Muon Relaxation Rate 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.

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.

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.

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.

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.

Anomalous local magnetism in the 4f-localized ferromagnets CeRu2X2B (X = Al, Ga) revealed by using ZF-μSR

We report zero-field muon spin relaxation/rotation (ZF-μSR) measurements on the 4f-localized ferromagnets CeRu2X2B (X = Al, Ga) with Ising-type anisotropy. Our ZF-μSR spectra of CeRu2Ga2B with a Curie temperature at T C = 16.3 K show a well-defined muon procession at temperatures below T C . The extracted critical exponent of β = 0.533 is close to the mean-field value of β = 0.5. On the other hand, the isomorphic CeRu2Al2B exhibits an intriguing evolution of the ZF-μSR spectrum through a spin density wave/ferromagnetic transition at T C = 12.8 K with a subsequent magnetic anomaly at T* = 6 K. Strikingly, the muon frequency decreases upon cooling to temperatures below T C and can be no longer resolved at temperatures below T*. At the same time, the muon relaxation rate increases continuously at temperatures below T C . These give an indication of the development of an inhomogeneous and dynamic ferromagnetic state. The contrasting ferromagnetism between CeRu2Ga2B and CeRu2Al2B evidences that a certain type of intrinsic/extrinsic perturbation, for example, exchange frustration and defects/impurities, can exert a drastic impact on the local magnetic properties in a family of 4f-localized magnetic materials with frustration.

Perturbation on hyperfine-enhancedPr141nuclear spin dynamics associated with antiferroquadrupolar order inPrV2Al20

The nature of multipolar order and hyperfine-enhanced (HE) $^{141}$Pr nuclear spin dynamics in PrV$_2$Al$_{20}$ was investigated using the muon spin relaxation technique. No explicit sign of time-reversal symmetry breaking was found below the multipolar order temperature $T_Q\sim 0.6$ K in a zero applied field as anticipated on the basis of the antiferroquadrupolar (AFQ) order picture proposed by Sakai and Nakatsuji [J. Phys. Soc. Jpn. 80, 063701 (2011)]. Further evidence of the nonmagnetic ground state was obtained from the observation of HE $^{141}$Pr nuclear spin fluctuations in the MHz scale. A marked increase in the muon spin-lattice relaxation rate (1/$T_{\rm 1,\mu}$) was observed below 1 K with decreasing temperature, which was attributed to the perturbation on the HE $^{141}$Pr nuclear spin dynamics associated with the development of AFQ correlations. The longitudinal field dependence of 1/$T_{\rm 1,\mu}$ revealed that the enhanced $^{141}$Pr nuclear spin accidentally has an effective gyromagnetic ratio close to that of the muon.

Thermodynamic phase transitions in a frustrated magnetic metamaterial.

Materials with interacting magnetic degrees of freedom display a rich variety of magnetic behaviour that can lead to novel collective equilibrium and out-of-equilibrium phenomena. In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour. Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory. We use low energy muon spectroscopy to probe the dynamic behaviour of the interacting nanomagnets and observe peaks in the muon relaxation rate that can be identified with the critical temperatures of the predicted phase transitions. This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

Magnetic order and muon motion in VO2

We report the first transverse, longitudinal and zero field measurements performed on Vanadium Dioxide (VO2) where we find a significant local magnetic field below T = 34.7 ± 0.16 K at the muon site and Mud motion above 340 K. Distinct shifts in the muon relaxation rates and Kubo-Toyabe delta parameters, near the metal to semiconductor and structural transition (TMST ≈ 340 K), show that μ+SR measurements may provide additional means to further characterize the mechanisms contributing to these transitions that are yet to be understood.

Microscopic studies of the normal and superconducting state of Ca3Ir4Sn13

We report on muon spin rotation (muSR) studies of the superconducting and magnetic properties of the ternary intermetallic stannide Ca3Ir4Sn13. This material has recently been the focus of intense research activity due to a proposed interplay of ferromagnetic spin fluctuations and superconductivity. In the temperature range T=1.6-200 K, we find that the zero-field muon relaxation rate is very low and does not provide evidence for spin fluctuations on the muSR time scale. The field-induced magnetization cannot be attributed to localized magnetic moments. In particular, our muSR data reveal that the anomaly observed in thermal and transport properties at T*~38 K is not of magnetic origin. Results for the transverse-field muon relaxation rate at T=0.02-12 K, suggest that superconductivity emerges out of a normal state that is not of a Fermi-liquid type. This is unusual for an electronic system lacking partially filled f-electron shells. The superconducting state is dominated by a nodeless order parameter with a London penetration depth of lambda=385(1) nm and the electron-phonon pairing interaction is in the strong-coupling limit.

Possible Quantum Diffusion of Polaronic Muons inDy2Ti2O7Spin Ice

We interpret recent measurements of the zero field muon relaxation rate in the magnetic pyrochlore Dy(2)Ti(2)O(7) as resulting from the quantum diffusion of muons in the material. In this scenario, the plateau observed at low temperature (< 7 K) in the relaxation rate is due to coherent tunneling of muons through a spatially disordered spin state and not to any magnetic fluctuations persisting at low temperature. Two further regimes either side of a maximum relaxation rate at T* = 50 K correspond to a crossover between tunneling and incoherent activated hopping motion of the muon. Our fit of the experimental data is compared with the case of muonium diffusion in KCl.

Evolution of spin relaxation processes in LiY1−xHoxF4studied via ac-susceptibility and muon spin relaxation

We present measurements of magnetic field and frequency dependence of the low-temperature ($T$ = 1.8 K) ac-susceptibility and temperature and field dependence of the longitudinal field positive muon spin relaxation (\ensuremath{\mu}SR) for LiY${}_{1\ensuremath{-}x}$Ho${}_{x}$F${}_{4}$ with $x$ = 0.0017, 0.0085, 0.0408, and 0.0855. The fits of numerical simulations to the susceptibility data for the $x$ = 0.0017, 0.0085, and 0.0408 show that Ho-Ho cross-relaxation processes become more important at higher concentrations, signaling the crossover from single-ion to correlated behavior. We simulate the muon spin depolarization using the parameters extracted from the susceptibility, and the simulations agree well with our data for samples with $x$ = 0.0017 and 0.0085. The \ensuremath{\mu}SR data for samples with $x$ = 0.0408 and 0.0855 at low temperatures ($T$ 10 K) cannot be described within a single-ion picture of magnetic field fluctuations and give evidence for additional mechanisms of depolarization due to Ho${}^{3+}$ correlations. We also observe an unusual peak in the magnetic field dependence of the muon relaxation rate in the temperature interval 10--20 K that we ascribe to a modification of the Ho${}^{3+}$ fluctuation rate due to a field induced shift of the energy gap between the ground and the first excited doublet crystal field states relative to a peak in the phonon density of states centered near 63 cm${}^{\ensuremath{-}1}$.