Radio-frequency muon spin resonance (RFμSR) experiments on condensed matter

In this paper we present an overview of the radio-frequency muon spin resonance (RFμSR) technique, an analogue to continuous-wave NMR, and an introduction to time-integral (TI) and time-differential (TD) RFμSR on muons in diamagnetic or in paramagnetic environments. The general form of the resonance line for TI-RFμSR as well as the expression for the time-dependence of the longitudinal muon spin polarization at resonance are given. Since RFμSR does not require phase coherence of the muon spin ensemble, this technique allows us to investigate muon species that are generated by transitions from, or in the course of reactions of, a precursor muon species even if in transverse-field (TF) μSR measurements the signal is lost due to dephasing. This ability of RFμSR is clearly demonstrated by measurements on doped Si. In this example, at low temperatures, a very pronounced signal from a muon species in diamagnetic environment has been found in RFμSR measurements, whereas in TFμSR experiments only a very small signal from muons in diamagnetic environment could be detected and a large fraction of the implanted muons escaped detection. These findings could be interpreted in terms of the delayed formation of a diamagnetic muonium-dopant complex, and, due to the large diamagnetic RFμSR signal, the RFμSR technique is a unique tool to study how the variation of parameters and experimental conditions such as illumination affects formation and behavior of these complexes. First results obtained on illuminated boron doped Si are reported. However, as illustrated by the example of experiments on the muonated radical in solid C₆₀, results from conventional TI-RFμSR cannot always be interpreted unambiguously since different parameters, namely the fraction of muons forming the investigated muon species, the longitudinal and the transverse relaxation rates, have similar effects on height and shape of the RFμSR resonance line. These ambiguities, however, may be resolved by collecting time-differential data. With this extension RFμSR becomes a very powerful complementary method to TFμSR in the studies of dynamic effects.     

Radio-frequency μSR experiments at the ISIS pulsed muon facility

This paper explores the use of pulsed radio-frequency (RF) techniques to remove the frequency limitations imposed on conventional transverse muon spin rotation (μSR) experiments at a pulsed muon source by the finite muon pulse width. The implementation of the 90° pulse technique is demonstrated by observing the free precession signal of diamagnetic muons implanted in polythene, the change in signal amplitude as a function of RF pulse length is plotted and the precise condition for a 90° pulse determined. The technique is evaluated by comparing measurements made using conventional spin rotation experiments to those employing pulsed RF methods. The potential for applying standard NMR multiple-pulse methods to the μSR experiment is considered and the use of two-pulse RF sequences (90° _x ?τ?90° _x and 90° _x ?τ?180° _x ) to form a muon spin echo demonstrated.     

β-NMR

The β-NMR facility at ISAC is constructed specifically for experiments in condensed matter physics with radioactive ion beams. Using co-linear optical pumping, a ⁸Li^?+? ion beam having a large nuclear spin polarisation and low energy (nominally 30 keV) can be generated. When implanted into materials these ions penetrate to shallow depths comparable to length scales of interest in the physics of surfaces and interfaces between materials. Such low-energy ions can be decelerated with simple electrostatic optics to enable depth-resolved studies of near-surface phenomena over the range of about 2–200 nm. Since the β-NMR signal is extracted from the asymmetry intrinsic to beta-decay and therefore monitors the polarisation of the radioactive probe nuclear magnetic moments, this technique is fundamentally a probe of local magnetism. More generally though, any phenomena which affects the polarisation of the implanted spins by, for example, a change in resonance frequency, line width or relaxation rate can be studied. The β-NMR program at ISAC currently supports a number of experiments in magnetism and superconductivity as well as novel ultra-thin heterostructures exhibiting properties that cannot occur in bulk materials. The general purpose zero/low field and high field spectrometers are configured to perform CW and pulsed RF nuclear magnetic resonance and spin relaxation experiments over a range of temperatures (3–300 K) and magnetic fields (0–9 T).     

Measurement of the gluon polarisation with COMPASS

The COMPASS experiment at CERN is investigating the nucleon spin structure in polarised deep inelastic muon scattering, mainly the gluon polarisation .     

MuSR method and tomographic-probability representation of spin states

The muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. The time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. The entanglement phenomenon of a bipartite muon–electron system is investigated, in view of the tomographic analogs of the Bell number and the positive partial transpose (PPT) criterion. Reconstruction of the muon–electron spin state as well as the total spin tomography of the composed system is discussed.     

