Recent progress in neutron spin-echo spectroscopy by means of longitudinal Modulation of IntEnsity with Zero Effort (MIEZE) is reviewed. Key technical characteristics are summarized which highlight that the parameter range accessible in momentum and energy, as well as its limitations, are extremely well understood and controlled. Typical experimental data comprising quasi-elastic and inelastic scattering are presented, featuring magneto-elastic coupling and crystal field excitations in Ho 2 Ti 2 O 7 , the skyrmion lattice to paramagnetic transition under applied magnetic field in MnSi, ferromagnetic criticality and spin waves in Fe. In addition bench marking studies of the molecular dynamics in H 2 O are reported. Taken together, the advantages of MIEZE spectroscopy in studies at small and intermediate momentum transfers comprise an exceptionally wide dynamic range of over seven orders of magnitude, the capability to perform straight forward studies on depolarizing samples or under depolarizing sample environments, as well as on incoherently scattering materials.

We report an experimental study of the emergence of non-trivial topological winding and longrange order across the paramagnetic to skyrmion lattice transition in the transition metal helimagnet MnSi. Combining measurements of the susceptibility with small angle neutron scattering, neutron resonance spin echo spectroscopy and all-electrical microwave spectroscopy, we find evidence of skyrmion textures in the paramagnetic state exceeding 10 3Å with lifetimes above several 10 −9 s. Our experimental findings establish that the paramagnetic to skyrmion lattice transition in MnSi is well-described by the Landau soft-mode mechanism of weak crystallization, originally proposed in the context of the liquid to crystal transition. As a key aspect of this theoretical model, the modulation-vectors of periodic small amplitude components of the magnetization form triangles that add to zero. In excellent agreement with our experimental findings, these triangles of the modulation-vectors entail the presence of the non-trivial topological winding of skyrmions already in the paramagnetic state of MnSi when approaching the skyrmion lattice transition. I. MOTIVATIONA pre-requisite for the definition of topological magnetic textures is the presence of a continuous magnetization field with a finite amplitude in space and time. An example par excellence of such textures are magnetic skyrmions, representing topologically nontrivial whirls of this magnetization field [1]. The notions of topological winding and topological stability of such skyrmions are only meaningful when the magnetization is sufficiently smooth on local scales. This condition may be readily satisfied in systems exhibiting long-range magnetic order for temperatures far below the transition temperature T c . In contrast, changes of the topological properties require that the magnetization is capable of vanishing on short length and time scales. The associated microscopic mechanisms underlying the transition of skyrmions into different types of conventional long-range magnetic order have been explored in a large number of theoretical and experimental studies [2][3][4][5][6][7][8].A major unresolved question concerns, in contrast, the formation of skyrmion lattice order when starting from a state that is essentially paramagnetic and dominated by an abundance of fluctuations such that the local magnetization, on a coarse-grained level, practically vanishes on average [9][10][11][12][13][14][15]. This alludes to the question whether topologically non-trivial characteristics exist already in * a paramagnetic state, and how they may be accounted for in the framework of the present-day classification of phase transitions [16][17][18]. It connects also with the relevance of non-trivial topological properties in the search for novel electronic properties of solids, e.g., at quantum phase transitions [19,20].Magnetic skyrmions are ideally suited to address this question. However, they are typically portrayed from either one of two seemingly contrary points of view. On the one hand...