Fig. 2

Spin wave spectroscopy on the nonreciprocal magnon transport in a chiral magnet. a Asymmetric spin wave dispersions for the collinear ferromagnetic state in a chiral magnet MnSi according to Eq. (3); a sharp spike around k~0 is due to the dipolar interaction. b The experimental setup to detect the nonreciprocity for the magnon transport between the coplanar microwave guides (ports 1 and 2). c Imaginary part spectra of the mutual inductance ΔL₁₂ (ΔL₂₁), representing the transport of the magnons from 1 to 2 (from 2 to 1) for magnetic fields applied parallel (+H) or antiparallel (–H) to the propagation direction; the result for the enantiomer D-body crystal. Another enantiomer L-body crystal shows the opposite behaviors for the exchange between ΔL₁₂ and ΔL₂₁. d Magnetic field dependence of spin wave nonreciprocity between ΔL₁₂ and ΔL₂₁ (i.e., +k and −k), measured for the D-body crystal of Cu₂OSeO₃ with the H // k // [001] configuration at 30 K. Here, ν_p indicates the magnetic resonance frequency giving the peak value of |ΔLnm|, and Δν_p the difference between ±k, respectively. |ΔL^p_nm | and v^p_g indicate the corresponding peak value and the group velocity at the frequency ν_p. The right panel shows the schematic illustration of collinear ferromagnetic state and helical spin state, respectively. The nonreciprocal spin wave propagation between ±k is discerned only in the former spin state. Reprinted figure with permission from ref²⁹. Copyright (2016) by the American Physical Society