Chiral Damping Research Articles

Chiral Damping of Magnons.

Chiral magnets have garnered significant interest due to the emergence of unique phenomena prohibited in inversion-symmetric magnets. While the equilibrium characteristics of chiral magnets have been extensively explored through the Dzyaloshinskii-Moriya interaction (DMI), nonequilibrium properties like magnetic damping have received comparatively less attention. We present the inaugural direct observation of chiral damping through Brillouin light scattering (BLS) spectroscopy. Employing BLS spectrum analysis, we independently deduce both the DMI and chiral damping, extracting them from the frequency shift and linewidth of the spectrum peak, respectively. The resulting linewidths exhibit clear odd symmetry with respect to the magnon wave vector, unambiguously confirming the presence of chiral damping. Our study introduces a novel methodology for quantifying chiral damping, with potential ramifications on diverse nonequilibrium phenomena within chiral magnets.

Control of chiral damping in magnetic trilayers using He+ ion irradiation

In the forefront of spintronic advancements, structures with strong perpendicular magnetic anisotropy (PMA) such as Pt/Co/Pt are essential for the miniaturization and performance enhancement of high-density magnetic storage technologies. The robust PMA characteristic of these systems facilitates the development of scalable spintronic devices, crucial for next-generation magnetic memory applications. This study investigates the interplay between PMA and the Dzyaloshinskii-Moriya interaction (DMI)—an antisymmetric exchange interaction prevalent in non-centrosymmetric magnetic systems—and its dissipative counterpart, chiral damping. While chiral damping arises from the same broken inversion symmetry as DMI, it typically introduces an additional energy dissipation channel, reducing device efficiency. Our research examines the effects of controlled helium ion (He+) irradiation on a Pt/Co/Pt system. We find that ion beam irradiation enhances interfacial intermixing, which correlates with a decrease in PMA. However, domain wall velocity measurements indicate a concurrent reduction in both DMI and chiral damping, along with enhanced velocities as irradiation fluence increases. These observations suggest that ion beam irradiation can be judiciously applied to achieve a balance between lower DMI, chiral damping, and reasonable PMA, thereby optimizing the system for improved device performance.

Decoupling the influences of chiral damping and Dzyaloshinskii-Moriya interaction in chiral magnetic domain walls

We revisit the nature and impact of both the chiral damping (CD) and Dzyaloshinskii-Moriya interaction (DMI) in uniaxial chiral ferromagnetic nanowires with broken inversion symmetry. We propose that CD, akin to its chiral energy counterpart (DMI), can be described in terms of the Lifshitz invariants permissible by the underlying symmetry of the system. This representation offers a clearer foundation for integrating CD into the dynamics of various chiral magnetic textures. We theoretically investigate the current-induced motion of chiral domain walls (DWs), driven by both spin-transfer torque and the spin Hall effect in the presence of CD. We demonstrate that it is possible to unambiguously separate the influence of CD from that of DMI by analyzing the current-induced dynamics. In particular, below the Walker breakdown (WB), the DMI does not affect the DW velocity, whereas increases in the strength of CD result in a decrease in the DW velocity. Moreover, for the spin-orbit torque driven motion, while the DMI enhances both the WB current density and the maximum attainable velocity below the WB, the CD only enhances the WB without affecting the maximum attainable velocity below the WB. Our findings open up intriguing opportunities for exploitation in exotic magnetic textures. Published by the American Physical Society 2024

Theory of tensorial Gilbert damping in antiferromagnets

Although the magnetic Gilbert damping was considered as a scalar quantity in micromagnetic and atomistic spin simulations, recent investigations show that the Gilbert damping parameter is a tensor. Here, we investigate the effect of anisotropic and chiral damping in one-sublattice ferromagnets and two-sublattice antiferromagnets. We employ linear response theory to calculate the susceptibility with the damping tensor and determine the ferromagnetic and antiferromagnetic resonance frequencies together with the effective damping. Our results show that apart from the scalar Gilbert damping, the antisymmetric chiral damping has a significant contribution to the spin dynamics that it breaks the antiparallel alignment of two sublattices in antiferromagnets even in the absence of an applied field. To this end, we also compare the tensorial damping and cross-sublattice scalar damping in antiferromagnets.

Quantum dynamics of dissipative Chern insulator

For open quantum systems, a short-time evolution is usually well described by the effective non-Hermitian Hamiltonians, while long-time dynamics requires the Lindblad master equation,in which the Liouvillian superoperators characterize the time evolution. In this paper, we constructed an open system by adding suitable gain and loss operators to the Chen insulator to investigate the time evolution of quantum states at long times by numerical simulations. Finally, we also propose a topolectrical circuits to realize the dissipative system for experimental observation. It is found that the opening and closing of the Liouvillian gap leads to different damping behaviours of the system and that the presence of non-Hermitian skin effects leads to a phenomenon of chiral damping with sharp wavefronts. Our study deepens the understanding of quantum dynamics of dissipative system.

