Spin Relaxation Studies Research Articles

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.

Anomalous quantum critical spin dynamics in YFe2Al10

We report results of a muon spin relaxation ($\mu$SR) study of YFe$_2$Al$_{10}$, a quasi-2D nearly-ferromagnetic metal in which unconventional quantum critical behavior is observed. No static Fe$^{2+}$ magnetism, with or without long-range order, is found down to 19~mK\@. The dynamic muon spin relaxation rate~$\lambda$ exhibits power-law divergences in temperature and magnetic field, the latter for fields that are too weak to affect the electronic spin dynamics directly. We attribute this to the proportionality of $\lambda(\omega_\mu,T)$ to the dynamic structure factor~$S(\omega_\mu,T)$, where $\omega_\mu \approx 10^5$--$10^7~\mathrm{s}^{-1}$ is the muon Zeeman frequency. These results suggest critical divergences of $S(\omega_\mu,T)$ in both temperature and frequency. Power-law scaling and a 2D dissipative quantum XY (2D-DQXY) model both yield forms for $S(\omega,T)$ that agree with neutron scattering data ($\omega \approx 10^{12}~\mathrm{s}^{-1}$). Extrapolation to $\mu$SR frequencies agrees semi-quantitatively with the observed temperature dependence of $\lambda(\omega_\mu,T)$, but predicts frequency independence for $\omega_\mu \ll T$ in extreme disagreement with experiment. We conclude that the quantum critical spin dynamics of YFe$_2$Al$_{10}$ are not well understood at low frequencies.

Muon spin relaxation study of spin dynamics in the extended kagome systems YBaCo4O7+δ (δ=0,0.1)

We present muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements of the extended kagome systems ${\mathrm{YBaCo}}_{4}{\mathrm{O}}_{7+\ensuremath{\delta}}$ ($\ensuremath{\delta}=0,0.1$), comprising two interpenetrating kagome sublattice of $\mathrm{Co}{(\mathrm{I})}^{3+}$ ($S=3/2$) and a triangle sublattice of $\mathrm{Co}{(\mathrm{II})}^{2+}$ ($S=2$). The zero- and longitudinal-field $\ensuremath{\mu}\mathrm{SR}$ spectra of the stoichiometric compound ${\mathrm{YBaCo}}_{4}{\mathrm{O}}_{7}$ unveil that the triangular subsystem orders at ${T}_{N}=101$ K. In contrast, the muon spin relaxation rate pertaining to the kagome subsystem shows persistent spin dynamics down to $T=20$ K and then a sublinear decrease $\ensuremath{\lambda}(T)\ensuremath{\sim}{T}^{0.66(5)}$ on cooling towards $T=4$ K. In addition, the introduction of interstitial oxygen ($\ensuremath{\delta}=0.1$) is found to drastically affect the magnetism. For the fast-cooling experiment ($g10$ K/min), ${\mathrm{YBaCo}}_{4}{\mathrm{O}}_{7.1}$ enters a regime characterized by persistent spin dynamics below 90 K. For the slow-cooling experiment (1 K/min), evidence is obtained for the phase separation into interstitial oxygen-poor and oxygen-rich regions with distinct correlation times. The observed temperature, cooling rate, and oxygen content dependencies of spin dynamics are discussed in terms of a broad range of spin-spin correlation times, relying on a different degree of frustration between the kagome and triangle sublattices as well as of oxygen migration.

Circularly polarized photoluminescence and Hanle effect measurements of spin relaxation in organic–inorganic hybrid perovskite films

Partial circularly polarized photoluminescence with polarization degree of 2% from CH3NH3PbBr3 film at 77 K is observed, excited using a circularly polarized 532 nm laser. Moreover, the Hanle effect is measured to study spin relaxation in CH3NH3PbBr3 film, yielding a spin lifetime of ∼240 ps at 77 K.

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.

