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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 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 nanosized topological spin textures stabilized by a delicate balance of magnetic energy terms. The chemical substitution of the underlying crystal structure of skyrmion-hosting materials offers a route to manipulate these energy contributions but also introduces additional effects such as disorder and pinning. While the effects of doping and disorder have been well studied in B20 metallic materials such as ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{Si}$ and ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Si}$, the consequences of chemical substitution in the magnetoelectric insulator ${\mathrm{Cu}}_{2}\mathrm{O}\mathrm{Se}{\mathrm{O}}_{3}$ have not been fully explored. In this work we utilize a combination of AC magnetometry and small-angle neutron scattering to investigate the magnetic phase transition dynamics in pristine and Zn-substituted ${\mathrm{Cu}}_{2}\mathrm{O}\mathrm{Se}{\mathrm{O}}_{3}$. The results demonstrate that the first-order helical-conical phase transition exhibits two thermally separated behavioral regimes: at high temperatures, the helical and conical domains transform by large-scale, continuous rotations, while at low temperatures, the two phases coexist. Remarkably, the effects of pinning in the substituted sample are less prevalent at low temperatures compared to high temperatures, despite the reduction of available thermal activation energy. We attribute this behavior to the large, temperature-dependent, cubic anisotropy unique to ${\mathrm{Cu}}_{2}\mathrm{O}\mathrm{Se}{\mathrm{O}}_{3}$, which becomes strong enough to overcome the pinning energy at low temperatures. Consideration and further exploration of these effects will be crucial when engineering skyrmion materials towards future applications.

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.

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.

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.

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#

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 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 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.

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.

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, ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}=1.1\ifmmode\pm\else\textpm\fi{}0.1$.

In ${\mathrm{V}}_{3}\mathrm{Si}$, a first-order structural phase transition from hexagonal to square flux-line lattice occurs at approximately 1 T with $H\ensuremath{\Vert}$ to the $a$ axis. In this paper, we demonstrate the reentrant structural transition in the flux-line lattice, which reverts to hexagonal symmetry as the magnetic field approached ${H}_{c2}(T)$. This behavior is described very well by a nonlocal London theory with thermal fluctuations. The phase diagram of the flux lattice topology is mapped out for this geometry.

We report on detailed small-angle neutron scattering measurements with polarization analysis from the flux-line lattice in the anisotropic superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ When the field was applied at an angle to the principal axes we have observed spin-flip neutron diffraction consistent with local transverse field components. From a detailed study of the angle dependence of the magnitude of the spin-flip neutron-scattered intensity we have found that the transverse-field components are larger than predicted by an anisotropic London model for reasonable mass anisotropy values. The transverse-field components are consistent with a reduced c-axis coherence length at low temperature.

Systematic measurements of the magnetic moment per Ni atom in Cu/Ni/Cu/Si(001) structures have been made using polarized neutron reflection (PNR) for Ni thicknesses in the range 30Å, , perpendicular anisotropy strength, and surface in-plane Ni lattice constant, respectively, during epitaxial growth. RHEED measurements show that the in-plane lattice constant falls by 1.7% in the Ni thickness range 30 Å, , and total moment per atom versus Ni thickness as found for the total moment by PNR. Polar MOKE measurements confirmed the transition from a perpendicular easy axis towards an in-plane magnetic easy axis as has already been extensively studied in the literature. Comparison of the PNR results with RHEED measurements reveal a striking correlation between the increase of in-plane strain and reduction in magnetic moment per atom with decreasing Ni thickness. While a direct strain-induced variation of the moment based on bulk phase calculations cannot account for the magnitude of the moment variations we observe, we show that the results cannot be attributed to sample contamination, interdiffusion, or a reduction of the Curie temperature with decreasing Ni thickness. Furthermore, the presence of a magnetically dead layer in the samples is not consistent with the PNR results. The strong moment variation partially explains the large thickness range for which perpendicular anisotropy is observed in this system.