Muon Knight Shift Research Articles

Kondo screening in a Majorana metal

Kondo impurities provide a nontrivial probe to unravel the character of the excitations of a quantum spin liquid. In the S = 1/2 Kitaev model on the honeycomb lattice, Kondo impurities embedded in the spin-liquid host can be screened by itinerant Majorana fermions via gauge-flux binding. Here, we report experimental signatures of metallic-like Kondo screening at intermediate temperatures in the Kitaev honeycomb material α-RuCl3 with dilute Cr3+ (S = 3/2) impurities. The static magnetic susceptibility, the muon Knight shift, and the muon spin-relaxation rate all feature logarithmic divergences, a hallmark of a metallic Kondo effect. Concurrently, the linear coefficient of the magnetic specific heat is large in the same temperature regime, indicating the presence of a host Majorana metal. This observation opens new avenues for exploring uncharted Kondo physics in insulating quantum magnets.

Magnetic Susceptibility Study of Hole-Doped Organic Metal κ-(ET)<sub>4</sub>Hg<sub>3-δ</sub>Cl<sub>8, </sub>δ=22% and κ-(ET)<sub>4</sub>Hg<sub>3-δ</sub>Br<sub>8, </sub>δ=11%

The Non-Fermi-Liquid (NFL) state has been one of central issues in the strongly correlated electrons systems. This deviates from conventional Fermi Liquid (FL) behavior. In the hole-doped triangular lattice organic metal κ-(ET)4Hg3-δBr8, δ = 11% (κ-HgBr), the NFL state is observed as a linear temperature dependence of the resistivity which changed to the temperature square dependence behavior by pressure. The spin susceptibility dependence of the muon Knight shift, K(c), is not linear in the region below 50 K, unlike in other k-type organic superconductors. Furthermore, 13C-NMR study under pressure concluded that strong antiferromagnetic spin fluctuations (AFSF) contribute to the origin of NFL. To understand the underlying correlation of the enhanced AFSF and NFL state in k-HgBr, the K(c) plot study in the sister compound κ-(ET)4Hg3-δCl8, δ=22% (κ-HgCl) which shows metal to insulator transition at TMI ~ 20 K is desirable. In this study, we report a precise susceptibility measurement in both k-HgBr and k-HgCl. Furthermore, we summarize the c(T) data of k-HgBr and k-HgCl and discuss them from the viewpoint of the triangular and square lattice models.

Freezing out of a low-energy bulk spin exciton in SmB6

The Kondo insulator SmB6 is purported to develop into a robust topological insulator at low temperatures. Yet there are several puzzling and unexplained physical properties of the insulating bulk. It has been proposed that bulk spin excitons may be the source of these anomalies and may also adversely affect the topologically protected metallic surface states. Here, we report muon spin rotation measurements of SmB6 that show thermally activated behavior for the temperature dependence of the transverse-field relaxation rate below 20 K and a decreasing contact hyperfine field contribution to the positive muon Knight shift below 5–6 K. Our data are consistent with the freezing out of a bulk low-energy (~1 meV) spin exciton concurrent with the appearance of metallic surface conductivity. Furthermore, our results support the idea that spin excitons play some role in the anomalous low-temperature bulk properties of SmB6.

Electronic correlation in the quasi-two-dimensional electride Y2C

Magnetic properties of the electride compound Y$_2$C were investigated by muon spin rotation and magnetic susceptibility on two samples with different form (poly- and single-crystalline), to examine the theoretically-predicted Stoner ferromagnetism for the electride bands. There was no evidence of static magnetic order in both samples even at temperatures down to 0.024 K. For the poly-crystalline sample, the presence of a paramagnetic moment at Y sites was inferred from the Curie-Weiss behavior of the muon Knight shift and susceptibility, whereas no such tendency was observed in the single-crystalline sample. These observations suggest that the electronic ground state of Y$_2$C is at the limit between weak-to-strong electronic correlation, where onsite Coulomb repulsion is sensitive to a local modulation of the electronic state or a shift in the Fermi level due to the presence of defects/impurities.

Spin and Time-Reversal Symmetries of Superconducting Electron Pairs Probed by the Muon Spin Rotation and Relaxation Technique

Unconventional superconductivity based on the strong correlation of electrons is one of the central issues of solid-state physics. Although many experimental techniques are appropriate for investigating unconventional superconductivity, a complete perspective has not been established yet. The symmetries of electron pairs are crucial properties for understanding the essential state of unconventional superconductivity. In this review, we discuss the investigation of the time-reversal and spin symmetries of superconducting electron pairs using the muon spin rotation and relaxation technique. By detecting a spontaneous magnetic field under zero field and/or the temperature dependence of the muon Knight shift in the superconducting phase, the time-reversal symmetry and spin parity of electron pairs have been determined for several unconventional superconductors.

