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Muon spin rotation (muSR) spectra recorded for manganese silicide MnSi and interpreted in terms of a quantitative analysis constrained by symmetry arguments were recently published. The magnetic structures of MnSi in zero-field at low temperature and in the conical phase near the magnetic phase transition were shown to substantially deviate from the expected helical and conical structures. Here, we present material backing the previous results obtained in zero-field. First, from simulations of the field distributions experienced by the muons as a function of relevant parameters we confirm the uniqueness of the initial interpretation and illustrate the remarkable complementarity of neutron scattering and muSR for the MnSi magnetic structure determination. Second we present the result of a muSR experiment performed on MnSi crystallites grown in a Zn-flux and compare it with the previous data recorded with a crystal obtained from Czochralski pulling. We find the magnetic structure for the two types of crystals to be identical within experimental uncertainties. We finally address the question of a possible muon-induced effect by presenting transverse field muSR spectra recorded in a wide range of temperature and field intensity. The field distribution parameters perfectly scale with the macroscopic magnetization, ruling out a muon-induced effect.

We present the results of muon-spin spectroscopy ($\mu^{+}$SR) measurements on the molecular spin ladder system (Hpip)$_{2}$CuBr$_{4(1-x)}$Cl$_{4x}$, [Hpip=(C$_{5}$H$_{12}$N)]. Using transverse field $\mu^{+}$SR we are able to identify characteristic behaviour in each of the regions of the phase diagram of the $x=0$ strong-rung spin ladder system (Hpip)$_{2}$CuBr$_4$. Comparison of our results to those of the dimer-based molecular magnet Cu(pyz)(gly)(ClO$_{4}$) shows several common features. We locate the crossovers in partially disordered (Hpip)$_{2}$CuBr$_{4(1-x)}$Cl$_{4x}$ ($x=0.05$), where a region of behaviour intermediate between quantum disordered and Luttinger liquid-like is identified. Our interpretation of the results incorporates an analysis of the probable muon stopping states in (Hpip)$_{2}$CuBr$_4$ based on density functional calculations and suggests how the muon plus its local distortion can lead to a local probe unit with good sensitivity to the magnetic state. Using longitudinal field $\mu^{+}$SR we compare the dynamic response of the $x=1$ strong-rung material (Hpip)$_{2}$CuCl$_{4}$ to that of the strong-leg material (C$_{7}$H$_{10}$N)$_{2}$CuBr$_{4}$ (known as DIMPY) and demonstrate that our results are in agreement with predictions based on interacting fermionic quasiparticle excitations in these materials.

A nematic transition preceding a long-range spin density wave antiferromagnetic phase is a common feature of many Fe based superconductors. However, in the FeSe system with a nematic transition at $T_{\rm s} \approx$ 90 K no evidence for long-range static magnetism down to very low temperature was found. The lack of magnetism is a challenge for the theoretical description of FeSe. Here, we investigated high-quality single crystals of FeSe using high-field (up to 9.5 Tesla) muon spin rotation ($\mu$SR) measurements. The $\mu$SR Knight shift and the bulk susceptibility linearly scale at high temperatures but deviate from this behavior around $T^{*} \sim 10$ K, where the Knight shift exhibits a kink. This behavior hints to an essential change of the electronic and/or magnetic properties crossing the region near $T^{*}$. In the temperature range $T_{\rm s} \gtrsim T \gtrsim T^{*}$ the muon spin depolarization rate follows a critical behavior $\Lambda \propto T^{-0.4}$. The observed non-Fermi liquid behavior with a cutoff at $T^{*}$ indicates that FeSe is in the vicinity to a antiferromagnetic quantum critical point. Our analysis is suggestive for $T^{*}$ triggered by the Lifshitz transition.

Pressure, together with temperature and magnetic field, is an important thermodynamical parameter in physics. Investigating the response of a compound or of a material to pressure allows to elucidate ground states, investigate their interplay and interactions and determine microscopic parameters. Pressure tuning is used to establish phase diagrams, study phase transitions and identify critical points. Muon spin rotation/relaxation (muSR) is now a standard technique making increasing significant contribution in condensed matter physics, material science research and other fields. In this review, we will discuss specific requirements and challenges to perform muSR experiments under pressure, introduce the high-pressure muon facility at the Paul Scherrer Institute (PSI, Switzerland) and present selected results obtained by combining the sensitivity of the muSR technique with pressure.

