Enhanced Sensitivity at Magnetic High-Order Exceptional Points and Topological Energy Transfer in Magnonic Planar Waveguides

Abstract

Controlling the low-energy excitations in magnetically active materials is the key to numerous phenomena in magnonics and spintronics. This study demonstrates a generic scheme for highly efficient control of magnonic signals in a stack of magnetic slabs separated by current-carrying metallic nanoscale spacer layers. We demonstrate analytically and confirm full numerically that the proposed structure has a magnonic spectrum that is highly susceptible to external perturbations and is governed by a parity-time ($\mathcal{P}\mathcal{T}$) symmetric Hamiltonian. The enhanced sensitivity can be tuned by the dc charge currents, the number of stacking layers or/and by the intrinsic properties of the stacking layers. Physically, the currents in the spacer layers cause spin-orbit torques acting on the adjacent magnetic layers. Effectively, these torques damp or antidamp magnonic excitations. Depending on the spacer-charge current density and the number of stacking layers, a point can be reached where damping and antidamping are balanced. Beyond this exceptional point (EP) the magnonic system enters a $\mathcal{P}\mathcal{T}$-symmetry-broken phase. Near EP we show analytically and numerically that the system exhibits a nonlinear response even to weak perturbing fields. Scanning the external fields in a loop to enclose the EP in the dispersion manifold, we identify a nonreciprocal topological energy transfer between different magnon modes. The results point to a promising route in magnonics and spintronics as well as to a versatile testing ground for $\mathcal{P}\mathcal{T}$-symmetry-driven phenomena.