Metal-insulator transition and pseudogap inBi1.76Pb0.35Sr1.89CuO6+δhigh-Tccuprates

It is inferred from bulk-sensitive muon Knight shift measurement for a Bi$_{1.76}$Pb$_{0.35}$Sr$_{1.89}$CuO$_{6+\delta}$ single-layer cuprate that metal-insulator (MI) transition (in the low temperature limit, $T\rightarrow0$) occurs at the critical hole concentration $p=p_{\rm MI}=0.09(1)$, where the electronic density of states (DOS) at the Fermi level is reduced to zero by the pseudogap irrespective of the N\'eel order or spin glass magnetism. Superconductivity also appears for $p>p_{\rm MI}$, suggesting that this feature is controlled by the MI transition. More interestingly, the magnitude of the DOS reduction induced by the pseudogap remains unchanged over a wide doping range ($0.1\le p\le0.2$), indicating that the pseudogap remains as a hallmark of the MI transition for $p>p_{\rm MI}$.

Muon Knight shift in d-electron heavy fermion compound Y0.95Sc0.05Mn2

We report on the muon Knight shift in a polycrystalline sample of Y0.95Sc0.05Mn2 that is known as one of the d-electron heavy fermion compounds. Since the muon site is presumed to have a trigonal symmetry, it is expected that the Fourier-transformed (FT) spectrum line shape would exhibit a uni-axial powder pattern which has two edges determined by the parallel and perpendicular components of the Knight shift, K|| and K⊥, where K|| (K⊥) is proportional to the parallel (perpendicular) component of the spin susceptibility, χ|| (χ⊥). The observed FT spectrum at 2 K largely disagrees with the calculated line shape in isotropic (χ|| = χ⊥) and anisotropic (χ|| ≠ χ⊥) cases, suggesting that there must be field- induced staggered magnetization due to strong antiferromagnetic spin correlations.

Unconventional magnetic ground state in Yb2Ti2O7

We report low temperature specific heat and muon spin relaxation/rotation ($\mu$SR) measurements on both polycrystalline and single crystal samples of the pyrochlore magnet Yb$_2$Ti$_2$O$_7$. This system is believed to possess a spin Hamiltonian supporting a Quantum Spin Ice (QSI) ground state and to display sample variation in its low temperature heat capacity. Our two samples exhibit extremes of this sample variation, yet our $\mu$SR measurements indicate a similar disordered low temperature state down to 16 mK in both. We report little temperature dependence to the spin relaxation and no evidence for ferromagnetic order, in contrast to recent reports by Chang \emph{et al.} (Nat. Comm. {\bf 3}, 992 (2012)). Transverse field (TF) $\mu$SR measurements show changes in the temperature dependence of the muon Knight shift which coincide with heat capacity anomalies. We are therefore led to propose that Yb$_2$Ti$_2$O$_7$ enters a hidden order ground state below $T_c\sim265$ mK where the nature of the ordered state is unknown but distinct from simple long range order.

Magnetic transition and spin fluctuations in the unconventional antiferromagnetic compoundYb3Pt4

Muon spin rotation and relaxation measurements have been carried out on the unconventional antiferromagnetYb3Pt4. Oscillations areobserved below TN = 2.22(1) K, consistent with the antiferromagnetic (AFM) Néel temperature observed in bulkexperiments. In agreement with neutron diffraction experiments the oscillation frequencyωμ(T)/2π followsan S = 1/2 mean-field temperature dependence, yielding a quasistatic local field of 1.71(2) kOe atT = 0. A crude estimate gives an ordered moment of ∼ 0.66 μB atT = 0, comparableto 0.81 μB from neutron diffraction. As from above the dynamic relaxation rateλd exhibits no critical slowing down, consistent with a mean-field transition. In the AFM phase aT-linearfit to λd(T), appropriate to a Fermi liquid, yields highly enhanced values ofλd/T and the Korringaconstant Kμ2T/λd, with Kμ the estimated muon Knight shift. A strong suppression ofλd by applied field is observed in the AFM phase. These properties are consistentwith the observed large Sommerfeld–Wilson and Kadowaki–Woods ratios inYb3Pt4 (although the data do not discriminate between Fermi-liquidand non-Fermi-liquid states), and suggest strong enhancement ofq≈0 spin correlations between large-Fermi-volume band quasiparticles in the AFM phase ofYb3Pt4.

