Muon Spin Rotation Studies Research Articles

The pairing symmetry in quasi-one-dimensional superconductor Rb[formula omitted]Mo[formula omitted]As[formula omitted

Quasi-one-dimensional electron systems display intrinsic instability towards long-range ordered phases at sufficiently low temperatures. The superconducting orders are of particular interest as they can possess either singlet or triplet pairing symmetry and frequently compete with magnetism. Here we report on muon spin rotation and relaxation (μSR) study of Rb2Mo3As3 characterised by one of the highest critical temperatures Tc=10.4 K among quasi-one-dimensional superconductors. The transverse-field μSR signal shows enhanced damping below Tc due to the formation of vortex lattice. Comparison of vortex lattice broadening against single gap s−, p− and d−wave models shows the best agreement for the s−wave scenario but with the anomalously small superconducting gap, Δ0, to Tc ratio of 2Δ0/kBTc=2.74(1). The alternative nodal p−wave or d−wave scenarios with marginally worse goodness of fit would yield more realistic 2Δ0/kBTc=3.50(2) and 2Δ0/kBTc=4.08(1), respectively, and thus they cannot be ruled out when accounting for the superconducting state in Rb2Mo3As3.

Confirming the high pressure phase diagram of the Shastry-Sutherland model

A Muon Spin Rotation (µ + SR) study was conducted to investigate the magnetic properties of SrCu2(BO3)2 (SCBO) as a function of temperature/pressure. Measurements in zero field and transverse field confirm the absence of long range magnetic order at high pressures and low temperatures. These measurements suggest changes in the Cu spin fluctuations characteristics above 21 kbar, consistent with the formation of a plaquette phase as previously suggested by inelastic neutron scattering measurements. SCBO is the only known realisation of the Shatry-Sutherland model, thus the ground state mediating the dimer and antiferromagnetic phase is likekly to be a plaquette state.

Muon spin rotation and relaxation study on Nb1−yFe2+y

We present a detailed study of the magnetic properties of weakly ferromagnetic/quantum critical Nb$_{1-y}$Fe$_{2+y}$ using muon spin rotation and relaxation ($\mu$SR). By means of an angular dependent study of the muon spin rotation signal in applied magnetic fields on a single crystal in the paramagnetic state we establish the muon stopping site in the crystallographic lattice of NbFe$_2$. With this knowledge we develop models to describe the muon spin rotation and relaxation signals in the weakly ferromagnetic, spin density wave and quantum critical phases of Nb$_{1-y}$Fe$_{2+y}$ and fit the corresponding experimental data. In particular, we quantify the $\mu$SR response for quantum critical behavior in Nb$_{1.0117}$Fe$_{1.9883}$ and extract the influence of residual weak structural disorder. From our analysis, Nb$_{1-y}$Fe$_{2+y}$ emerges to be uniquely suited to study quantum criticality close to weak itinerant ferromagnetic order.

Hydrogen-Ti<sup>3+</sup> Complex as a Possible Origin of Localized Electron Behavior in Hydrogen-Irradiated SrTiO<sub>3</sub>

A recent muon spin rotation ($\mu^+$SR) study on a paramagnetic defect complex formed upon implantation of $\mu^+$ pseudo-proton into SrTiO$_3$ is reviewed with a specific focus on the relation with experimental signatures of coexisting delocalized and localized electrons in hydrogen-irradiated metallic SrTiO$_3$ films. The paramagnetic defect complex, composed of interstitial $\mu^+$ and Ti$^{3+}$ small polaron, is characterized by a small dissociation energy of about 30 meV. Density functional theory (DFT) calculations in the generalized gradient approximation (GGA) +$U$ scheme for a corresponding hydrogen defect complex reveal that a thermodynamic donor level associated with electron transfer from an H$^+$-Ti$^{3+}$ complex to the conduction band can form just below the conduction band minimum for realistic $U$ values. These findings suggest that the coexistence of delocalized and localized electrons can be realized in hydrogen-irradiated SrTiO$_3$ in electron-rich conditions.

