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We present the results of a study of the vortex lattice in the heavy fermion superconductor ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$, using small-angle neutron scattering (SANS). In this material at temperatures well below ${T}_{\mathrm{c}}\ensuremath{\sim}0.6$ K, the value of the upper critical field ${B}_{\mathrm{c}2}\ensuremath{\sim}2.2$ T is strongly limited by the Pauli paramagnetism of the heavy fermions. In this temperature region, our SANS data show an increase in the magnetization of the flux line cores with field, followed by a rapid fall near ${B}_{\mathrm{c}2}$. This behavior is the effect of Pauli paramagnetism and we present a theory-based model, which can be used to describe this effect in a range of materials. The pairing in ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$ appears to arise from the effect of magnetic fluctuations, but the evidence for a $d$-wave order parameter is rather weak. We find that the vortex lattice structure in ${\mathrm{CeCu}}_{2}{\mathrm{Si}}_{2}$ is close to regular hexagonal. There are no phase transitions to square or rhombic structures; such transitions are expected for $d$-wave superconductors and observed in ${\mathrm{CeCoIn}}_{5}$; however, the temperature dependence of the SANS intensity indicates that both large and small gap values are present, most likely due to multiband $s$-wave superconductivity, rather than a nodal gap structure.

We study the evolution of the low-temperature field-induced magnetic defects observed under an applied magnetic field in a series of frustrated amorphous ferromagnets (Fe$_{1-x}$Mn$_{x}$)$_{75}$P$_{16}$B$_{3}$Al$_{3}$ (a-FeMn). Combining small-angle neutron scattering and Monte Carlo simulations, we show that the morphology of these defects resemble that of quasi-bidimensional spin vortices. They are observed in the reentrant spin-glass (RSG) phase, up to the critical concentration $x_{\rm C} \approx 0.36$ which separates the RSG and "true" spin glass (SG) within the low temperature part of the magnetic phase diagram of a-FeMn. These vortices systematically decrease in size with increasing magnetic field or decreasing the average exchange interaction, and they finally disappear in the SG sample ($x = 0.41$), being replaced by field-induced correlations over finite length scales. We argue that the study of these nanoscopic defects could be used to probe the nature of the critical line between the RSG and SG phases., Comment: 23 pages, 14 figures, includes supplement

The Guinier law for magnetic SANS on bulk ferromagnets is introduced and applied to the analysis of nanocrystalline cobalt. The magnetic-field-dependent Guinier radius reflects the characteristic microstructural size and depends on the magnetic interactions., Small-angle scattering of X-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g. soft-matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, the Guinier law is introduced for the case of magnetic small-angle neutron scattering and its applicability is experimentally demonstrated for the example of nanocrystalline cobalt. It is well known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometre length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e. these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics) and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets.

In this paper we study consequences of the results of Kang et al. [Monoidal categorification of cluster algebras, J. Amer. Math. Soc. 31 (2018), 349–426] on a monoidal categorification of the unipotent quantum coordinate ring $A_{q}(\mathfrak{n}(w))$ together with the Laurent phenomenon of cluster algebras. We show that if a simple module $S$ in the category ${\mathcal{C}}_{w}$ strongly commutes with all the cluster variables in a cluster $[\mathscr{C}]$, then $[S]$ is a cluster monomial in $[\mathscr{C}]$. If $S$ strongly commutes with cluster variables except for exactly one cluster variable $[M_{k}]$, then $[S]$ is either a cluster monomial in $[\mathscr{C}]$ or a cluster monomial in $\unicode[STIX]{x1D707}_{k}([\mathscr{C}])$. We give a new proof of the fact that the upper global basis is a common triangular basis (in the sense of Qin [Triangular bases in quantum cluster algebras and monoidal categorification conjectures, Duke Math. 166 (2017), 2337–2442]) of the localization $\widetilde{A}_{q}(\mathfrak{n}(w))$ of $A_{q}(\mathfrak{n}(w))$ at the frozen variables. A characterization on the commutativity of a simple module $S$ with cluster variables in a cluster $[\mathscr{C}]$ is given in terms of the denominator vector of $[S]$ with respect to the cluster $[\mathscr{C}]$.

