Most $\mu$SR is done with the $\mu^+$ because 100% polarized surface muons have a fixed lifetime and usually retain their full polarization upon stopping in the sample, whereas the $\mu^-$ has higher energy, loses most of its polarization through $LS$ coupling during its cascade to the ground state of the muonic atom, and is then subject to capture on the nucleus, so its lifetime is variable...
Since the first measurements of muon quadrupolar level crossing resonance (QLCR) in Cu [1], the technique has been extended to various other quadrupolar atoms. For example, recent QLCR studies with N looked at a charge transfer salt [2] and the quantum delocalisation of the muon in solid N$_2$ [3]. Another recent study measured the kagome superconductor RbV$_3$Sb$_5$ and this has provided the...
In perovskite Ta oxynitrides $A$TaO$_2$N ($A$=Ba, Sr), a new degree of freedom, $cis/trans$, is introduced by the anion configuration. In these materials, a dielectric constant of about 10$^2$-10$^3$ has been observed at room temperature. However, powder X-ray diffractions show structures such as $Pm\bar{3}m$ and ${I4/mcm}$, which have central symmetry and do not exhibit dielectric...
NiI$_2$ is a layered van der Waals magnet which has recently been proposed to host a novel form of skyrmion phase in the 2D limit$^1$. $\mu$SR has proven to be a sensitive probe of magnetic dynamics resulting from such topological excitations. I will present the results$^2$ of $\mu$SR measurements of NiI$_2$, which probe magnetic phase transitions at $T_{\rm{N1}}=73$ K and $T_{\rm{N2}}=62$ K....
A silicon strip detector has been developed for positron tracking from muon decay at the J-PARC muon g-2/EDM experiment. The detector is composed of silicon strip sensors with a strip pitch of 190 μm and features a readout with a 200 MHz sampling clock. It can be operated at 25 Hz on the J-PARC MLF muon beam line. The application of the detector to μSR measurement at J-PARC MLF is being...
The bulk heterostructure 6R-TaS$_{2}$ offers a unique platform to study the interplay of charge density waves, superconductivity, and electronic transport anomalies. Notably, nematic Ising superconductivity has been recently proposed, and a hidden order accompanied by a large anomalous Hall effect at $T^{*}$ ${\simeq}$ 35 K has been identified, raising fundamental questions about the nature...
Muonium is a pure leptonic binary system consisting of a positive muon and an electron, and its level structure can be calculated with high precision. The Muonium Spectroscopy Experiment Using Microwave (MuSEUM) experiment aims to verify the quantum electromagnetic dynamics theory and determine the positive muon magnetic moment and mass by precise measurements of the ground-state hyperfine...
In recent years, there has been an influx of research surrounding the kagome AV$_3$Sb$_5$ (A = K, Rb, Cs) compounds which display both superconductivity and charge order [1,2]. The onset of charge order has been associated with the breaking of time-reversal symmetry (TRS), but the extent to which TRS breaking can be tuned is relatively unexplored. To address this, we employ muon spin rotation...
High-speed charged particles (such as electrons) are scattered in matter by the electric field of the atomic nucleus producing the Bremsstrahlung X-rays (light). Since the efficiency of Bremsstrahlung is inversely proportional to the square of the mass, in principle, $\mu^{\pm}$ which is 200 times heavier than an electron, can produce 40000 times less Bremsstrahlung than an electron. On the...
The interplay between superconductivity and charge or spin order is a key focus in condensed matter physics, with kagome lattice systems providing unique insights [1-9]. We recently discovered that the kagome superconductor LaRu$_{3}$Si$_{2}$ ($T_{\rm c} \simeq 7$ K) exhibits a characteristic kagome band structure and a hierarchy of charge-order transitions at 400 K and 80 K, as well as an...
$\mu$SR in high magnetic fields is a powerful technique for probing material structures, enabling detailed measurements such as the muon Knight shift and level-crossing resonance (LCR). To advance such studies, we are developing a high-field µSR spectrometer named CYCLOPS, designed to operate in magnetic fields up to 5 tesla in the Materials and Life Science Experimental Facility (MLF) at...
Internal nuclear magnetic fields in various battery materials have been predicted using density functional theory (DFT) calculations to interpret the $\mu^+$SR results, particularly for identifying the diffusing species responsible for the dynamic behavior observed. In materials where Li$^+$ and Na$^+$ ions are mobile, these cations readily change positions to minimize electrostatic repulsion...
DGEBA is used in many dielectric systems. Understanding factors that influence its performance and longevity require a knowledge of charge dynamics, which intrinsically are linked to the molecular structure and dynamics. Bulk techniques have been used to determine structural relaxations and activation energies; however, these methods only provide information on processes, not on the causal...
Equilateral spin triangles are pivotal in quantum magnetism to explore frustration, spin–electric coupling, and multiferroic ordering. Achieving ideal triangular spin networks is difficult due to structural distortions, but the organic compound TNN·CH3CN overcomes these limitations with isotropic spins free from Jahn–Teller effects, enabling uniform exchange interactions and making it an...
