Non-reciprocal spin excitations across the skyrmion-paramagnetic phase transition in MnSi

TL;DR

MnSi hosts a skyrmion lattice whose spin excitations are non-reciprocal due to the Dzyaloshinskii–Moriya interaction under field. The study uses inelastic neutron scattering with momentum transfers beyond the Brillouin-zone center and resolution-convolved linear spin-wave theory to track how these magnons evolve across the skyrmion-paramagnetic transition. Elastic scans locate the skyrmion region up to $T_c \approx 29\,\mathrm{K}$, while increasing temperature causes the skyrmion satellites to fade into a fluctuation-disordered paramagnetic state and the inelastic spectrum to reorganize into paramagnon-like excitations; notably, non-reciprocity persists into the paramagnetic regime under finite field. In zero-field, the helimagnetic-paramagnetic transition shows no non-reciprocity, highlighting the role of broken time-reversal symmetry in sustaining directional spin dynamics. The results suggest potential for high-temperature magnonic devices exploiting unidirectional spin transport and provide insight into the persistence of skyrmion-like correlations near phase boundaries.

Abstract

The magnetic excitations of the skyrmion lattice in MnSi comprise a multitude of individual modes, which are non-reciprocal and thereby propagate unidirectionally. We report inelastic neutron scattering experiments for temperatures near and above the skyrmion-paramagnetic phase transition in the chiral magnet MnSi tracking the evolution from the skyrmion lattice towards the high-temperature paramagnetic state. Within the resolution of the triple-axis measurements the excitations vary smoothly across the skyrmion-paramagnetic boundary, and, the quasi-elastic paramagnetic signal under applied field retains the non-reciprocal character seen in the skyrmion phase even far above the critical temperature. Using a resolution-convolution our results are consistent with linear spin-wave theory.

Figures (5)

• Figure 1: Experimental set-up showing the two principal momentum transfers, $Q_{(i)}$ and $Q_{(ii)}$. We measured in the $\left<hk0\right>$ scattering plane at total momentum transfers $Q = G + q$ and external field $B$ transverse to the $G = \left( 110 \right)$ Bragg peak.
• Figure 2: Calculations using our previously developed linear spin-wave model Garst2017Waizner2016phdWeber2022Skyrmi for the skyrmion order at $28.3\,\mathrm{K}$. The plots show the magnon modes propagating along $\left(110\right) + q \cdot \left[1\bar{1}0\right]$. Spin-flip (SF) and non-spin-flip (NSF) components of the scattering cross sections are depicted as red and black curves, respectively. The experiment itself was unpolarised, summing the NSF and SF channels. The thickness of the lines symbolises the spectral weights of the modes. The grey bars labelled (i) and (ii) mark the positions of the scans in Fig. \ref{['fig:IN12_skx_T']}. Panels (a) and (b) depict the dispersion for $B = -195\ \mathrm{mT}$ and $B = +195\ \mathrm{mT}$, respectively.
• Figure 3: (a) Longitudinal elastic scan around $\left( 110 \right)$. (b) Transversal elastic scan around $\left( 110 \right)$. (c) and (d): Inelastic scans showing the temperature-dependent evolution of the magnon modes starting from the skyrmion phase at $T=28.3\,\mathrm{K}$ and up to the nonmagnetic phase. The scans in panels (c) and (d) correspond to respective positions (i) and (ii) marked in Fig. \ref{['fig:theo_skx']}. The complicated magnon structure in the skyrmion phase is lost when increasing the temperature. The solid lines for the skyrmion phase at $T_{skx}=28.3\,\mathrm{K}$ are resolution-convolution simulations of the magnon model Garst2017Weber2022Skyrmi, all the other solid lines are Lorentzian fits. The label s1 marks the position where the first excitation of the skyrmion lattice is expected. (e) and (f): The non-reciprocity that is characteristic of the ordered magnetic phases is retained throughout the paramagnetic phase and only disappears in the clearly non-magnetic regime for $T>80\,\mathrm{K}$. It manifests itself via a time-reversal asymmetry that is evident when flipping the polarity of the magnetic field. Panel (e) shows the paramagnons for $T=30.4\,\mathrm{K}$. Here, the solid lines are Lorentzian fits. In panel (f) the asymmetric energy maxima are plotted against temperature.
• Figure 4: (a) Elastic scan of one of the helimagnetic satellites vs. temperature. The phase transition towards paramagnetism is observed at $T_c = 29\,\mathrm{K}$. The vertical dashed lines mark the scan temperatures. (b) Magnon modes in the multi-domain helical ($T=28.5\,\mathrm{K}$) and in the paramagnetic ($T=30.5\,\mathrm{K}$) phase at $Q = \left(1.06,\; 1.06,\; 0 \right)$ close to their phase boundary. The solid lines are Lorentzian fits.
• Figure 5: Unsubtracted data sets with panels (a) and (b) corresponding to Fig. \ref{['fig:IN12_skx_T']} (c) and (d), respectively. Here, we also show the high-temperature non-magnetic reference scan at $T = 79\,\mathrm{K}$ explicitly. The solid lines for the skyrmion phase at $T_{skx}=28.3\,\mathrm{K}$ are resolution-convolution simulations of the magnon model Garst2017Weber2022Skyrmi plus Gaussian profiles modeling the incoherent-elastic contribution, all the other solid lines are Lorentzian fits.