The itinerant-electron compound MnSi features a skyrmion order  for temperatures in the range T ≈ 28 − 29 K and for magnetic fields B ≈ 0.16 − 0.21 T. Its non-centrosymmetric P213 space group has profound consequences for spin-wave dynamics in all ordered magnetic phases of MnSi. Namely, it introduces a Dzyaloshinskii-Moriya term which -- at reduced momentum transfers parallel to a helimagnetic propagation vector -- leads to magnon creation at energies that are different from the energies for magnon annihilation at the same momentum transfer q. The dynamical magnetic structure factor S(q, E, B), with q = Q - G and lattice vector G, is thus asymmetric ("non-reciprocal") with respect to changing the sign of either the reduced momentum transfer q, the energy transfer E, or the magnetic field B, but is symmetric upon interchanging the signs of two of these variables . Such an asymmetric behavior has been observed for the field-polarized [3, 4], the paramagnetic , the conical , and the skyrmion  phase of MnSi.
In a recent series of experiments at the instrument ThALES , we discovered an asymmetric separation of the non-reciprocal skyrmion dynamics into different polarization channels, which signify a flip from spin-down to spin-up (“SF-+”), from up to down (“SF+-”) or no spin-flip (“NSF”). Theoretically, we succeeded to describe our results utilizing a mean-field linear spin-wave model. Correcting the theory for instrumental resolution effects yields a virtually perfect quantitative agreement between experiment and theory.
Our new results are intriguing, as they not only confirm the previously determined  asymmetric nature of the skyrmion dynamical structure factor with respect to q, E, and B, but moreover extend the asymmetry to the flipping direction of the spin. We could furthermore show a close relationship between the dynamics in the skyrmion phase and all other ordered magnetic phases in MnSi.
Upcoming publication: T. Weber, D. Fobes, J. Waizner, L. Beddrich, P. Steffens, G. Tucker, R. Bewley, R. Georgii, A. Bauer, C. Pfleiderer, P. Böni, M. Janoschek, and M. Garst, in preparation. (The present work will be published as part of a general investigation into skyrmion dynamics.)
 S. Mühlbauer, et al., Science 323 (5916), 915–919 (2009).
 T. Weber, et al., AIP Advances 8, 101328 (2018).
 S. V. Grigoriev, et al., Phys. Rev. B, 92, 220415 (2015).
 T. J. Sato, et al., Phys. Rev. B, 94, 144420 (2016).
 B. Roessli, et al., Phys. Rev. Lett. 88, 237204 (2002).
 T. Weber, et al., Phys. Rev. B, 97, 224403 (2018).
 M. Böhm, et al., Neutron News 26 (3), 18–21 (2015).
Dr. Alexandros Koutsioumpas
Dr. Markos Skoulatos