Microscopic study of antiferromagnetic ground state and possible high-field ordered state inCeOs4Sb12using muon spin rotation and relaxation

An antiferromagnetic (AFM) ground state and a possible high-field ordered state in magnetic fields $H>1\text{ }\text{T}$ of a filled-skutterudite compound ${\text{CeOs}}_{4}{\text{Sb}}_{12}$ were investigated by the muon spin rotation and relaxation method. In a zero applied field, a spontaneous local field due to the weak AFM ordering was observed below $\ensuremath{\sim}1.6\text{ }\text{K}$. The magnetic volume fraction gradually increases below 1.6 K with decreasing temperature, suggesting that this phase is sensitive to sample quality. The magnitude of the ordered dipole moment in the AFM state was estimated to be in the range of $0.11--0.17\text{ }{\ensuremath{\mu}}_{B}/\text{Ce}$ at 0.1 K. In a field of 2 T applied along the [001] direction, clear anomalies in the muon Knight shift and linewidth were observed at $\ensuremath{\sim}1.5\text{ }\text{K}$, consistent with the phase-transition scenario into the high-field ordered state suggested from specific-heat, resistivity, elastic, and NMR anomalies. The possibility of multipole ordering in the high-field phase was discussed.

Muon knight shift measurements in CeCoIn5 below 17 kOe

We report muon Knight shift measurements in single crystals of CeCoIn5 below 17 kOe. The muon Knight shift decreases with decreasing temperature below Tc and the reduction of the Knight shift is roughly explained by the Fermi liquid relation. The magnetic field dependence of the reduction of the muon Knight shift is not in proportion to . This fact is inconsistent with simple expectation for a d-wave superconductor.

Field-Induced Coupled Superconductivity and Spin Density Wave Order in the Heavy Fermion CompoundCeCoIn5

The high-field superconducting state in CeCoIn(5) has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c axis close to the upper critical field mu(0)H(c2) = 4.97 T. At magnetic fields mu(0)H > or = 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < or = mu(0)H < 4.8 T. In the normal state close to H(c2) correlated spin fluctuations as described by the self-consistent renormalization theory are observed. The results support the formation of a mode-coupled superconducting and antiferromagnetically ordered phase in CeCoIn(5) for H directed parallel to the c axis.

Muon Knight shift study of pseudogap state in underdoped (Bi,Pb)2201

We performed zero-field muon spin rotation/relaxation (ZF-μSR) measurements on high-quality single-crystalline samples of Bi1.76Pb0.35Sr1.89CuO6+δ [(Bi,Pb)2201] over a wide doping region controlled by oxygen depletion (δ). We find that there is no static magnetic order above ∼2K in any of these samples including underdoped samples. The absence of slow antiferromagnetic fluctuation in the underdoped region allows reliable muon Knight shift measurements, which provides a direct evidence of reduced density of states at lower temperatures or “pseudogap”.

Development of the heavy-fermion state inCe2IrIn8and the effects of Ce dilution in(Ce1−xLax)2IrIn8

We report a study of muon Knight shifts to investigate the formation of the heavy-fermion state in single crystals of ${({\text{Ce}}_{1\ensuremath{-}x}{\text{La}}_{x})}_{2}{\text{IrIn}}_{8}$. Two different kinds of Knight-shift anomalies (deviations from a linear relation between the Knight shift and the susceptibility) are found: (1) a high-temperature effect arising from depopulation of crystalline electric field levels with temperature, and (2) a lower-temperature anomaly arising from the onset of the heavy-fermion state below a characteristic temperature ${T}^{\ensuremath{\ast}}$, in agreement with the ``two-fluid'' model of heavy-fermion formation. In ${\text{Ce}}_{2}{\text{IrIn}}_{8}$, we find ${T}_{c}^{\ensuremath{\ast}}=20.0(6)\text{ }\text{K}$ and ${T}_{a}^{\ensuremath{\ast}}=15.2(1.2)\text{ }\text{K}$ for applied field $H\ensuremath{\parallel}c$ axis and $H\ensuremath{\parallel}a$ axis, respectively. For the Ce diluted systems ${({\text{Ce}}_{1\ensuremath{-}x}{\text{La}}_{x})}_{2}{\text{IrIn}}_{8}$, $x=0.1$, 0.25, 0.50, 0.70, and 0.90, ${T}^{\ensuremath{\ast}}$ decreases linearly for $x\ensuremath{\le}0.5$, reaching zero near $x=0.7$, indicating the reduction in intersite $f$-spin correlations with Ce dilution. A comparison with nuclear magnetic-resonance measurements of Knight-shift anomalies in several other heavy-fermion compounds suggests that the observed small anisotropy in ${T}^{\ensuremath{\ast}}$ may be induced by the applied field, and that ${T}^{\ensuremath{\ast}}$ may be inherently isotropic, even in highly anisotropic materials.