The intercalated transition-metal dichalcogenides (TMDCs) are formed through the insertion of transition-metal ions between weakly bonded hexagonal layers. The low dimensionality of these systems leads to the realisation of a wide range of magnetic phenomena, which is further enhanced by varying the species and stoichiometry of the intercalate [1]. The sensitivity of muons to local magnetism...
We study the magnetic properties of the metallic kagome system (Fe$_{1-x}$Co$_x$)Sn by a combination of $\mu$SR, magnetic susceptibility and STM measurements, in single crystal specimens with Co concentrations $x=0,0.11,0.8$. In FeSn, we find possible signatures for a previously unidentified phase that sets in at $T^*\sim 50$ K, well beneath the Neel temperature $T_N \sim 376$ K, as indicated...
The μSR experiment has been used to measure diffusion coefficients and activation energies of ions in cathode materials such as LiCoO2. [1] However, direct determination can be challenging due to the use of models such as the Kubo-Toyabe dynamic function, as well as difficulties in distinguishing muon diffusion itself from Li+ diffusion at high temperatures.
First principles calculations...
A superconductor’s intrinsic length scales – the London penetration depth λL and Bardeen-Cooper-Schrieffer (BCS) coherence length ξ0 – are closely connected to its electronic structure and govern salient features such at its Meissner response. Leveraging recent advances in the preparation [1] and characterization [2] of Nb metal for technical applications (e.g.,...
The F--$\mu$--F state is observed in many fluorides via the quantum coherent oscillatory muon polarization resulting from entanglement between the spins of the muon and nearby fluorine nuclei [1,2,3]. The usual method to treat muon hopping in this system is to use the strong-collision approximation to dynamicize the standard F--$\mu$--F relaxation function [4]. This approach neglects...
We report on the magnetic properties of two sets of superlattices composed of antiferromagnetic LaFeO$_3$, separated by either SrTiO$_3$ or LaAlO$_3$. The superlattices consist of 1, 2, or 3 unit cells of LaFeO$_3$, separated by 5 unit cells of SrTiO$_3$ in one set, and 5 unit cells of LaAlO$_3$ in the other, each repeated 10 times. The magnetic behavior was investigated using low-energy muon...
One of the key challenges in performing experiments is knowing which temperatures and applied fields to measure at, and how many statistics should be measured at each temperature/field combination. We have recently developed a technique which uses Fisher information which, for a given muon asymmetry function, can analytically calculate the number of muon statistics required to have an error of...
The standard interpretation of superconductivity (S) is based on the London theory (LT) with minor modifications adopted in the GL and BCS. In all theories the sample bulk is totally inert and microscopic parameters of the S state can be obtained exclusively from the surface properties, i.e., the penetration depth $\lambda$ and the induction profile B vs depth z. Herewith, $B(z)$ is or close...
Battery materials can undergo a series of structural phase transitions during cycling that significantly change the ionic diffusion. In-operando $\mu$SR measurements provide a powerful new tool to investigate the ionic diffusion in these intermediate phases that affect both the performance and longevity of batteries.
Here we report in-operando $\mu$SR measurements of the battery...
Si:P offers a versatile setting for exploring quantum many-body effects. At intermediate impurity concentrations, Si:P hosts a Kondo condensate—a quantum state featuring an energy gap in the electronic density of states. In this regime, overlapping Kondo clouds interact via RKKY exchanges, though the nature of the magnetic ground state has remained unclear.
In this presentation, we combine...
The search for states of matter such as quantum spin-liquids involves the characterization of disordered magnetic ground states, and spinons or topological excitations, along with signatures of entanglement [1]. Examples of these features are also found in one-dimensional spin chains. Here we describe our recent $\mu$SR work on such systems built from metal centres linked by molecules.
We...
The $\mu$SR method has been widely used in recent years to study ion diffusion in battery materials. In data analysis, a dynamic Kubo-Toyabe function is often used in which the internal magnetic field distribution $n(B)$ fluctuates with frequency $\nu$. The model also presumes that $n(B)$ at the muon site remains constant and uncorrelated between fluctuations [1]. However, it has been pointed...
The performance of superconducting cavities in particle accelerators is limited by magnetic flux behavior in the near-surface region, where radiofrequency currents flow. Muon spin rotation (μSR) and beta-detected nuclear magnetic resonance (β-NMR) are uniquely suited to investigate this regime, offering access to local magnetic properties with depth resolution on the nanometer scale. This...
YbBO₃ is an intriguing example of a geometrically frustrated magnet. Early muon spin spectroscopy study reported an increase in the muon depolarization rate below 400 mK, but no oscillations indicative of long-range order were detected [1]. In contrast, subsequent investigations using other experimental techniques revealed that YbBO₃ does indeed undergo magnetic ordering [2]. A recent proposal...
Conventional μSR lacks external control over local muon–spin interactions; to overcome this limitation, we employed pulsed RF techniques to manipulate spin populations in muon-coupled fluoride systems at precisely controlled times after muon implantation, utilizing the ISIS pulsed muon beamline—well suited for such experiments. In ionic fluoride insulators, implanted μ$^+$ forms an F–μ–F...