Muon addition to nitrogen,oxygen and other atoms: Considerations for level crossing resonance studies

The purpose of this note is to examine the conditions under which muon level crossing resonance with quadrupolar nuclei may be used to characterise the elusive diamagnetic fraction which is formed when positive muons are stopped in various media and associated chemically with the host molecules. A potential difficulty is identified for nuclei having integral spin, which may explain why cross polarisation to¹⁴N has not yet been detected. The general suitability of nuclei with half-integral spin (I≥3/2) is illustrated with the case of¹⁷O, and suggestions are made for future studies with other nuclei, including species such as molecular ions and defect complexes (muon-impurity pairs).     

Muon spin resonance — A variant of magnetic resonance

Spin polarized positive muons injected in matter serve as magnetic probes for the investigation of various properties. The evolution of muon spin polarization rests on the same basis as in conventional magnetic resonance techniques. The background of the technique, different variants of the experimental set-up, and potential and limitations of the muon as a probe are described.     

Adiabatic Mixing in the Liquid State

Adiabatic spin inversion has been used in the liquid state very efficiently for decoupling purposes. Here we show that it can also be adapted for spin mixing experiments, such as the TOCSY and clean TOCSY experiment, and is superior to previously employed mixing sequences. The main advantage of adiabatic mixing sequences over the conventional mixing schemes used in liquid state experiments is an extremely low sensitivity to RF field inhomogeneity and miscalibration of theB₁field strength. The method is evaluated experimentally by comparing results obtained with different mixing schemes in the basic 2D TOCSY experiment. In addition to higher reliability, adiabatic mixing provides a sensitivity improvement of ca. 20% as compared to conventional mixing schemes. This is explained by higher signal losses due to RF inhomogeneity in the experiments employing traditional mixing schemes. More significant sensitivity improvements can be expected in situations where RF homogeneity is traditionally poor, for example, in large volume probes and magnetic resonance imaging experiments.     

Observation of “decoupled” diamagnetic muon states in Alkali halides by muon spin resonance

The states of positive muons in KCl, NaCl and KI were studied with the muon spin resonance method under a 3 kG decoupling longitudinal field, revealing a considerably larger fraction of diamagnetic muon state than observed by the conventional spin rotation method. The origin of this fraction, which increases with temperature, is attributed to a muonium to muon transition in solids.     

Muon spin resonance by strong pulsed r.f. field with pulsed muons

Muon spin resonance experiments have been performed for the ⁺ in H₂O and for some other cases, and the first observation has been made of the time-differential pattern of muon spin resonance, namely, spin precession around the r.f. field vector under various resonance conditions. In the present experiment, a high-power pulsed r.f. field was effectively applied to the pulsed muon beam in our laboratory of the KEK-Booster Meson Facility (BOOM). Potential uses of muon spin resonance, particularly for research in the border regions of solid state and nuclear physics, are discussed in comparison with the conventional spin rotation method.     

Radio-frequency muon spin resonance studies of endohedral and exohedral muonium adducts of fullerenes

The radio-frequency muon spin resonance technique (RF-μSR) is described, with examples drawn from muon studies of fullerences. Two distinct species can be detected by RF-μSR when solid C₆₀ is irradiated with positive muons. Endohedral muonium (Mu@C₆₀) is characterized by a muon hyperfine constant (A _μ) close to the vacuum value. A remarkable feature of the RF-μSR spectrum is the double quantum transition, which appears when the allowed transitions are saturated. The exohedral muonium adduct (C₆₀Mu) is also detected, and has a much smaller value ofA _μ typical of a carbon-centred organic radical. It has been studied by RF-μSR in dilute solution, which is not possible for transverse field muon spin rotation (TF-μSR). There is a significant difference inA _μ of C₆₀Mu in the solid and in solution, a result of great import to the analysis of avoided-level crossing experiments on¹³C₆₀Mu.     

量子自旋液体候选材料的缪子自旋弛豫研究

量子自旋液体是一种新奇的磁性物态。由于极强的量子涨落,直至零温都不会出现长程序。量子自旋液体的基态不能用序参量描述,并且缺少对称性破缺,因此该物态的实现打破朗道理论的范式。对于量子自旋液体的研究有助于理解高温超导的机理,并且可以被应用在量子计算和量子信息中。目前,尽管理论上有了长足的发展,但仍旧没有任何一个材料被证实为量子自旋液体。因此,探测和确认一个真正的量子自旋液体材料是当前的研究重点。缪子自旋弛豫是一个对磁场极为敏感的实验技术,被广泛应用于量子自旋液体候选材料的研究中。该技术可以观测基态中是否存在磁有序,测量系统中的涨落频率,这两点都是表征量子自旋液体的重要性质。本文简要介绍了量子自旋液体态和缪子自旋弛豫技术,回顾了近期在不同体系的量子自旋液体候选材料中的实验结果,特别是缪子自旋弛豫的成果。这些体系包括一维反铁磁海森堡链（苯甲酸铜）,三角格子（YbMgGaO4,NaYbO2 和TbInO3）,笼目格[ZnCu3(OH)6Cl2 和 m3Sb3Zn2O14],蜂窝状格子（Na2IrO3 和 α-RuCl3）,以及烧绿石结构（Tb2Ti2O7,Pr2Ir2O7 和Ce2Zr2O7）。     

