We discuss the interaction between a polarized neutron beam and chiral magnetism with emphasis on magnetic chirality. Without any loss of generality, we adopt a simple approach to formalism that pinpoints to the salient features of chiral magnetic scattering and can be easily used to plan and interpret experiments. We also discuss the unique information that can be derived on the topology of chiral magnetic correlations and consider the example of the skyrmion hosting system MnSi. This is one of the most simple realisations of chiral magnetism and at the same time a system, where the interaction between magnetic chirality and a polarized neutron beam is most clearly noticeable. In a next step we address the interplay between chiral magnetism and paramagnetic Neutron Spin Echo spectroscopy and then focus on the ferromagnetic Spin Echo method, which has not been discussed in the literature so far. Finally, we discuss the implications of the vector nature of the (dipole) interaction between a neutron beam polarization and a magnetic sample for the quantum mechanical description of Larmor precession-based methods.@en

The bulk helimagnet Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets exhibiting a tilted spiral and skyrmion phase at low temperatures when the magnetic field is applied along the easy (001) crystallographic direction. Here we present a systematic study of the stability and ordering of these low-temperature magnetic states. We focus our attention on the temperature and field dependencies of the tilted spiral state that we observe persisting up to above T=35 K, i.e., up to higher temperatures than reported so far. We discuss these results in the frame of the phenomenological theory introduced by Dzyaloshinskii in an attempt to reach a quantitative description of the experimental findings. We find that the anisotropy constants, which are the drivers behind the observed behavior, exhibit a pronounced temperature dependence. This explains the differences in the behavior observed at high temperatures (above T=18 K), where the cubic anisotropy is weak, and at low temperatures (below T=18 K), where a strong cubic anisotropy induces an abrupt appearance of the tilted spirals out of the conical state and enhances the stability of skyrmions.

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We present a systematic study of tilted spiral states obtained theoretically within the classical Dzyaloshinskii model for magnetic states in cubic non-centrosymmetric ferromagnets. Such tilted spirals are shown to stabilize under the competing effect of cubic and exchange anisotropies inherent to cubic helimagnets. By focusing on the internal structure of these spirals and their field-driven behaviour for different aspect ratios of the anisotropy coefficients, we are able to capture the main features of the experimental findings in a bulk cubic helimagnet Cu₂OSeO₃ and to make a step further towards a complete quantitative model of this chiral magnet. In particular, we show that for strong anisotropy values (which experimentally correspond to low temperatures near zero) there exist an angular separation between the conical and tilted spirals, i.e., the conical spiral flips into a tilted state and immediately composes some finite angle with respect to the field direction. As the anisotropy ratio decreases, such a transition between two spiral states becomes almost continuous and corresponds to higher temperatures at the experiments. In addition, we investigate the field-driven reorientation of metastable skyrmion lattices induced by the competing anisotropies, which may be responsible for some peculiarities at the experimental phase diagrams of Cu₂OSeO₃.

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A novel spin echo small-angle neutron scattering (SESANS) concept based on a rotationally symmetric magnetic field geometry is introduced. The proposed method is similar to the conventional linear SESANS technique but uses
longitudinal precession fields and field gradients in a radial direction, as typically found in neutron spin echo (NSE) spectrometers. Radial SESANS could thus be implemented as an add-on to NSE setups. The neutron trajectory through the
instrument is encoded with the help of radial gradients generated by radial shifters, which are coils placed in the beam area similar to Fresnel coils. The present work introduces the setup of the instrument and explores its performance and the relationship between the encoded momentum transfer and the precession angle. The results indicate that radial SESANS is only sensitive to scattering along the radial direction and thus measures the projected correlation function along this direction as a function of the spin echo length, defined similarly to linear SESANS. For an evaluation of the performance of the setup, the case of scattering from solid spheres is considered and the results calculated for the radial and linear SESANS cases are compared. Also discussed is the implementation of the radial magnetic field geometry in spin echo modulated small-angle neutron scattering.@en

