We present data on the magnetic and magnetoelastic coupling in the hexagonal multiferroic manganite LuMnO 3 from inelastic neutron scattering, magnetization, and thermal-expansion measurements. We measured the magnon dispersion along the main symmetry directions and used this data to determine the principal exchange parameters from a spin-wave model. An analysis of the magnetic anisotropy in terms of the crystal field acting on the Mn is presented. We compare the results for LuMnO 3 with data on other hexagonal RMnO 3 compounds.The in-plane ͑J 1 , J 2 ͒ and out-of-plane ͑J 1 Ј,J 2 Ј͒, Mn-Mn exchange couplings used in the spin-wave model are shown. Arrows on the Mn atoms show the probable magnetic structure of LuMnO 3 based on neutron diffraction ͑Ref. 10͒ and optical second-harmonic generation ͑Ref. 17͒.

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 observed showing that the magnetic structure is more complex. Synthetic NaFeSi2O6 shows a single muon precession frequency but with a far larger damping rate than in the lithium compound. Heat capacity measurements reproduce the phase diagrams previously derived from other techniques and demonstrate that the magnetic entropy is mostly associated with the build up of correlations in the quasi-one-dimensional Fe 3+ chains.

Transverse-field muon-spin rotation measurements performed on two samples of LiFeAs demonstrate that the superfluid stiffness of the superconducting condensate in relation to its superconducting transition temperature is enhanced compared to other pnictide superconductors. Evidence is seen for a field-induced magnetic state in a sample with a significantly suppressed superconducting transition temperature. The results in this system highlight the role of direct Fe-Fe interactions in frustrating pairing mediated by antiferromagnetic fluctuations and indicate that, in common with other pnictide superconductors, the system is close to a magnetic instability.The relationship between critical temperature T c and superfluid stiffness s in a superconductor ͑SC͒ provides important information concerning the balance between the strength of the pairing and the efficiency of electromagnetic screening. In many SCs these two parameters are related by Uemura scaling, 1,2 though deviations from this are found for overdoped cuprates 3 and organic SCs. 4 The recently discovered oxypnictide SCs ͑Ref. 5͒ containing FeAs layers show a wide range of T c , 6-10 and those studied so far have shown behavior broadly consistent with Uemura scaling, 11-19 as observed for hole-doped cuprates. In this Brief Report we test this relationship for LiFeAs, 20-22 a recently discovered variant of pnictide SC where Li replaces the lanthanide-oxide layer. In LiFeAs the closest Fe-Fe separation in the FeAs layers is significantly shorter than in previously studied pnictide SC compounds. This produces additional frustrating magnetic interactions which are expected to weaken the strength of the antiferromagnetic coupling through Fe-As bonds, which has been suggested to mediate the superconducting pairing. 23 We find that this produces a departure from the previously observed scaling behavior which can provide some insight into the nature of the pairing in this family of compounds.LiFeAs crystallizes in a tetragonal space group ͑P4 / nmm͒ with a = 0.378 nm and c = 0.635 nm and contains FeAs layers, based on edge-sharing tetrahedral FeAs 4 units, interspersed with layers containing Li ions. The tetrahedra are compressed in the basal plane relative to those in LaFeAsO and SrFeAs 2 . This implies that although the Fe-As bond distance 0.2414 nm in LiFeAs is similar to the other compounds, the Fe-Fe distance of 0.268 nm is considerably shorter. Superconductivity can be obtained at up to 18 K in this compound, though differences have been observed even between samples with similar cell volumes, probably connected with slight compositional variation, as described previously for compositions close to LiFeAs. 24 In contrast with the oxypnictides, no further doping is necessary to induce superconductivity, and from studies to date the spin-density wave ͑SDW͒ state has appeared to be notably absent.Transverse-field ͑TF͒ muon-spin rotation ͑SR͒ ͑TF-SR͒ is a method for accurately measuring the internal magnetic field distribution within the vortex lattice ͑VL͒ of a t...

We present a muon-spin relaxation investigation of the Ising chain magnet Ca 3 Co 2−x Mn x O 6 ͑x Ϸ 0.95͒. We find dynamic spin fluctuations persisting down to the lowest measured temperature of 1.6 K. The previously observed transition at around 18 K is interpreted as a subtle change in dynamics for a minority of the spins coupling to the muon that we interpret as spins locking into clusters. The dynamics of this spin fraction freeze below a temperature T SF Ϸ 8 K, while a majority of spins continue to fluctuate. An explanation of the lowtemperature behavior is suggested in terms of the predictions of the anisotropic next-nearest-neighbor Ising model.The magnetic chain multiferroic Ca 3 Co 2−x Mn x O 6 ͑x Ϸ 1͒ has been the subject of considerable recent investigation. [1][2][3][4] This material is based on the Ising spin chain magnet Ca 3 Co 2 O 6 , with ͑close to͒ half of the cobalt ions replaced with manganese. 5-7 The observation of up-up-down-down ͑↑↑ ↓↓͒ order in this system has led to the proposal that, at low temperatures, Ca 3 Co 2−x Mn x O 6 may be described by the anisotropic next-nearest-neighbor Ising ͑ANNNI͒ model. 1 This model 8-11 describes Ising spins on a three-dimensional lattice in which, along one direction, there is nearestneighbor ferromagnetic exchange ͑J FM ͒ and next-nearestneighbor antiferromagnetic ͑AFM͒ exchange ͑J AFM ͒. For ͉J AFM / J FM ͉ Ͼ 1 / 2 the ground-state magnetic order is of the ↑↑ ↓↓ type. As temperature is increased from T = 0 the magnetic behavior is determined by the existence of domain wall solitons, which separate regions with different commensurate AFM spin arrangements. 9,10 Although a continuum description of the ANNNI model predicts an infinity of high order commensurate AFM phases ͑known as the devil's staircase͒ a description in terms of a discrete Hamiltonian shows the possibility of metastable states of randomly pinned solitons. In magnetic systems, these so-called "chaotic states" are expected to lead to frozen-in disorder or spin-glasslike behavior. 8 Here we present an investigation of the lowtemperature static and dynamic magnetism in Ca 3 Co 2−x Mn x O 6 ͑x Ϸ 1͒ that we have observed at a local level using muon-spin relaxation ͑ + SR͒. We find that the low-temperature magnetic state of Ca 3 Co 2−x Mn x O 6 is reached through a complex freezing out of dynamic processes, and we conjecture that the existence of chaotic states provides an explanation for the disordered magnetism and persistent dynamics that we observe at low temperature.Ca 3 Co 2−x Mn x O 6 is formed from chains of magnetic ions arranged along the c axis in alternating oxygen cages of faceshared trigonal prisms and octahedra. Mn 4+ ions preferentially occupy the octahedral sites while the trigonal prisms are occupied by Co 2+ ions. The magnetic chains form a triangular lattice in the ab plane separated by Ca 2+ ions. While it is agreed that 3d 3 Mn 4+ is in the S =3/ 2 high-spin configuration, the spin state of 3d 7 Co 2+ has been questioned. Although fits to magnetic neutron diffraction dat...

We present the results of muon-spin relaxation (µ + SR) measurements on the hexagonal manganite HoMnO3. Features in the temperature-dependent relaxation rate λ correlate with the magnetic transitions at 76 K, 38 K and 34 K. The highest temperature transition, associated with the ordering of Mn 3+ moments has the largest effect on λ. The application of a static electric field of E = 10 4 Vm −1 below T = 50 K causes a small reduction in λ which is suggestive of coupling between ferroelectric and magnetic domain walls in the ordered state of the material.