Spin order and fluctuations in the EuAl4 and EuGa4 topological antiferromagnets: A μSR study

We report on systematic muon-spin rotation and relaxation ($\mu$SR) studies of the magnetic properties of EuAl$_4$ and EuGa$_4$ single crystals at a microscopic level. Transverse-field $\mu$SR measurements, spanning a wide temperature range (from 1.5 to 50 K), show clear bulk AFM transitions, with an almost 100% magnetic volume fraction in both cases. Zero-field $\mu$SR measurements, covering both the AFM and the paramagnetic (PM) states, reveal internal magnetic fields $B_\mathrm{int}(0) = 0.33$ T and 0.89 T in EuAl$_4$ and EuGa$_4$, respectively. The transverse muon-spin relaxation rate $\lambda_\mathrm{T}$, a measure of the internal field distribution at the muon-stopping site, shows a contrasting behavior. In EuGa$_4$, it decreases with lowering the temperature, reaching its minimum at zero temperature, $\lambda_\mathrm{T}(0) = 0.71$ $\mu$s$^{-1}$. In EuAl$_4$, it increases significantly below $T_\mathrm{N}$, to reach 58 $\mu$s$^{-1}$ at 1.5 K, most likely reflecting the complex magnetic structure and the competing interactions in the AFM state of EuAl$_4$. In both compounds, the temperature-dependent longitudinal muon-spin relaxation $\lambda_\mathrm{L}(T)$, an indication of the rate of spin fluctuations, diverges near the onset of AFM order, followed by a significant drop at $T < T_\mathrm{N}$. In the AFM state, spin fluctuations are much stronger in EuAl$_4$ than in EuGa$_4$, while being comparable in the PM state. The evidence of robust spin fluctuations against the external magnetic fields provided by $\mu$SR may offer new insights into the origin of the topological Hall effect and the possible magnetic skyrmions in the EuAl$_4$ and EuGa$_4$ compounds.

Magnetic structure determination of high-moment rare-earth-based laminates

The laminate (Mo${}_{2/3}$Gd${}_{1/3}$)${}_{2}$AlC, based on high-moment Gd, grows as pristine crystals and might exfoliate or be etched into two-dimensional magnets, but its properties are unknown since Gd is a strong neutron absorber. Bypassing this difficulty, the authors succeed in determining the magnetic structure by combining neutron diffraction studies on isostructural compounds with muon spin rotation studies including first-principles site calculations and, most importantly, initial muon spin polarization variations.

Electron–phonon superconductivity in C-doped topological nodal-line semimetal Zr5Pt3: a muon spin rotation and relaxation (μSR) study

In the present work, we demonstrate that C-doped Zr5Pt3 is an electron–phonon superconductor (with critical temperature T C = 3.8 K) with a nonsymmorphic topological Dirac nodal-line semimetal state, which we report here for the first time. The superconducting properties of Zr5Pt3C0.5 have been investigated by means of magnetization, resistivity, specific heat, and muon spin rotation and relaxation (μSR) measurements. We find that at low temperatures, the depolarization rate is almost constant and it can be well described by a single-band s‐wave model with a superconducting gap of 2Δ(0)/k B T C = 3.84, somewhat higher than the value of BCS theory. From the transverse field μSR analysis, we estimate the London penetration depth λ L = 469 nm, superconducting carrier density n s = 1.83 × 1026 m−3, and effective mass m* = 1.428m e. The zero field μSR confirms the absence of any spontaneous magnetic field in the superconducting ground state. In order to gain additional insights into the electronic ground state of C-doped Zr5Pt3, we also performed first-principles calculations within the framework of density functional theory (DFT). The observed homogenous electronic character of the Fermi surface as well as the mutual decrease of T C and density of states at the Fermi level are consistent with the experimental findings of this study. However, the band structure reveals the presence of robust, gapless fourfold-degenerate nodal lines protected by 63 screw rotations and glide mirror planes. Therefore, Zr5Pt3 represents a novel, unprecedented condensed matter system to investigate the intricate interplay between superconductivity and topology.

