Muon Relaxation Research Articles

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field μSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Effect of Co-Doping on the Magnetic Ground State of the Heavy-Fermion System CeCu2Ge2 Studied by Neutron Diffraction

The antiferromagnetic phase transition of the heavy-fermion system Ce(Cu1−xCox)2Ge2 for x = 0.05 and 0.2, showing up in specific heat, magnetic susceptibility, and muon spin relaxation (μSR) data, has been further investigated. The neutron diffraction (ND) results show that Co-doping drastically reduces the moment size of Ce, without a qualitative change in the magnetic structure of the undoped compound CeCu2Ge2. An incommensurate magnetic propagation vector k = (0.2852, 0.2852, 0.4495) with a cycloidal magnetic structure with a Ce moment of 0.55 μB in the ab-plane has been observed for x = 0.05. Although for x = 0.2 the specific heat and magnetic susceptibility data reflect a phase transition with a broad peak and the muon relaxation rate shows a sharp peak at T = 0.9 K, our ND data dismiss the possibility of a long-range magnetic ordering down to 50 mK. The ND data, along with previously reported results for x = 0.2, are interpreted in terms of the reduced ordered state magnetic moments of the Ce3+ ion by Kondo screening and the presence of dynamical short-range magnetic correlations.

Impact of Mn-Pn intermixing on magnetic properties of an intrinsic magnetic topological insulator: the µSR perspective

We investigated the magnetic properties of polycrystalline samples of the intrinsic magnetic topological insulators MnPn2Te4, with pnictogen Pn = Sb, Bi, by bulk magnetization and µSR. DC susceptibility detects the onset of magnetic ordering at TN = 27 K and 24 K and a field dependence of the macroscopic magnetization compatible with ferri- (or ferro-) and atiferro- magnetic ordering, respectively. Weak transverse field (wTF) Muon Spin Rotation (µSR) confirms the homogeneous bulk nature of magnetic ordering at the same two distinct transition temperatures. Zero Field (ZF) µSR shows that the Sb based material displays a broader distribution of internal field at the muon, in accordance with a larger deviation from the stoichiomectric composition and a higher degree of positional disorder (Mn at the Pn(6c) site), which however does not affect significantly the sharpness of the thermodynamic transition, as detected by the muon magnetic volume fraction and the observability of a critical divergence in the longitudinal and transverse muon relaxation rates.

Improving the study of atoms under pressure

Instrumentation to probe muon rotation and relaxation under hydrostatic pressure proposed.

Two-step Mott transition in Ni(S,Se)2 : μSR studies and charge-spin percolation model

A pyrite system ${\mathrm{NiS}}_{2\ensuremath{-}x}{\mathrm{Se}}_{x}$ exhibits a bandwidth controlled Mott transition via (S,Se) substitutions in a two-step process: the antiferromagnetic insulator (AFI) to antiferromagnetic metal (AFM) transition at $x\ensuremath{\sim}0.45$ followed by the AFM to paramagnetic metal (PMM) transition at $x\ensuremath{\sim}1.0$. Among a few other Mott systems which exhibit similar two-step transitions, $\mathrm{Ni}{(\mathrm{S},\mathrm{Se})}_{2}$ is of particular interest because a large intermediate AFM region in the phase diagram would provide unique opportunities to study the interplay between the spin and charge order. Muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements on ${\mathrm{NiS}}_{2\ensuremath{-}x}{\mathrm{Se}}_{x}$ have been carried out on seven different Se concentrations from $x=0$ to 1.0. The results on quantum evolution demonstrate significantly random spin correlations in the AFM region associated with a rapid reduction of the average local static Ni moment size with increasing $x$, yet without signatures of macroscopic phase separation as confirmed by nearly full volume fraction participating in the static muon relaxation process up to $x\ensuremath{\sim}$ 0.9 at low temperatures. The observed time spectra in the AFM region indicate Lorentzian distribution of static internal field expected for a spatially dilute spin structure. No signature of dynamic critical behavior was observed in thermal phase transitions. The previous neutron scattering studies found sharp magnetic Bragg peaks with a slower reduction of the average ordered moment size in the AFM region. By comparing and combining the muon and neutron results, here we propose a picture where the spin order is maintained by the percolation of ``nonmetallic'' localized and dangling Ni moments surrounded by S, while the charge transition from AFI to AFM is caused by the percolation of the conducting paths generated by the Ni-Se-Ni bonds. This model of interpenetrating charge and spin percolation captures the behavior of experimental results on (a) Se concentration for the insulator to metal transition, (b) Se concentration for the AFM to PMM transition, (c) variation of Hall effect in the AFM region due to conducting Ni charges on the backbone of the percolating charge network, (d) evolution of the neutron Bragg intensity, (e) evolution of the muon static local fields, and (f) spatial variation of the local conductance observed by STM.

