Muon Relaxation Rate Research Articles

Kapellasite: A Kagome Quantum Spin Liquid with Competing Interactions

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.

μSR studies of superconductivity in eutectically grown mixed ruthenates

The low-temperature magnetic behavior of the double-layered ruthenate Sr${}_{3}$Ru${}_{2}$O${}_{7}$, as grown from a eutectic Sr${}_{2}$RuO${}_{4}$-Sr${}_{3}$Ru${}_{2}$O${}_{7}$ system, was investigated via zero- and transverse-field muon-spin rotation. The gradual increase of the muon relaxation rate observed below 2.5 K, even in the absence of applied magnetic fields, indicates the occurrence of a spontaneous breaking of time-reversal symmetry. The onset of the latter at a temperature above 1.5 K, the ${T}_{c}$ of the single phase Sr${}_{2}$RuO${}_{4}$, provides evidence about an unconventional superconducting state in the eutectic phase, which most likely takes place at the interface between the Sr${}_{2}$RuO${}_{4}$ and Sr${}_{3}$Ru${}_{2}$O${}_{7}$ domains, or even inside the Sr${}_{3}$Ru${}_{2}$O${}_{7}$ phase. We show that the superconducting state manifests a two-component behavior in the transverse-field response with change-over at about $T=2.5$ K and $T=1.5$ K. The comparison with zero-field $\ensuremath{\mu}$SR data in the Ru-Sr${}_{2}$RuO${}_{4}$ eutectic system rules out the possibility of spurious effects due to embedded Ru islands.

μSR investigation of magnetism and magnetoelectric coupling in Cu2OSeO3

A detailed zero and transverse field (ZF&TF) muon spin rotation (muSR) investigation of magnetism and the magneto-electric coupling in Cu2OSeO3 is reported. An internal magnetic field B_int(T=0) = 85.37(25) mT was found, in agreement with a ferrimagnetic state below Tc = 57.0(1) K. The temperature dependence of the magnetic order parameter is well described by the relation B_int = B(0)(1-(T/Tc)^2)^b with an effective exponent b = 0.39(1) which is close to the critical exponent B ~ 1/3 for a three dimensional (3D) magnetic system. Just above Tc the muon relaxation rate follows the power low \lambda (T)\propto (T/Tc - 1)^\omega with \omega = 1.06(9), which is characteristic for 3D ferromagnets. Measurements of B_int(T) with and without an applied electrostatic field E = 1.66 x 10^5 V/m suggest a possible electric field effect of magnitude \Delta Bv = Bv(0 V)-Bv(500 V) = - 0.4(4) mT.

Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earthpyrochlore Gd2Sn2O7 antiferromagnet

The magnetic insulator Gd2Sn2O7 is one of many geometrically frustrated magnetic materials knownto exhibit a nonzero muon spin polarization relaxation rate,λ(T), down to the lowesttemperature (T) studied. Such behaviour is typically interpreted as signalling the presenceof persistent spin dynamics (PSD) of the host material. In the case ofGd2Sn2O7, such PSD comes as a surprise since magnetic specific heat measurements suggestconventional gapped magnons, which would naively lead to an exponentially vanishingλ(T) as T → 0. In contrast to most materials that display PSD, the ordered phase ofGd2Sn2O7 is well characterized and both the nature and the magnitude of the interactions have beeninferred from the magnetic structure and the temperature dependence of themagnetic specific heat. Based on this understanding, the temperature dependenceof the muon spin polarization relaxation through the scattering of spin waves(magnons) is calculated. The result explicitly shows that, despite the unusualextensive number of weakly dispersive (gapped) excitations characterizingGd2Sn2O7, a remnant of the zero modes of the parent frustrated pyrochloreHeisenberg antiferromagnet, the temperature dependence of the calculatedλ(T) differs dramatically from the experimental one. Indeed, the calculationconforms to the naive expectation of an exponential collapse ofλ(T) at temperaturesbelow ∼ 0.7 K. This result, for the first time, illustrates crisply and quantitatively the paradox thatpresents itself with the pervasive occurrence of PSD in highly frustrated magnetic systemsas evinced by muon spin relaxation measurements.