Thermal Annealing Driven Enhancement of Perpendicular Magnetic Anisotropy and the Interfacial Dzyaloshinskii–Moriya Interaction in Ultrathin Ru/Co/W/Ru Films

Spin-related effects discovered in ultrathin magnetic films generally have an interfacial nature. The quality of interfaces between a heavy metal and a ferromagnet is the main driver of surface anisotropy, antisymmetric exchange, chiral damping, spin Hall effect, and spin–orbit torques. To understand the physics and usage of these phenomena for future atomic-scale devices, one has to study systems with disordered interfaces and search there for novel practically desirable effects, which lie beyond the atomic order and surface flatness. Here, we report the interface-related effects in Ru/Co/W/Ru ultrathin films treated by thermal annealing in vacuum. The surface roughness and degree of atomic intermixing at Ru/Co and Co/W interfaces change with increasing annealing temperature up to 240 °C, promoting an enhancement of perpendicular magnetic anisotropy and the interfacial Dzyaloshinskii–Moriya interaction (i-DMI). Further annealing at higher temperatures brings the interface deterioration and, consequently, a drastic degradation of the magnetic properties. Our first-principles calculations qualitatively support the experimental findings, providing an understanding of the i-DMI enhancement nature.

Effect of Chiral Damping on the dynamics of chiral domain walls and skyrmions

Friction plays an essential role in most physical processes that we experience in our everyday life. Examples range from our ability to walk or swim, to setting boundaries of speed and fuel efficiency of moving vehicles. In magnetic systems, the displacement of chiral domain walls (DW) and skyrmions (SK) by Spin Orbit Torques (SOT), is also prone to friction. Chiral damping (αc), the dissipative counterpart of the Dzyaloshinskii Moriya Interaction (DMI), plays a central role in these dynamics. Despite experimental observation, and numerous theoretical studies confirming its existence, the influence of chiral damping on DW and SK dynamics has remained elusive due to the difficulty of discriminating from DMI. Here we unveil the effect that αc has on the flow motion of DWs and SKs driven by current and magnetic field. We use a static in-plane field to lift the chiral degeneracy. As the in-plane field is increased, the chiral asymmetry changes sign. When considered separately, neither DMI nor αc can explain the sign reversal of the asymmetry, which we prove to be the result of their competing effects. Finally, numerical modelling unveils the non-linear nature of chiral dissipation and its critical role for the stabilization of moving SKs.

Damping transition in an open generalized Aubry-André-Harper model

We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as "chiral damping". Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase transition with the inclusion of the hopping amplitude modulation. By using the spectral topology and a finite-size scaling analysis in the commensurate case, we show there exists a phase transition of the skin effect with non-Bloch anti-parity-time symmetry breaking. For the incommensurate case, we find richer phases with the coexistence of the non-Hermitian skin effect and the Anderson localization, which are separated by a generalized mobility edge. We reveal the transition of the damping dynamics as a consequence of the phase transition. Furthermore, we propose a possible scheme with ultracold atoms in a dissipative momentum lattice to realize and detect the damping dynamics.

Asymmetric magnetic domain wall motion under lateral and normal space inversion asymmetry with interfacial Dzyaloshinskii–Moriya interaction

The magnetic anisotropy of a typical magnetic sample with an easy axis perpendicular to the surface has many advantages over an in-plane easy axis due to advantages like better thermal stability, higher data storage density, lower energy consumption, etc. The perpendicular magnetic anisotropy arises due to the spatial inversion asymmetry (SIA) at the interfaces between a ferromagnet (FM) and a heavy metal (HM). In such systems, one can achieve a current-induced magnetization reversal (CIMR) via spin–orbit torque with the assistance of an in-plane (IP) magnetic field. This IP field requirement for the CIMR process is an obstacle for the practical application. Recent studies on CIMR at magnetic fields free condition are achieved by breaking the lateral structural symmetry by achieving thickness-gradient in a particular layer. In previous reports, the SIA normal to the surface in a heterostructure leads to an asymmetric contribution as chiral damping. In this work, a system Ta/Pt/CoFeB/Pt with normal and lateral SIA has been prepared by introducing a thickness-gradient in the FM CoFeB layer, which leads to create a tilted perpendicular magnetic anisotropy. The presence of the lateral SIA gives rise to another asymmetric component besides the chiral damping component. In this study, the total asymmetric component of the Ta/Pt/CoFeB/Pt heterostructure has been calculated into two contributions Ht and Hch, to extract the distinct information of the tilt asymmetry due to the lateral SIA and the chiral damping due to the normal SIA, respectively. In this study, by varying the bottom Pt thickness of the Ta/Pt/CoFeB/Pt heterostructures we have observed that the two asymmetry contributions Ht and Hch both decreased with increasing bottom Pt thickness.