A quantum critical point (QCP) occurs upon chemical doping of the weak itinerant ferromagnet Sc_3.1In. Remarkable for a system with no local moments, the QCP is accompanied by non-Fermi liquid (NFL) behavior, manifested in the logarithmic divergence of the specific heat both in the ferro- and the paramagnetic states. Sc_3.1In displays critical scaling and NFL behavior in the ferromagnetic state, akin to what had been observed only in f-electron, local moment systems. With doping, critical scaling is observed close to the QCP, as the critical exponents, and delta, gamma and beta have weak composition dependence, with delta nearly twice, and beta almost half of their respective mean-field values. The unusually large paramagnetic moment mu_PM~1.3 mu_B/F.U. is nearly composition-independent. Evidence for strong spin fluctuations, accompanying the QCP at x_c = 0.035 +- 0.005, may be ascribed to the reduced dimensionality of Sc_3.1In, associated with the nearly one-dimensional Sc-In chains.

We report muon spin relaxation/rotation (uSR) measurements of single crystal Ba(Fe1-xCox)2As2 with x=0.038 and 0.047. Zero field (ZF)-uSR and Transverse field (TF)-iSR measurements of these underdoped samples find the presence of magnetism and superconductivity. We find internal fields along the c-axis whose magnitude decreases with increasing doping. We find evidence for a low-temperature volume fraction that is only weakly magnetic, where that volume fraction increases with increasing Co doping of the sample. TF-uSR measurements show slight changes in the spectra that indicate magnetic inhomogeneities due to the loss of Fe moments in the system, the effect of which is larger in the higher Co doping. We discuss the existence of superconductivity in these samples in close proximity to strong magnetic order.

EuTiO_3, which is a G-type antiferromagnet below T_N = 5.5 K, has some fascinating properties at high temperatures, suggesting that macroscopically hidden dynamically fluctuating weak magnetism exists at high temperatures. This conjecture is substantiated by magnetic field dependent magnetization measurements, which exhibit pronounced anomalies below 200 K becoming more distinctive with increasing magnetic field strength. Additional results from muon spin rotation (${\mu}$SR) experiments provide evidence for weak fluctuating bulk magnetism induced by spin-lattice coupling which is strongly supported in increasing magnetic field.

We use muon spin relaxation (muSR) to investigate the magnetic properties of a bulk form diluted ferromagnetic semiconductor (DFS) Li1.15(Zn0.9Mn0.1)P with T_C ~ 22 K. MuSR results confirm the gradual development of ferromagnetic ordering below T_C with a nearly 100% magnetic ordered volume. Despite its low carrier density, the relation between static internal field and Curie temperature observed for Li(Zn,Mn)P is consistent with the trend found in (Ga,Mn)As and other bulk DFSs, indicating these systems share a common mechanism for the ferromagnetic exchange interaction. Li1+y(Zn1-xMnx)P has the advantage of decoupled carrier and spin doping, where Mn2+ substitution for Zn2+ introduces spins and Li+ off-stoichiometry provides carriers. This advantage enables us to investigate the influence of overdoped Li on the ferromagnetic ordered state. Overdoping Li suppresses both T_C and saturation moments for a certain amount of spins, which indicates that more carriers are detrimental to the ferromagnetic exchange interaction, and that a delicate balance between charge and spin densities is required to achieve highest T_C.