Probing the superconducting ground state near the charge density wave phase transition inCu0.06TiSe2

We have investigated the nature of the superconducting ground state of ${\text{Cu}}_{0.06}{\text{TiSe}}_{2}$ using muon spin rotation and muon spin relaxation measurements. The temperature dependence of the magnetic penetration depth of ${\text{Cu}}_{0.06}{\text{TiSe}}_{2}$ is consistent with a single gap $s$-wave BCS superconductor in the clean limit. The gap energy is $\ensuremath{\Delta}(0)=0.27(1)\text{ }\text{meV}$, which corresponds to a gap to ${T}_{C}$ ratio of $[2\ensuremath{\Delta}(0)/{k}_{B}{T}_{C}]=2.5$. The estimated magnetic penetration depth, $\ensuremath{\lambda}$, and the coherence length, $\ensuremath{\xi}$, are 660(10) and 15(5) nm, respectively. Furthermore, we observe an irreversibility line in the temperature dependence of the superconducting part of the muon relaxation rate, ${\ensuremath{\sigma}}_{sc}(T)$, indicating the presence of strong pinning in ${\text{Cu}}_{0.06}{\text{TiSe}}_{2}$. Interestingly, at low temperatures we have found clear evidence of the presence of low-energy spin fluctuations that coexist with superconductivity and have an Arrhenius temperature dependence.

Muon spin relaxation investigation of tetranuclear iron(III)Fe4(OCH3)6(dpm)6molecular cluster

We present a study of the spin dynamics of ${\text{Fe}}_{4}{({\text{OCH}}_{3})}_{6}{(\text{dpm})}_{6}$ single molecule magnet by means of SQUID magnetization and muon relaxation $({\ensuremath{\mu}}^{+}SR)$ measurements. In longitudinal field ${\ensuremath{\mu}}^{+}SR$ experiments performed at magnetic fields $H=200$, 1000 Oe, the muon asymmetry $P(t)$ could be fitted by means of three components, the first constant, the second fast relaxing through a quasiexponential decay, and the third, the slowest relaxing, showing an exponential decay. The slowest muon relaxation rate $\ensuremath{\lambda}$ studied as a function of temperature $T$ displayed two structures, a broad peak at $T\ensuremath{\sim}15/20\text{ }\text{K}$ and a shoulder at $T<5\text{ }\text{K}$, both decreasing in amplitude and displacing toward higher temperatures as the field is increased. To mimic qualitatively the temperature behavior $\ensuremath{\lambda}(T)$ at the investigated fields, we used a function expressed as the sum of two Bloembergen-Purcell-Pound (BPP)-like laws, reproducing the mechanism of relaxation. The exponential data resulted well fitted by means of a heuristic model which takes into account two correlation times ${\ensuremath{\tau}}^{\ensuremath{'}}$ and $\ensuremath{\tau}$, related to the ground-state multiplet barrier $({\ensuremath{\Delta}}^{\ensuremath{'}}/{k}_{B}=7.25\text{ }\text{K})$ and to the intermultiplet separation $(\ensuremath{\Delta}/{k}_{B}=86.4\text{ }\text{K})$ between $\text{S}=5$ and $\text{S}=4$.

Magnetic-field-induced reentrance of Fermi-liquid behavior and spin-lattice relaxation rates in [formula omitted

A strong departure from Landau–Fermi liquid (LFL) behavior have been recently revealed in observed anomalies in both the magnetic susceptibility χ and the muon and 63Cu nuclear spin-lattice relaxation rates 1 / T 1 of YbCu 5 − x Au x ( x = 0.6 ). We show that the above anomalies along with magnetic-field-induced reentrance of LFL properties are indeed determined by the dependence of the quasiparticle effective mass M ∗ on magnetic field B and temperature T and demonstrate that violations of the Korringa law also come from M ∗ ( B , T ) dependence. We obtain this dependence theoretically utilizing our approach based on fermion condensation quantum phase transition (FCQPT) notion. Our theoretical analysis of experimental data on the base of FCQPT approach permits not only to explain the above two experimental facts in a unified manner, but to unveil their universal properties, relating the peculiar features of both longitudinal magnetoresistance and specific heat in YbRh 2Si 2 to the behavior of spin-lattice relaxation rates.

