconductors

Synthesis in 1% oxygen at 930°C leads to non-superconducting RuSr 2GdCu 2O 8 in which superconductivity subsequently can be induced with oxygen annealings without observable stoichiometric changes. Detailed ac susceptibility and zero-field muon-spin rotation experiments reveal that the superconducting compounds always exhibit a lower temperature of the magnetic transition and larger values of the internal magnetic field in the ordered state of the Ru sublattice. The same annealings in oxygen, however, lead to non-superconducting RuSr 2EuCu 2O 8. The magnetic properties of a newly discovered series of Ru 1− x Sr 2GdCu 2+ x O 8− y superconductors (maximum T c=72 K for x=0.4) are reported. Low temperature behavior of the magnetization shows a significant contribution of the paramagnetic system of Gd ions to the magnetic response below the superconducting transition. Muon-spin rotation experiments reveal the presence of the magnetic transitions at low temperatures below the superconducting transition. XANES CuK absorption edge data show an increase in Cu valence with x.

Crystal structure assignment for the heavy-fermion superconductorUPt3

Understanding the normal and superconducting states in ${\mathrm{UPt}}_{3}$ depends critically on its crystal structure. Based on high-energy x-ray diffraction and transmission electron microscopy, we have determined that the crystal structure of ${\mathrm{UPt}}_{3}$ is trigonal, not hexagonal as traditionally held. Its trigonal structure provides an interpretation of recent high-field muon spin rotation experiments and may be relevant to the existence of the symmetry-breaking field required by most theoretical models of heavy-fermion superconductivity.

Muon Spin Rotation and Relaxation Experiments on Thin Films

The recent development at the Paul Scherrer Institute of a beam of low energy muons allows depth dependent muon spin rotation and relaxation investigations in thin samples, multilayers and near surface regions (low energy μSR, LE-μSR). After a brief overview of the LE-μSR method, some representative experiments performed with this technique will be presented. The first direct determination of the field profile just below the surface of a high-temperature superconductor in the Meissner phase illustrates the power and sensitivity of low energy muons as near-surface probe and is an example of general application to depth profiling of magnetic fields. The evolution of the flux line lattice distribution across the surface of a YBa2Cu3O7 film in the vortex phase has been investigated by implanting muons on both sides of a normal-superconducting boundary. A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters, embedded in a silver thin film matrix (500nm), demonstrates the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional μSR. Other experiments investigated the magnetic properties of thin Cr(001) layers at thicknesses above and below the collapse of the spin density wave.

μ–H Interaction in Hydrogen Bonding Systems

Muon spin rotation (μSR) experiments were performed on single crystal samples of KH2PO4(KDP) and KD2PO4(dKDP) to study the dynamics of hydrogen in hydrogen bonding systems. At low temperature, the nuclear dipole interaction of muon and proton was confirmed from the angular dependence of precession frequency of the muon spin under zero magnetic field. The muon occupation site was also determined. A clear change in μSR spectra was observed at the antiferroelectric transition temperature (123 K). At 90 K well below the transition temperature, the muon spin starts to relax, possibly due to muon dynamics.

Effective "penetration depth" in the vortex state of a d-wave superconductor.

The temperature and the field dependence of the effective magnetic penetration depth (lambdaeff) in the vortex state of a d-wave superconductor, as measured by muon spin rotation (muSR) experiments, is calculated using a nonlocal London model. We show that at temperatures below [EQUATION: SEE TEXT], the linear T dependence of lambda-2eff crosses over to a T3 dependence. This could provide an explanation for the low temperature flattening of the lambda-2eff curve observed in a recent muSR experiment.

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.

μ −SR investigations in silicon

Results on the temperature dependence of the residual polarization of negative muons in silicon with phosphorus ( 4.5×10 18, 2.3×10 15 , and 3.2×10 12 cm −3 ) and aluminium (2.4×10 18 and 2×10 14 cm −3 ) impurities are presented. The muon spin rotation (μSR) experiments were carried out in a magnetic field of 0.2 T and in the temperature range 4.2–300 K. In all investigated samples a relaxation of the muon spin and a shift of the spin-precession frequency were observed. The frequency shift (relative to the room-temperature value) amounts to 7×10 −3 at 15 K. In the sample with a high concentration of phosphorus impurity ( 4.5×10 18 cm −3 ) damped and undamped components of the muon spin polarization were observed at T<30 K . Hyperfine interaction between the magnetic moments of the muon and that of the electron shell of the muonic atom (acceptor centre – μAl) is estimated on the basis of the muon spin precession frequency shift data. The temperature dependence of the spin-lattice relaxation rate of the magnetic moment of the shallow acceptor centre in silicon in the absence of external stress is determined for the first time. It is found that the relaxation rate is well approximated by the power function ν( T)= CT q , where the parameter q lies between 2 and 3.

Oxygen-related muon species in crystalline silicon

A new muonium centre, termed Mu X , with anisotropic hyperfine interaction has been discovered recently in crystalline silicon in transverse-field muon spin rotation experiments (Schefzik et al., Philos. Mag. B 79 (1999) 1561). Its hyperfine tensor is very close to that of bond centred muonium (Mu BC). The signature of Mu X is only observable in samples containing oxygen in a concentration which is higher than that of the donors or acceptors. This indicates that Mu X is related to an oxygen–muonium centre. In the present work we have carried out a study of the temperature behaviour of the Mu X signal on a sample showing a very pronounced Mu X signature. The observations clearly show that the Mu X signal, on the one hand, and the Mu BC signals, on the other, have an identical temperature dependence.