[1] Pure ferrimagnetic greigite (Fe 3 S 4 ) has been synthesized by reacting ferric chloride with thiourea and formic acid at 170°C. Sample purity was confirmed by X-ray diffraction, neutron diffraction and Mössbauer spectroscopy, coupled with magnetic measurements. Scanning electron microscope observations indicate clear cubo-octahedral and polyhedral crystal morphologies. The grain sizes are as large as 44 mm. Detailed low-and high-temperature magnetic measurements document the previously poorly known magnetic properties of greigite. The synthetic greigite samples are dominated by pseudo-single-domain and multi-domain behavior. The saturation magnetization (M s ) at room temperature is $59 Am 2 kg À1 (3.13 m B per formula unit), which is higher than any value previously reported for greigite in the literature largely because of the high purity of this sample compared to others. No low-temperature magnetic transition has been detected; however, a local coercivity minimum is observed at around 130 K, which is probably associated with domain walls present in the studied samples. The high-temperature magnetic properties of greigite are dominated by chemical decomposition above around 250°C, which precludes determination of the Curie temperature, but our evidence indicates that it must exceed 350°C. On the basis of the Bloch spin wave expansion, the spin wave stiffness of greigite was determined for the first time as $193 meVÁÅ 2 from low-temperature M s measurements, with the corresponding exchange constant J AB of $1.03 meV.

We study the low-energy spin fluctuations and superfluid density of a series of pure and Zn-substituted high-T c superconductors ͑HTS͒ using the muon spin relaxation and ac-susceptibility techniques. At a critical doping state, p c , we find ͑i͒ simultaneous abrupt changes in the magnetic spectrum and in the superconducting ground state and ͑ii͒ that the slowing down of spin fluctuations becomes singular at Tϭ0. These results provide experimental evidence for a quantum transition that separates the superconducting phase diagram of HTS into two distinct ground states. DOI: 10.1103/PhysRevB.66.064501 PACS number͑s͒: 74.72.Ϫh, 74.25.Ha, 75.40.Ϫs, 76.75.ϩi Quantum phase transitions occur at zero temperature at a critical electron density separating distinct ground states. Near a quantum critical point, electrons in metals are highly correlated and the diverging fluctuations may induce unconventional superconductivity. [1][2][3][4][5][6][7][8] For example, in certain heavy fermion compounds a ''bubble'' of superconductivity occurs around the quantum critical point at which itinerant antiferromagnetism is suppressed by applied pressure. 9 The search for an underlying quantum phase transition in high-T c superconductors ͑HTS͒ is motivated by the potential for quantum fluctuations to bind electronic carriers into superconducting Cooper pairs and also to cause the celebrated linear temperature dependence of their electrical resistivity. [1][2][3][4][5][6][7][8]10 HTS exhibit a common generic phase diagram in which the superconducting transition temperature, T c , rises to a maximum at an optimal doping of approximately 0.16 holes per planar copper atom and then falls to zero on the overdoped side. In addition the underdoped normal state exhibits correlations, which introduce a gap in the density of states that strongly affects all physical properties. There is no phase transition associated with the opening of this gap and so it is called a pseudogap. Analysis of specific heat data, for example, suggests that the pseudogap energy decreases with doping and falls to zero at a critical doping of p c Ӎ0.19, just beyond optimal doping, 10,11 a behavior rather analogous to the quantum-critical heavy-fermion materials. 9 Many fundamental physical quantities such as the superconducting condensation energy, 10,11 the superfluid density, 12,13 and the quasiparticle weight, 10,14 show abrupt changes as p→p c . While compelling in their totality, 10,11 none of the results can be considered as evidence of a quantum transition. In particular there is no evidence for an associated order parameter and slowing down of the relevant fluctuations. With this in mind we examined the evolution with doping of the low-energy spin fluctuation spectrum using muon spin relaxation ( SR) combined with low-field ac-susceptibility measurements of the superfluid density.The samples studied were: ͑i͒ La 2Ϫx Sr x Cu 1Ϫy Zn y O 4 ͑LSCO͒ (xϭ0.03-0.24 and yϭ0, 0.01, and 0.02͒. Samples were synthesized using solid-state reaction and where necessary follow...

The absolute values and temperature, T, dependence of the in-plane magnetic penetration depth, λ ab , of La2−xSrxCuO4 and HgBa2CuO 4+δ have been measured as a function of carrier concentration. We find that the superfluid density, ρs, changes substantially and systematically with doping. The values of ρs(0) are closely linked to the available low energy spectral weight as determined by the electronic entropy just above Tc and the initial slope of ρs(T )/ρs(0) increases rapidly with carrier concentration. The results are discussed in the context of a possible relationship between ρs and the normal-state (or pseudo) energy gap.

The extraction of particle size distributions from small-angle neutron scattering data is an example of a practical linear inverse problem. Additional assumptions are necessary to obtain a unique solution. The application of the maximum entropy method to select a realistic size distribution is discussed. Principal features of the method include a proper treatment of experimental errors, no interpolation or smoothing of data, no fitting to empirical models, and guaranteed positivity of the solution everywhere in spite of statistical noise in the data. The resulting solution is the most uniform consistent with the data. Model data results are presented to show that the maximum entropy criterion proves very useful in problems of this type.

We have investigated the superconducting properties of the noncentrosymmetric superconductor LaRhSi 3 by performing magnetization, specific heat, electrical resistivity and muon spin relaxation (µSR) measurements. LaRhSi 3 crystallizes with the BaNiSn 3 -type tetragonal structure (space group I4 mm) as confirmed through our neutron diffraction study. Magnetic susceptibility, electrical resistivity and specific heat data reveal a sharp and well defined superconducting transition at T c = 2.16 ± 0.08 K. The low temperature specific heat data reveal that LaRhSi 3 is a weakly coupled bulk BCS superconductor and has an s-wave singlet ground state with an isotropic energy gap of ∼ 0.3 meV, 2∆ 0 /k B T c = 3.24. The specific heat data measured in applied magnetic field strongly indicate a type-I behaviour. Type-I superconductivity in this compound is also inferred from the Ginzburg-Landau parameter, κ = 0.25. Various superconducting parameters, including the electron-phonon coupling strength, penetration depth and coherence length, characterize LaRhSi 3 as a moderate dirty-limit superconductor. A detailed study of the magnetic field-temperature (H − T ) phase diagram is presented and from a consideration of the free energy, the thermodynamic critical field, H c0 is estimated to be 17.1 ± 0.1 mT, which is in very good agreement with that estimated from the transverse field µSR measurement that gives H c0 = 17.2 ± 0.1 mT. The transverse field µSR results are consistent with conventional type-I superconductivity in this compound. Further, the zero-field µSR results indicate that time reversal symmetry is preserved when entering the superconducting state, also supporting a singlet pairing superconducting ground state in LaRhSi 3 .