Quantum disordered state in the J1−J2 square-lattice antiferromagnet Sr2Cu(Te0.95W0.05)O6

The $B$-site ordered double perovskites ${\mathrm{Sr}}_{2}\mathrm{Cu}({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{W}}_{x}){\mathrm{O}}_{6}$ provide an excellent arena for investigating exotic phases expected for the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square-lattice Heisenberg antiferromagnet. Here, combining magnetic susceptibility and specific-heat measurements with electron spin resonance (ESR) and muon spin rotation/relaxation $(\ensuremath{\mu}\mathrm{SR})$ techniques, we explore a spin-liquid-like state in the vicinity of the N\'eel critical end point $(x=0.05--0.1)$. The specific heat and the ESR and muon relaxation rates give evidence for an energy hierarchy of low-energy excitations, reminiscent of randomness-induced singlet states. In addition, the weak transverse $\ensuremath{\mu}\mathrm{SR}$ data show a fraction of frozen magnetic moments in the random-singlet background. The origin of a random-singlet-like state near the phase boundary is discussed in terms of concomitant exchange randomness and local strain generated by the ${\mathrm{W}}^{6+}\text{\ensuremath{-}}\mathrm{for}\text{\ensuremath{-}}{\mathrm{Te}}^{6+}$ substitution.

Magnetic structure of the quantum magnet SrCuTe2O6

SrCuTe$_2$O$_6$ consists of a 3-dimensional arrangement of spin-$\frac{1}{2}$ Cu$^{2+}$ ions. The 1st, 2nd and 3rd neighbor interactions respectively couple Cu$^{2+}$ moments into a network of isolated triangles, a highly frustrated hyperkagome lattice consisting of corner sharing triangles and antiferromagnetic chains. Of these, the chain interaction dominates in SrCuTe$_2$O$_6$ while the other two interactions lead to frustrated inter-chain coupling giving rise to long range magnetic order at suppressed temperatures. In this paper, we investigate the magnetic properties in SrCuTe$_2$O$_6$ using muon relaxation spectroscopy and neutron diffraction and present the low temperature magnetic structure.

Magnetic Phase Diagram of Cu4–xZnx(OH)6FBr Studied by Neutron-Diffraction and μSR Techniques*Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302900, 2016YFA0300500, 2018YFA0704200, 2017YFA0303100, and 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 11874401, 11674406, 11674372, 11961160699, 11774399, 12061130200, 11974392, and 11822411), the Strategic Priority Research Program(B) of the Chinese Academy of Sciences (Grant Nos.

We systematically investigate the magnetic properties of Cu4 – xZnx(OH)6FBr using the neutron diffraction and muon spin rotation and relaxation (μSR) techniques. Neutron-diffraction measurements suggest that the long-range magnetic order and the orthorhombic nuclear structure in the x = 0 sample can persist up to x = 0.23 and 0.43, respectively. The temperature dependence of the zero-field μSR spectra provides two characteristic temperatures, TA0 and Tλ, which are associated with the initial drop close to zero time and the long-time exponential decay of the muon relaxation, respectively. Comparison between TA0 and TM from previously reported magnetic-susceptibility measurements suggest that the former comes from the short-range interlayer-spin clusters that persist up to x = 0.82. On the other hand, the doping level where Tλ becomes zero is about 0.66, which is much higher than threshold of the long-range order, i.e., ∼0.4. Our results suggest that the change in the nuclear structure may alter the spin dynamics of the kagome layers and a gapped quantum-spin-liquid state may exist above x = 0.66 with the perfect kagome planes.