Comment on “Muon spin relaxation study of spin dynamics in poly(triarylamine)”

He et al. studied the muoniated radicals formed by muonium (Mu) addition to the low-molecular-weight polymer poly(triarylamine) (PTAA) (He et al., 2015) [1], an organic semiconductor, using avoided level crossing muon spin resonance (ALC-μSR) (McKenzie and Roduner, 2013; McKenzie, 2009) [2,3]. The goal of these experiments was to study the electron spin relaxation of a paramagnetic defect in PTAA using a local probe. Our main issue with this paper is the claim that parameters relating to the electronic structure of the muoniated radicals have been measured with greater precession than we believe is possible considering the quality of the ALC-μSR spectra presented.

Reply to “Comment on ‘Muon spin relaxation study of spin dynamics in poly(triarylamine)”’

Reply to “Comment on ‘Muon spin relaxation study of spin dynamics in poly(triarylamine)”’

Neutron diffraction and μSR studies of two polymorphs of nickel niobate NiNb2O6

Neutron diffraction and muon spin relaxation ($\mu$SR) studies are presented for the newly characterized polymorph of NiNb$_2$O$_6$ ($\beta$-NiNb$_2$O$_6$) with space group P4$_2$/n and $\mu$SR data only for the previously known columbite structure polymorph with space group Pbcn. The magnetic structure of the P4$_2$/n form was determined from neutron diffraction using both powder and single crystal data. Powder neutron diffraction determined an ordering wave vector $\vec{k}$ = ($\frac{1}{2},\frac{1}{2},\frac{1}{2}$). Single crystal data confirmed the same $\vec{k}$-vector and showed that the correct magnetic structure consists of antiferromagnetically-coupled chains running along the a or b-axes in adjacent Ni$^{2+}$ layers perpendicular to the c-axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related tri-rutile phases, NiSb$_2$O$_6$ and NiTa$_2$O$_6$. $\mu$SR data finds a transition temperature of $T_N \sim$ 15 K for this system, while the columbite polymorph exhibits a lower $T_N =$ 5.7(3) K. Our $\mu$SR measurements also allowed us to estimate the critical exponent of the order parameter $\beta$ for each polymorph. We found $\beta =$ 0.25(3) and 0.16(2) for the $\beta$ and columbite polymorphs respectively. The single crystal neutron scattering data gives a value for the critical exponent $\beta =$~0.28(3) for $\beta$-NiNb$_2$O$_6$, in agreement with the $\mu$SR value. While both systems have $\beta$ values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. In other words, although both systems appear to well-described by $S = 1$ spin chains, the interchain interactions in the $\beta$-polymorph are likely much larger.

Monte Carlo method for studies of spin relaxation in degenerate electron gas: Application to monolayer graphene

Monte Carlo method allowing to account for the effect of Pauli Exclusion Principle in the case of spin polarized electron gas is demonstrated. Modeling requires calculation of electron states occupancy accounting for the direction of the spin of the scattered electron. As an example of application, calculations for the case of spin and energy relaxation of initially polarized electrons in monolayer graphene have been performed. Model includes D'yakonov-Perel' and Elliot-Yafet relaxation mechanisms. It is demonstrated that electron distribution function and energy relaxation follow the spin polarization relaxation and they are mainly governed by spin related scattering processes.

Signature of multigap nodeless superconductivity in CaKFe4As4

A newly discovered family of high-Tc Fe-based superconductors, AeAFe4As4 (Ae = Ca, Sr, Eu and A = K, Rb, Cs), offers further opportunities to understand unconventional superconductivity in these materials. In this Rapid Communication, we report on the superconducting and magnetic properties of CaKFe4As4, studied using muon spectroscopy. Zero-field muon spin relaxation studies carried out on the CaKFe4As4 superconductor do not show any detectable magnetic anomaly at Tc or below, implying that time-reversal symmetry is preserved in the superconducting ground state. The temperature dependence of the superfluid density of CaKFe4As4 is found to be compatible with a two-gap s + s-wave model with gap values of 8.6(4) and 2.5(3) meV, similar to the other Fe-based superconductors. The presence of two superconducting energy gaps is consistent with theoretical and other experimental studies on this material. The value of the penetration depth at T = 0 K has been determined as 289(22) nm.