We report β-NMR spin-lattice relaxation of 8Li+ implanted at 25 keV into polycrystal samples of the high entropy oxides (Co1/5 Cu1/5Mg1/5 Ni1/5Zn1/5 )O with the rocksalt (RS) structure and (Co1/5 Cr1/5Fe1/5Mn1/5Ni1/5 )3 O4 with the spinel (Sp) structure in a high applied longitudinal field of 5.65 T. Both are magnetic materials with a high degree of cation disorder. In the RS, occupation of...
Repeated recharging of lithium-ion batteries leads to the deposition of metallic lithium (m-Li) on the anode surface. Visualizing the spatial distribution of m-Li is challenging with existing techniques. Furthermore, lithium can also be deposited in the form of insoluble salts (s-Li) within the battery, making it essential f for visualization methods that distinguish between these two lithium...
Altermagnetism has recently emerged as a third fundamental class of magnetism [1], with spin-spilt bands but no net magnetisation. As well as being of fundamental interest, this magnetic state has some properties of both ferromagnets and antiferromagnets which are particularly interesting for spintronic applications [2]. Key to altermagnetism is rotational symmetry between flipped magnetic...
LaAlO$_3$ (LAO) is, alongside SrTiO$_3$ (STO), and sapphire one of the most commonly used substrates for complex metal-oxide thin film growth. LAO plays a crucial role in inducing interesting physical properties, such as in LaNiO$_3$/LAO superlattices and interface superconductivity at STO/LAO interfaces. While $\mu$SR studies have characterized STO, sapphire, and LSAT regarding Muonium...
Due to the highest electronegativity of F ions, the highest electrical conductivity of fluorides [1] and the higher energy density (estimated theoretically [2]) than Li-ion batteries, metal fluorides attracted the attentions for all-solid-state battery materials for next generation. Since muon spin rotation and relaxation ($\mu$SR) method is used to study the dynamics of ions in battery...
The use of a Si pixel-based particle tracking scheme in μSR will, among others, allow measurements using a ten-fold increased stopped muons rate and samples ten times smaller than currently possible at continuous muon source facilities. In this contribution we present simulation results to assess the effects of magnetic fields on two spectrometer configurations using a two-layered tracking...
The Kubo-Toyabe (KT) function has long been a mainstay of studies of ionic diffusion in solids. Its usefulness has extended far beyond its expected range of applicability. One of the assumptions of the KT theory is that there is a Gaussian distribution of internal fields reflecting the contributions of a dense array of nuclear spins surrounding the muon site. In many cases this is clearly not...
We study the μ+ dynamics in CaF2 in a wide temperature range between 10K and 290K using ZF and LF μ+SR experiments. The analysis of the muon spin polarization function A(t) at all temperatures in zero field (figure (a)) and longitudinal magnetic field is done by a quantum simulation of the static muon spin interacting with 2 nearest neighbor and 8 next-nearest neighbor flourine nuclear moments...
The fineness and quality of a state’s coinage is often used as a proxy for its fiscal health, meaning the purity and chemical composition of coins are of real historical interest. Sampling of such objects is often at the surface or near-surface, but, in ancient coinages, these areas can be unrepresentative of the bulk alloy. Investigations on Roman gold and silver coinage using negative muons...
Copper-exchanged zeolites have emerged as promising catalysts for the direct conversion of methane to methanol, yet the precise nature and dynamics of the active copper species remain elusive. In this study, we apply muon spin spectroscopy (µSR) to investigate local magnetic and electronic environments in Cu-loaded SSZ-13 zeolites, a technique uniquely sensitive to "slow" and local dynamic...
LiNi$_{0.8}$Mn$_{0.1}$Co$_{0.1}$O$_2$, commonly known as NMC811, is widely used as a cathode material in Li-ion batteries for electric vehicles due to its high energy density. Despite this, NMC811 and other Ni-rich layered cathode materials suffer from poor cycle life when compared to their lower Ni-containing analogues. This is caused by mechanical stress induced by anisotropic evolution of...
A new beamline called "β-SRF" has been built at TRIUMF, allowing for the near surface characterization of materials with β-radiation-detected nuclear magnetic resonance (β-NMR) in applied magnetic fields up to 200 mT parallel to the sample surface. These capabilities are relevant for the study of Nb superconducting radiofrequency (SRF) cavities - common components in particle accelerators -...
In muon spin rotation/relaxation ($\mu$SR) experiment, the time evolution of muon spin polarization, $P(t)$, is analyzed to evaluate the internal magnetic fields and their temporal fluctuations sensed by the muons at their stopping sites. In conventional data analysis, a phenomenological model for $P(t)$—typically based on general spin relaxation theory (e.g. that by Kubo and Toyabe) —is used...
To extend μSR to driven samples, we employ a microwave stimulus to excite the sample by ferromagnetic resonance (FMR) and probe the resultant effect with the muon. The experiments were performed on the helimagnet Cu$_2$OSeO$_3$, which exhibits distinct FMR and μSR signatures throughout its magnetic phase diagram. FMR excitations in the helical state cause precession, which is characterized by...