We present a comprehensive investigation of the magnetic properties of stage-1 graphite intercalated FeCl3 using a combination of DC and AC magnetic susceptibility, thermoremanent magnetization, and field-dependent magnetization measurements. This van der Waals system, with a centrosymmetric honeycomb lattice, combines frustration and disorder, due to intercalation, and may be hosting topologically nontrivial magnetic phases. Our study identifies two magnetic phase transitions at Tf1≈4.2 K and at Tf2≈2.7 K. We find that the paramagnetic state, for T>Tf1, is dominated by short-range ferromagnetic correlations. These build up well above Tf1 and lead to a significant change in magnetic entropy, which reaches ΔSMPk=-5.52 J kg-1K-1 at 7 T. Between Tf1 and Tf2, we observe slow spin dynamics characteristic of a cluster glasslike state, whereas for T<Tf2, our results indicate the onset of a low-temperature long-range ordered state. The analysis of the experimental results leads to a complex phase diagram, which may serve as a reference for future investigations searching for topological nontrivial phases in this system.

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Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets with a tilted spiral and a low-temperature skyrmion phase arising for magnetic fields applied along the easy crystallographic (100) axes. Although the stabilization mechanism of these phases can be accounted for by cubic magnetic anisotropy, the skyrmion nucleation process is still an open question, since the stability region of the skyrmion phase displays strongly hysteretic behavior with different phase boundaries for increasing and decreasing magnetic fields. Here, we address this important point using micromagnetic simulations and come to the conclusion that skyrmion nucleation is underpinned by the reorientation of spiral domains occurring near the critical magnetic fields of the phase diagrams: HC1, the critical field of the transition between the helical and conical/tiled spiral phase, and HC2, the critical field between the conical/tiled spiral and the homogenous phase. By studying a wide variety of cases we show that domain walls may have a 3D structure. Moreover, they can carry a finite topological charge stemming from half-skyrmions (merons) also permitting along-the-field and perpendicular-to-the-field orientation. Thus, domain walls may be envisioned as nucleation source of skyrmions that can form thermodynamically stable and metastable lattices as well as skyrmion networks with misaligned skyrmion tubes. The results of numerical simulations are discussed in view of recent experimental data on chiral magnets, in particular, for the bulk cubic helimagnet Cu2OSeO3.

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We present a comprehensive investigation of the evolution of helimagnetic correlations in Mn1−xFexSi with increasing doping. By combining polarized neutron scattering and high resolution neutron spin echo spectroscopy we investigate three samples with x = 0.09, 0.11, and 0.14, i.e., with compositions on both sides of the concentration x∗∼0.11 where the helimagnetic Bragg peaks disappear and between x∗ and the quantum critical concentration xC∼0.17, where TC vanishes. We find that the abrupt disappearance of the long range helical periodicity at x∗ does not affect the precursor fluctuating correlations. These build up with decreasing temperature in a similar way as for the parent compound MnSi. Also the dynamics bears strong similarities to MnSi. The analysis of our results indicates that frustration, possibly due to achiral Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, increases with increasing Fe doping. We argue that this effect explains both the expansion of the precursor phase with increasing x and the abrupt disappearance of long range helimagnetic periodicity at x∗.@en

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-xMn_x)₇₅P₁₆B₃Al₃ (“a-Fe_1-xMn_x”). 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 so-called “reentrant” spin-glass (RSG) phase, up to the critical concentration x_C≈ 0.36 which separates the RSG and “true” spin glass (SG) within the low temperature part of the magnetic phase diagram of a-Fe_1−xMn_x. These textures 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 critical line between the RSG and SG phases.

