We report muon spin relaxation measurements on two Ti3+ containing perovskites, LaTiO3 and YTiO3, which display long range magnetic order at low temperature. For both materials, oscillations in the time-dependence of the muon polarization are observed which are consistent with three-dimensional magnetic order. From our data we identify two magnetically inequivalent muon stopping sites. The muon spin relaxation results are compared with the magnetic structures of these compounds previously derived from neutron diffraction and muon spin relaxation studies on structurally similar compounds.
We present the results of muon-spin relaxation measurements on ferromagnetic BiMnO3. Below T_C=98.0(1) K oscillations in the time-dependence of the muon polarization are observed, characteristic of a quasistatic magnetic field at a single muon site, allowing us to probe the critical behaviour associated with the magnetic phase transition. We are able to suggest candidate muon sites on the basis of dipole field calculations. Close to T_C, fluctuations of the Mn^3+ moments are characteristic of critical behaviour while there is a sharp crossover to a region of fast dynamic fluctuations at higher…
We review examples of muon-spin relaxation measurements on molecule-based magnetic coordination polymers, classified by their magnetic dimensionality. These include the one-dimensional s=1/2 spin chain Cu(pyz)(NO3)2 and the two-dimensional s=1/2 layered material [Cu(HF2)(pyz)2]BF4. We also describe some of the more exotic ground states that may become accessible in the future given the ability to tune the interaction strengths of our materials through crystal engineering.
Muon spin relaxation measurements on the filled skutterudite compound SmRu4P12 have been carried out in zero- and longitudinal-fields. Temperature dependence of both initial asymmetry and muon-spin depolarization rate show the appearance of a magnetically ordered state below the metal-insulator transition temperature TMI. The present study indicates that the ordering below TMI is not a non-magnetic antiferro-quadrupolar ordering but a magnetic one, which supports a scenario that a magnetic octupolar ordering occurs below TMI in SmRu4P12.
We present the results of muon-spin relaxation (muSR) measurements on the hexagonal manganite HoMnO3. Features in the temperature-dependent relaxation rate, lambda, correlate with the magnetic transitions at 76 K, 38 K and 34 K. The highest temperature transition, associated with the ordering of Mn3+ moments has the largest effect on lambda. The application of a static electric field of E=10^4 Vm^-1 below T=50 K causes a small reduction in lambda which is suggestive of coupling between ferroelectric and magnetic domain walls in the ordered state of the material.
We demonstrate that quantum-critical spin dynamics can be probed in high magnetic fields using muon-spin relaxation ($μ^{+}$SR). Our model system is the strong-leg spin ladder bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). In the gapless Tomonaga-Luttinger liquid phase we observe finite-temperature scaling of the $μ^{+}$SR $1/T_1$ relaxation rate which allows us to determine the Luttinger parameter $K$. We discuss the benefits and limitations of local probes compared with inelastic neutron scattering.