We report the magnetic field dependence of the THz absorption and non-reciprocal directional dichroism spectra of BiFeO$_3$ measured on the three principal crystal cuts for fields applied along the three principal directions of each cut. From the systematic study of the light polarization dependence we deduced the optical selection rules of the spin-wave excitations. Our THz data, combined with small-angle neutron scattering results showed that i) an in-plane magnetic field rotates the $\mathbf{q}$ vectors of the cycloids perpendicular to the magnetic field, and ii) the selection rules are mostly determined by the orientation of the $\mathbf{q}$ vector with respect to the electromagnetic fields. We observed a magnetic field history dependent change in the strength and the frequency of the spin-wave modes, which we attributed to the change of the orientation and the length of the cycloidal $\mathbf{q}$ vector, respectively. Finally, we compared our experimental data with the results of linear spin-wave theory that reproduces the magnetic field dependence of the spin-wave frequencies and most of the selection rules, from which we identified the spin-polarization coupling terms relevant for the optical magnetoelectric effect.

We report spatially resolved small-angle neutron-scattering measurements of the conical and skyrmion states of a bulk single crystal of nickel-substituted ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$, with a nominal concentration of Ni of 14%. We observe a significant spatial dependence of the structure of these magnetic states, characterized by increased disorder and misalignment with respect to the applied field as we approach the edge of the sample. Remarkably, the edge skyrmion state is also characterized by an extended stability towards lower temperatures. Surprisingly, in the same region of the sample, the metastable skyrmion state did not show simple decay. Instead, only a fraction of the scattered intensity appeared to decay, and the intensity therefore did not approach zero during our measurements. We suggest that the increased local disorder and the coexistence of conical and skyrmion states, induced by demagnetization effects at the edge of the sample, are responsible for the increased stability of this skyrmion state. We also infer that the unclear metastable behavior of the skyrmion lattice at the edge of the sample is due to the local geometry of the sample, which induces coexistence of different skyrmion states whose lifetimes are superimposed and difficult to separate in the data.

Magnetic skyrmions are vortex-like topological spin textures often observed in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Among them, Co-Zn-Mn alloys with a $\beta$-Mn-type chiral structure host skyrmions above room temperature. In this system, it has recently been found that skyrmions persist over a wide temperature and magnetic field region as a long-lived metastable state, and that the skyrmion lattice transforms from a triangular lattice to a square one. To obtain perspective on chiral magnetism in Co-Zn-Mn alloys and clarify how various properties related to the skyrmion vary with the composition, we performed systematic studies on Co$_{10}$Zn$_{10}$, Co$_9$Zn$_9$Mn$_2$, Co$_8$Zn$_8$Mn$_4$ and Co$_7$Zn$_7$Mn$_6$ in terms of magnetic susceptibility and small-angle neutron scattering measurements. The robust metastable skyrmions with extremely long lifetime are commonly observed in all the compounds. On the other hand, preferred orientation of a helimagnetic propagation vector and its temperature dependence dramatically change upon varying the Mn concentration. The robustness of the metastable skyrmions in these materials is attributed to topological nature of the skyrmions as affected by structural and magnetic disorder. Magnetocrystalline anisotropy as well as magnetic disorder due to the frustrated Mn spins play crucial roles in giving rise to the observed change in helical states and corresponding skyrmion lattice form., Comment: 70 pages, 19 figures

We investigate the macroscopic and microscopic physical properties of the solid solution of ${\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x}\mathrm{AlGe}$. The series tunes from CeAlGe with its multi-$\stackrel{P\vec}{k}$ structure and a major moment in the $ab$ plane, to PrAlGe with an easy $c$-axis ferromagnetic ground state coexisting with a low density of nanoscale textured magnetic domain walls. Using AC, DC susceptibility, resistivity, specific heat, muon spin relaxation/rotation, and neutron scattering we analyze the magnetic ground state of the series. We provide further evidence supporting our previous claim for spin-glass-like properties in pure PrAlGe. With the introduction of Pr to CeAlGe the finite magnetic field required to stabilize the topological multi-$\stackrel{P\vec}{k}$ magnetic phase for $x=0$ becomes suppressed. The crossover between the two end-member ground states occurs in the vicinity of $x=0.3$, a region where we further anticipate the field-induced topological magnetic phase for $xl0.3$ to become the zero field ground state.

