Magnetic Fluctuations, Precursor Phenomena, and Phase Transition in MnSi under a Magnetic Field.

The reference chiral helimagnet MnSi is the first system where Skyrmion lattice correlations have been reported. At a zero magnetic field the transition at T_{C} to the helimagnetic state is of first order. Above T_{C}, in a region dominated by precursor phenomena, neutron scattering shows the buildup of strong chiral fluctuating correlations over the surface of a sphere with radius 2π/ℓ, where ℓ is the pitch of the helix. It has been suggested that these fluctuating correlations drive the helical transition to first order following a scenario proposed by Brazovskii for liquid crystals. We present a comprehensive neutron scattering study under magnetic fields, which provides evidence that this is not the case. The sharp first order transition persists for magnetic fields up to 0.4 T whereas the fluctuating correlations weaken and start to concentrate along the field direction already above 0.2 T. Our results thus disconnect the first order nature of the transition from the precursor fluctuating correlations. They also show no indication for a tricritical point, where the first order transition crosses over to second order with increasing magnetic field. In this light, the nature of the first order helical transition and the precursor phenomena above T_{C}, both of general relevance to chiral magnetism, remain an open question.

Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8.

Following the early prediction of the skyrmion lattice (SkL)--a periodic array of spin vortices--it has been observed recently in various magnetic crystals mostly with chiral structure. Although non-chiral but polar crystals with Cnv symmetry were identified as ideal SkL hosts in pioneering theoretical studies, this archetype of SkL has remained experimentally unexplored. Here, we report the discovery of a SkL in the polar magnetic semiconductor GaV4S8 with rhombohedral (C3v) symmetry and easy axis anisotropy. The SkL exists over an unusually broad temperature range compared with other bulk crystals and the orientation of the vortices is not controlled by the external magnetic field, but instead confined to the magnetic easy axis. Supporting theory attributes these unique features to a new Néel-type of SkL describable as a superposition of spin cycloids in contrast to the Bloch-type SkL in chiral magnets described in terms of spin helices.

Anisotropy of the superconducting state in Sr2RuO4.

Despite intense studies the exact nature of the order parameter in superconducting Sr2RuO4 remains unresolved. We have used small-angle neutron scattering to study the vortex lattice in Sr2RuO4 with the field applied close to the basal plane, taking advantage of the transverse magnetization. We measured the intrinsic superconducting anisotropy between the c axis and the Ru-O basal plane (~60), which greatly exceeds the upper critical field anisotropy (~20). Our result imposes significant constraints on possible models of triplet pairing in Sr2RuO4 and raises questions concerning the direction of the zero spin projection axis.

Persistence of metastable vortex lattice domains in MgB2 in the presence of vortex motion.

Recently, extensive vortex lattice metastability was reported in MgB2 in connection with a second-order rotational phase transition. However, the mechanism responsible for these well-ordered metastable vortex lattice phases is not well understood. Using small-angle neutron scattering, we studied the vortex lattice in MgB2 as it was driven from a metastable to the ground state through a series of small changes in the applied magnetic field. Our results show that metastable vortex lattice domains persist in the presence of substantial vortex motion and directly demonstrate that the metastability is not due to vortex pinning. Instead, we propose that it is due to the jamming of counterrotated vortex lattice domains which prevents a rotation to the ground state orientation.

Chiral properties of structure and magnetism in Mn(1-x)Fe(x)Ge compounds: when the left and the right are fighting, who wins?

Magnetic susceptibility measurements have shown that the compounds Mn(1-x)Fe(x)Ge are magnetically ordered through the whole range of concentrations x = [0.0,1.0]. Small-angle neutron scattering reveals the helical nature of the spin structure with a wave vector, which changes from its maximum (|k| = 2.3 nm(-1)) for pure MnGe, through its minimum (|k| → 0) at x(c) ≈ 0.75, to the value of |k| = 0.09 nm(-1) for pure FeGe. The macroscopic magnetic measurements confirm the ferromagnetic nature of the compound with x = x(c). The observed transformation of the helix structure to the ferromagnet at x = x(c) is explained by different signs of chirality for the compounds with x > x(c) and x

Graphical reduction and analysis small-angle neutron scattering program: GRASP.