Spin dynamics in the neutral rare-earth single-molecule magnets[TbPc2]0and[DyPc2]0fromμSRand NMR spectroscopies

The spin dynamics in [TbPc$_{2}$]$^{0}$ and [DyPc$_{2}$]$^{0}$ single molecule magnets have been investigated by means of muon and nuclear spin-lattice relaxation rate measurements. The correlation time for the spin fluctuations was found to be close to 0.1 ms already at 50 K, about two orders of magnitude larger than the one previously found in other lanthanide based single molecule magnets. In [TbPc$_{2}$]$^{0}$ two different regimes for the spin fluctuations have been evidenced: a high temperature activated one involving spin fluctuations across a barrier $\Delta\simeq 880 K$ separating the ground and first excited states and a low temperature regime involving quantum fluctuations within the twofold degenerate ground-state. In [DyPc$_{2}$]$^{0}$ a high temperature activated spin dynamics is also evidenced which, however, cannot be explained in terms of a single spin-phonon coupling constant.

Muon-spin-rotation study of the superconducting properties ofMo3Sb7

We present the microscopic properties of superconducting state in ${\text{Mo}}_{3}{\text{Sb}}_{7}$ $({T}_{c}=2.2\text{ }\text{K})$ using muon-spin rotation measurements. The zero-field-cooled and field-cooled (FC) data with an applied transverse field of 40 mT reveal an irreversibility in the muon relaxation rates and precessional frequencies below 2 K. We have also found an anomaly around 0.5 K, which may be related to a process of the vortex melting or some change in vortex-lattice symmetry. The temperature dependence of FC muon relaxation rate can be analyzed using a phenomenological double-gap $s$-wave model. The observation of a nonlinear field dependence of the muon relaxation rate is consistent with the occurrence of two superconducting gaps. Moreover, the magnetic penetration depth $\ensuremath{\lambda}$, coherence length $\ensuremath{\xi}$, superconducting carrier density ${n}_{s}$, and effective-mass enhancement ${m}^{\ensuremath{\ast}}$ have been found to be $\ensuremath{\lambda}\ensuremath{\approx}665\text{ }\text{nm}$, $\ensuremath{\xi}\ensuremath{\approx}12.5\text{ }\text{nm}$, ${n}_{s}\ensuremath{\approx}1.2\ifmmode\times\else\texttimes\fi{}{10}^{27}\text{ }\text{carriers}/{\text{m}}^{3}$, and ${m}^{\ensuremath{\ast}}\ensuremath{\approx}18.7{m}_{e}$, respectively.

A zero-field [formula omitted]SR study of glassy spin dynamics in [formula omitted]-MnCu

We have performed zero-field muon spin relaxation ( μ SR) measurements of a number of γ - Mn x Cu 1 - x alloys around the critical concentration ( x = 0.72 ) in order to investigate the dynamical properties of the system as it moves from short-range to long-range magnetic order. Above the critical concentration the muon spin relaxation is exponential in form, whilst for Mn concentrations ⩽ 71 at % the relaxation is stretched-exponential, with the “stretch” exponent β decreasing from unity at high temperatures (i.e. a simple monopolar Lorentzian relaxation regime) to around 1 3 at the transition temperature—indicated by a divergence in the muon relaxation rate, λ . This behaviour is indicative of a concentrated spin-glass ground state. For a Mn concentration of 73 at % we find a re-entrant transition, from a cluster-glass phase at T g ≈ 260 K to an AF phase at T N ≈ 140 K .

Slow inhomogeneous spin dynamics in the frustrated antiferromagnet [formula omitted

Muon spin relaxation experiments in the geometrically frustrated antiferromagnet NiGa 2 S 4 indicate strong slow spin fluctuations at low temperatures. The muon relaxation rate is strongly field dependent, in contrast with the field independence of the gapless excitations indicated by the observed specific heat.

Low-energy excitations in theS=12molecular nanomagnetK6[V15IVAs6O42(H2O)]∙8H2Ofrom proton NMR andμSR