Information constraint in open quantum systems

We propose an effect called information constraint which is characterized by the existence of different decay rates of signal strengths propagating along opposite directions. It is an intrinsic property of a type of open quantum systems, which does not rely on boundary conditions. We define the value of information constraint $({I}_{C})$ as the ratio of different decay rates and derive the analytical representation of ${I}_{C}$ for general quadratic Lindbladian systems. Based on information constraint, we can provide a simple and elegant explanation of chiral and helical damping, and get the local maximum points of relative particle number for the periodical boundary system, consistent with numerical calculations. Inspired by information constraint, we propose and prove the correspondence between edge modes and damping modes. A new damping mode called Dirac damping is constructed, and chiral/helical damping can be regarded as a special case of Dirac damping.

Competition between Chiral Energy and Chiral Damping in the Asymmetric Expansion of Magnetic Bubbles

AG gratefully acknowledges the support from Khalifa University, UAE and PSE Division, KAUST, Saudi Arabia. In addition, GD and AG acknowledge the support of the Khalifa University internal funding FSU-2020-08 (8474000233).

Asymmetric magnetic domain wall motion in quasi-perpendicularly magnetized Pt/Co/Pt trilayer with interfacial Dzyaloshinskii-Moriya interaction

Field-induced domain wall motion has been observed in quasi-perpendicularly magnetized Pt/Co/Pt trilayers with interfacial Dzyaloshinskii-Moriya interaction (iDMI) using differential Kerr microscopy method in the creep regime. An oblique angle sputter deposition technique had introduced a thickness gradient in one of the layers of a trilyer, results in a small tilt of magnetic anisotropy from the film normal. The tilt angle has been estimated in each trilayer by determining the shift in the out-of-plane magnetization hysteresis measurements under bias magnetic field applied along various in-plane directions. The effective in-plane field at the domain wall due to iDMI has been determined by decomposing the symmetric and asymmetric contributions of the domain wall motion. Furthermore, the asymmetric contribution has been decomposed into two contributions due to the tilted magnetic anisotropy and the exponentially decaying chiral damping. The nature of the asymmetric contribution owing to the tilted anisotropy was studied by the collective coordinate model and a functional form of the total asymmetric contribution has been determined and used to fit the asymmetric contribution.

Dzyaloshinskii-Moriya interaction and chiral damping effect in symmetric epitaxial Pd/Co/Pd(111) trilayers

We investigate the creep of domain walls (DWs) in the combination of in-plane (IP) and out-of-plane magnetic fields in a series of epitaxial Cu(2 nm)/Pd(0--3 nm)/Co(0.7 nm)/Pd(3 nm) samples. Measured velocity curves, $v({H}_{x})$, are fitted with an extended dispersive elasticity model, which considers the dependence of both the elastic energy of the DWs and a velocity prefactor in the creep law on the IP magnetic field. The results of the calculations indicate that strong asymmetry in the $v({H}_{x})$ curves in the investigated system is primarily defined by the dependence of the velocity prefactor on the IP magnetic field, which may be related to a chiral damping effect. The effective energy of the Dzyaloshinskii-Moriya interaction (DMI) increases with increasing thickness of the Pd bottom layer from \ensuremath{-}0.16 \ifmmode\pm\else\textpm\fi{} 0.03 to $0.19\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$. We attribute the complex dependence of the effective DMI energy on the thickness of the Pd bottom layer in the epitaxial Pd/Co/Pd(111) system and the existence of the nonzero DMI in the symmetric Pd(3 nm)/Co(0.7 nm)/Pd(3 nm) samples to unequal strains in the bottom Pd/Co and top Co/Pd interfaces. The elastic strains in the interfaces varying depending on the thickness of the Pd bottom layer strongly influence the magnitude and even the sign of the contributions to the net DMI energy from each interface.

Generalized Brillouin zone and non-Hermitian band theory

The energy band theory is one of the cornerstones of condensed matter physics. It also has wide applications in other branches of physics. Recently, a number of questions from non-Hermitian physics call for a generalization of energy band theory to non-Hermitian systems. In the study of non-Hermitian topological states, it has been found that such a generalization necessitates redefinitions of certain fundamental concepts of band theory. In particular, the non-Hermitian skin effect (NHSE) causes the breakdown of Bloch-band picture and conventional bulk-boundary correspondence. To calculate the energy spectra and define topological invariants, the standard Brillouin zone gives way to the generalized Brillouin zone (GBZ). Many intriguing non-Hermitian phenomena, including the non-Hermitian skin effect, can be precisely characterized in terms of the generalized Brillouin zone. The non-Hermitian band theory based on the concept of generalized Brillouin zone, now generally known as the non-Bloch band theory, has successfully described and predicted a number of novel non-Hermitian phenomena. The present article provides a brief introduction to the main concepts of non-Bloch band theory, and its applications in the non-Hermitian bulk-boundary correspondence, Green’s functions, wave dynamics, chiral damping, and non-Bloch parity-time symmetry.