The B-site ordered double perovskite Ba2CaOsO6 was studied by d.c. magnetic susceptibility, powder neutron diffraction and muon spin relaxation methods. The lattice parameter is a = 8.3619(6) A at 280K and cubic symmetry (Fm-3m) is retained to 3.5K with a = 8.3426(5) A. Curie-Weiss susceptibility behavior is observed for T > 100K and the derived constants are C = 0.3361(1)emu-K/mole and T_CW = -156.2(3) K, in excellent agreement with literature values. This Curie constant is much smaller than the spin-only value of 1.00 emu-K/mole for a 5d^2 Os6+ configuration, indicating a major influence of spin-orbit coupling. Previous studies had detected both susceptibility and heat capacity anomalies near 50K but no definitive conclusion was drawn concerning the nature of the ground state. While no ordered Os moment could be detected by powder neutron diffraction, muon spin relaxation (muSR) data show clear long-lived oscillations indicative of long-range magnetic order below T_C = 50K. An estimate of the ordered moment on Os6+ is ~0.2 mu_B, based upon a comparison with muSR data for Ba2YRuO6 with a known ordered moment of 2.2 mu_B. These results are compared with those for isostructural Ba2YReO6 which contains Re5+, also 5d^2, and has a nearly identical unit cell constant, a = 8.3628(2) A. In contrast, Ba2YReO6 shows T_CW = -616 K, and a complex spin-disordered and, ultimately, spin-frozen ground state below 50 K, indicating a much higher level of geometric frustration than in Ba2CaOsO6. A comparison is made to recent theory on d^2 double perovskites.

We report the discovery of a new diluted magnetic semiconductor, Li(Zn,Mn)P, in which charge and spin are introduced independently via lithium off-stoichiometry and the isovalent substitution of Mn2+ for Zn2+, respectively. Isostructural to (Ga,Mn)As, Li(Zn,Mn)P was found to be a p-type ferromagnetic semiconductor with excess Lithium providing charge doping. First principles calculations indicate that excess Li is favored to partially occupy the Zn site, leading to hole doping. Ferromagnetism is mediated in semiconducting samples of relative low mobile carriers with a small coercive force, indicating an easy spin flip.

We report the synthesis and characterization of a bulk diluted magnetic semiconductor (La1-xBax)(Zn1-xMnx)AsO (0 <= x <= 0.2) with a layered crystal structure identical to that of the "1111" FeAs superconductors. No ferromagnetic order occurs for (Zn,Mn) substitution in the parent compound LaZnAsO without charge doping. Together with carrier doping via (La,Ba) sub- stitution, a small amount of Mn substituting for Zn results in ferromagnetic order with TC up to ~40 K, although the system remains semiconducting. Muon spin relaxation measurements confirm the development of ferromagnetic order in the entire volume, with the relationship between the internal field and TC consistent with the trend found in (Ga,Mn)As, the "111" Li(Zn,Mn)As, and the "122" (Ba,K)(Zn,Mn)2As2 systems.

Diluted magnetic semiconductors (DMS) have received much attention due to its potential applications to spintronics devices. A prototypical system (Ga,Mn)As has been widely studied since 1990s. The simultaneous spin and charge doping via hetero-valence (Ga3+,Mn2+) substitution, however, resulted in severely limited solubility without availability of bulk specimens. Previously we synthesized a new diluted ferromagnetic semiconductor of bulk Li(Zn,Mn)As with Tc up to 50K, where isovalent (Zn,Mn) spin doping was separated from charge control via Li concentrations. Here we report the synthesis of a new diluted ferromagnetic semiconductor (Ba1-xKx)(Zn1-yMny)2As2, isostructural to iron 122 system, where holes are doped via (Ba2+, K1+), while spins via (Zn2+,Mn2+) substitutions. Bulk samples with x=0.1-0.3 and y=0.05-0.15 exhibit ferromagnetic order with TC up to 180K, comparable to that of record high Tc for Ga(MnAs), significantly enhanced than Li(Zn,Mn)As. Moreover the (Ba,K)(Zn,Mn)2As2 shares the same 122 crystal structure with semiconducting BaZn2As2, antiferromagnetic BaMn2As2, and superconducting (Ba,K)Fe2As2, which makes them promising to the development of multilayer functional devices.