μSR study of an layered organic superconductor κ-(BEDT-TTF)4Hg2.89Br8

Abstract Zero-field muon spin relaxation and high-field transverse muon spin rotation have been measured for an organic superconductor κ - ( BEDT - TTF ) 4 Hg 2.89 Br 8 . No anomaly is found in zero-field relaxation spectrum at the superconducting transition temperature, 4.2 K. The muon Knight shift determined by transverse muon spin rotation at 6 T exhibits Curie–Weiss like behavior down to 2 K, whereas static magnetic susceptibility shows a peak around 30 K. The muon Knight shift does not scale with the magnetic susceptibility at low temperatures.

Magnetism and superconductivity in heavy fermion superconductor

Abstract Zero field (ZF) and transverse field (TF) muon spin relaxation and rotation ( μ SR ) experiments have been carried out in the Cd-doped heavy fermion superconductor CeCoIn 5 to investigate its superconducting state. The ZF- μ SR results in CeCo ( In 0.97 Cd 0.03 ) 5 revealed that no spontaneous magnetic field was induced below its superconducting transition temperature ( T c ), indicating no evidence for time reversal symmetry breaking. The muon Knight shifts obtained from TF- μ SR measurements decrease significantly below T c , consistent with a spin-singlet state as in the parent compound CeCoIn 5 , which is a d-wave superconductor.

Muon Knight shift measurements in possible octupole ordering system [formula omitted

We performed muon Knight shift measurements on randomly aligned single crystalline samples of SmRu 4 P 12 in a magnetic field of 6 T. A marked increase in the muon spin relaxation rate was observed below a metal-insulator transition temperature, interpreted as an occurrence of finite local fields due to a dipole and/or octupole ordering. An expected magnetic anomaly at around 14 K in high fields was still obscure in a field of 6 T.

Formula omitted] study of the effects of Ce dilution on the development of the heavy-fermion state in [formula omitted

We have performed muon Knight shift measurements in the heavy-fermion compound ( Ce 1 - x La x ) 2 IrIn 8 , x = 0.1 , in 1 T magnetic field applied along the crystalline c-axis. Although the Knight shift K scales linearly with susceptibility χ above T ∼ 20 K , a breakdown of this relationship was observed below a temperature T * = 20.1 ( 8 ) K . It was found that this Knight shift anomaly occurs due to a low-temperature susceptibility component χ cf ∼ ( 1 - T / T * ) ln ( T * / T ) , corresponding to the formation of a coherent heavy-fermion state below T * , as found previously in the x = 0 compound. The characteristic temperature T * is reduced by about 4 K for 10% La doping, indicating a reduction in the strength of the intersite Ce fluctuations associated with the heavy electron state.

The search for magnetic order in [formula omitted]-Pu metal using muon spin relaxation

We review results from previous muon spin relaxation ( μ SR) measurements in applied fields of H 0 = 0 and 0.25 T which established an upper limit for the ordered or disordered frozen spin moment above T = 4 K in δ -Pu (4.3 at.% Ga) of μ ord ≤ 1 0 − 3 μ B . In addition, we present new data in H 0 = 0.25 and 2 T applied field on a highly annealed δ -Pu (4.3 at.% Ga) sample. Neither the muon Knight shift ( H 0 = 2 T) nor the inhomogeneous linewidths in the new sample show appreciable temperature dependence below about T = 60 K, also consistent with no spin freezing. Recent theoretical arguments advanced to explain these results are mentioned.

Spin-triplet superconductivity inPrOs4Sb12probed by muon Knight shift

We report a muon spin rotation study in single-crystalline samples of the heavy fermion superconductor $\mathrm{Pr}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$. The muon Knight shift is independent of temperature passing through ${T}_{c}$ down to $20\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ at 3 and $17\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$, indicating that the local spin susceptibility does not decrease in the superconducting state. This result is evidence that spin-triplet superconductivity is realized in $\mathrm{Pr}{\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$.