We present the results of a study of the vortex lattice (VL) of the nickel chalcogenide superconductor ${\mathrm{TlNi}}_{2}{\mathrm{Se}}_{2}$, using small angle neutron scattering. This superconductor has the same crystal symmetry as the iron arsenide materials. Previous work points to it being a two-gap superconductor, with an unknown pairing mechanism. No structural transitions in the vortex lattice are seen in the phase diagram, arguing against $d$-wave gap symmetry. Empirical fits of the temperature dependence of the form factor and penetration depth rule out a simple $s$-wave model, supporting the presence of nodes in the gap function. The variation of the VL opening angle with field is consistent with earlier reports of multiple gaps.

The vertical sample-plane reflectometer D17 at the Institut Laue–Langevin in Grenoble, France, has undergone several major upgrades since its commissioning, which are summarized in this article. The three major improvements are (i) a new focusing guide, increasing the usable flux on the sample by a factor of 2.5; (ii) a new beam polarizer and new spin flippers, allowing for the use of polarized neutrons in time-of-flight mode; and (iii) a new detector with a particularly uniform response under homogeneous exposure, improved stability and state-of-the-art detector electronics. The combination of these factors has paved the road to new possibilities in fast kinetic measurements, magnetism and off-specular scattering. Examples and scientific references for the new capabilities are presented.

We report a magnetic state in GaV4Se8 which emerges exclusively in samples with mesoscale polar domains and not in polar mono-domain crystals. It is manifested by a sharp anomaly in the magnetic susceptibility and the magnetic torque, distinct from other anomalies observed also in polar mono-domain samples upon transitions between the cycloidal, the Néel-type skyrmion lattice and the ferromagnetic states. We ascribe this additional transition to the transformation of distinct magnetic textures, confined to polar domain walls (DW), to the ferromagnetic (FM) state. The emergence of these DW-confined magnetic states is likely driven by the mismatch of different spin spirals, hosted by the adjacent domains. A clear anomaly in the magneto-current indicates that the DW-confined magnetic states also have strong contributions to the magnetoelectric response. We expect polar DWs to commonly host such confined magnetic edge states and, thus, offer a fertile ground to explore novel forms of magnetism.

We observe a hysteretic reorientation of the magnetic vortex lattice in the noncentrosymmetric superconductor ${\mathrm{Ru}}_{7}{\mathrm{B}}_{3}$, with the change in orientation driven by altering the magnetic field below ${T}_{\mathrm{c}}$. Normally a vortex lattice chooses either a single or degenerate set of orientations with respect to a crystal lattice at any given field or temperature, a behavior well described by prevailing phenomenological and microscopic theories. Here, in the absence of any typical VL structural transition, we observe a continuous rotation of the vortex lattice which exhibits a pronounced hysteresis and is driven by a change in magnetic field. We propose that this rotation is related to the spontaneous magnetic fields present in the superconducting phase, which are evidenced by the observation of time-reversal symmetry breaking, and the physics of broken inversion symmetry. Finally, we develop a model from the Ginzburg-Landau approach which shows that the coupling of these to the vortex lattice orientation can result in the rotation we observe.

Magnetic skyrmions are topologically protected nanoscale spin textures with particle-like properties. In bulk cubic helimagnets, they appear under applied magnetic fields and condense spontaneously into a lattice in a narrow region of the phase diagram just below the magnetic ordering temperature, the so-called A-phase. Theory, however, predicts skyrmions to be locally stable in a wide range of magnetic fields and temperatures. Our neutron diffraction measurements reveal the formation of skyrmion states in large areas of the magnetic phase diagram, from the lowest temperatures up to the A-phase. We show that nascent and disappearing spiral states near critical lines catalyze topological charge changing processes, leading to the formation and destruction of skyrmionic states at low temperatures, which are thermodynamically stable or metastable depending on the orientation and strength of the magnetic field. Skyrmions are surprisingly resilient to high magnetic fields: the memory of skyrmion lattice states persists in the field polarized state, even when the skyrmion lattice signal has disappeared. These findings highlight the paramount role of magnetic anisotropies in stabilizing skyrmionic states and open up new routes for manipulating these quasi-particles towards energy-efficient spintronics applications.