GRASP is a scientific software application designed for the graphical inspection, reduction and analysis of multidetector data produced by the small-angle neutron scattering (SANS) instruments at the Institut Laue-Langevin and other neutron sources around the world. The first developments of GRASP began more than 20 years ago and were written in MATLAB, allowing rapid development of scientific code, with much of the data handling, matrix manipulation, mathematical tools, user interface and graphical tools integrated at a high level in the underlying MATLAB platform. By their very nature, multidimensional data are often best appreciated in graphical form. GRASP deals with many of the diverse requirements for data reduction and analysis of SANS data using a general set of tools and reduction algorithms suited to 2D multidetector data. A further fundamental architectural inclusion is a third dimension of data manipulation, thereby easily allowing parametric analysis and cross referencing of series data such as composition, kinetic measurements, temperature, magnetic field, angle or time of flight, often considered as a single 'measurement'. This article serves as a reference document for users of the software, and outlines the architecture and strategy of the program. An overview of some of the features, capabilities, peripheral user modules and neutron scattering tools is presented.

First-order reorientation transition of the flux-line lattice in CaAlSi.

The flux-line lattice in CaAlSi has been studied by small-angle neutron scattering. A well-defined hexagonal flux-line lattice is seen just above H(c1) in an applied field of only 54 Oe. A 30° reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be first-order and could be explained by nonlocal effects. The magnetic field dependence of the form factor is well-described by a single penetration depth of λ=1496(1) Å and a single coherence length of ξ=307(1) Å at 2 K. At 1.5 K, the penetration depth anisotropy is γ(λ)=2.7(1), with the field applied perpendicular to the c axis, and agrees with the coherence length anisotropy determined from critical field measurements.

Observation of well-ordered metastable vortex lattice phases in superconducting MgB2 using small-angle neutron scattering.

The vortex lattice (VL) symmetry and orientation in clean type-II superconductors depends sensitively on the host material anisotropy, vortex density and temperature, frequently leading to rich phase diagrams. Typically, a well-ordered VL is taken to imply a ground-state configuration for the vortex-vortex interaction. Using neutron scattering we studied the VL in MgB(2) for a number of field-temperature histories, discovering an unprecedented degree of metastability in connection with a known, second-order rotation transition. This allows, for the first time, structural studies of a well-ordered, nonequilibrium VL. While the mechanism responsible for the longevity of the metastable states is not resolved, we speculate it is due to a jamming of VL domains, preventing a rotation to the ground-state orientation.

Small-angle neutron scattering study of mesoscale magnetic disordering and skyrmion phase suppression in the frustrated chiral magnet Co6.75Zn6.75Mn6.5.

Co-Zn-Mn chiral cubic magnets display versatile magnetic skyrmion phases, including equilibrium phases stable far above and far below room temperature, and the facile creation of robust far-from-equilibrium skyrmion states. In this system, compositional disorder and magnetic frustration are key ingredients that have profound effects on the chiral magnetism. Reported here are studies of the magnetism in Co6.75Zn6.75Mn6.5 by magnetometry, small-angle neutron scattering (SANS), magnetic diffuse neutron scattering and Lorentz transmission electron microscopy (LTEM). While features in magnetometry and LTEM often give standard indications for skyrmion formation, they are not readily observed from the measurements on this system. Instead, skyrmion lattice correlations are only revealed by SANS, and they are found to form an orientationally disordered structure in a minority fraction of the sample. The majority fraction of the sample always displays orientationally disordered helical spin correlations, which undergo further disordering along the radial direction on cooling below the critical temperature (T c ≃ 102 K). The near-complete suppression of the skyrmion phase, and the process of disordering on cooling, are attributed to competing magnetic interactions that dominate over the ferromagnetic interaction expected to favour chiral magnetism in this system. These competing interactions start to develop above T c and become further enhanced towards low temperatures. The present observations of co-existing and disordered magnetic correlations over multiple length scales are not unique to Co6.75Zn6.75Mn6.5 but are seemingly common to the family of Co-Zn-Mn compounds with finite Mn, and their accurate description presents a challenge for theoretical modelling. In addition, this study highlights a need for neutron instrumentation capable of the comprehensive measurement of magnetic correlations over expanded ranges of momentum transfer in such multiple-length-scale magnets.