We present a detailed study of the magnetic properties of weakly ferromagnetic/quantum critical Nb$_{1-y}$Fe$_{2+y}$ using muon spin rotation and relaxation ($μ$SR). By means of an angular dependent study of the muon spin rotation signal in applied magnetic fields on a single crystal in the paramagnetic state we establish the muon stopping site in the crystallographic lattice of NbFe$_2$. With this knowledge we develop models to describe the muon spin rotation and relaxation signals in the weakly ferromagnetic, spin density wave and quantum critical phases of Nb$_{1-y}$Fe$_{2+y}$ and fit the c…
Muon spin relaxation experiments have been carried out in the Kondo compound PrInAg_2. The zero-field muon relaxation rate is found to be independent of temperature between 0.1 and 10 K, which rules out a magnetic origin (spin freezing or a conventional Kondo effect) for the previously-observed specific heat anomaly at \sim0.5 K. The low-temperature muon relaxation is quantitatively consistent with nuclear magnetism including hyperfine enhancement of the ^{141}Pr nuclear moment. This is strong evidence against a Pr^{3+} electronic magnetic moment, and for the Γ_3 crystalline-electric-field-spl…
Zero-field muon-spin-relaxation (ZF-{\boldmath $μ$}SR) measurements were carried out down to 80 mK on the randomness bond system Tl$_{1-x}$K$_x$CuCl$_3$ with $x$ = 0.44. Time spectra are well fitted by the stretched exponential function $\exp (-λt)^β$. The muon spin relaxation rate $λ$ increases rapidly with decreasing temperature, and $β$ tends to 0.5 at 80 mK. The divergent increase of $λ$ suggests the critical slowing down of the frequency of the Cu-3{\it d} spin fluctuations toward a spin frozen state below 80 mK, and the root-exponential-like behavior of the time spectrum indicates that t…
Zero- and longitudinal-field muon spin relaxation (MuSR) experiments have been carried out in the alloy series Pr(Os1-xRux)4Sb12 and Pr1-yLayOs4Sb12 to elucidate the anomalous dynamic muon spin relaxation observed in these materials. The damping rate associated with this relaxation varies with temperature, applied magnetic field, and dopant concentrations x and y in a manner consistent with the ``hyperfine enhancement'' of 141Pr nuclear spins first discussed by Bleaney in 1973. This mechanism arises from Van Vleck-like admixture of magnetic Pr3+ crystalline-electric-field-split excited states …
Muon-spin-rotation and relaxation studies have been performed on (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x$=0.85 and 0.95, which are solid solutions of the two isomorphic spin-gap systems (CH$_3$)$_2$CHNH$_3$CuCl$_3$ and (CH$_3$)$_2$CHNH$_3$CuBr$_3$ with different spin gaps. The sample with $x$=0.85 showed a clear muon spin rotation under zero-field below $T_{\rm N}$=11.65K, indicating the existence of a long-range antiferromagnetic order. A critical exponent of the hyperfine field was obtained to be $β$=0.33, which agrees with 3D-Ising model. In the other sample with $x$=0.95, an a…
We report muon spin relaxation (muSR) and magnetic susceptibility investigations of two Ti3+ chain compounds which each exhibit a spin gap at low temperature, NaTiSi2O6 and TiOCl. From these we conclude that the spin gap in NaTiSi2O6 is temperature independent, with a value of 2*Delta=660(50)K, arising from orbital ordering at Too = 210K; the associated structural fluctuations activate the muon spin relaxation rate up to temperatures above 270K. In TiOCl we find thermally activated spin fluctuations corresponding to a spin gap 2*Delta=420(40)K below Tc1=67K. We also compare the methods used to…
Muon spin relaxation measurements are reported on samples of dimethylammonium metal formates containing magnetic divalent nickel, cobalt, manganese, and copper ions. These hybrid organic-inorganic perovskites exhibit weak ferromagnetism and are, apart from the copper system, multiferroics with well separated magnetic and antiferroelectric transitions. We use muons to follow the sublattice magnetization, observing the effect of the spin reorientation transitions below TN and the criticality approaching TN. The multiferroic samples have three-dimensional antiferromagnetic interactions, but the c…
We report a study of the triangular lattice Heisenberg magnet NiGa2S4 by the positive muon spin rotation and relaxation technique. We unravel three temperature regimes: (i) below T_c = 9.2(2) K a spontaneous static magnetic field at the muon site is observed and the spin dynamics is appreciable: the time scale of the modes we probe is ~ 7 ns; (ii) an unconventional stretched exponential relaxation function is found for T_c < T < T_{cross} where T_{cross} = 12.6 K, which is a signature of a multichannel relaxation for this temperature range; (iii) above T_{cross}, the relaxation is exponential …
We report the results of muon-spin relaxation measurements on the low-dimensional antiferromagnet Rb4Cu(MoO4)3. No long-range magnetic order is observed down to 50 mK implying a ratio T_N/J<0.005 (where J is the principal exchange strength along the spin chains) and an effective ratio of interchain to intrachain exchange of |J_perp/J|<2 x 10^-3, making the material an excellent realization of a one-dimensional quantum Heisenberg antiferromagnet. We probe the persistent spin excitations at low temperatures and find that ballistic spin transport dominates the excitations detected below 0.3 K.
