Non-reciprocal mu-near-zero mode in PT-symmetric magnetic domains

We find that a new type of non-reciprocal modes exist at an interface between two \emph{parity-time} ($\mathcal{PT}$) symmetric magnetic domains (MDs) near the frequency of zero effective permeability. The new mode is non-propagating and purely magnetic when the two MDs are semi-infinite while it becomes propagating in the finite case. In particular, two pronounced nonreciprocal responses could be observed via the excitation of this mode: one-way optical tunneling for oblique incidence and unidirectional beam shift at normal incidence. When the two MDs system becomes finite in size, it is found that perfect-transmission mode could be achieved if $\mathcal{PT}$-symmetry is maintained. The unique properties of such an unusual mode are investigated by analytical modal calculation as well as numerical simulations. The results suggest a new approach to the design of compact optical isolator.