Muon level-crossing resonance in magnetically ordered materials

The positive muon is widely used as a microscopic probe of internal fields at interstitial sites in magnetically ordered materials. Recently, we have demonstrated that the hyperfine fields on the neighboring host nuclear spins can be measured using a novel muon level-crossing resonance technique, thus providing a more detailed picture of the electronic and magnetic environment around the muon. In this paper I will describe the fundamentals of muon level-crossing resonance as applied to magnetically ordered materials, and report an example in MnF₂.     

μSR at new accelerators

In this paper I speculate upon the potential of muon spin rotation/relaxation/resonance (μSR) for future refinement and/or exploitation at large accelerators like KAON, which might generate muon beams a hundred times more intense than today's best. Several schemes for efficient utilisation of such beams might be well worth implementing on existing muon channels. Work supported by NRC and NSERC.     

Laser polarized muonic atoms

Lasers are an important tool in the field of muon physics. A new application of lasers, namely producing polarized muonic atoms, is the subject of a new program at LAMPF. One technique already demonstrated is stopping unpolarized muons in a laser polarized³He target. A more promising idea is to polarize neutral muonic helium by collisions with laser polrized Rb vapor. These methods for producing polarized muonic helium will be useful for measuring the spin dependence of nuclear muon capture and for determining the induced pseudoscalar coupling.     

Electrical generation of pure spin current with oscillating spin-orbit interaction

We propose an electrical scheme for the generation of a pure spin current without a charge current in a two-terminal device, which consists of a scattering region of a two-dimensional electron gas (2DEG) with Rashba (R) and/or Dresselhaus (S) spin-orbit interaction (SOI) and two normal leads. The SOI is modulated by a time-dependent gate voltage to pump a spin current. Based on a tight-binding model and the Keldysh Green’s function technique, we obtain the analytical expression of the spin current. It is shown that a pure spin current can be pumped out, and its magnitude could be modulated by device parameters such as the oscillating frequency of the SOI, as well as the SOI strength. Moreover, the spin polarisation direction of the spin current could also be tuned by the strength ratio between RSOI and DSOI. Our proposal provides not only a fully electrical means to generate a pure spin current but also a way to control the spin polarisation direction of the generated spin current.     

Electron spin polarisation in laser induced autoionisation

The electron spin polarisation in the strong laser light induced autoionisation is discussed in the simple model. It is shown that confluence of coherences manifests itself in the dependence of polarisation on the laser detuning as a field strength dependent resonance, which enables verification of the phenomenon by means of the spin polarisation measurement. The separation of the confluence of coherences point and the point at which the maximal slowing down of the ionisation process (population trapping) occurs is showed.     

Muon state dynamics in germanium and silicon

We have carried out implanted positive muon studies on the molecular metal system d_n- (DMe-DCNQI)₂ Cu in order to understand better its novel magnetic properties. Examples of these salts at different levels of deuteration were studied. The fully deuterated ( d₈) salt shows a metal–insulator (MI) transition around 80 K and a magnetic transition around 7 K. The muon spin relaxation rate is enhanced below the MI transition, reflecting the localisation of spins along the Cu columns, however, the increase in muon spin relaxation rate occurs well above the metal–insulator (MI) transition and suggests a slowdown of the spin fluctuations around 120 K. At temperatures below 7 K a zero field precession signal was observed as a result of the 3D magnetic ordering of the Cu spins. For a muon site associated with the ring of the DCNQI molecule, the local field distribution was found to be consistent with the previously proposed magnetic structure. A sharp nuclear quadrupolar level crossing resonance (QLCR) was observed at 50 G which was assigned to resonance with the imine nitrogen on the DCNQI molecule. This revised version was published online in July 2006 with corrections to the Cover Date.     

Muonium acoustic resonance

Theoretical consideration is given to the effect of ultrasonic oscillations on the spin polarization of the positive muon of muonium present in matter. The resonant action of the periodic acoustic perturbation on the muonium hyperfine structure levels is shown to result in characteristic oscillations and to modify the muon spin precession pattern considerably. The possibilities for experimental detection of the muonium acoustic resonance are discussed