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Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. Deep physical relations and common physical features of a large variety of very different solitonic states in these systems arise from the mathematical similarity of phenomenological equations.
During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for the experimental investigation of topological solitons and the understanding of their nonsingular field configurations. This is directly related to the discovery of particle-like chiral skyrmions, which are also considered as promising
ingredients for technological applications. Here we introduce a paradigm of facile skyrmionic networks with mutually orthogonal orientations of constituent isolated skyrmions. On the one hand, such networks are envisioned as a novel concept of spintronic devices based, e.g., on gapless skyrmion motion along each other, and are presumably responsible for precursor phenomena near the ordering temperatures of bulk cubic helimagnets. In particular, we demonstrate an interconversion between mutually orthogonal skyrmions: horizontal skyrmions may swirl into an intermediate spring-like state and subsequently squeeze into vertical skyrmions with both polarities. On the other hand, skyrmion tubes are considered as building blocks for particle-like states with more involved internal structure. A family of target-skyrmions, which includes a so far overlooked type with a multiple topological charge, is formed owing to the tendency to minimize the interaction energy between vertical
and horizontal skyrmions. The conical phase serves as a suitable background for considered skyrmion evolution.
It substantializes the attracting skyrmion-skyrmion interaction in the skyrmionic networks, shapes their internal
structure, and guides the nucleation processes. Alternatively, intricate textural changes of isolated skyrmions
result not only in the structural deformations of a host conical state, but may lead to the formation of an exotic
skyrmion order with pairs of merons being the core of the game. Generically, the fundamental insights provided
by this work emphasize a three-dimensional character of skyrmion metamorphoses and can also be extended to
three-dimensional solitons, such as hopfions@en

This chapter is mainly devoted to the distinctive properties of spiral and skyrmion states accounted by the cubic anisotropy in bulk cubic helimagnets such as MnSi and Cu2OSeO3. We start by systematizing the main features of the universal phase diagrams at the critical fields Hc1 and Hc2. We first discuss the influence of cubic anisotropy on the reversible, or irreversible, alignment of oblique spiral states into the conical phase at Hc1. We then address the phase transition between the conical and field-polarized state at Hc2, which may be of both first order and second order depending on the orientation of the applied magnetic field with respect to easy anisotropy axes. We show that the effect of cubic anisotropy is more subtle than assumed so far, as it may induce new elliptically distorted spiral states and phase transitions between them. Finally, we show how this distortion of the spiral states by cubic anisotropy opens up the way to skyrmion stabilization.@en

In-situ Neutron Diffraction and Small-Angle Neutron Scattering (SANS) are employed for the first time simultaneously in order to reveal the interaction between the austenite to ferrite phase transformation and the precipitation kinetics during isothermal annealing at 650 and at 700 °C in three steels with different vanadium (V) and carbon (C) concentrations. Austenite-to-ferrite phase transformation is observed in all three steels at both temperatures. The phase transformation is completed during a 10 h annealing treatment in all cases. The phase transformation is faster at 650 than at 700 °C for all alloys. Additions of vanadium and carbon to the steel composition cause a retardation of the phase transformation. The effect of each element is explained through its contribution to the Gibbs free energy dissipation. The austenite-to-ferrite phase transformation is found to initiate the vanadium carbide precipitation. Larger and fewer precipitates are detected at 700 than at 650 °C in all three steels, and a larger number density of precipitates is detected in the steel with higher concentrations of vanadium and carbon. After 10 h of annealing, the precipitated phase does not reach the equilibrium fraction as calculated by ThermoCalc. The external magnetic field applied during the experiments, necessary for the SANS measurements, causes a delay in the onset and time evolution of the austenite-to-ferrite phase transformation and consequently on the precipitation kinetics.

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In-situ Small-Angle Neutron Scattering (SANS) is used to determine the time evolution of the chemical composition of precipitates at 650 °C and 700 °C in three micro-alloyed steels with different vanadium (V) and carbon (C) concentrations. Precipitates with a distribution of substoichiometric carbon-to-metal ratios are measured in all steels. The precipitates are initially metastable with a high iron (Fe) content, which is gradually being substituted by vanadium during isothermal annealing. Eventually a plateau in the composition of the precipitate phase is reached. Faster changes in the precipitate chemical composition are observed at the higher temperature in all steels because of the faster vanadium diffusion at 700 °C. At both temperatures, the addition of more vanadium and more carbon to the steel has an accelerating effect on the evolution of the precipitate composition as a result of a higher driving force for precipitation. Addition of vanadium to the nominal composition of the steel leads to more vanadium rich precipitates, with less iron and a smaller carbon-to-metal ratio. Atom Probe Tomography (APT) shows the presence of precipitates with a distribution of carbon-to-metal ratios, ranging from 0.75 to 1, after 10 h of annealing at 650 °C or 700 °C in all steels. These experimental results are coupled to ThermoCalc equilibrium calculations and literature findings to support the Small-Angle Neutron Scattering results.

