Perturbation spreading in a non-reciprocal classical isotropic magnet

We consider a classical Heisenberg spin magnet with precessional dynamics governed by an asymmetric exchange coupling along one spatial direction, i.e., different couplings for left and right neighbors [Das et al., EPL 60, 418-424 (2002)]. This breaks both energy and spin conservation while retaining O(3) symmetry. We quantify the effects of a localized perturbation by means of a "decorrelator", the classical equivalent of an out-of-time-ordered correlator, and show that it spreads ballistically and -- for a purely antisymmetric coupling -- symmetrically about the perturbed site. We present results on spreading speed, entropy production and related quantities.