Pseudo-Hermitian Magnon Dynamics

TL;DR

This work surveys pseudo-Hermitian and PT-symmetric physics with a focus on magnons in magnetically ordered materials, explaining how balanced gain and loss can yield real spectra and EPs in open magnonic systems. It integrates theory and experiments across ferromagnets, synthetic antiferromagnets, metamaterials, and hybrid platforms, showing how STT, SOT, RKKY, and DMI enable engineered non-Hermitian Hamiltonians and tunable EPs. Key contributions include demonstrations of EPs in planar ferromagnetic waveguides, magnonic crystals, and cavity/magnon-polariton systems, as well as Floquet-engineered EPs and higher-order EPs with topological energy transfer and nonreciprocal transport. The findings advance the design of electrically controllable, highly sensitive, and directionally selective magnonic devices with potential applications in spintronics, sensing, and non-Hermitian topological physics.

Abstract

A defining quantity of a physical system is its energy which is represented by the Hamiltonian. In closed quantum mechanical or/and 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 spanning the space where the 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 behaviour 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 wave length spin excitations (spin waves) with magnons being the energy quanta of these excitations. Various setups including ferromagnetic, antiferromagnetic, magnonic crystals, and hybride 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 amplifications, non-reciprocal propagation, magnon cloaking, non-Hermitian skin effect, PT-symmetric assisted Floquet engineering, topological energy transfer, and field-induced enhanced sensitivity.

Figures (26)

• Figure 1: Pseudo-Hermitian systems across different physical domains.
• Figure 2: Typical dispersion of dipolar surface spin waves (wave vector $\mathbf{k}$ perpendicular to magnetization $\mathbf{M}$), and backward volume spin waves (wave vector $\mathbf{k}$ parallel to magnetization $\mathbf{M}$) in a thin ferromagnetic stripe.
• Figure 3: In the synthetic antiferromagnet (c.f. model of Fig. \ref{['pseudomodels']}(c)), (a) real and (b) imaginary parts of the two magnon frequencies as functions of the wavevector $k _{\rm x}$.apl50029523
• Figure 4: For dipolarly coupled waveguides with antiparallel and parallel magnetization (c.f. model of Fig. \ref{['pseudomodels']}(d)), (a) real and (b) imaginary parts of the two magnon frequencies as functions of the wavevector $k _{\rm x}$.PhysRevApplied.18.024080
• Figure 5: Several schematics for model magnonic pseudo-Hermitian setups. (a) Two coupled magnets with symmetric gain and loss in magnon amplitudes.PhysRevB.91.094416 (b)Coupled FM bilayers with balanced gain (red layer) and loss (green layer) with equilibrium magnetizations along the $x$ direction.PhysRevLett.121.197201 (c) Two coupled FM layers with different damping.Haoliangsciadveaax9144 (d) Two RKKY coupled magnonic waveguides. The charge current in the spacer layer results in spin-orbit torque(SOT)-induced magnonic gain and loss in magnon density in the waveguides.Wang2020nc (e) Schematics for synthetic antiferromagnetic heterostructure with gain-loss, and loss-more loss.apl50029523 (f) Schematics of two dipolarly coupled magnonic waveguides WG1 and WG2 with SOT induced gain and loss.PhysRevApplied.18.024080