Zero- and longitudinal-field muon-spin-rotation $(\ensuremath{\mu}\mathrm{SR})$ and $^{1}\mathrm{H}$ NMR measurements on the $S=\frac{1}{2}$ molecular nanomagnet ${\mathrm{K}}_{6}[{\mathrm{V}}_{15}^{IV}{\mathrm{As}}_{6}{\mathrm{O}}_{42}({\mathrm{H}}_{2}\mathrm{O})]∙8{\mathrm{H}}_{2}\mathrm{O}$ are presented. In LF experiments, the muon asymmetry $P(t)$ was fitted by the sum of three different exponential components with fixed weights. The different muon relaxation rates ${\ensuremath{\lambda}}_{i}$ $(i=1,2,3)$ and the low-field $H=0.23\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ $^{1}\mathrm{H}$ NMR spin-lattice relaxation rate $1∕{T}_{1}$ show a similar behavior for $T>50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$: starting from room temperature they increase as the temperature is decreased. The increase of ${\ensuremath{\lambda}}_{i}$ and $1∕{T}_{1}$ can be attributed to the ``condensation'' of the system toward the lowest-lying energy levels. The gap $\ensuremath{\Delta}\ensuremath{\sim}550\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ between the first and second $S=\frac{3}{2}$ excited states was determined experimentally. For $T<2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the muon relaxation rates ${\ensuremath{\lambda}}_{i}$ stay constant, independently of the field value $H\ensuremath{\leqslant}0.15\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The behavior for $T<2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ strongly suggests that, at low $T$, the spin fluctuations are not thermally driven but rather originate from quasielastic intramolecular or intermolecular magnetic interactions. We suggest that the very-low-temperature relaxation rates could be driven by energy exchanges between two almost degenerate $S=\frac{1}{2}$ ground states and/or by quantum effects.

Spin Dynamics and Magnetic Order in Magnetically FrustratedTb2Sn2O7

We report a study of the geometrically frustrated magnetic material Tb2Sn2O7 by the positive muon-spin relaxation technique. No signature of a static magnetically ordered state is detected while neutron magnetic reflections are observed in agreement with a published report. This is explained by the dynamical nature of the ground state of Tb2Sn2O7: the Tb3+ magnetic moment characteristic fluctuation time is approximately 10(-10) s. The strong effect of the magnetic field on the muon-spin-lattice relaxation rate at low fields indicates a large field-induced increase of the magnetic density of states of the collective excitations at low energy.

Role of disorder and competing ferromagnetic and antiferromagnetic interactions in the magnetic, electrical, and dynamic properties ofLa0.7Pb0.3(Mn1−xFex)O3,0⩽x⩽0.2manganites

The effect of Fe doping on the magnetic properties of ${\mathrm{La}}_{0.7}{\mathrm{Pb}}_{0.3}{\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{O}}_{3}(0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.2)$ colossal magnetoresistance perovskites is studied by muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ spectroscopy and macroscopic static magnetization measurements. The latter quantities show a cusp at temperatures below that signaling magnetic ordering (Curie temperature ${T}_{C}$) as well as a kink at lower temperatures which are taken as signatures of magnetic irreversibility. Random substitution of Mn by Fe ions gives rise to antiferromagnetic couplings mediated by conventional superexchange interaction. This manifests itself by the decrease of Curie temperatures and a concomitant decrease of the spontaneous magnetization with increased doping. The muon relaxation data under zero and applied longitudinal fields is interpreted in terms of progressive spin freezing concomitant with a reduction of the ferromagnetic component as Fe substitution is increased. The spin dynamics as ${T}_{C}$ is crossed from above shows clear departures from those expected for exchange-coupled Heisenberg or Ising systems but rather it displays features common to magnetically interacting-cluster systems. This effect leads to the appearance of a peak in the muon relaxation rate versus temperature curves that is located at temperatures below that signaling magnetic ordering $({T}_{C})$. Finally, direct evidence of the existence of antiferromagnetic and ferromagnetically short-range-ordered regions within the $x=0.2$ sample is provided by polarized neutron diffraction. The picture that emerges from our study identifies competing positive (double exchange) and negative (superexchange) interactions at random sites as the entities responsible for the low-temperature freezing monitored by using $\ensuremath{\mu}\mathrm{SR}$ spectroscopy.

Formula omitted] studies of the electron-doped [formula omitted

We have performed muon spin relaxation ( μ SR ) experiments on undoped CaMnO 3 and electron-doped Ca 1 - x Sm x MnO 3 for x = 0.1 , 0.15 and 0.3. Undoped CaMnO 3 is a G-type antiferromagnet with a Néel temperature of T N ≈ 122 K . The μ SR signal shows three well-defined frequencies, which decrease continuously with temperature and becomes zero at T N ≈ 122 K . The electron-doped Ca 0.85Sm 0.15MnO 3 which shows colossal magnetoresistive (CMR) behaviour, undergoes a structural and magnetic transition at T c ≈ 125 K . The μ SR signal shows heavily damped oscillating signal. The frequency decreases continuously with increasing temperature. Ca 0.9Sm 0.1MnO 3 and Ca 0.7 Sm 0.3MnO 3 show only relaxation and do not show any frequency. We have determined temperature variation of the muon relaxation rates below and above the magnetic and charge order transitions under zero and longitudinal magnetic fields, which give important information about the nature of these transitions.