Neutron spin-flip scattering of nanocrystalline cobalt.

We report results of longitudinal (one-dimensional) neutron polarization analysis on polycrystalline bulk Co with an average crystallite size of D = 10 nm. The spin-flip small-angle neutron scattering (SANS) data are analyzed in the approach-to-saturation regime within the framework of micromagnetic theory. In particular, we provide a closed-form expression for the spin-flip SANS cross section [Formula: see text]. From the data analysis, we find a room-temperature value of A = (2.6 ± 0.1) × 10( - 11) J m( - 1) for the exchange-stiffness constant, which agrees well with earlier data.

Weak superconducting pairing and a single isotropic energy gap in stoichiometric LiFeAs.

We report superconducting (SC) properties of stoichiometric LiFeAs (T(c)=17 K) studied by small-angle neutron scattering (SANS) and angle-resolved photoemission (ARPES). Although the vortex lattice exhibits no long-range order, well-defined SANS rocking curves indicate better ordering than in chemically doped 122 compounds. The London penetration depth lambda(ab)(0)=210+/-20 nm, determined from the magnetic field dependence of the form factor, is compared to that calculated from the ARPES band structure with no adjustable parameters. The temperature dependence of lambda(ab) is best described by a single isotropic SC gap Delta(0)=3.0+/-0.2 meV, which agrees with the ARPES value of Delta(0)(ARPES)=3.1+/-0.3 meV and corresponds to the ratio 2Delta/k(B)T(c)=4.1+/-0.3, approaching the weak-coupling limit predicted by the BCS theory. This classifies LiFeAs as a weakly coupled single-gap superconductor.

Distinct vortex-glass phases in Yb3Rh4Sn13 at high and low magnetic fields.

The vortex lattice (VL) in the mixed state of the stannide superconductor Yb3Rh4Sn13 has been studied using small-angle neutron scattering (SANS). The field dependences of the normalized longitudinal and transverse correlation lengths of the VL, ξ(L)/a0 and ξ(T)/a0, reveal two distinct anomalies that are associated with vortex-glass phases below µ0Hl ≈ 700 G and above µ0Hh ∼ 1.7 T (a0 is the intervortex distance). At high fields, around 1.7 T, the longitudinal correlation decreases abruptly with increasing fields indicating a weakening (but not a complete destruction) of the VL due to a phase transition into a glassy phase, below µ0Hc2 (1.8 K) ≈2.5 T. ξ(L)/a0 and ξ(T)/a0, gradually decrease for decreasing fields of strengths less than 1 T and tend towards zero. The shear elastic modulus c66 and the tilting elastic modulus c44 vanish at a critical field µ0Hl ≈ 700 G, providing evidence for a disorder-induced transition into a vortex-glass. A 'ring' of scattered intensity is observed for fields lower than 700 G, i.e. µ0Hc1 = 135 G < µ0H < 700 G. This low-field phenomenon is of different nature than the one observed at high fields, where ξ(L)/a0 but not ξ(T)/a0, decreases abruptly to an intermediate value.

Magnetic field dependent small-angle neutron scattering on a Co nanorod array: evidence for intraparticle spin misalignment.

The structural and magnetic properties of a cobalt nanorod array have been studied by means of magnetic field dependent small-angle neutron scattering (SANS). Measurement of the unpolarized SANS cross section dΣ/dΩ of the saturated sample in the two scattering geometries where the applied magnetic field H is either perpendicular or parallel to the wavevector ki of the incoming neutron beam allows one to separate nuclear from magnetic SANS, without employing the usual sector-averaging procedure. The analysis of the SANS data in the saturated state provides structural parameters (rod radius and centre-to-centre distance) that are in good agreement with results from electron microscopy. Between saturation and the coercive field, a strong field dependence of dΣ/dΩ is observed (in both geometries), which cannot be explained using the conventional expression of the magnetic SANS cross section of magnetic nanoparticles in a homogeneous nonmagnetic matrix. The origin of the strong field dependence of dΣ/dΩ is believed to be related to intradomain spin misalignment, due to magnetocrystalline and magnetoelastic anisotropies and magnetostatic stray fields.