The D33 small-angle neutron scattering (SANS) instrument at the Institut Laue–Langevin (ILL) is the most recent SANS instrument to be built at the ILL. In a project beginning in 2005 and lasting seven years, the concept has been developed, and the instrument designed, manufactured and installed. D33 was commissioned with neutrons during the second half of 2012, fully entering the ILL user programme in 2013. The scientific case required that D33 should provide a wide dynamic range of measured scattering vector magnitudeq, flexibility with regard to the instrument resolution, and the provision of polarized neutrons and3He spin analysis to facilitate and expand studies in magnetism. In monochromatic mode, a velocity selector and a flexible system of inter-collimation apertures define the neutron beam. A double-chopper system enables a time-of-flight (TOF) mode of operation, allowing an enhanced dynamicqrange (qmax/qmin) and a flexible wavelength resolution. Two large multitube detectors extend the dynamicqrange further, givingqmax/qmin≃ 25 in monochromatic mode and a very largeqmax/qmin> 1000 in TOF mode. The sample zone is large and flexible in configuration, accommodating complex and bulky sample environments, while the position of D33 is such as to allow high magnetic fields at the sample position. The instrument is of general purpose with a performance rivalling that of D22, and is well adapted for SANS studies in scientific disciplines as diverse as solution scattering in biology and soft matter and studies of physics, materials science and magnetism. This article provides a detailed technical description of D33 and its performance and characterization of the individual components, and serves as a technical reference for users of the instrument.

It was recently proposed that multiferroic GaV${}_{4}$S${}_{8}$ hosts a new N\'eel-type of magnetic skyrmion lattice in its bulk, though direct microscopic experimental evidence of this type of skyrmion state has been absent up to now. By using polarized small-angle neutron scattering, the authors show unambiguously that the spins twist cycloidally in all modulated phases of GaV${}_{4}$S${}_{8}$, consistent with that expected for N\'eel-type skyrmions. In a further contrast to any other skyrmion host material, all of the spiral and skyrmion phases in GaV${}_{4}$S${}_{8}$ are shown to be stable only at finite temperature due to a delicate interplay between thermal agitation and a strong magnetic anisotropy.

The calculation of neutron reflectivity from raw time-of-flight data including instrumental corrections and an improved resolution calculation is presented. The theoretical calculations are compared with experimental data measured on the vertical sample plane reflectometer D17 and the horizontal sample plane reflectometer FIGARO at the Institut Laue–Langevin (ILL), Grenoble, France. This article comprises the mathematical body of the time-of-flight reflectivity data-reduction software COSMOS which is used on D17 and FIGARO.

Reentrant spin glasses are frustrated disordered ferromagnets developing vortex-like textures under an applied magnetic field. Our study of a Ni$_{0.81}$Mn$_{0.19}$ single crystal by small angle neutron scattering clarifies their internal structure and shows that these textures are randomly distributed. Spin components transverse to the magnetic field rotate over length scales of 3-15 nm in the explored field range, decreasing as field increases according to a scaling law. Monte-Carlo simulations reveal that the internal structure of the vortices is strongly distorted and differs from that assumed for "frustrated" skyrmions, built upon a competition between symmetric exchange interactions. Isolated vortices have small non-integer topological charge. The vortices keep an anisotropic shape on a 3 dimensional lattice, recalling "croutons" in a "ferromagnetic soup". Their size and number can be tuned independently by the magnetic field and concentration x (or heat treatment), respectively. This opens an original route to understand and control the influence of quenched disorder in systems hosting non trivial spin textures., Comment: 23 pages, 15 figures, includes supplement

Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Recently $\beta$-Mn structure-type Co-Zn-Mn alloys were identified as a new class of chiral magnet to host such skyrmion crystal phases, while $\beta$-Mn itself is known as hosting an elemental geometrically frustrated spin liquid. Here we report the intermediate composition system Co$_7$Zn$_7$Mn$_6$ to be a unique host of two disconnected, thermal-equilibrium topological skyrmion phases; one is a conventional skyrmion crystal phase stabilized by thermal fluctuations and restricted to exist just below the magnetic transition temperature $T_\mathrm{c}$, and the other is a novel three-dimensionally disordered skyrmion phase that is stable well below $T_\mathrm{c}$. The stability of this new disordered skyrmion phase is due to a cooperative interplay between the chiral magnetism with Dzyaloshinskii-Moriya interaction and the frustrated magnetism inherent to $\beta$-Mn., Comment: 57 pages, 16 figures

