Vortex-antivortex proliferation from an obstacle in thin film ferromagnets

Magnetization dynamics in thin film ferromagnets can be studied using a dispersive hydrodynamic formulation. The equations describing the magnetodynamics map to a compressible fluid with broken Galilean invariance parametrized by the longitudinal spin density and a magnetic analog of the fluid velocity that define spin-density waves. A direct consequence of these equations is the determination of a magnetic Mach number. Micromagnetic simulations reveal nucleation of nonlinear structures from an impenetrable object realized by an applied magnetic field spot or a defect. In this work, micromagnetic simulations demonstrate vortex-antivortex pair nucleation from an obstacle. Their interaction establishes either ordered or irregular vortex-antivortex complexes. Furthermore, when the magnetic Mach number exceeds unity (supersonic flow), a Mach cone and periodic wavefronts are observed, which can be well-described by solutions of the steady, linearized equations. These results are reminiscent of theoretical and experimental observations in Bose-Einstein condensates, and further supports the analogy between the magnetodynamics of a thin film ferromagnet and compressible fluids. The nucleation of nonlinear structures and vortex-antivortex complexes using this approach enables the study of their interactions and effects on the stability of spin-density waves.Comment: 23 pages, 7 figure

Symmetry-broken dissipative exchange flows in thin-film ferromagnets with in-plane anisotropy

Planar ferromagnetic channels have been shown to theoretically support a long-range ordered and coherently precessing state where the balance between local spin injection at one edge and damping along the channel establishes a dissipative exchange flow, sometimes referred to as a spin superfluid. However, realistic materials exhibit in-plane anisotropy, which breaks the axial symmetry assumed in current theoretical models. Here, we study dissipative exchange flows in a ferromagnet with in-plane anisotropy from a dispersive hydrodynamic perspective. Through the analysis of a boundary value problem for a damped sine-Gordon equation, dissipative exchange flows in a ferromagnetic channel can be excited above a spin current threshold that depends on material parameters and the length of the channel. Symmetry-broken dissipative exchange flows display harmonic overtones that redshift the fundamental precessional frequency and lead to a reduced spin pumping efficiency when compared to their symmetric counterpart. Micromagnetic simulations are used to verify that the analytical results are qualitatively accurate, even in the presence of nonlocal dipole fields. Simulations also confirm that dissipative exchange flows can be driven by spin transfer torque in a finite-sized region. These results delineate the important material parameters that must be optimized for the excitation of dissipative exchange flows in realistic systems.Comment: 20 pages, 5 figure

Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy

Stripe domains are narrow, elongated, reversed regions that exist in magnetic materials with perpendicular magnetic anisotropy. Stripe domains appear as a pair of domain walls that can exhibit topology with a nonzero chirality. Recent experimental and numerical investigations identify an instability of stripe domains in the long direction as a means of nucleating isolated magnetic skyrmions. Here, the onset and nonlinear evolution of transverse instabilities for a dynamic stripe domain known as the bion stripe are investigated. Both non-topological and topological variants of the bion stripe are shown to exhibit a long-wavelength transverse instability with different characteristic features. In the former, small transverse variations in the stripe's width lead to a neck instability that eventually pinches the non-topological stripe into a chain of two-dimensional breathers composed of droplet soliton pairs. In the latter case, small variations in the stripe's center results in a snake instability whose topological structure leads to the nucleation of dynamic magnetic skyrmions and antiskyrmions as well as perimeter-modulated droplets. Quantitative, analytical predictions for both the early, linear evolution and the long-time, nonlinear evolution are achieved using an averaged Lagrangian approach that incorporates both exchange (dispersion) and anisotropy (nonlinearity). The method of analysis is general and can be applied to other filamentary structures.Comment: 8 figures, 13 page

Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: the role of dispersion, nonlinearity, and damping

Nonlocal compensation of magnetic damping by spin injection has been theoretically shown to establish dynamic, noncollinear magnetization states that carry spin currents over micrometer distances. Such states can be generically referred to as dissipative exchange flows (DEFs) because spatially diffusing spin currents are established by the mutual exchange torque exerted by neighboring spins. Analytical studies to date have been limited to the weak spin injection assumption whereby the equation of motion for the magnetization is mapped to hydrodynamic equations describing spin flow and then linearized. Here, we analytically and numerically study easy-plane ferromagnetic channels subject to spin injection of arbitrary strength at one extremum under a unified hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile along the channel accompanied by a nonlinear frequency tuneability. At large injection strengths, we fully characterize a novel magnetization state we call a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the injection site, which smoothly transitions into a DEF and exhibits a negative frequency tuneability. The transition between a DEF and a CS-DEF occurs at the maximum precessional frequency and coincides with the Landau criterion: a subsonic to supersonic flow transition. Leveraging the hydraulic-electrical analogy, the current-voltage characteristics of a nonlinear DEF circuit are presented. Micromagnetic simulations of nanowires that include magnetocrystalline anisotropy and non-local dipole fields are in qualitative agreement with the analytical results. The magnetization states found here along with their characteristic profile and spectral features provide quantitative guidelines to pursue an experimental demonstration of DEFs in ferromagnetic materials and establishes a unified description for long-distance spin transport

