Pseudo-Hermitian magnon dynamics

A defining quantity of a physical system is its energy which is represented by the Hamiltonian. In closed quantum mechanical or/and fully coherent wave-based systems the Hamiltonian is introduced as a Hermitian operator which ensures real energy spectrum and secures the decomposition of any state over a complete basis set that spans the space where states live. Pseudo-Hermitian, or PT symmetric, systems are a special class of non-Hermitian ones. They describe open systems but may still have real energy spectrum. The eigenmodes are however not orthogonal in general. This qualitative difference to Hermitian physics has a range of consequences for the physical behavior of the system in the steady state or when it is subjected to external perturbations. This overview reviews the recent progress in the field of pseudo-Hermitian physics as it unfolds when applied to low-energy excitations of magnetically ordered materials. The focus is mainly on long wavelength spin excitations (spin waves) with magnons being the energy quanta of these excitations. Various setups including ferromagnetic, antiferromagnetic, magnonic crystals, and hybrid structures with different types of coupling to the environments as well as spatio-temporally engineered systems will be discussed with a focus on the particular aspects that are brought about by the pseudo-Hermiticity such as mode amplification, non-reciprocal propagation, magnon cloaking, non-Hermitian skin effect, PT-symmetric assisted Floquet engineering, topological energy transfer, and field-induced enhanced sensitivity.