Theory of strain-induced magnetic order and splitting of Tc and TTRSB in Sr2RuO4

The internal structure of the superconducting state in Sr$_2$RuO$_4$ remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\rm TRSB}$ with applied strain [Grinenko et al., arXiv:2001.08152]. In addition, static magnetic order is induced by the uniaxial strain beyond $\sim$1 GPa, indicating that unstrained Sr$_2$RuO$_4$ is close to a magnetic quantum critical point. Here, we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. It is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain-dependence of accidentally degenerate pair states in unstrained Sr$_2$RuO$_4$. In addition, while unstrained Sr$_2$RuO$_4$ features mainly $(2\pi/3,2\pi/3)$ magnetic fluctuations, uniaxial strain promotes $(\pi,\pm\pi/2)$ magnetism.

Persistent spin dynamics in the pressurized spin-liquid candidate YbMgGaO4

Single-crystal x-ray diffraction, density-functional band-structure calculations, and muon spin relaxation ($\mu$SR) are used to probe pressure evolution of the triangular spin-liquid candidate YbMgGaO$_4$. The rhombohedral crystal structure is retained up to at least 10 GPa and shows a nearly uniform compression along both in-plane and out-of-plane directions, whereas local distortions caused by the random distribution of Mg$^{2+}$ and Ga$^{3+}$ remain mostly unchanged. The $\mu$SR data confirm persistent spin dynamics up to 2.6 GPa and down to 250 mK with no change in the muon relaxation rate. Longitudinal-field $\mu$SR reveals power-law behavior of the spin-spin autocorrelation function, both at ambient pressure and upon compression.

Penetration depth and gap structure in the antiperovskite oxide superconductor Sr3−xSnO revealed by μSR

We report a $\mu$SR study on the antiperovskite oxide superconductor Sr$_{3-x}$SnO. With transverse-field $\mu$SR, we observed the increase of the muon relaxation rate upon cooling below the superconducting transition temperature $T_{\mathrm{c}}=5.4$ K, evidencing bulk superconductivity. The exponential temperature dependence of the relaxation rate $\sigma$ at low temperatures suggests a fully gapped superconducting state. We evaluated the zero-temperature penetration depth $\lambda(0)\propto1/\sqrt{\sigma(0)}$ to be around 320-1020 nm. Such a large value is consistent with the picture of a doped Dirac semimetal. Moreover, we revealed that the ratio $T_{\mathrm{c}}/\lambda(0)^{-2}$ is larger than those of ordinary superconductors and is comparable to those of unconventional superconductors. The relatively high $T_{\mathrm{c}}$ for small carrier density may hint at an unconventional pairing mechanism beyond the ordinary phonon-mediated pairing. In addition, zero-field $\mu$SR did not provide evidence of broken time-reversal symmetry in the superconducting state. These features are consistent with the theoretically proposed topological superconducting state in Sr$_{3-x}$SnO, as well as with $s$-wave superconductivity.

Two-band superconductivity with unconventional pairing symmetry in HfV2Ga4

In this letter, we have examined the superconducting ground state of the HfV$_2$Ga$_4$ compound using resistivity, magnetization, zero-field (ZF) and transverse-field (TF) muon-spin relaxation and rotation ($\mu$SR) measurements. Resistivity and magnetization unveil the onset of bulk superconductivity with $T_{\bf c}\sim$ 3.9~K, while TF-$\mu$SR measurements show that the temperature dependence of the superfluid density is well described by a nodal two-gap $s$+$d$-wave order parameter model. In addition, ZF muon relaxation rate increases with decreasing temperature below 4.6 K, indicating the presence of weak spin fluctuations. These observations suggest an unconventional multiband nature of the superconductivity possibly arising from the distinct $d$-bands of V and Hf ions with spin fluctuations playing an important role. To better understand these findings, we carry out first-principles electronic-structure calculations, further highlighting that the Fermi surface consists of multiple disconnected sheets with very different orbital weights and spin-orbit coupling, bridging the way for a nodal multiband superconductivity scenario. In this vein, therefore, HfV$_2$Ga$_4$-family stands out as an open avenue to novel unexplored unconventional superconducting compounds, such as ScV$_2$Ga$_4$ and ZrV$_2$Ga$_4$, and other many rare earths based materials.