Magnetic ordering and dynamics in the XY pyrochlore antiferromagnet: a muon-spin relaxation studyof Er2Ti2O7 and Er2Sn2O7

Spin dynamics in Er2Ti2O7 and Er2Sn2O7 have been probed by means of muon-spin relaxation(μ+SR) in the temperature range K. Both compounds are thought to constitute experimental realizationsof the highly frustrated XY antiferromagnet on the pyrochlore lattice, forwhich theory predicts fluctuation-induced magnetic order. Our results forEr2Ti2O7 are consistent with a transition into an ordered state at K, in agreement with previous neutron measurements. Below this temperature, the muon relaxationrate λ(T) remains large ( MHz) and temperature independent, in contrast to the behaviour in conventional magnets. The thermalevolution of λ(T) for Er2Sn2O7 is somewhat similar to that of the Ti material. However, the depolarization curves remainexponential over the entire temperature range, suggesting a dense distribution of rapidly fluctuatingmagnetic moments, and, thus, are compatible with the absence of long-range order at least forT>0.02 K.

Thermal Behaviour of the μSR Relaxation Rate at High Temperature in Insulators

We show that, in rare earth based insulators, measurement of the thermal dependence of the muon spin-lattice relaxation rate at high temperature provides information on the nature of the magnetic correlations and on the crystal-field energy splitting, if any.

μSRStudy of the Quantum Dynamics in the FrustratedS=32Kagomé Bilayers

We present muSR experiments in the S=3/2 kagomé bilayer compound Ba(2)Sn(2)ZnGa(10-7p)Cr(7p)O22 [BSZCGO(p)] and compare it to the isostructural SrCr(9p)Ga(12-9p)O19 [SCGO(p)], including for the latter new results for p > or =0.89. Quantum-dynamical low energy magnetic excitations are evidenced in this novel compound. We study the evolution of the muon relaxation rate with p, T, and field. A phenomenological model for the muon relaxation based on sporadic dynamics due to spin excitations in a singlet sea proposed by Uemura et al. is extended to all fields and T range. Its connection to the RVB picture is discussed, and we argue that such coherent states might mediate the interactions between "impurities" which induce the spin glass freezing.

Investigation of Eu 6C 60 magnetic properties

A representative rare earth doped fulleride, Eu 6C 60, has been studied using several spectroscopic and magnetometry techniques. We find that europium ions are present both in their magnetic bivalent state and nonmagnetic trivalent state. The Eu 2+/Eu 3+ ratio seems to critically depend on sample preparation conditions. Muon relaxation rates show a large magnetic field distribution near the ordered phase, whereas 13C NMR lineshapes at room temperature are consistent with dipolar field broadening (∼100 G) from neighbouring Eu 2+ magnetic moments.

Low-temperature magnetic order and spin dynamics inYbRh2Si2

Muon spin rotation and relaxation experiments have been carried out in single crystals of ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2},$ a compound that exhibits non-Fermi-liquid (NFL) behavior associated with a quantum critical point (QCP) at $T=0.$ The zero-field muon relaxation rate is found to be independent of temperature down to 100 mK but to increase below $\ensuremath{\sim}70\mathrm{mK},$ which suggests magnetic order at low temperatures. From the relation between the internal field at the ${\ensuremath{\mu}}^{+}$ stopping site and the hyperfine coupling constant the ordered ${\mathrm{Yb}}^{3+}$ moment is very small, $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{\ensuremath{\mu}}_{B}.$ Muon spin rotation linewidths in a transverse field of 6 kOe indicate a homogeneous susceptibility down to 2 K, which is an order of magnitude lower than the characteristic (Kondo) temperature ${T}_{K}\ensuremath{\approx}25\mathrm{K}.$ This is evidence against the importance of disorder-driven NFL mechanisms in ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}.$ In longitudinal magnetic fields the muon spin-lattice relaxation function $G(t)$ is exponential, again indicative of a homogeneous system. The relaxation obeys the time-field scaling relation $G(t,H)=G(t/H),$ which suggests long-lived spin correlations at low temperatures. The ${\mathrm{Yb}}^{3+}$ spin dynamics derived from muon spin relaxation appear to be intimately related to critical magnetic fluctuations near the QCP.