The magnetic field induced rearrangement of the cycloidal spin structure in ferroelectric monodomain single crystals of the room-temperature multiferroic ${\mathrm{BiFeO}}_{3}$ is studied using small-angle neutron scattering. The cycloid propagation vectors are observed to rotate when magnetic fields applied perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value of $\ensuremath{\sim}5\text{ }\text{ }\mathrm{T}$. In light of these experimental results, a phenomenological model is proposed that captures the rearrangement of the cycloidal domains, and we revisit the microscopic origin of the magnetoelectric effect. A new coupling between the magnetic anisotropy and the polarization is proposed that explains the recently discovered magnetoelectric polarization perpendicular to the rhombohedral axis.

We present small-angle neutron scattering (SANS) measurements of the vortex lattice (VL) in single crystal MgB 2 ––a two-band superconductor. Bragg diffraction of neutrons visualizes the structure and orientation of the VL while the scattered intensity probes the super-carrier density. Superconductivity in the π-band is rapidly suppressed with increasing field with a corresponding decrease in scattered intensity and a re-orientation of the VL between 0.5 and 0.9 T. Both these observations are consistent with superconductivity in the π-band being weaker than in the σ-band ( Δ π Δ σ ), and a changing influence of different parts of the Fermi surface determining the VL orientation. SANS measurements of the VL for fields applied at an angle to the c -axis allow the penetration depth anisotropy, γ λ , to be estimated.

FIGARO (http://www.ill.eu/instruments-support/instruments-groups/instruments/figaro/) is the ILL's new horizontal time-of-flight neutron reflectometer dedicated to the study of free liquid surfaces, launched in April 2009 [1] (see FIGARO team in Figure 1). During 2009, FIGARO has seen a busy schedule of user experiments employing the full range of sample environments available, as well as several experiments employing some of the special features of the instrument, which include variable wavelength resolution and neutron flux, positive and negative incidence angles relative to horizontal and a 2D area detector. A range of sample environments exists on the instrument including a Langmuir trough and heated/cooled adsorption troughs for studying the molecules at the air-liquid interface, as well as a number of sample cells for studying the solid/liquid and liquid/liquid interfaces. Some of the exiting highlights from the first experiments using a range of instrument configurations are described in this report.

Recent experimental results indicate that superconductivity in Sr2RuO4 is described by the p-wave E_u representation of the D_{4h} point group. Results on the vortex lattice structures for this representation are presented. The theoretical results are compared with experiment., Comment: 4 pages, 3 figures, M2S-HTSC-VI proceedings

We have measured the diffracted neutron scattering intensities from the square magnetic flux lattice in the perovskite superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, which is thought to exhibit $p$-wave pairing with a two-component order parameter. The relative intensities of different flux lattice Bragg reflections over a wide range of field and temperature have been shown to be inconsistent with a single component Ginzburg-Landau theory but qualitatively agree with a two-component $p$-wave Ginzburg-Landau theory.

Small-angle neutron scattering (SANS) is an extremely powerful probe of the vortex state in type II superconductors. The technique may be further enhanced by the use of polarised neutrons and the application of the neutron spin-echo method. We discuss some recent applications of these techniques to the study of both conventional and unconventional superconducting materials, and describe the unique information which SANS can provide on the vortex state. ( 2000 Elsevier Science B.V. All rights reserved.

There are several ways of investigating#ux lines with polarised neutrons. We shall describe our recent work on IN15 at ILL, investigating spatially varying "elds perpendicular to the #uxoid axes, which are present with tilted "elds in anisotropic superconductors. These "eld components may be detected by polarisation analysis of neutrons di!racted by the #ux line lattice, and allow a detailed investigation of #ux structure in such materials as YBCO and NbSe 2 . A further application of polarised neutrons is the use of neutron spin-echo techniques to measure the speed of moving #ux lines. We have recently demonstrated this in an Nb}Ta alloy on instruments IN11 and IN15, by measuring the energy change of neutrons di!racted by #ux lines, which are moving under the in#uence of a transport current. We shall also comment on others’ work on the search for interference terms between #ux lattice and nuclear di!raction signals, and the use of neutron depolarisation for investigation of #ux distributions in superconductors. ( 1999 Elsevier Science B.V. All rights reserved.