We report low temperature specific heat and muon spin relaxation/rotation ($\mu$SR) measurements on both polycrystalline and single crystal samples of the pyrochlore magnet Yb$_2$Ti$_2$O$_7$. This system is believed to possess a spin Hamiltonian supporting a Quantum Spin Ice (QSI) ground state and to display sample variation in its low temperature heat capacity. Our two samples exhibit extremes of this sample variation, yet our $\mu$SR measurements indicate a similar disordered low temperature state down to 16 mK in both. We report little temperature dependence to the spin relaxation and no evidence for ferromagnetic order, in contrast to recent reports by Chang \emphet al. (Nat. Comm. \bf 3, 992 (2012)). Transverse field (TF) $\mu$SR measurements show changes in the temperature dependence of the muon Knight shift which coincide with heat capacity anomalies. We are therefore led to propose that Yb$_2$Ti$_2$O$_7$ enters a hidden order ground state below $T_c\sim265$ mK where the nature of the ordered state is unknown but distinct from simple long range order.

We respond to the comment of Bramwell et al (arXiv:1111.4168v1) to our original publication (S. R. Dunsiger et al, Phys. Rev. Lett. 107, 207207 (2011)), detailing muon spin rotation measurements of the Spin Ice compound Dy2Ti2O7.

Theory predicts the low-temperature magnetic excitations in spin ices consist of deconfined magnetic charges, or monopoles. A recent transverse-field (TF) muon spin rotation (muSR) experiment [S T Bramwell et al, Nature 461, 956 (2009)] reports results claiming to be consistent with the temperature and magnetic field dependence anticipated for monopole nucleation - the so-called second Wien effect. We demonstrate via a new series of muSR experiments in Dy_2Ti_2O_7 that such an effect is not observable in a TF muSR experiment. Rather, as found in many highly frustrated magnetic materials, we observe spin fluctuations which become temperature independent at low temperatures, behavior which dominates over any possible signature of thermally nucleated monopole excitations.

We have studied the magnetism in superconducting single crystals of EuFe2 As1.4 P0.6 by using the local probe techniques of zero-field muon spin rotation/relaxation and 151 Eu/57 Fe Mössbauer spec- troscopy. All of these measurements reveal magnetic hyperfine fields below the magnetic ordering temperature TM = 18 K of the Eu2+ moments. The analysis of the data shows that there is a coexistence of ferromagnetism, resulting from Eu2+ moments ordered along the crystallographic c-axis, and superconductivity below TSC ≈15 K. We find indications for a change in the dynamics of the small Fe magnetic moments (∼0.07 \mu B) at the onset of superconductivity: below TSC the Fe magnetic moments seem to be "frozen" within the ab-plane.

Static magnetic order of quasi two-dimensional FeAs compounds Sr4A2O6-xFe2As2, with A = Sc and V, has been detected by 57Fe Moessbauer and muon spin relaxation (\muSR) spectroscopies. The non-superconducting stoichiometric (x = 0) A = Sc system exhibits a static internal/hyperfine magnetic field both at the 57Fe and \mu+ sites, indicating antiferromagnetic order of Fe moments below TN = 35 K with ~ 0.1 Bohr magneton per Fe at T = 2 K. The superconducting and oxygen deficient (x = 0.4) A = V system exhibits a static internal field only at the \mu+ site below TN ~ 40 K, indicating static magnetic order of V moments co-existing with superconductivity without freezing of Fe moments. These results suggest that the 42622 FeAs systems belong to the same paradigm with the 1111 and 122 FeAs systems with respect to magnetic behavior of Fe moments.

We present muon-spin rotation measurements on polycrystalline samples of the complete family of the antiferromagnetic (AF) $zigzag$ chain compounds, Na$_x$Ca$_{1-x}$V$_2$O$_4$. In this family, we explore the magnetic properties from the metallic NaV$_2$O$_4$ to the insulating CaV$_2$O$_4$. We find a critical $x_c(\sim0.833)$ which separates the low and high Na-concentration dependent transition temperature and its magnetic ground state. In the $x<x_c$ compounds, the magnetic ordered phase is characterized by a single homogenous phase and the formation of incommensurate spin-density-wave order. Whereas in the $x>x_c$ compounds, multiple sub-phases appear with temperature and $x$. Based on the muon data obtained in zero external magnetic field, a careful dipolar field simulation was able to reproduce the muon behavior and indicates a modulated helical incommensurate spin structure of the metallic AF phase. The incommensurate modulation period obtained by the simulation agrees with that determined by neutron diffraction.