Intertwined magnetic sublattices in the double perovskite compound LaSrNiReO6

We report a muon spin rotation ($\mu^{+}$SR) study of the magnetic properties of the double perovskite compound LaSrNiReO$_{6}$. Using the unique length and time scales of the $\mu^{+}$SR technique, we successfully clarify the magnetic ground state of LaSrNiReO$_{6}$, which was previously deemed as a spin glass state. Instead, our $\mu^{+}$SR results point towards a long-range dynamically ordered ground state below $T_{\rm C}= 23$ K, for which a static limit is foreseen at $T=0$. Furthermore, between 23 K$<T\leq$300 K, three different magnetic phases are identified: a dense ($23$ K$<T\leq75$ K), a dilute ($75$ K$<T\leq250$ K), and a paramagnetic ($T>250$ K) state. Our results reveal how two separate, yet intertwined magnetic lattices interact within the unique double perovskite structure and the importance of using complementary experimental techniques to obtain a complete understanding of the microscopic magnetic properties of complex materials.

Observation of a Charge-Neutral Muon-Polaron Complex in Antiferromagnetic Cr2O3

We report a comprehensive muon spin rotation ($\mu$SR) study of the prototypical magnetoelectric antiferromagnet Cr$_2$O$_3$. We find the positively charged muon ($\mu^+$) occupies several distinct interstitial sites, and displays a rich dynamic behavior involving local hopping, thermally activated site transitions and the formation of a charge-neutral complex composed of a muon and an electron polaron. The discovery of such a complex has implications for the interpretation of $\mu$SR spectra in a wide range of magnetic oxides, and opens a route to study the dopant characteristics of interstitial hydrogen impurities in such materials. We address implications arising from implanting a $\mu^+$ into a linear magnetoelectric, and discuss the challenges of observing a local magnetoelectric effect generated by the charge of the muon.

Charge-stripe order, antiferromagnetism, and spin dynamics in the cuprate-analog nickelate La4Ni3O8

We report a muon spin rotation ($\mu$SR) study of the cuprate-analog nickelate La$_4$Ni$_3$O$_8$, which undergoes a transition at 105 K to a low-temperature phase with charge-stripe and antiferromagnetic (AFM) order on square planar NiO$_2$ layers. Zero-field $\mu$SR shows that this transition is abrupt and that the AFM configuration is commensurate. Comparison of observed muon precession frequencies with Ni dipolar field calculations yields Ni moments $\lesssim 0.5\mu_B$. Dynamic muon spin relaxation above 105 K suggests critical slowing of Ni spin fluctuations, but is inconsistent with corresponding $^{139}$La NMR results. Critical slowing and an abrupt transition are also observed in the planar cuprate AFM La$_2$CuO$_{4+\delta}$, where they are evidence for weakly interplanar-coupled two-dimensional AFM spin fluctuations, but our $\mu$SR data do not agree quantitatively with theoretical predictions for this scenario.

Nodeless superconductivity and its evolution with pressure in the layered dirac semimetal 2M-WS2

Recently, the transition metal dichalcogenide (TMD) system 2M-WS2 has been identified as a Dirac semimetal exhibiting both superconductivity with the highest Tc ~ 8.5 K among all the TMD materials and topological surface states. Here we report on muon spin rotation (μSR) and density functional theory studies of microscopic SC properties and the electronic structure in 2M-WS2 at ambient and under hydrostatic pressures (pmax = 1.9 GPa). The SC order parameter in 2M-WS2 is determined to have single-gap s-wave symmetry. We further show a strong negative pressure effect on Tc and on the SC gap Δ. This may be partly caused by the pressure induced reduction of the size of the electron pocket around the Γ-point. We also find that the superfluid density ns is weakly affected by pressure. The absence of a strong pressure effect on ns and the absence of a correlation between ns and Tc in 2M-WS2, in contrast to the other SC TMDs Td-MoTe2 and 2H-NbSe2, is explained in terms of its location in the optimal (ambient pressure) and above the optimal (under pressure) superconducting regions of the phase diagram and its large distance to the other possible competing or cooperating orders.