Magnonic Band Structure Established by Chiral Spin-Density Waves in Thin Film Ferromagnets

Recent theoretical studies have demonstrated the possibility to excite and sustain noncollinear magnetization states in ferromagnetic nanowires. The resulting state is referred to as a spin-density wave (SDW). SDWs can be interpreted as hydrodynamic states with a constant fluid density and fluid velocity in systems with easy-plane anisotropy. Here, we consider the effect of the nonlocal dipole field arising from the finite thickness of magnetic thin films on the spatial profile of the SDW and on the associated magnon dispersion. Utilizing a hydrodynamic formulation of the Larmor torque equation, it is found that the nonlocal dipole field modulates the fluid velocity. Such a modulation induces a magnonic band structure unlike the typical dispersion relation for magnons on uniform magnetization. The analytical results are validated by micromagnetic simulations. Band gaps on the order of GHz are numerically observed to depend on the SDW fluid velocity and film thickness for realistic material parameters. The presented results suggest that SDWs can find applications as reconfigurable magnonic crystals.Comment: 5 pages, 5 figure

Deterministic drift instability and stochastic thermal perturbations of magnetic dissipative droplet solitons

The magnetic dissipative droplet is a strongly nonlinear wave structure that can be stabilized in a thin film ferromagnet exhibiting perpendicular magnetic anisotropy by use of spin transfer torque. These structures have been observed experimentally at room temperature, showcasing their robustness against noise. Here, we quantify the effects of thermal noise by deriving stochastic equations of motion for a droplet based on soliton perturbation theory. First, it is found that deterministic droplets are linearly unstable at large bias currents, subject to a drift instability. When the droplet is linearly stable, our framework allows us to analytically compute the droplet's generation linewidth and center variance. Additionally, we study the influence of nonlocal and Oersted fields with micromagnetic simulations, providing insight into their effect on the generation linewidth. These results motivate detailed experiments on the current and temperature-dependent linewidth as well as drift instability statistics of droplets, which are important figures-of-merit in the prospect of droplet-based applications

Oscillatory transient regime in the forced dynamics of a spin torque nano-oscillator

We demonstrate that the transient non-autonomous dynamics of a spin torque nano-oscillator (STNO) under a radio-frequency (rf) driving signal is qualitatively different from the dynamics described by the Adler model. If the external rf current $I_{rf}$ is larger than a certain critical value $I_{cr}$ (determined by the STNO bias current and damping) strong oscillations of the STNO power and phase develop in the transient regime. The frequency of these oscillations increases with $I_{rf}$ as $\propto\sqrt{I_{rf} - I_{cr}}$ and can reach several GHz, whereas the damping rate of the oscillations is almost independent of $I_{rf}$. This oscillatory transient dynamics is caused by the strong STNO nonlinearity and should be taken into account in most STNO rf applications.Comment: 4 page, 3 figure

A high-speed single sideband generator using a magnetic tunnel junction spin torque nano-oscillator

An important property of spin-torque nano-oscillators (STNOs) is their ability to produce a frequency modulated (FM) signal, which is very critical for communication applications. We here demonstrate a novel single sideband (SSB) modulation phenomenon using a magnetic tunnel junction (MTJ)-based STNO, which saves transmission bandwidth and in principle should minimize attenuation for wireless communication. Experimentally, lower single sidebands (LSSBs) have been successfully demonstrated over a wide range of modulation frequency, f m  = 150 MHz-1 GHz. The observed LSSBs are determined by the intrinsic properties of the device, which can be modeled well by a nonlinear frequency and amplitude modulation formulation and reproduced in macrospin simulations. Moreover, our macrospin simulation results show that the range of modulation current and modulation frequency for generating SSBs can be controlled by the field-like torque and biasing conditions

Spin-Injection-Generated Shock Waves and Solitons in a Ferromagnetic Thin Film

Unsteady nonlinear magnetization dynamics are studied in an easy-plane ferromagnetic channel subject to spin injection at one edge. The Landau-Lifshitz equation is known to support steady-state solutions, termed dissipative exchange flows (DEFs) or spin superfluids. In this work, by means of numerical simulations and theoretical analysis, we provide a full description of the injection-induced, large-amplitude, nonlinear magnetization dynamics up to the steady state. The dynamics prior to reaching steady state are driven by spin injection, a perpendicular applied magnetic field, the exchange interaction, and local demagnetizing fields. We show that the dynamics result in well-defined profiles in the form of rarefaction waves (RWs), dispersive shock waves (DSWs), and solitons. The realization of these coherent structures depends on the interplay between the spin injection strength and the applied magnetic field. A soliton at the injection boundary, signaling the onset of the magnetic 'supersonic' condition, rapidly develops and persists in the steady-state configuration of a contact soliton DEF. We also demonstrate the existence of sustained soliton-train dynamics in long time that can only arise in a nonzero applied magnetic field scenario. The dynamical evolution of spin-injection-induced magnetization dynamics presented here may help guide observations in long-distance spin transport experiments