Muon-spin relaxation results on the pyrochlore iridate Nd$_2$Ir$_2$O$_7$ are reported. Spontaneous coherent muon-spin precession below the metal-insulator transition (MIT) temperature of about 33 K is observed, indicating the appearance of a long-ranged magnetic ordering of Ir$^{4+}$ moments. With further decrease in temperature, the internal field at the muon site increases again below about 9 K. The second increase of internal field suggests the ordering of Nd$^{3+}$ moments, which is consistent with a previous neutron experiment. Our results suggest that the MIT and magnetic ordering of Ir$…
We present the results of a muon-spin relaxation study of the high-Tc analogue material Cs2AgF4. We find unambiguous evidence for magnetic order, intrinsic to the material, below T_C=13.95(3) K. The ratio of inter- to intraplane coupling is estimated to be |J'/J|=1.9 x 10^-2, while fits of the temperature dependence of the order parameter reveal a critical exponent beta=0.292(3), implying an intermediate character between pure two- and three- dimensional magnetism in the critical regime. Above T_C we observe a signal characteristic of dipolar interactions due to linear F-mu-F bonds, allowing t…
We present a detailed local probe study of the magnetic order in the oxychalcogenide La2O2Fe2OSe2 utilizing 57Fe Moessbauer, 139La NMR, and muon spin relaxation spectroscopy. This system can be regarded as an insulating reference system of the Fe arsenide and chalcogenide superconductors. From the combination of the local probe techniques we identify a non-collinear magnetic structure similar to Sr2F2Fe2OS2. The analysis of the magnetic order parameter yields an ordering temperature TN = 90.1 K and a critical exponent of beta = 0.133, which is close to the 2D Ising universality class as report…
The results of muon-spin relaxation and heat capacity measurements on two pyroxene compounds LiFeSi2O6 and NaFeSi2O6 demonstrate that despite their underlying structural similarity the magnetic ordering is considerably different. In LiFeSi2O6 a single muon precession frequency is observed below TN, consistent with a single peak at TN in the heat capacity and a commensurate magnetic structure. In applied magnetic fields the heat capacity peak splits in two. In contrast, for natural NaFeSi2O6, where multiferroicity has been observed in zero-magnetic-field, a rapid Gaussian depolarization is obse…
A crystal structure that cannot be superposed on its mirror image by any combination of rotations and translations is classified as chiral. Such crystal structures have gained importance in recent years since they are prone to host unconventional magnetic orders and to exhibit topological magnetic textures. These properties result from the Dzyaloshinskii-Moriya antisymmetric exchange interaction which is authorized when space inversion is broken. While recent reports have shown the muon spin rotation and relaxation technique to provide unique information about structural and dynamical properti…
We present the results of zero-field muon-spin relaxation measurements made on the double perovskite insulators Sr$_{2}B$OsO$_6$ ($B={\rm Fe, Y, In}$). Spontaneous muon-spin precession indicative of quasistatic long range magnetic ordering is observed in Sr$_{2}$FeOsO$_6$ within the AF1 antiferromagnetic phase for temperatures below $T_{\rm N}=135 \pm 2~{\rm K}$. Upon cooling below $T_2 \approx 67~{\rm K}$ the oscillations cease to be resolvable owing to the coexistence of the AF1 and AF2 phases, which leads to a broader range of internal magnetic fields. Using density functional calculations …
The stretched diamond lattice material LiYbO2 has recently been reported to exhibit two magnetic transitions ($T_{N1} = 1.1 K$, $T_{N2} = 0.45 K$) via specific heat, magnetization, and neutron scattering measurements [Bordelon et al., Phys. Rev. B 103, 014420 (2021)]. Here we report complementary magnetic measurements down to T = 0.28 K via the local probe technique of muon spin relaxation. While we observe a rapid increase in the zero-field muon depolarization rate at $T_{N1}$, we do not observe any spontaneous muon precession for $T < T_{N1}$, which is typically associated with long-range ma…