Anisotropic Hanle line shape via magnetothermoelectric phenomena

We observe anisotropic Hanle lineshape with unequal in-plane and out-of-plane non-local signals for spin precession measurements carried out on lateral metallic spin valves with transparent interfaces. The conventional interpretation for this anisotropy corresponds to unequal spin relaxation times for in-plane and out-of-plane spin orientations as for the case of 2D materials like graphene, but it is unexpected in a polycrystalline metallic channel. Systematic measurements as a function of temperature and channel length, combined with both analytical and numerical thermoelectric transport models, demonstrate that the anisotropy in the Hanle lineshape is magneto-thermal in origin, caused by the anisotropic modulation of the Peltier and Seebeck coefficients of the ferromagnetic electrodes. Our results call for the consideration of such magnetothermoelectric effects in the study of anisotropic spin relaxation.

A Site-Specific Study of the Magnetic Field-Dependent Proton Spin Relaxation of an Iridium N-Heterocyclic Carbene Complex

Abstract We report a study of proton spin relaxation of an Iridium N-heterocyclic carbene complex [Ir(COD)(IMes)Cl] complex (where COD=1,5-cyclooctadiene, Imes=1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene). This compound is a pre-catalyst of the most efficient complex allowing the signal amplification by reversible exchange (SABRE) effect, relevant for enhancing weak signals in nuclear magnetic resonance (NMR). An important feature of the study is a combination of relaxation measurements over a wide field range with high-resolution NMR detection. As a result, we are able to measure nuclear magnetic relaxation dispersion (NMRD) curves in the field range 0.1 mT–16.4 T (corresponding to the frequency range 4 kHz–700 MHz) for individual protons in the complex under study. This attractive possibility enables determination of the motional correlation times, τc , for the individual protons by analyzing the features in the NMRD curves (increase of the relaxation times) appearing at the magnetic fields where ωτc ≈1 (here ω is the proton Larmor precession frequency at a given field strength). The following correlation times were determined: (1.3±0.1) ns for the protons of imidazol-2-ylidene, (0.96±0.1) ns for the ortho-protons of two phenyl moieties and (0.95±0.2) ns for the protons of methyl groups. Additionally, we report low-field features coming from “strong coupling” of the protons. One should note that such features must not be misinterpreted by associating them with motional features. From the low-field features we obtain consistent estimates for the proton spin-spin interactions. The analysis of motional correlation times is also of importance for interpretation of spin order transfer from parahydrogen to various substrates in transient organometallic complexes (termed the SABRE effect) at high magnetic field.

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...

Quantum limited heterodyne detection of spin noise.

Spin noise spectroscopy is a powerful technique for studying spin relaxation in semiconductors. In this article, we propose an extension of this technique based on optical heterodyne detection of spin noise, which provides several key advantages compared to conventional spin noise spectroscopy: detection of high frequency spin noise not limited by detector bandwidth or sampling rates of digitizers, quantum limited sensitivity even in case of very weak probe power, and possible amplification of the spin noise signal. Heterodyne detection of spin noise is demonstrated on insulating n-doped GaAs. From measurements of spin noise spectra up to 0.4 Tesla, we determined the distribution of g-factors, Δg/g = 0.49%.

Spin dynamics of the ordered dipolar-octupolar pseudospin-12pyrochloreNd2Zr2O7probed by muon spin relaxation

We present a muon spin relaxation study on the Ising pyrochlore Nd$_2$Zr$_2$O$_7$ which develops an "all-in-all-out" magnetic order below 0.4~K. At 20~mK far below the ordering transition temperature, the zero-field muon spin relaxation spectra show no static features and can be well described by a dynamical Gaussian-broadened Gaussian Kubo-Toyabe function indicating strong fluctuations of the ordered state. The spectra of the paramagnetic state (below 4.2~K) reveal anomalously slow paramagnetic spin dynamics and show only small difference with the spectra of the ordered state. We find that the fluctuation rate decreases with decreasing temperature and becomes nearly temperature independent below the transition temperature indicating persistent slow spin dynamics in the ground state. The field distribution width shows a small but sudden increase at the transition temperature and then becomes almost constant. The spectra in applied longitudinal fields are well fitted by the conventional dynamical Gaussian Kubo-Toyabe function, which further supports the dynamical nature of the ground state. The fluctuation rate shows a peak as a function of external field which is associated with a field-induced spin-flip transition. The strong dynamics in the ordered state are attributed to the transverse coupling of the Ising spins introduced by the multipole interactions.