Quantum Griffiths phase near an antiferromagnetic quantum critical point: Muon spin relaxation study of Ce(Cu1−xCox)2Ge2

The antiferromagnetic order in the heavy-fermion compound ${\mathrm{CeCu}}_{2}{\mathrm{Ge}}_{2}$ can be suppressed by Co-doping, and at critical composition ${x}_{c}=0.6$ (${T}_{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}0$ K) a quantum critical point has been observed. We have performed zero-field (ZF) and longitudinal-field muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements on polycrystalline samples of $\mathrm{Ce}{({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{Ge}}_{2}$ ($x=0,0.2,0.6,1$) over a temperature range of 100 mK to 10 K and in applied fields from 0 up to 3000 G. Above any ordering temperature, the muon relaxation spectra can be described by a Gaussian-Kubo-Toyabe times exponential line shape. Below the magnetic ordering temperature (i.e., for $x<0.6$), an additional Gaussian relaxation is observed. The zero-field muon relaxation rate suggests the presence of antiferromagnetic ordering below 4 and 0.8 K for $x=0$ and 0.2 samples, respectively. For $x=0.6$, the magnetic order is completely suppressed, and the quantum critical point is accompanied by non-Fermi-liquid behavior, manifested in the power-law divergence of exponential depolarization, i.e., $\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{T}^{0.55}$. The relaxation rate of $x=0.6$ obeys the time-field scaling relation ${G}_{z}(t,H)={G}_{z}(t/{H}^{\ensuremath{\gamma}})$, which is considered to be a characteristic feature of quantum critical magnetic fluctuations. Furthermore, for $x=0.6$, the exponent of isotherm magnetization, $M\ensuremath{\sim}{H}^{\ensuremath{\eta}}$, and magnetization-field-temperature scaling is consistent with the ZF-$\ensuremath{\mu}\mathrm{SR}$ data. These results provide strong evidence for the formation of a quantum Griffiths phase near the antiferromagnetic quantum phase transition.

μSR and neutron diffraction studies on the tuning of spin-glass phases in the partially ordered double perovskites SrMn1−xWxO3

Tunability of the partially ordered double perovskite (PODP) and coexisting spin-glass phase in SrMn1-xWxO3 (x=0.20 to 0.40) have been studied using neutron powder diffraction (NPD), muon spin relaxation (MuSR), and magnetic susceptibility (X) measurements. Structural studies reveal that SrMn1-xWxO3 undergoes a quasi-continuous transformation from simple perovskite (Pm-3m) to PODP (P21/n) phase as x increases. Xdc(T) and Xac(T) measurements show a sharp cusp-like peak at a spin glass transition, Tg. The muon relaxation rate ({\lambda}) peaks at Tg following a critical growth, given by {\lambda}={\lambda}(0).t-w [t=(T-Tg)/Tg]. However, no long-range magnetic order is observed in NPD below Tg. These measurements confirm a tunable spin-glass freezing in SrMn1-xWxO3 with Tg monotonously decreasing with W content, which we attribute to tuning the relative concentration of the coexisting Mn-O-Mn and Mn-O-W-O-Mn anti-ferromagnetic super-exchange pathways altering the geometric frustration.

Spin dynamics in the single-ion magnet [Er(W5O18)2]9−

In this work we present a detailed NMR and ${\ensuremath{\mu}}^{+}\mathrm{SR}$ investigation of the spin dynamics in the new hydrated sodium salt containing the single-ion magnet ${[\mathrm{Er}{({\mathrm{W}}_{5}{\mathrm{O}}_{18})}_{2}]}^{9\ensuremath{-}}$. The $^{1}\mathrm{H}\phantom{\rule{0.16em}{0ex}}\mathrm{NMR}$ absorption spectra at various applied magnetic fields present a line broadening on decreasing temperature which indicates a progressive spin freezing of the single-molecule magnetic moments. The onset of quasistatic local magnetic fields, due to spin freezing, is observed also in the muon relaxation curves at low temperature. Both techniques yield a local field distribution of the order of 0.1--0.2 T, which appears to be of dipolar origin. On decreasing the temperature, a gradual loss of the $^{1}\mathrm{H}\phantom{\rule{0.16em}{0ex}}\mathrm{NMR}$ signal intensity is observed, a phenomenon known as wipe-out effect. The effect is analyzed quantitatively on the basis of a simple model which relies on the enhancement of the NMR spin-spin, ${T}_{2}^{\ensuremath{-}1}$, relaxation rate due to the slowing down of the magnetic fluctuations. Measurements of spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ for $^{1}\mathrm{H}\phantom{\rule{0.16em}{0ex}}\mathrm{NMR}$ and of the muon longitudinal relaxation rate \ensuremath{\lambda} show an increase as the temperature is lowered. However, while for the NMR case the signal is lost before reaching the very slow fluctuation region, the muon spin-lattice relaxation \ensuremath{\lambda} can be followed until very low temperatures and the characteristic maximum, reached when the electronic spin fluctuation frequency becomes of the order of the muon Larmor frequency, can be observed. At high temperatures, the data can be well reproduced with a simple model based on a single correlation time $\ensuremath{\tau}={\ensuremath{\tau}}_{0}\phantom{\rule{0.16em}{0ex}}\mathrm{exp}(\mathrm{\ensuremath{\Delta}}/\mathrm{T})$ for the magnetic fluctuations. However, to fit the relaxation data for both NMR and ${\ensuremath{\mu}}^{+}\mathrm{SR}$ over the whole temperature and magnetic field range, one has to use a more detailed model that takes into account spin-phonon transitions among the $\mathrm{E}{\mathrm{r}}^{3+}$ magnetic sublevels. A good agreement for both proton NMR and ${\ensuremath{\mu}}^{+}\mathrm{SR}$ relaxation is obtained, which confirms the validity of the energy level scheme previously calculated from an effective crystal field Hamiltonian.

Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa 2 Cu 3 O y

The origin of the pseudogap region below a temperature T* is at the heart of the mysteries of cuprate high-temperature superconductors. Unusual properties of the pseudogap phase, such as broken time-reversal and inversion symmetry are observed in several symmetry-sensitive experiments: polarized neutron diffraction, optical birefringence, dichroic angle-resolved photoemission spectroscopy, second harmonic generation, and polar Kerr effect. These properties suggest that the pseudogap region is a genuine thermodynamic phase and are predicted by theories invoking ordered loop currents or other forms of intra-unit-cell (IUC) magnetic order. However, muon spin rotation (μSR) and nuclear magnetic resonance (NMR) experiments do not see the static local fields expected for magnetic order, leaving room for skepticism. The magnetic resonance probes have much longer time scales, however, over which local fields could be averaged by fluctuations. The observable effect of the fluctuations in magnetic resonance is then dynamic relaxation. We have measured dynamic muon spin relaxation rates in single crystals of YBa2Cu3O y (6.72 < y < 6.95) and have discovered "slow" fluctuating magnetic fields with magnitudes and fluctuation rates of the expected orders of magnitude that set in consistently at temperatures Tmag ≈ T*. The absence of any static field (to which μSR would be linearly sensitive) is consistent with the finite correlation length from neutron diffraction. Equally important, these fluctuations exhibit the critical slowing down at Tmag expected near a time-reversal symmetry breaking transition. Our results explain the absence of static magnetism and provide support for the existence of IUC magnetic order in the pseudogap phase.

Low-field spin dynamics of Cr7Ni and Cr7Ni−Cu−Cr7Ni molecular rings as detected by μSR

Muon spin rotation measurements were used to investigate the spin dynamics of heterometallic ${\mathrm{Cr}}_{7}\mathrm{Ni}$ and ${\mathrm{Cr}}_{7}\mathrm{Ni}$-Cu-${\mathrm{Cr}}_{7}\mathrm{Ni}$ molecular clusters. In ${\mathrm{Cr}}_{7}\mathrm{Ni}$ the magnetic ions are arranged in a quasiplanar ring and interact via an antiferromagnetic exchange coupling constant $J$, while ${\mathrm{Cr}}_{7}\mathrm{Ni}$-Cu-${\mathrm{Cr}}_{7}\mathrm{Ni}$ is composed of two ${\mathrm{Cr}}_{7}\mathrm{Ni}$ linked by a bridging moiety containing one Cu ion, that induces an inter-ring ferromagnetic interaction ${J}^{\ensuremath{'}}\ensuremath{\ll}J$. The longitudinal muon relaxation rate $\ensuremath{\lambda}$ collected at low magnetic fields ${\ensuremath{\mu}}_{0}Hl0.15$ Tesla, shows that the two systems present differences in spin dynamics vs temperature. While both samples exhibit a main peak in the muon relaxation rate vs temperature, at $T\ensuremath{\sim}10$ K for ${\mathrm{Cr}}_{7}\mathrm{Ni}$ and $T\ensuremath{\sim}8$ K for ${\mathrm{Cr}}_{7}\mathrm{Ni}$-Cu-${\mathrm{Cr}}_{7}\mathrm{Ni}$, the two compounds have distinct additional features: ${\mathrm{Cr}}_{7}\mathrm{Ni}$ shows a shoulder in $\ensuremath{\lambda}(T)$ for $Tl8$ K, while ${\mathrm{Cr}}_{7}\mathrm{Ni}$-Cu-${\mathrm{Cr}}_{7}\mathrm{Ni}$ shows a flattening of $\ensuremath{\lambda}(T)$ for $Tl2$ K down to temperatures as low as $T=20$ mK. The main peak of both systems is explained by a Bloembergen-Purcell-Pound (BPP)-like heuristic fitting model that takes into account of a distribution of electronic spin characteristic times for $Tg5$ K, while the shoulder presented by ${\mathrm{Cr}}_{7}\mathrm{Ni}$ can be reproduced by a BPP function that incorporates a single electronic characteristic time theoretically predicted to dominate for $Tl5$ K. The flattening of $\ensuremath{\lambda}(T)$ in ${\mathrm{Cr}}_{7}\mathrm{Ni}$-Cu-${\mathrm{Cr}}_{7}\mathrm{Ni}$ occurring at very low temperature can be tentatively attributed to field-dependent quantum effects and/or to an inelastic term in the spectral density of the electronic spin fluctuations.