We present the results of a muon-spin relaxation (muSR) investigation into magnetic ordering in several families of layered quasi-two-dimensional molecular antiferromagnets based on transition metal ions such as S=1/2 Cu2+ bridged with organic ligands such as pyrazine. In many of these materials magnetic ordering is difficult to detect with conventional magnetic probes. In contrast, muSR allows us to identify ordering temperatures and study the critical behavior close to T_N . Combining this with measurements of in-plane magnetic exchange J and predictions from quantum Monte Carlo simulations …
We present muon spin relaxation ($μ$SR) and specific-heat versus temperature $C(T)$ measurements on polycrystalline and single-crystal samples of the pyrochlore magnet Yb$_2$Ti$_2$O$_7$. $C(T)$ exhibits a sharp peak at a $T_\mathrm{C}$ of 0.21 and 0.26~K for the single-crystal and polycrystalline samples respectively. For both samples, the magnetic entropy released between 50~mK and 30~K amounts to $R\ln2$ per Yb. At temperatures below $T_\mathrm{C}$ we observe a steep drop in the asymmetry of the zero-field $μ$SR time spectra at short time scales, as well as a decoupling of the muon spins fro…
We report the results of a muon-spin relaxation ($μ$SR) investigation of La$_{2-x}$Sr$_{x}$CoO$_{4}$, an antiferromagnetic insulating series which has been shown to support charge ordered and magnetic stripe phases and an hourglass magnetic excitation spectrum. We present a revised magnetic phase diagram, which shows that the suppression of the magnetic ordering temperature is highly sensitive to small concentrations of holes. Distinct behavior within an intermediate $x$ range ($0.2 \leq x \lesssim 0.6$) suggests that the putative stripe ordered phase extends to lower $x$ than previously thoug…
We report predominantly zero field muon spin relaxation measurements in a series of Ca-doped LaMnO_3 compounds which includes the colossal magnetoresistive manganites. Our principal result is a systematic study of the spin-lattice relaxation rates 1/T_1 and magnetic order parameters in the series La_{1-x}Ca_xMnO_3, x = 0.0, 0.06, 0.18, 0.33, 0.67 and 1.0. In LaMnO_3 and CaMnO_3 we find very narrow critical regions near the Neel temperatures T_N and temperature independent 1/T_1 values above T_N. From the 1/T_1 in LaMnO_3 we derive an exchange integral J = 0.83 meV which is consistent with the …
We report a muon spin rotation/relaxation ($μ$SR) study of single-crystalline samples of the $α$-RuCl$_3$ honeycomb magnet, which is presumed to be a model compound for the Kitaev-Heisenberg interaction. It is inferred from magnetic susceptibility and specific-heat measurements that the present samples exhibit successive magnetic transitions at different critical temperatures $T_{\rm N}$ with decreasing temperature, eventually falling into the $T_{\rm N}=7$ K antiferromagnetic (7 K) phase that has been observed in only single-crystalline specimens with the least stacking fault. Via $μ$SR measu…
The nature of the magnetic transition of the Na-rich thermoelectric Na$_{0.75}$CoO$_2$ at 22K was studied by positive muon-spin-rotation and relaxation ($μ^+$SR) spectroscopy, using a polycrystalline sample in the temperature range between 300 and 2.5 K. Zero field $μ$SR measurements indicated the existence of a static internal magnetic field at temperatures below 22 K (= $T_{\rm m}$). The observed muon spin precession signal below $T_{\rm m}$ consisted of three components with different precession frequencies, corresponding to three inequivalent muon$^+$ sites in the Na$_{0.75}$CoO$_2$ lattic…
