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Abstract
We report an experimental study of the emergence of non-trivial topological winding and long-range 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 $10^3$\AA 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.
Highlights
MOTIVATIONA prerequisite for the definition of topological magnetic textures is the presence of a continuous magnetization field with a finite amplitude in space and time
There is no evidence for hysteresis in any of the properties studied in the temperature and field range of interest here, we find it helpful to confirm spectroscopically that there are no static remnants of the skyrmion lattice causing the sixfold intensity modulation in the fluctuation disordered (FD) regime
For increasing temperature, the magnetic-field dependence of the microwave spectra is dominated by an excitation in the FD regime that is reminiscent of the counterclockwise mode of the skyrmion lattice phase
Summary
A prerequisite for the definition of topological magnetic textures is the presence of a continuous magnetization field with a finite amplitude in space and time. 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 case alludes to the question of whether topologically nontrivial 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]. The order emerges from a disordered state in terms of a weak crystallization of fluctuating skyrmion textures with topologically nontrivial character
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