Structure and magnetism in the bond-frustrated spinelZnCr2Se4

The crystal and magnetic structures of stoichiometric ZnCr2Se4 have been investigated using synchrotron X-ray and neutron powder diffraction, muon spin relaxation (muSR) and inelastic neutron scattering. Synchrotron X-ray diffraction shows a spin-lattice distortion from the cubic spinel to a tetragonal I41/amd lattice below TN = 21 K, where powder neutron diffraction confirms the formation of a helical magnetic structure with magnetic moment of 3.04(3) {\mu}B at 1.5 K; close to that expected for high-spin Cr3+. MuSR measurements show prominent local spin correlations that are established at temperatures considerably higher (< 100 K) than the onset of long range magnetic order. The stretched exponential nature of the relaxation in the local spin correlation regime suggests a wide distribution of depolarizing fields. Below TN, unusually fast (> 100 {\mu}s-1) muon relaxation rates are suggestive of rapid site hopping of the muons in static field. Inelastic neutron scattering measurements show a gapless mode at an incommensurate propagation vector of k = (0 0 0.4648(2)) in the low temperature magnetic ordered phase that extends to 0.8 meV. The dispersion is modelled by a two parameter Hamiltonian, containing ferromagnetic nearest neighbor and antiferromagnetic next nearest neighbor interactions with a Jnnn/Jnn = -0.337.

μSR study of stoichiometric NbFe2

The magnetic ground state of nominally stoichiometric single crystalline NbFe2 is investigated by bulk magnetisation and muon spin relaxation techniques. Magnetic order clearly emerges below the critical temperature TN=10.3K and is dominated by randomly orientated quasi-static moments. The local field distribution observed by muons can be explained by the phenomenological Gaussian-broadened-Gaussian Kubo Toyabe relaxation function. The observed short range order could be used to describe a new magnetic ground state, but a helical spin density wave with an incommensurate amplitude modulation cannot be ruled out. The sensitivity of μSR to the local magnetic field distribution in the vicinity of the quantum critical point (QCP) in NbFe2 is clearly demonstrated via comparison with already published work. This suggests detailed measurements of the muon relaxation as the QCP is approached will reveal further details of the field distribution and fluctuations in Nb1−yFe2+y.

Gapless quantum spin liquid ground state in the spin-1 antiferromagnet 6HB-Ba3NiSb2O9

We present an in-depth study of the magnetic properties of the spin-1 antiferromagnet 6HB-${\mathrm{Ba}}_{3}{\mathrm{NiSb}}_{2}{\mathrm{O}}_{9}$. $\ensuremath{\mu}\mathrm{SR}$ measurements demonstrate that this material shows no static magnetism down to temperatures as low as 20 mK, making it a likely candidate for a quantum spin liquid state. $^{121}\mathrm{Sb}$ NMR shift measurements show that the local, intrinsic susceptibility levels off at temperatures below $\ensuremath{\sim}60$ K. The NMR spin-lattice relaxation rate $1/{T}_{1}$ is essentially constant in temperature and the muon relaxation rate exhibits a low-temperature relaxation plateau, all indications of gapless spin excitations. Our local probe measurements are discussed in the context of several theories proposed for this material.