Probing fractal magnetic domains on multiple length scales in Nd2Fe14B.

Using small-angle neutron scattering, we demonstrate that the complex magnetic domain patterns at the surface of Nd2Fe14B, revealed by quantitative Kerr and Faraday microscopy, propagate into the bulk and exhibit structural features with dimensions down to 6 nm, the domain wall thickness. The observed fractal nature of the domain structures provides an explanation for the anomalous increase in the bulk magnetization of Nd2Fe14B below the spin-reorientation transition. These measurements open up a rich playground for studies of fractal structures in highly anisotropic magnetic systems.

Fermi surface and order parameter driven vortex lattice structure transitions in twin-free YBa2Cu3O7.

We report on small-angle neutron scattering studies of the intrinsic vortex lattice (VL) structure in detwinned YBa2Cu3O7 at 2 K, and in fields up to 10.8 T. Because of the suppressed pinning to twin-domain boundaries, a new distorted hexagonal VL structure phase is stabilized at intermediate fields. It is separated from a low-field hexagonal phase of different orientation and distortion by a first-order transition at 2.0(2) T that is probably driven by Fermi surface effects. We argue that another first-order transition at 6.7(2) T, into a rhombic structure with a distortion of opposite sign, marks a crossover from a regime where Fermi surface anisotropy is dominant, to one where the VL structure and distortion is controlled by the order-parameter anisotropy.

Kinetic neutron diffraction and SANS studies of phase formation in bioactive machinable glass ceramics.

Bioactive fluormica-fluorapatite glass-ceramic materials offer a very encouraging solution to the problem of efficient restoration and reconstruction of hard tissues. To produce material with the desired crystalline phases, a five-stage heat treatment must be performed. This thermal processing has a large impact on the microstructure and ultimately the final mechanical properties of the materials. We have examined the thermal processing of one of our most promising machinable biomaterials, using time-resolved small angle neutron scattering and neutron diffraction to study the nucleation and growth of crystallites. The processing route had already been optimized by studying the properties of quenched samples using x-ray diffraction, mechanical measurements and differential thermal analysis. However these results show that the heat treatment can be further optimized in terms of crystal nucleation, and we show that these techniques are the only methods by which a truly optimized thermal processing route may be obtained.

Pauli paramagnetic effects on vortices in superconducting TmNi2B2C.

The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.

Field dependent coherence length in the superclean, high-kappa superconductor CeCoIn5.

Using small-angle neutron scattering, we have studied the flux-line lattice (FLL) in the superclean, high-kappa superconductor CeCoIn5. The FLL undergoes a first-order symmetry and reorientation transition at approximately 0.55 T at 50 mK. In addition, the FLL form factor in this material is found to be independent of the applied magnetic field, in striking contrast to the exponential decrease usually observed in superconductors. This result is consistent with a strongly field-dependent coherence length, proportional to the vortex separation.

Spontaneous symmetry-breaking vortex lattice transitions in pure niobium.

We report an extensive investigation of magnetic vortex lattice (VL) structures in single crystals of pure niobium with the magnetic field applied parallel to a fourfold symmetry axis, so as to induce frustration between the cubic crystal symmetry and hexagonal VL coordination expected in an isotropic situation. We observe new VL structures and phase transitions; all the VL phases observed (including those with an exactly square unit cell) spontaneously break some crystal symmetry. One phase even has the lowest possible symmetry of a two-dimensional Bravais lattice. This is quite unlike the situation in high-Tc or borocarbide superconductors, where VL structures orient along particular directions of high crystal symmetry. The causes of this behavior are discussed.

Intrinsic behavior of flux lines in pure niobium near the upper critical field.

We report small-angle neutron-scattering (SANS) measurements of flux line properties near H(c2) in an ultrapure sample of niobium with weak pinning of flux in the bulk. These confirm in detail the Abrikosov picture of the flux line lattice to within 20 mK of the upper critical field line. However, it has recently been claimed [X. S. Ling et al., Phys. Rev. Lett. 86, 712 (2001)], on the basis of SANS observations of a disordering of flux lines in niobium, that the flux lattice melts at temperatures clearly separated from the upper critical field line. This discrepancy may possibly arise from differences in sample purity and pinning.