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Neutron Spin Echo methods (NSE) use Larmor labelling to measure the precession phase of the neutron beam polarization around well-defined magnetic fields. Scattering by a sample can affect the resulting precession phase providing information on the sample's structure and dynamics with high accuracy and resolution. A major limitation for the performance of Neutron Spin Echo instruments is the homogeneity of the precession magnetic fields. Here we investigate the influence of the new 'pancake' moderator, which is being built at the European Spallation Source, on the design of a Neutron Spin Echo spectrometer. The calculations show clear gains when the height to width ratios of the rectangular beam cross-sections mimic those of the ESS 'pancake' moderator beams. In such a case the homogeneity of the magnetic field integrals could improve by at least 30%. However, the calculations show that will not be possible to preserve a high resolution and at the same time reduce the length of the instrument. Consequently, NSE spectrometers will perform better at the ESS but they will not be substantially compacter than at other neutron sources e.g. ILL or FRM2.

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SESANS data analysis has been implemented in the SasView software package, allowing SESANS experiments to be analyzed using a numerical Hankel transformation of isotropic small-angle scattering (SAS) models. The error of the numerical approximation is three orders of magnitude below typical experimental errors. All advanced data fitting features of SasView (multi-model fitting, batch fitting, and simultaneous/constrained fitting) are now also available for SESANS and this is demonstrated by examples of fitting SAS models to SESANS measurements.

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We discuss distinctive features of spiral states in bulk chiral magnets such as MnSi and Cu2OSeO3 that stem from the effect of the cubic magnetocrystalline anisotropy. First of all, at both the helical-to-conical and theconical-to-ferromagnetic transitions, taking place at Hc1 and Hc2, respectively, the cubic anisotropy leads to reversible or irreversible jumplike reorientations of the spiral wave vectors. The subtle interplay between the easy and hard anisotropy axes gives rise to a phase transition between elliptically distorted conical states almost without any detectable change in the period. We show that the competition between on-site cubic and exchange anisotropy terms can also lead to oblique spiral states. Our work gives clear directions for further experimental studies to reveal theoretically predicted spiral states in cubic helimagnets beyond the aforementioned well-
established states and thus it can help to understand the magnetic phase diagram of these archetypal skyrmion hosts. In addition, we show that properties of isolated skyrmions such as interskyrmion attraction, orientation, and/or nucleation are also rooted in the properties of host spiral states, in which skyrmions are stabilized@en

Interphase precipitation occurring during solid-state phase transformations in micro-alloyed steels is generally studied through transmission electron microscopy, atom probe tomography, and ex situ measurements of Small-Angle Neutron Scattering (SANS). The advantage of SANS over the other two characterization techniques is that SANS allows for the quantitative determination of size distribution, volume fraction, and number density of a statistically significant number of precipitates within the resulting matrix at room temperature. However, the performance of ex situ SANS measurements alone does not provide information regarding the probable correlation between interphase precipitation and phase transformations. This limitation makes it necessary to perform in situ and simultaneous studies on precipitation and phase transformations in order to gain an in-depth understanding of the nucleation and growth of precipitates in relation to the evolution of austenite decomposition at high temperatures. A furnace is, thus, designed and developed for such in situ studies in which SANS measurements can be simultaneously performed with neutron diffraction measurements during the application of high-temperature thermal treatments. The furnace is capable of carrying out thermal treatments involving fast heating and cooling as well as high operation temperatures (up to 1200 °C) for a long period of time with accurate temperature control in a protective atmosphere and in a magnetic field of up to 1.5 T. The characteristics of this furnace give the possibility of developing new research studies for better insight of the relationship between phase transformations and precipitation kinetics in steels and also in other types of materials containing nano-scale microstructural features.