We report muon-spin relaxation measurements of highly homogeneous samples of FeAs and FeAs2, both previously found as impurity phases in some samples of recently synthesized pnictide superconductors. We observe well defined muon precession in the FeAs sample with two precession frequencies of 38.2(3) and 22.7(9) MHz at 7.5 K, with the majority of the amplitude corresponding to the lower frequency component. In FeAs2 we confirm previous measurements showing that no long-ranged magnetic order occurs above 2 K and measure the muon spin relaxation rate, which increases on cooling. Our results excl…
The existing theory of the microscopic interpretation of the dynamical contribution to zero-field muon depolarization spectra in a longitudinal geometry is developed. The predicted relaxation of the muon depolarization is calculated from two forms of the spin correlation function. First, when the spin correlation function has an exponential form with a single wave vector dependent relaxation rate is considered, it is shown that this form of the spin correlation function reproduces the slow and fast fluctuation limits of stochastic spin theory regardless of the choice of microscopic spin model.…
We have observed an electronic energy level crossing in a molecular nanomagnet (MNM) using muon-spin relaxation. This effect, not observed previously despite several muon studies of MNM systems, provides further evidence that the spin relaxation of the implanted muon is sensistive to the dynamics of the electronic spin. Our measurements on a broken ring MNM [H_{2}N^{t}Bu^{is}Pr][Cr_{8}CdF_{9}(O_{2}CC(CH_{3})_{3})_{18}] (hereafter Cr_{8}Cd), which contains eight Cr ions, show clear evidence for the S=0 to S=1 transition that takes place at B_{c}=2.3 T. The crossing is observed as a resonance-li…
We present longitudinal-field muon-spin relaxation (LF $μ$SR) measurements on two systems that stabilize a skyrmion lattice (SkL): Cu$_2$OSeO$_3$, and Co$_x$Zn$_y$Mn$_{20-x-y}$ for $(x,y)~=~(10,10)$, $(8,9)$ and $(8,8)$. We find that the SkL phase of Cu$_2$OSeO$_3$ exhibits emergent dynamic behavior at megahertz frequencies, likely due to collective excitations, allowing the SkL to be identified from the $μ$SR response. From measurements following different cooling protocols and calculations of the muon stopping site, we suggest that the metastable SkL is not the majority phase throughout the …
Positive-muon ($μ^+$) Knight shifts have been measured in the paramagnetic states of Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloys, where $x =$ 0, 0.25, 0.45, 0.50, 0.55, 0.75, and 1.00. In Pr-substituted NdOs$_4$Sb$_{12}$ ($x \le$ 0.75), but not in NdOs$_4$Sb$_{12}$, Clogston-Jaccarino plots of $μ^+$ Knight shift~$K$ versus magnetic susceptibility~$χ$ exhibit an anomalous saturation of $K(χ)$ at $\sim-$0.5% for large susceptibilities (low temperatures), indicating a reduction of the coupling strength between $μ^+$ spins and $4f$ paramagnetism for temperatures $\lesssim$ 15~K. We speculate that itine…
We have carried out neutron diffraction, muon spin relaxation (muSR) and inelastic neutron scattering investigations on a polycrystalline sample of CeOs2Al10 to investigate the nature of the phase transition observed near 29 K in the resistivity and heat capacity. Our muSR data clearly reveal coherent frequency oscillations below 28 K, indicating the presence of an internal field at the muon site, which confirms the long-range magnetic ordering of the Ce-moment below 28 K. Upon cooling the sample below 15 K, unusual behaviour of the temperature dependent muSR frequencies may indicate either a …
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 …
We report on muon spin relaxation measurements of the 4f^2-based heavy-fermion superconductor filled-skutterudite PrOs4Sb12. The results reveal the spontaneous appearance of static internal magnetic fields below the superconducting transition temperature, providing unambiguous evidence for the breaking of time-reversal symmetry in the superconducting state. A discussion is made on which of the spin or orbital component of Cooper pairs carries a nonzero momentum.