A small angle neutron scattering study of the flux-line lattice in a large untwinned single crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is presented. In fields parallel to the $c$ axis, diffraction spots are observed corresponding to four orientations of a hexagonal lattice, distorted by the $a\ensuremath{-}b$ anisotropy. A value for the anisotropy, the penetration depth ratio, of ${\ensuremath{\lambda}}_{a}/{\ensuremath{\lambda}}_{b}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.18\left(2\right)$ was obtained. The high quality of the data is such that second-order diffraction is observed, indicating a well ordered FLL. With the field at 33\ifmmode^\circ\else\textdegree\fi{} to $c$, a field dependent reorientation of the lattice is observed around 3 T.

Using the technique of small angle neutron scattering (SANS) the vortex lattice of ultra-pure niobium has been investigated on an extremely fine temperature scale. As the temperature is increased towards T c 2 the longitudinal correlations of the vortices along their length improve, up to the resolution limited value of 100 μ m .

The phenomenon of superconductivity continues to be of considerable scientific and practical interest. Underlying this phenomenon is the formation of electron pairs, which in conventional superconductors do not rotate about their centre of mass (‘s -wave’ pairing; refs 1, 2). This contrasts with the situation in high-temperature superconductors, where the electrons in a pair are believed to have two units of relative angular momentum (‘d -wave’ pairing; ref. 3 and references therein). Here we report small-angle neutron-scattering measurements of magnetic flux lines in the perovskite superconductor Sr2RuO4 (ref. 4), which is a candidate for another unconventional paired electron state—‘p -wave’ pairing, which has one unit of angular momentum5,6,7. We find that the magnetic flux lines form a square lattice over a wide range of fields and temperatures, which is the result predicted by a recent theory8,9 of p -wave superconductivity in Sr2RuO4. This theory also indicates that only a fraction of the electrons are strongly paired and that the orientation of the square flux lattice relative to the crystal lattice will determine which parts of the three-sheet Fermi surface of this material are responsible for superconductivity. Our results suggest that superconductivity resides mainly on the ‘γ’ sheet9.

A neutron small-angle scattering study of the flux-line lattice in heavily twinned YBa2Cu3O72x is presented. It is found that the diffraction signal disappears at temperatures well below Tc , associated with a melting of the flux lattice. The shape of the melting line is consistent with both a Lindemann criterion and the scaling expected for a vortex-glass transition with the superconducting parameters from the three-dimensional XY model. The influence of twin planes on the structure of the vortex lattice and its melting is studied by applying the field at different angles to the c axis. The results are compared with recent specific heat measurements on similar crystals. @S0163-1829~98!03022-7#

High resolution, neutron small angle scattering studies have been performed to investigate the low field $(Bl250\mathrm{mT})$ region of the phase diagram for the vortex lattice in the superconducting state of ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$. The data present clear evidence for a vortex lattice reorientation transition from a state with the diagonal of the rhombic unit cell along a $[110]$ direction to a $[100]$ direction. Above this transition the lattice distorts under the influence of the applied field until the apex angle becomes constant at some higher field. For $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$ a square lattice configuration is formed. These experiments confirm qualitatively many of the predictions of a general model based on nonlocal corrections to the London model as applied to this and similar materials.

A detailed study has been made of a transition in the flux lattice of the superconductor ${\mathrm{Bi}}_{2.15}$${\mathrm{Sr}}_{1.85}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ using the technique of muon-spin rotation. The results are in excellent agreement with a recent theoretical analysis on the low-field phase diagram of highly anisotropic superconductors. In particular, the important role of electromagnetic interactions between vortex segments is demonstrated. The form of the phase boundary suggests that the transition may be identified with a simultaneous melting and decoupling of the vortices in adjacent layers.