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The archetype cubic chiral magnet MnSi is home to some of the most fascinating states in condensed matter, such as skyrmions and a non-Fermi-liquid behavior in conjunction with a topological Hall effect under hydrostatic pressure. Using small angle neutron scattering, we study the evolution of the helimagnetic, conical, and skyrmionic correlations with increasing hydrostatic pressure. We show that the helical propagation vector smoothly reorients from (111) to (100) at intermediate pressures. At higher pressures, above the critical pressure, the long-range helimagnetic order disappears at zero magnetic field. Nevertheless, skyrmion lattices and conical spirals form under magnetic fields, in a part of the phase diagram where a topological Hall effect and a non-Fermi-liquid behavior have been reported. These unexpected results shed light on the puzzling behavior of MnSi at high pressures and the mechanisms that destabilize the helimagnetic long-range order at the critical pressure.

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Recent experimental findings in the bulk cubic helimagnet and Mott insulator Cu2OSeO3 highlight the paramount role of cubic anisotropy in stabilizing novel chiral and skyrmion phases. It was indeed found that if a magnetic field is applied along the easy 001 crystallographic direction, competing cubic and
exchange anisotropies tilt the wave vector of the conical spiral away from the magnetic field [Qian et al., Sci. Adv. 4, eaat7323 (2018)]. Furthermore, in this configuration skyrmions have been observed in a broad range of temperatures and magnetic fields [Chacon et al., Nat. Phys. 14, 936 (2018)]. Starting from these
experimental observations and on the basis of a phenomenological Dzyaloshinskii theory, we investigate additional implications of the cubic anisotropy for this specified field direction. By including cubic anisotropy we show that the phase transition between the conical and field-polarized or homogeneous states becomes first order. Furthermore, we show that this transition is accompanied by the formation of conical droplets—domains of the conical phase in the homogeneous state. We investigate the internal structure of these droplets, which at their boundaries encompass alternating regions of positive and negative energy densities with respect to
the homogeneous state. We thus deduce that these droplets may be zipped and unzipped in phase during the first-order phase transition that occurs by either increasing or decreasing the magnetic field. On the other hand, we show that in the conical phase skyrmions may form clusters due to their attractive mutual interaction. However, in
the homogeneous state, the skyrmion-skyrmion interaction becomes repulsive, and the skyrmion clusters expand and disperse isolated skyrmions. This mutual skyrmion repulsion prevents the stabilization of skyrmion clusters even if the energy of isolated skyrmions is lower than that of the homogeneous state. Yet this skyrmion dispersal
may be prevented if skyrmions are surrounded by the circular spiral state and form skyrmion bags. Such a scenario could explain the existence of skyrmions in the field-polarized state reported experimentally.@en

The precipitation kinetics of vanadium carbides and its interaction with the austenite-to-ferrite phase transformation is studied in two micro-alloyed steels that differ in vanadium and carbon concentrations by a factor of two, but have the same vanadium-to-carbon atomic ratio of 1:1. Dilatometry is used for heat-treating the specimens and studying the phase transformation kinetics during annealing at isothermal holding temperatures of 900, 750 and 650 °C for up to 10 h. Small-Angle Neutron Scattering (SANS) and Atom Probe Tomography (APT) measurements are performed to study the vanadium carbide precipitation kinetics. Vanadium carbide precipitation is not observed after annealing for 10 h at 900 and 750 °C, which is contrary to predictions from thermodynamic equilibrium calculations. Vanadium carbide precipitation is only observed during or after the austenite-to-ferrite phase transformation at 650 °C. The precipitate volume fraction and mean radius continuously increase as holding time increases, while the precipitate number density starts to decrease after 20 min, which corresponds to the time at which the austenite-to-ferrite phase transformation is finished. This indicates that nucleation and growth are dominant during the first 20 min, while later precipitate growth with soft impingement (overlapping diffusion fields) and coarsening take place. APT shows gradual changes in the precipitate chemical composition during annealing at 650 °C, which finally reaches a 1:1 atomic ratio of vanadium-to-carbon in the core of the precipitates after 10 h.@en