We report muon spin rotation ($\mu$SR) measurements of single crystal Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$. From measurements of the magnetic field penetration depth $\lambda$ we find that for optimally- and over-doped samples, $1/\lambda(T\to 0)^2$ varies monotonically with the superconducting transition temperature T$_{\rm C}$. Within the superconducting state we observe a positive shift in the muon precession signal, likely indicating that the applied field induces an internal magnetic field. The size of the induced field decreases with increasing doping but is present for all Co concentrations studied.

We have searched for time-reversal symmetry breaking fields in the non-centrosymmetric superconductor Mg$_{10}$Ir$_{19}$B$_{16}$ via muon spin relaxation in zero applied field, and we measured the temperature dependence of the superfluid density by muon spin rotation in transverse field to investigate the superconducting pairing symmetry in two polycrystalline samples of signficantly different purities. In the high purity sample, we detected no time-reversal symmetry breaking fields greater than 0.05 G. The superfluid density was also found to be exponentially-flat as T$\to $0, and so can be fit to a single-gap BCS model. In contrast, the lower purity sample showed an increase in the zero-field $\mu$SR relaxation rate below T$_c$ corresponding to a characteristic field strength of 0.6 G. While the temperature-dependence of the superfluid density was also found to be consistent with a single-gap BCS model, the magnitude as T$\to $0 was found to be much lower for a given applied field than in the case of the high purity sample. These findings suggest that the dominant pairing symmetry in high quality Mg$_{10}$Ir$_{19}$B$_{16}$ samples corresponds to the spin-singlet channel, while sample quality drastically affects the superconducting properties of this system.

We have performed transverse field muon spin rotation measurements of single crystals of Ba(Fe$_{0.93}$Co$_{0.07})_2$As$_2$ with the applied magnetic field along the $\hat{c}$ direction. Fourier transforms of the measured spectra reveal an anisotropic lineshape characteristic of an Abrikosov vortex lattice. We have fit the $\mu$SRSR spectra to a microscopic model in terms of the penetration depth $\lambda$ and the Ginzburg-Landau parameter $\kappa$. We find that as a function of temperature, the penetration depth varies more rapidly than in standard weak coupled BCS theory. For this reason we first fit the temperature dependence to a power law where the power varies from 1.6 to 2.2 as the field changes from 200G to 1000G. Due to the surprisingly strong field dependence of the power and the superfluid density we proceeded to fit the temperature dependence to a two gap model, where the size of the two gaps is field independent. From this model, we obtained gaps of $2\Delta_1=3.7k_BT_c$ and $2\Delta_2=1.6k_BT_c$, corresponding to roughly 6 meV and 3 meV respectively.

The recent discovery and subsequent developments of FeAs-based superconductors have presented novel challenges and opportunities in the quest for superconducting mechanisms in correlated-electron systems. Central issues of ongoing studies include interplay between superconductivity and magnetism as well as the nature of the pairing symmetry reflected in the superconducting energy gap. In the cuprate and RE(O,F)FeAs (RE = rare earth) systems, the superconducting phase appears without being accompanied by static magnetic order, except for narrow phase-separated regions at the border of phase boundaries. By muon spin relaxation measurements on single crystal specimens, here we show that superconductivity in the AFe$_{2}$As$_{2}$ (A = Ca,Ba,Sr) systems, in both the cases of composition and pressure tunings, coexists with a strong static magnetic order in a partial volume fraction. The superfluid response from the remaining paramagnetic volume fraction of (Ba$_{0.5}$K$_{0.5}$)Fe$_{2}$As$_{2}$ exhibits a nearly linear variation in T at low temperatures, suggesting an anisotropic energy gap with line nodes and/or multi-gap effects.

Zero-field (ZF) muon spin relaxation ($\mu$SR) measurements have revealed static commensurate magnetic order of Fe moments in NdOFeAs below $T_{N} \sim 135$ K, with the ordered moment size nearly equal to that in LaOFeAs, and confirmed similar behavior in BaFe$_{2}$As$_{2}$. In single crystals of superconducting (Ba$_{0.55}$K$_{0.45}$)Fe$_{2}$As$_{2}$, $\mu$SR spectra indicate static magnetism with incommensurate or short-ranged spin structure in $\sim$ 70 % of volume below $T_{N} \sim$ 80 K, coexisting with remaining volume which exhibits superfluid-response consistent with nodeless gap below $T_{c}\sim 30$ K.