A systematic muon-spin-rotation ({mu}{sup +}SR) study is presented of the temperature dependence of the London penetration depth in sintered powder samples of the YBa{sub 2}Cu{sub 3}O{sub {ital x}} system and related compounds. The in-plane penetration depth {lambda}{sub {ital a}{ital b}} is estimated from the {mu}{sup +}SR depolarization rate of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}}, YBa{sub 2}Cu{sub 4}O{sub 8}, and a series of samples of the YBa{sub 2}Cu{sub 3}O{sub {ital x}} family, respectively. It is found that not only the low-temperature value {lambda}{sub {ital a}{ital b}}(0), but also the temperature behavior {lambda}{sub {ital a}{ital b}}({ital T}) is specific to each compound. The form of {lambda}{sub {ital a}{ital b}}({ital T}) can be well characterized by a simple power law. In particular, the YBa{sub 2}Cu{sub 3}O{sub {ital x}} family shows a systematic variation of the form of {lambda}{sub {ital a}{ital b}}({ital T}) with the oxygen content {ital x} which points to a varying coupling strength, whereas {lambda}{sub {ital a}{ital b}}(0) as a function of {ital x} suggests a positive charge transfer into the CuO{sub 2} planes with increasing oxygen doping. Furthermore, our data is consistent with an empirical ansatz which has been proposed in the framework of a Bose-gas picture of high-temperature superconductivity.more » As a consequence, the pressure and the isotope coefficients can be extracted from the {mu}{sup +}SR depolarization rate and compared to direct measurements of these quantities, showing good agreement. Moreover, in the Bose-gas picture the variation of {lambda}{sub {ital a}{ital b}}({ital T}) in the YBa{sub 2}Cu{sub 3}O{sub {ital x}} family may be interpreted as a crossover from a dense (high-{ital T}{sub {ital c}}) to a dilute (low-{ital T}{sub {ital c}}) system of weakly interacting local pairs.« less

The reflectometer D17 has been operational for a year and has already proved to be an excellent tool for investigating surfaces and interfaces in the realms of physics, biology and chemistry. The instrument has two modes of operation, time-of-flight and monochromatic, the latter incorporating the polarised-neutron option. Both modes are flexible in the wave-vector-transfer (q) resolution. The loosest resolution required to resolve the sample structure can be chosen (and hence the highest flux), enabling the lowest reflectivities and hence the widest q-range to be measured.

The vortex lattice (VL) in the high-κ superconductor YBa2Cu3O7, at 2 K and with the magnetic field parallel to the crystal c axis, undergoes a sequence of transitions between different structures as a function of applied magnetic field. However, from structural studies alone, it is not possible to determine precisely the system anisotropy that governs the transitions between different structures. To address this question, here we report new small-angle neutron scattering measurements of both the VL structure at higher temperatures and the field and temperature dependence of the VL form factor. Our measurements demonstrate how the influence of anisotropy on the VL, which in theory can be parameterized as nonlocal corrections, becomes progressively important with increasing magnetic field, and suppressed by increasing the temperature toward Tc. The data indicate that nonlocality due to different anisotropies plays an important role in determining the VL properties.

By neutron scattering, we have observed a well-ordered magnetic vortex lattice (VL) in KFe${}_{2}$As${}_{2}$ single crystals. With the field along the $c$ axis, a nearly isotropic hexagonal VL is formed, with no symmetry transitions up to high fields, indicating a small anisotropy of the superconducting state around this axis. This rules out line nodes parallel to the $c$ axis, and thus $d$-wave or anisotropic $s$-wave pairing. However, the strong temperature dependence of the signal at $T\ensuremath{\ll}{T}_{c}$ shows that extremely small gap values exist; these may arise from nodal lines perpendicular to the $c$ axis.

The microscopic magnetic field distribution in the mixed state of single-crystal ${\mathrm{Bi}}_{2.15}$${\mathrm{Sr}}_{1.85}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ has been measured using the muon spin rotation technique. A study of the line shapes as a function of temperature and magnetic field gives evidence for an abrupt change of flux-lattice structure which is attributed to the presence of a flux-lattice melting line in the B-T phase diagram. In addition, the data suggest the existence of a crossover field above which the flux structure is more 2D in nature.

We report on small angle neutron scattering observations of the flux line lattice (FLL) in a single crystal of YBa[sub 2]Cu[sub 3]O[sub 7]. To probe the mass anisotropy ratio, [ital m][sub 3]/[ital m][sub 1], measurements were made as a function of angle, [Theta], between the 8 kOe applied field and the crystallographic (001) axis for 0[degree][le][Theta][le]80[degree]. With the rotation about an [ital a]/[ital b] (or [ital y]) axis, two symmetry-related distorted hexagonal FLL domains formed. Contrary to theoretical prediction, the lattices formed are consistent with a rotation of the short basis vector, [bold a][sub 1], from the [ital x] axis by 15[degree], after the effects of anisotropy are removed. The mass ratio is 20[plus minus]2, which is slightly lower than published values. The temperature dependence of the intensity is not conventional.

