Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

Abstract

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...

Megahertz dynamics in skyrmion systems probed with muon-spin relaxation

“…We find that the enhanced relaxation rate in Co 8 Zn 8 Mn 4 is found at those fields that stabilize the SkL in the B-T phase diagram, even at temperatures lower than those that stabilize the SkL state. It is notable both that similar behavior is seen in lightly substituted GaV 4 S 8−y Se y [31] and that individual skyrmion formation has been reported in MnSi above T c at those fields that stabilize the SkL [62]. These three systems, all crystallographically distinct (and, in the case of GaV 4 S 8−y Se y , hosting a different type of skyrmion), all therefore suggest that the important parameter for skyrmion creation in the Hamiltonian is the applied field, with, as is the current consensus [1,2], thermal fluctuations stabilizing the SkL phase.…”

Evolution of magnetocrystalline anisotropies in Mn1−xFexSi and Mn1−xKindervater1, Adams2, Bauer3 et al. 2020Phys. Rev. BSelf Cite214170View full textAdd to dashboardCite

“…As long as the cubic MCAs are weak, the concomitant enhancement of the fluctuations suppresses the helimagnetic order until a fluctuation-induced first-order transition takes place at T c , leaving behind a fluctuation-disordered (FD) regime below a crossover, T 2 . This so-called Brazovskii scenario is in excellent agreement with neutron scattering, specific heat and ultrasound attenuation [45][46][47][48][49][50][51][52][53][54].…”

Topological energy barrier for skyrmion lattice formation in MnSi

“…This so-called rocking curve is well fitted by a Lorentzian line shape, indicating that it is dominated by spatial or temporal fluctuations of the SkL rather than experimental resolution [23]. We believe it unlikely that these fluctuations are temporal like those associated with critical fluctuations observed above T c [31][32][33], but rather are a result of a finite skyrmion correlation length along the field direction due to crystal mosaicity as reported in other studies of MnSi [6].…”