We report muon spin relaxation ($\mu$SR) and magnetic susceptibility measurements on Cu(Cl,Br)La(Nb,Ta)$_{2}$O$_{7}$, which demonstrate: (a) the absence of static magnetism in (CuCl)LaNb$_{2}$O$_{7}$ down to 15 mK confirming a spin-gapped ground state; (b) phase separation between partial volumes with a spin-gap and static magnetism in (CuCl)La(Nb,Ta)$_{2}$O$_{7}$; (c) history-dependent magnetization in the (Nb,Ta) and (Cl,Br) substitution systems; (d) a uniform long-range collinear antiferromagnetic state in (CuBr)LaNb$_{2}$O$_{7}$; and (e) a decrease of Néel temperature with decreasing Br concentration $x$ in Cu(Cl$_{1-x}$Br$_{x}$)LaNb$_{2}$O$_{7}$ with no change in the ordered Cu moment size for $0.33 \leq x \leq 1$. Together with several other $\mu$SR studies of quantum phase transitions in geometrically-frustrated spin systems, the present results reveal that the evolution from a spin-gap to a magnetically ordered state is often associated with phase separation and/or a first order phase transition.

Muon spin relaxation (MuSR) measurements in iron oxy-pnictide systems have revealed: (1) commensurate long-range order in undoped LaOFeAs; (2) Bessel function line shape in La(O0.97F0.03)FeAs which indicates possible incommensurate or stripe magnetism; (3) anomalous weak magnetism existing in superconducting LaOFeP, Ce(O0.84F0.16)FeAs, and Nd(O0.88F0.12)FeAs but absent in superconducting La(O0.92F0.08)FeAs; and (4) scaling of superfluid density and Tc in the Ce, La, and Nd-FeAs superconductors following a nearly linear relationship found in cuprates.

Quantum phase transitions (QPTs) have been studied extensively in correlated electron systems. Characterization of magnetism at QPTs has, however, been limited by the volume-integrated feature of neutron and magnetization measurements and by pressure uncertainties in NMR studies using powderized specimens. Overcoming these limitations, we performed muon spin relaxation ($\mu$SR) measurements which have a unique sensitivity to volume fractions of magnetically ordered and paramagnetic regions, and studied QPTs from itinerant heli/ferro magnet to paramagnet in MnSi (single-crystal; varying pressure) and (Sr$_{1-x}$Ca$_{x}$)RuO$_{3}$ (ceramic specimens; varying $x$). Our results provide the first clear evidence that both cases are associated with spontaneous phase separation and suppression of dynamic critical behavior, revealed a slow but dynamic character of the ``partial order'' diffuse spin correlations in MnSi above the critical pressure, and, combined with other known results in heavy-fermion and cuprate systems, suggest a possibility that a majority of QPTs involve first-order transitions and/or phase separation.

We show that the pressure-temperature phase diagram of the Mott insulator Ca$_{2}$RuO$_{4}$ features a metal-insulator transition at 0.5GPa: at 300K from paramagnetic insulator to paramagnetic quasi-two-dimensional metal; at $T \leq$ 12K from antiferromagnetic insulator to ferromagnetic, highly anisotropic, three-dimensional metal. % We compare the metallic state to that of the structurally related p-wave superconductor Sr$_{2}$RuO$_{4}$, and discuss the importance of structural distortions, which are expected to couple strongly to pressure.

We have measured out-of-plane resistivity $\rho_c$ for La$_{2-x}$Sr$_{x}$CuO$_{4}$ under anisotropic pressure. c-axis compression, which decreases $\rho_c$, reduces $T_{\rm c}$ drastically, whereas c-axis extention, which increases $\rho_c$, enhances $T_{\rm c}$ from 38K at ambient pressure to 51.6K at 8GPa. We find that the variation of $T_{\rm c}$ scales as a function of $\rho_c$, and that the c-axis pressure coefficient is much stronger than the ab-axis one. These imply that $T_{\rm c}$ depends primarily on the interlayer, rather than the in-plane, lattice parameter.