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems.

One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.

Disentangling factors governing Dzyaloshinskii domain-wall creep in Co/Ni thin films using PtxIr1−x seed layers

We characterize asymmetric growth of magnetic bubble domains in perpendicularly magnetized Co/Ni multi-layers grown on Pt$_x$Ir$_{1-x}$ seedlayers by application of perpendicular and in-plane magnetic fields. Using a refined model of domain wall creep that incorporates contributions from the anisotropic elastic energy, $\varepsilon$, and a chirality-dependent prefactor, $v_0$, we elucidate factors that govern the mobility of Dzyaloshinskii domain walls as a function of seedlayer composition. The interfacial Dzyaloshinskii-Moriya Interaction magnitude is found to decrease monotonically with $x_{Ir}$, which is independently confirmed by Brillouin light scattering (BLS). Moreover, the persistence of significant asymmetry in velocity curves across the full composition range supports previous assertions that a chirality-dependent attempt frequency akin to chiral damping could play a critical role in the observed trends. This work helps resolve fundamental questions about the factors governing Dzyaloshinskii DW creep and demonstrates varying Pt-Ir seedlayer composition as a method to tune DMI.

Chirality-induced antisymmetry in magnetic domain wall speed

In chiral magnetic materials, numerous intriguing phenomena such as built-in chiral magnetic domain walls (DWs) and skyrmions are generated by the Dzyaloshinskii–Moriya interaction (DMI). The DMI also results in asymmetric DW speeds under an in-plane magnetic field, which provides a useful scheme to measure the strength of the DMI. However, recent findings of additional asymmetries such as chiral damping have inhibited the unambiguous determination of the DMI strength, and the underlying mechanism of overall asymmetries comes under debate. Here, we experimentally investigate the nature of the additional asymmetry by extracting the DMI-induced symmetric contribution from the DW speed. Our results reveal that the additional asymmetry has a truly antisymmetric nature with the typical behavior governed by the DW chirality. In addition, the antisymmetric contribution alters the DW speed by a factor of 100, dominating the overall variation in DW speed. Thus, experimental inaccuracies can be largely removed by calibration with such antisymmetric contributions, enabling the standard DMI measurement scheme.

Chiral damping, chiral gyromagnetism, and current-induced torques in textured one-dimensional Rashba ferromagnets

We investigate Gilbert damping, spectroscopic gyromagnetic ratio and current-induced torques in the one-dimensional Rashba model with an additional noncollinear magnetic exchange field. We find that the Gilbert damping differs between left-handed and right-handed N\'eel-type magnetic domain walls due to the combination of spatial inversion asymmetry and spin-orbit interaction (SOI), consistent with recent experimental observations of chiral damping. Additionally, we find that also the spectroscopic $g$ factor differs between left-handed and right-handed N\'eel-type domain walls, which we call chiral gyromagnetism. We also investigate the gyromagnetic ratio in the Rashba model with collinear magnetization, where we find that scattering corrections to the $g$ factor vanish for zero SOI, become important for finite spin-orbit coupling, and tend to stabilize the gyromagnetic ratio close to its nonrelativistic value.

Theory of magnon motive force in chiral ferromagnets

We predict that magnon motive force can lead to temperature dependent, nonlinear chiral damping in both conducting and insulating ferromagnets. We estimate that this damping can significantly influence the motion of skyrmions and domain walls at finite temperatures. We also find that in systems with low Gilbert damping moving chiral magnetic textures and resulting magnon motive forces can induce large spin and energy currents in the transverse direction.

Phenomenology of chiral damping in noncentrosymmetric magnets

A phenomenology of magnetic chiral damping is proposed in the context of magnetic materials lacking inversion symmetry breaking. We show that the magnetic damping tensor adopts a general form that accounts for a component linear in magnetization gradient in the form of Lifshitz invariants. We propose different microscopic mechanisms that can produce such a damping in ferromagnetic metals, among which spin pumping in the presence of anomalous Hall effect and an effective "$s$-$d$" Dzyaloshinskii-Moriya antisymmetric exchange. The implication of this chiral damping in terms of domain wall motion is investigated in the flow and creep regimes. These predictions have major importance in the context of field- and current-driven texture motion in noncentrosymmetric (ferro-, ferri-, antiferro-)magnets, not limited to metals.