Nonlinear Tellegen limit

Abstract

The Tellegen limit is the fundamental electromagnetic stability bound on magnetoelectric media. We show that nonlinear magnetoelectric coupling gives rise to a new Tellegen limit, which we term the \textit{nonlinear Tellegen limit}. Unlike the linear Tellegen limit, which is fixed by material parameters, the nonlinear Tellegen limit is field-tunable -- a static electric or magnetic field drives the system toward electromagnetic instability at a material-specific critical field determined by the symmetry-allowed nonlinear magnetoelectric couplings and electromagnetic response. The approach to this limit is accompanied by a field-tunable linear birefringence, whose maximum is bounded by the nonlinear Tellegen limit -- beyond which the medium becomes electromagnetically unstable. We demonstrate the nonlinear Tellegen limit and the field-space stability phase diagram in two magnetically ordered material systems -- a $d$-wave altermagnet and an M-type hexagonal ferrite -- showing that the symmetry of the magnetic point group governs both the structure of the nonlinear magnetoelectric tensor and the resulting electromagnetic instability.