The state of the vortex lattice extremely close to the superconducting to normal transition in an applied magnetic field is investigated in high-purity niobium. We observe that thermal fluctuations of the order parameter broaden the superconducting to normal transition into a crossover but no sign of a first-order vortex lattice melting transition is detected in measurements of the heat capacity or the small-angle neutron scattering (SANS) intensity. Direct observation of the vortices via SANS always finds a well-ordered vortex lattice. The fluctuation broadening is considered in terms of the lowest Landau-level theory of critical fluctuations and scaling is found to occur over a large ${H}_{c2}(T)$ range.

The non-centrosymmetric heavy fermion compound CePt3Si orders antiferromag-netically at TN = 2.2K, followed by a superconducting transition, where Ts = 0.45 K for high quality samples and Ts = 0.75K for lower quality samples. We have used neutron Larmor diffraction to measure the temperature dependence and distribution of the lattice constants in a single crystal of CePt3Si with Ts = 0.75K. In our study we observe an unusually wide range of lattice parameters for the a-axis and c-axis with Δa/a ≈ Δc/c ≈ 10−3. Small angle neutron scattering suggests an abundance of defects along the lattice planes. When taking into account the pressure dependence of Ts our study attributes the increased value of Ts in low quality samples to an effective negative pressure.

High-purity niobium exhibits a surprisingly rich assortment of vortex lattice (VL) structures for fields applied parallel to a fourfold symmetry axis, with all observed VL phases made up of degenerate domains that spontaneously break some crystal symmetry. Yet a single regular hexagonal VL domain is observed at all temperatures and fields parallel to a threefold symmetry axis. We report a detailed investigation of the transition between these lush and barren VL landscapes, discovering new VL structures and phase transitions at high fields. We show that the number and relative population of VL domains is intrinsically tied to the underlying crystal symmetry. We discuss how subtle anisotropies of the crystal may generate the remarkable VLs observed.

We describe the use of reverse Monte Carlo refinement to extract structural information from angle-resolved data of a Bragg peak. Starting with small-angle neutron scattering data, the positional order of an ensemble of flux lines in superconducting Nb is revealed. We discuss the uncovered correlation functions in the light of topical theories, in particular, the "Bragg glass" paradigm.

The flux line lattice in CeRu 2 has been studied by small-angle neutron scattering. The scattering potential is found to be well described in terms of a linear superposition of single flux-line profiles, while an increase in the mosaic spread of the diffraction peaks at low fields is consistent with the theory of weak collective pinning. The pinning parameter deduced from the data gives the correct onset field of a peak in the critical current observed at higher field.

Small-angle neutron scattering has been applied to study the vortex lattice in the intercalated graphite superconductor CaC6 (T-c=11.3 K). Scattering from the vortex lattice is in the form of a ring, most likely reflecting the absence of in-plane orientational order of the pyrolitic graphene planes. The temperature and field dependence of the scattered intensity allows the in-plane zero temperature value of the coherence length [xi=350(25) angstrom] and the London penetration depth [lambda=500(30) angstrom] to be estimated. Measurements with the applied field at 70 degrees to the c axis directly reveal the penetration depth anisotropy, gamma(lambda)=5.1(4), which, unlike MgB2, is equal to the anisotropy of the coherence length deduced from magnetization measurements. The orientation of the vortex lattice is fixed relative to the rotation axis of the crystal as predicted by anisotropic London theory.

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-${T}_{c}$ or borocarbide superconductors, where VL structures orient along particular directions of high crystal symmetry. The causes of this behavior are discussed.

Using small-angle neutron scattering, we have measured the misalignment between an applied field of $4\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ and the flux-line lattice in $\mathrm{Mg}{\mathrm{B}}_{2}$, as the field is rotated away from the $c$ axis by an angle $\ensuremath{\theta}$. The measurements, performed at $4.9\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, showed the vortices canting towards the $c$ axis for all field orientations. Using a two-band/two-gap model to calculate the magnetization, we are able to fit our results yielding a penetration depth anisotropy, ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}=1.1\ifmmode\pm\else\textpm\fi{}0.1$.