Non-Hermitian topology of one-dimensional spin-torque oscillator arrays

Abstract

Magnetic systems have been extensively studied both from a fundamental physics perspective and as building blocks for a variety of applications. Their topological properties, in particular those of excitations, remain relatively unexplored due to their inherently dissipative nature. The recent introduction of non-Hermitian topological classifications opens up new opportunities for engineering topological phases in dissipative systems. Here, we propose a magnonic realization of a non-Hermitian topological system. A crucial ingredient of our proposal is the injection of spin current into the magnetic system, which alters and can even change the sign of terms describing dissipation. We show that the magnetic dynamics of an array of spin-torque oscillators can be mapped onto a non-Hermitian Su-Schrieffer-Heeger model exhibiting topologically protected edge states. Using exact diagonalization of the linearized dynamics and numerical solutions of the nonlinear equations of motion, we find that a topological magnonic phase can be accessed by tuning the spin current injected into the array. In the topologically nontrivial regime, a single spin-torque oscillator on the edge of the array is driven into auto-oscillation and emits a microwave signal, while the bulk oscillators remain inactive. Our findings have practical utility for memory devices and spintronics neural networks relying on spin-torque oscillators as constituent units.

Quantum Engineering With Hybrid Magnonic Systems and Materials (Invited Paper)

“…As a ubiquitous phenomenon, non-Hermiticity has been studied in many different physical realizations based on platforms in electronics, [152][153][154] microwave, [155][156][157] acoustics, [158][159][160] optics/photonics, [161][162][163][164][165][166] optomechanics 167,168 and magnetics. 169 Exceptional point (EP) is one of the most intensively studied novel phenomena in non-Hermitian systems. 170, 171 An EP, sometimes also referred to as a branch point, is a singularity point on an Riemann surface for a system with two or more coupled modes.…”

Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model

“…These two coupling were already introduced in Ref. [29]. Additionally, in this work we also introduce the dipolar couplings between the STOs, which affect the non-linear dynamics [38,39].…”

“…Specifically, we consider the topology of the onedimensional (1D) array of spin-torque oscillators (STOs) as shown in Fig. 1, building on the work of Flebus et al [29]. Spin-torque oscillators are current-driven magnetic nanopillars, whose magnetization dynamics are determined by the balance of spin current injection and intrinsic (Gilbert-like) dissipation [30].…”

“…It has been experimentally shown that the coupling between STOs arranged in an array can be tuned [31,32]. Flebus et al [29] have shown that, by modulating the coupling between STOs and the local spin injection, the array can be driven into the topological phase of the non-Hermitian Su-Schrieffer-Heeger (SSH) model [33], known to host lasing edge states [34,35]. However, STOs also exhibit strong non-linear effects, such as a non-linear frequency shift [30].…”

Giant Microwave Sensitivity of Magnetic Array by Long-Range Chiral Interaction Driven Skin Effect

“…Chirality is a common ingredient in topological magnetic orders [10][11][12], but in terms of which realization of non-Hermitian topology is rarely addressed [13,14]. Chiral interaction between Kittel magnon of a magnetic wire (or sphere) has been recently discovered when they couple with the traveling modes such as the spin waves in films [15][16][17][18], waveguide microwaves [19,20], and surface acoustic waves [21][22][23], to name a few, in that the Kittel modes prefer to couple with the traveling waves propagating in one direction.…”