Nonreciprocal magnons and symmetry-breaking in the noncentrosymmetric antiferromagnet

Magnons, the spin-wave quanta, are disturbances that embody a wave propagating through a background medium formed by ordered magnetic moments. In an isotropic Heisenberg system, these disturbances vary in a continuous manner around an ordered spin structure, thus requiring infinitesimal energy as a wavevector approaches a magnetic zone centre. However, competing anisotropic interactions arising from broken symmetry can favour a distinct static and dynamic spin state causing a shift of the minimum point of the magnon dispersion to a nonreciprocal wavevector. Here we report the first direct evidence of these nonreciprocal magnons in an antiferromagnet. In the antiferromagnet we investigated, namely, noncentrosymmetric $\alpha$-Cu$_2$V$_2$O$_7$, they are caused by the incompatibility between anisotropic exchange and antisymmetric Dzyaloshinskii-Moriya interactions resulting in competing collinear and helical spin structures, respectively. The nonreciprocity introduces the difference in the phase velocity of the counter-rotating modes, causing the opposite spontaneous magnonic Faraday rotation of the left- and right-propagating spin-waves. The breaking of spatial inversion and time reversal symmetry is revealed as a magnetic-field-induced asymmetric energy shift, which provides a test for the detailed balance relation.