We report zero-field muon spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon spin precession frequency below the Curie temperature $T_C = 3$ K. The $μ^+$ precession frequency persists below the bulk superconducting transition temperature $T_{sc} = 0.5$ K, where it measures a local magnetic field $B_{loc} = 0.015$ T. The amplitude of the $μ$SR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on th…
Muon spin relaxation on Nd$_2$Ti$_2$O$_7$ (NTO) and NdLaTi$_2$O$_7$ (NLTO) compounds are presented. The time spectra for both compounds are as expected for the paramagnetic state at high temperatures, but deviate from the exponential function below about 100 K. The muon spin relaxation rate increases with decreasing temperature firstly, and then levels off below about 10 K, which is reminiscent of the frustrated systems. An enhancement of the relaxation rate by a longitudinal field in the paramagnetic state is observed for NTO, and eliminated by a magnetic dilution for the NLTO sample. This su…
We report muon spin relaxation rate measurements on films composed of aluminum grains having a size of a few nm, with a large energy level splitting of the order of 100 K. The films range from weakly metallic to insulating. In the insulating case the low temperature relaxation rate is consistent with the presence of single electron spins in grains having an odd number of electrons. The relaxation rate temperature dependence follows an activation law having an energy scale in agreement with the average level splitting. In weakly metallic films the relaxation rate is smaller and decreases faster…
We report results of a muon spin relaxation study of slow magnetic fluctuations in the pseudogap phase of underdoped single-crystalline YBa$_{2}$Cu$_{3}$O$_{y}$, $y = 6.77$ and 6.83. The dependence of the dynamic muon spin relaxation rate on applied magnetic field yields the rms magnitude~$B\mathrm{_{loc}^{rms}}$ and correlation time~$τ_c$ of fluctuating local fields at muon sites. The observed relaxation rates do not decrease with decreasing temperature~$T$ below the pseudogap onset at $T^\ast$, as would be expected for a conventional magnetic transition; both $B\mathrm{_{loc}^{rms}}$ and $τ_…
The magnetic ground state of an electron-doped cuprate superconductor Pr$_{1-x}$LaCe$_x$CuO$_{4+α-δ}$ ($x=0.11, α\simeq0.04$) has been studied by means of muon spin rotation/relaxation (\msr) over a wide variety of oxygen depletion, $0.03\leδ\le0.12$. Appearance of weak random magnetism over entire crystal volume has been revealed by a slow exponential relaxation. The absence of $δ$-dependence for the random magnetism and the multiplet pattern of muon Knight shift at higher fields strongly suggest that the random moments are associated with excited Pr$^{3+}$ ions under crystal electric field.
The muon spin relaxation method (μSR) is a powerful microscopic tool to probe electronic states of materials observing local magnetic field distributions on the muon. It often happens that a distribution of local magnetic fields shows intermediate state between Gaussian and Lorentzian shapes. In order to generally describe intermediate field distributions, we dealt the convolution of two isotropic distributions in the three dimension and derived exact muon-spin relaxation functions which can be applied to all crossover regimes between the Gaussian and Lorentzian.