Review of Muon Spin Rotation Studies of SRF Materials

Review of Muon Spin Rotation Studies of SRF Materials

Probing the superconducting ground state of ZrIrSi: A muon spin rotation and relaxation study

The superconducting ground state of newly reported ZrIrSi is probed by means of $\mu$SR technique along with resistivity measurement. The occurrence of superconductivity at $T_\mathrm{C}$ = 1.7 K is confirmed by resistivity measurement. ZF-$\mu$SR study revealed that below $T_\mathrm{C}$, there is no spontaneous magnetic field in the superconducting state, indicates TRS is preserved in case of ZrIrSi. From TF-$\mu$SR measurement, we have estimated the superfluid density as a function of temperature, which is described by an isotropic $s-$wave model with a superconducting gap $2\Delta(0)/k_\mathrm{B}T_\mathrm{C}$ = 5.1, indicates the presence of strong spin-orbit coupling. {\it Ab-initio} electronic structure calculation indicates that there are four bands passing through the Fermi level, forming four Fermi surface pockets. We find that the low-energy bands are dominated by the $4d$-orbitals of transition metal Zr, with substantially lesser weight from the $5d$-orbitals of the Ir-atoms.

Disentangling superconducting and magnetic orders in NaFe1−xNixAs using muon spin rotation

Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering.

Nodal superconductivity coexists with low-moment static magnetism in single-crystalline tetragonal FeS: A muon spin relaxation and rotation study

We report muon spin relaxation and rotation ($\mu$SR) measurements on hydrothermally-grown single crystals of the tetragonal superconductor~FeS, which help to clarify the controversial magnetic state and superconducting gap symmetry of this compound. $\mu$SR time spectra were obtained from 280~K down to 0.025~K in zero field (ZF) and applied fields up to 20 mT. In ZF the observed loss of initial asymmetry (signal amplitude) and increase of depolarization rate~$\Lambda_\mathrm{ZF}$ below 10~K indicate the onset of static magnetism, which coexists with superconductivity below $T_c$. Transverse-field $\mu$SR yields a muon depolarization rate $\sigma_\mathrm{sc} \propto \lambda_{ab}^{-2}$ that clearly shows a linear dependence at low temperature, consistent with nodal superconductivity. The $s{+}d$-wave model gives the best fit to the observed temperature and field dependencies. The normalized superfluid densities versus normalized temperature for different fields collapse onto the same curve, indicating the superconducting gap structure is independent of field. The $T=0$ in-plane penetration depth $\lambda_{ab}$(0) = 198(3) nm.

Macroscopic phase separation of superconductivity and ferromagnetism in Sr0.5Ce0.5FBiS2\u2212xSex revealed by \u03bcSR

The compound Sr0.5Ce0.5FBiS2 belongs to the intensively studied family of layered BiS2 superconductors. It attracts special attention because superconductivity at Tsc = 2.8 K was found to coexist with local-moment ferromagnetic order with a Curie temperature TC = 7.5 K. Recently it was reported that upon replacing S by Se TC drops and ferromagnetism becomes of an itinerant nature. At the same time Tsc increases and it was argued superconductivity coexists with itinerant ferromagnetism. Here we report a muon spin rotation and relaxation study (μSR) conducted to investigate the coexistence of superconductivity and ferromagnetic order in Sr0.5Ce0.5FBiS2−xSex with x = 0.5 and 1.0. By inspecting the muon asymmetry function we find that both phases do not coexist on the microscopic scale, but occupy different sample volumes. For x = 0.5 and x = 1.0 we find a ferromagnetic volume fraction of ~8 % and ~30 % at T = 0.25 K, well below TC = 3.4 K and TC = 3.3 K, respectively. For x = 1.0 (Tsc = 2.9 K) the superconducting phase occupies most (~64 %) of the remaining sample volume, as shown by transverse field experiments that probe the Gaussian damping due to the vortex lattice. We conclude ferromagnetism and superconductivity are macroscopically phase separated.