Muon Spin Relaxation and Neutron Diffraction Studies of Cluster-Glass States in Sr1−xLaxRuO3

To clarify the magnetic properties of cluster-glass states in Sr1-xLaxRuO3 (0.3 <= x <= 0.5), we report herein the results of muon spin relaxation (muSR) and neutron powder diffraction measurements. The muSR experiments showed that magnetic clusters start developing well above the peak temperature T^* in the ac susceptibility. The volume fraction of the magnetically ordered region increases continuously with decreasing temperature, showing no anomaly at T^*, and reaches nearly 100% at the lowest temperature. The temperature variation of the volume fraction is essentially independent of the La concentration in the x range presently investigated, although the dc magnetization is significantly suppressed with increasing x. Neutron powder diffraction experiments revealed that the ground state for x = 0.3 is a long-range ferromagnetic ordered state. These results indicate that, with decreasing temperature, cluster-glass states in Sr1-xLaxRuO3 gradually develop into long-range ferromagnetic ordered states with decreasing temperature, and that the magnetic ordering process differs strikingly from that expected for a conventional second-order ferromagnetic transition.

A fast field-cycling device for high-resolution NMR: Design and application to spin relaxation and hyperpolarization experiments

A device for performing fast magnetic field-cycling NMR experiments is described. A key feature of this setup is that it combines fast switching of the external magnetic field and high-resolution NMR detection. The field-cycling method is based on precise mechanical positioning of the NMR probe with the mounted sample in the inhomogeneous fringe field of the spectrometer magnet. The device enables field variation over several decades (from 100μT up to 7T) within less than 0.3s; progress in NMR probe design provides NMR linewidths of about 10−3ppm. The experimental method is very versatile and enables site-specific studies of spin relaxation (NMRD, LLSs) and spin hyperpolarization (DNP, CIDNP, and SABRE) at variable magnetic field and at variable temperature. Experimental examples of such studies are demonstrated; advantages of the experimental method are described and existing challenges in the field are outlined.

Questioning Antiferromagnetic Ordering in the Expanded Metal, Li(NH3)4: A Lack of Evidence from μSR.

We present the results of a muon spin relaxation study of the solid phases of the expanded metal, Li(NH3)4. No discernible change in muon depolarization dynamics is witnessed in the lowest temperature phase (≤25 K) of Li(NH3)4, thus suggesting that the prevailing view of antiferromagnetic ordering is incorrect. This is consistent with the most recent neutron diffraction data. Discernible differences in muon behavior are reported for the highest temperature phase of Li(NH3)4 (82-89 K), attributed to the onset of structural dynamics prior to melting.

Spin relaxation characteristics in Ag nanowire covered with various oxides

We have studied spin relaxation characteristics in a Ag nanowire covered with various oxide layers of Bi2O3, Al2O3, HfO2, MgO, or AgOx by using non-local spin valve structures. The spin-flip probability, a ratio of momentum relaxation time to spin relaxation time at 10 K, exhibits a gradual increase with an atomic number of the oxide constituent elements, Mg, Al, Ag, and Hf. Surprisingly, the Bi2O3 capping was found to increase the probability by an order of magnitude compared with other oxide layers. This finding suggests the presence of an additional spin relaxation mechanism such as Rashba effect at the Ag/Bi2O3 interface, which cannot be explained by the simple Elliott-Yafet mechanism via phonon, impurity, and surface scatterings. The Ag/Bi2O3 interface may provide functionality as a spin to charge interconversion layer.