We report Muon Spin Relaxation studies in weak transverse fields of the superconductivity in the metal cluster compound, Ga$\_{84}$[N(SiMe$\_{3}$)$\_{2}$]$\_{20}$-Li$\_{6}$Br$\_{2}$(thf)$\_{20}\cdot $2toluene. The temperature and field dependence of the muon spin relaxation rate and Knight shift clearly evidence type II bulk superconductivity below $T\_{\text{c}}\approx7.8$ K, with $B\_{\text{c1}}\approx 0.06$ T, $B\_{\text{c2}}\approx 0.26 $ T, $κ\sim 2$ and weak flux pinning. The data are well described by the s-wave BCS model with weak electron-phonon coupling in the clean limit. A qualitat…
We report muon spin relaxation and magnetometry studies of bulk Mn$_{1.4}$Pt$_{0.9}$Pd$_{0.1}$Sn and MnNiGa, two materials which have recently been proposed to host topological magnetic states in thin lamella (antiskyrmions for Mn$_{1.4}$Pt$_{0.9}$Pd$_{0.1}$Sn and biskyrmions for MnNiGa), and show spin reorientation transitions in bulk. These measurements shed light on the magnetic dynamics surounding the two magnetic phase transitions in each material. In particular, we demonstrate that the behaviour approaching the higher temperature transition in both samples is best understood by consideri…
We report muon-spin relaxation measurements on SrFeAsF, which is the parent compound of a newly discovered iron-arsenic-fluoride based series of superconducting materials. We find that this material has very similar magnetic properties to LaFeAsO, such as separated magnetic and structural transitions (TN = 120 K, Ts = 175 K), contrasting with SrFe2As2 where they are coincident. The muon oscillation frequencies fall away very sharply at TN, which suggests that the magnetic exchange between the layers is weaker than in comparable oxypnictide compounds. This is consistent with our specific heat m…
The magnetic and quadrupolar ordered states of polycrystalline YbRu2Ge2 have been investigated using zero-field muon spin relaxation (μSR) and neutron diffraction measurements. Specific heat measurements show three successive phase transitions, with decreasing temperature from a paramagnetic to a quadrupolar state at T0 ~ 10 K, from the quadrupolar to a magnetic state at T1 ~ 6.5 K and a possible change in the magnetic ground state at T2 ~ 5.5 K. Clear evidence for the magnetic transition below 7 K (spectrum at 8 K reveals paramagnetic state) and a likely change in the magnetic structure near …
Copper metaborate CuB$_2$O$_{4}$ was studied by muon spin relaxation measurements in order to clarify its static and dynamic magnetic properties. The time spectra of muon spin depolarization suggest that the local fields at the muon site contain both static and fluctuating components in all ordered phases down to 0.3 K. In the weak ferromagnetic phase (20 K~$>T>$~9.3 K), the static component is dominant. On the other hand, upon cooling the fluctuating component becomes dominant in the incommensurate helix phase (9.3K > T > 1.4K). The dynamical fluctuations of the local fields persist down to 0…
The effects of electron (Ir) and hole (Re) doping on the hybridization gap and antiferromagnetic order have been studied by magnetization, muon spin relaxation ($μ^+$SR), and inelastic neutron scattering on the polycrystalline samples of Ce(Os$_{1-x}$Ir$_x$)$_2$Al$_{10}$ ($x$ = 0.08 and 0.15) and CeOs$_{1.94}$Re$_{0.06}$Al$_{10}$. $μ^+$SR spectra clearly reveals magnetic ordering below 20 and 10 K for $x$ = 0.08 and 0.15 samples respectively with a very weak signature of oscillations of the muon initial asymmetry at very short time scale. Our important findings are that small amount of electro…
Using the transverse field muon spin relaxation technique we measure the temperature dependence of the magnetic field penetration depth $λ$, in the Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O system. We find that $λ,$ which is determined by superfluid density $n_{s}$ and the effective mass $m^{\ast}$, is very small and on the edge of the TF-$μ$SR sensitivity. Nevertheless, the results indicate that the order parameter in this system has nodes and that it obeys the Uemura relation. By comparing $λ$ with the normal state electron density we conclude that $m^{\ast}$ of the superconductivity carrier is 70 ti…
Muon spin relaxation ($μ$SR) measurements in high transverse magnetic fields ($\parallel \hat c$) revealed strong field-induced quasi-static magnetism in the underdoped and Eu doped (La,Sr)$_{2}$CuO$_{4}$ and La$_{1.875}$Ba$_{0.125}$CuO$_{4}$, existing well above $T_{c}$ and $T_{N}$. The susceptibility-counterpart of Cu spin polarization, derived from the muon spin relaxation rate, exhibits a divergent behavior towards $T \sim 25$ K. No field-induced magnetism was detected in overdoped La$_{1.81}$Sr$_{0.19}$CuO$_{4}$, optimally doped Bi2212, and Zn-doped YBa$_{2}$Cu$_{3}$O$_{7}$.