Pressure tuning of structure, superconductivity, and novel magnetic order in the Ce-underdoped electron-doped cuprate T′−Pr1.3−xLa0.7CexCuO4 ( x=0.1 )

High-pressure neutron powder diffraction, muon-spin rotation and magnetization studies of the structural, magnetic and the superconducting properties of the Ce-underdoped superconducting (SC) electron-doped cuprate system T'-Pr_1.3-xLa_0.7Ce_xCuO_4 with x = 0.1 are reported. A strong reduction of the lattice constants a and c is observed under pressure. However, no indication of any pressure induced phase transition from T' to T structure is observed up to the maximum applied pressure of p = 11 GPa. Large and non-linear increase of the short-range magnetic order temperature T_so in T'-Pr_1.3-xLa_0.7Ce_xCuO_4 (x = 0.1) was observed under pressure. Simultaneously pressure causes a non-linear decrease of the SC transition temperature T_c. All these experiments establish the short-range magnetic order as an intrinsic and a new competing phase in SC T'-Pr_1.2La_0.7Ce_0.1CuO_4. The observed pressure effects may be interpreted in terms of the improved nesting conditions through the reduction of the in-plane and out-of-plane lattice constants upon hydrostatic pressure.

Pressure-induced magnetic order in FeSe: A muon spin rotation study

The magnetic order induced by the pressure was studied in single crystalline FeSe by means of muon-spin rotation ($\mu$SR) technique. By following the evolution of the oscillatory part of the $\mu$SR signal as a function of angle between the initial muon-spin polarization and 101 axis of studied crystal it was found that the pressure induced magnetic order in FeSe corresponds either to the collinear (single-stripe) antiferromagnetic order as observed in parent compounds of various FeAs-based superconductors or to the Bi-Collinear order as obtained in FeTe system, but with the Fe spins turned by 45$^{\rm o}$. The value of the magnetic moment per Fe atom was estimated to be $\simeq 0.13-0.14$~$\mu_{\rm B}$ at $p\simeq 1.9$~GPa.

Recent μSR Studies of Insulating Rare-Earth Pyrochlore Magnets

We review recent muon spin rotation and relaxation (μSR) studies performed on insulating magnetic systems crystallizing in the pyrochlore structure and for which the only magnetic species are rare-earth ions. Different points are discussed: attempts to measure directly the magnetic charge of the monopoles in classical spin-ice systems, the frequency shift of Tb2Ti2O7 at 20 mK which is at variance with expectation for a quantum spin-ice system, and the detection of unexpected short-range magnetic correlations in the magnetically ordered state of Yb2Ti2O7, Yb2Sn2O7, and Er2Ti2O7. An explanation for the ubiquitous persistent spin dynamics is given in terms of spin loops. Their description requires to go beyond mean-field, i.e., at least Gaussian fluctuations have to be taken into account. While in the magnetically ordered state a spontaneous field is detected for some systems, such as Nd2Sn2O7, it is absent for others, such as Yb2Sn2O7. A theoretical work suggests this feature to be related to the magnetic s...

Anomalously slow spin dynamics and short-range correlations in the quantum spin ice systemsYb2Ti2O7andYb2Sn2O7

We report a positive muon spin relaxation and rotation (\muSR) study of the quantum spin ice materials Yb2Ti2O7 and Yb2Sn2O7 focusing on the low field response. In agreement with earlier reports, data recorded in small longitudinal fields evidence anomalously slow spin dynamics in the microsecond range below the temperature T_c at which the specific heat displays an intense peak, namely T_c = 0.24 K and 0.15 K, respectively, for the two systems. We found that slow dynamics extends above T_c up to at least 0.7 K for both compounds. The conventional dynamical Gaussian Kubo-Toyabe model describes the \muSR spectra recorded above T_c. At lower temperatures a published analytical extension of the Gaussian Kubo-Toyabe model provides a good description, consistent with the existence of short-range magnetic correlations. While the physical response of the two systems is qualitatively the same, Yb2Ti2O7 exhibits a much larger local magnetic susceptibility than Yb2Sn2O7 below T_c. Considering previously reported ac susceptibility, neutron scattering and \muSR results, we suggest the existence of anomalously slow spin dynamics to be a common physical property of pyrochlore magnetic materials. The possibility of molecular spin substructures to be associated to the slow dynamics and therefore the short-range correlations is mentioned. The slow spin dynamics observed under field does not exclude the presence of much faster dynamics detected in extremely low or zero field.