Floquet Engineering the Exceptional Points in Parity-Time-Symmetric Magnonics

Magnons serve as a testing ground for fundamental aspects of Hermitian and non-Hermitian wave mechanics and are of high relevance for information technology. This study presents setups for realizing spatiotemporally driven parity-time- (PT) symmetric magnonics based on coupled magnetic waveguides and magnonic crystals. A charge current in a metal layer with strong spin-orbit coupling sandwiched between two insulating magnetic waveguides leads to gain or loss in the magnon amplitude depending on the directions of the magnetization and the charge currents. When gain in one waveguide is balanced by loss in the other waveguide, a PT-symmetric system hosting non-Hermitian degeneracies [or exceptional points (EPs)] is realized. For ac current, multiple EPs appear for a certain gain-loss strength and mark the boundaries between the preserved PT-symmetry and the broken PT-symmetry phases. The number of islands of broken PT-symmetry phases and their extensions is tunable by the frequency and the strength of the spacer current. At EP and beyond, the induced and amplified magnetization oscillations are strong and self-sustained. In particular, these magnetization auto-oscillations in a broken PT-symmetry phase occur at low current densities and do not require further adjustments such as tilt angle between electric polarization and equilibrium magnetization direction in spin-torque oscillators, pointing to a new design of these oscillators and their utilization in computing and sensorics. It is also shown how the periodic gain-loss mechanism allows for the generation of high-frequency spin waves with low-frequency currents. For spatially periodic gain and loss acting on a magnonic crystal, magnon modes approaching each other at the Brillouin-zone boundaries are highly susceptible to PT symmetry, allowing for a wave-vector-resolved experimental realization at very low currents.