At low temperatures, spin dynamics in ideal spin ice is due mainly to dilute, thermally excited magnetic monopole excitations. I consider how these will affect the dynamics of a nuclear spin (the same theory applies to muon spin resonance if implanted muons do not diffuse). Up to the time scale for nearby monopoles to be rearranged, a stretched-exponential form of the relaxation functions is expected. I work out the expected exponent in that exponential and the formulas for the $T_1$ (longitudinal) and $T_2$ (dephasing) relaxations, as a function of the monopole density. Experimental NMR is in…
We interpret recent measurements of the zero field muon relaxation rate in the frustrated magnetic pyrochlore Dy$_2$Ti$_2$O$_7$ as resulting from the quantum diffusion of muons in the substance. In this scenario, the plateau observed at low temperature ($<7$ K) in the relaxation rate is due to coherent tunneling of the 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 tunnelling and incoherent activated hopping motion o…
Muon-spin-relaxation measurements have been performed for the partially Zn-substituted La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ with y=0-0.10 in the overdoped regime up to x=0.30. In the 3 % Zn-substituted samples up to x=0.27, exponential-like depolarization of muon spins has been observed at low temperatures, indicating Zn-induced slowing-down of the Cu-spin fluctuations. The depolarization rate decreases with increasing x and almost no fast depolarization of muon spins has been observed for x=0.30 where superconductivity disappears. The present results suggest that the dynamical stripe correlations exi…
We present measurements of magnetic field and frequency dependences of the low temperature (T = 1.8 K) AC-susceptibility, and temperature and field dependences of the longitudinal field positive muon spin relaxation (μSR) for LiY$_{1-x}$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 p…
Longitudinal-field muon-spin-relaxation measurements have revealed inhomogeneous distribution of the internal magnetic field at temperatures above the bulk superconducting (SC) transition temperature, $T_{\rm c}$, in slightly overdoped Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_{8+δ}$. The distribution width of the internal magnetic field, $Δ$, evolves continuously with decreasing temperature toward $T_{\rm c}$. The origin of the increase in $Δ$ is discussed in terms of the creation of SC domains in a sample.
We present longitudinal field muon spin relaxation ($μ$SR) measurements in the unilluminated state of the photo-sensitive molecular magnetic Co-Fe Prussian blue analogues M$_{1-2x}$Co$_{1+x}$[Fe(CN)$_6$]$\cdot z$ H$_2$O, where M=K and Rb with $x=0.4$ and $\simeq 0.17$, respectively. These results are compared to those obtained in the $x=0.5$ stoichiometric limit, Co$_{1.5}$[Fe(CN)$_6$]$\cdot 6$ H$_2$O, which is not photo-sensitive. We find evidence for correlation between the range of magnetic ordering and the value of $x$ in the unilluminated state which can be explained using a site percolat…
Muon spin relaxation measurements on some quantum spin ice candidate materials, the insulating pyrochlores Pr2B2O7 (B = Sn, Zr, Hf), have been performed for temperatures in the range 0.05-280 K. The results are indicative of a static distribution of magnetic moments which appears to grow on cooling and whose size at low temperatures is significantly larger than that expected for Pr nuclear moments. Using density functional theory we show how this effect can be explained via a hyperfine enhancement arising from a splitting of the non-Kramers doublet ground states on Pr ions close to the muon wh…
We present the results of muon-spin relaxation measurements of spin excitations in the one-dimensional quantum Heisenberg antiferromagnet Cu(pyz)(NO$_{3}$)$_{2}$. Using density-functional theory we propose muon sites and assess the degree of perturbation the muon probe causes on the system. We identify a site involving the muon forming a hydroxyl-type bond with an oxygen on the nitrate group that is sensitive to the characteristic spin dynamics of the system. Our measurements of the spin dynamics show that in the temperature range $T_{\mathrm{N}}<T<J$ (between the ordering temperature $T_{\mat…
