Engineering the Spectrum of Dipole Field-Localized Spin-Wave Modes to Enable Spin-Torque Antidamping

Abstract

Auto-oscillation of a ferromagnet due to spin-orbit torques in response to a dc current is of wide interest as a flexible mechanism for generating controllable high frequency magnetic dynamics. However, spin wave mode degeneracies and nonlinear magnon-magnon scattering impede coherent precession. Discretization of the spin wave modes can reduce this scattering. Spatial localization of the spin wave modes by the strongly inhomogeneous dipole magnetic field of a nearby spherical micromagnet provides variable spatial confinement, thus offering the option of systematic tunability of magnon spectrum for studying multi-mode interactions. Here we demonstrate that field localization generates a discrete spin wave mode spectrum observable as a series of well-resolved localized modes in the presence of imposed spin currents arising from the spin Hall effect (SHE) in a permalloy/platinum (Py/Pt) microstrip. The observation of linewidth reduction through damping control in this micromagnetically engineered spectrum demonstrates that localized modes can be controlled efficiently, an important step toward continuously tunable SHE driven auto-oscillators.

Giant nonlinear damping in nanoscale ferromagnets

“…Equations 3 and 4 also quantitatively explain the observed dependence of the quasi-uniform mode linewidth Δω 0,0 on direct bias current I dc . Assuming antidamping spin torque linear in bias current ( 27 , 38 , 39 ), α0,0→α0,0false(1−Idc/Icfalse∣0,0false〉false), αn,m→αn,mfalse(1−Idc/Icfalse∣n,mfalse〉false), where Icfalse∣n,mfalse〉>Icfalse∣0,0false〉 are the critical currents, we fit the measured bias dependence of ST-FMR linewidth in Fig. 3 by solving Eqs.…”

Spin orbit torque nano-oscillators by dipole field-localized spin wave modes

“…The microwave power emitted by the device is detected via anisotropic magnetoresistance (AMR) effect, and measured by a lownoise amplifier and spectrum analyzer [5,22]. We use a nearby micromagnetic particle to introduce a spatially localized minimum in the internal static fielda field well-in the sample [13][14][15][16]. The lowest-frequency spin wave modes at the bottom of the well are discrete localized modes (LM) whose frequencies lie well below the spin wave continuum.…”

“…The spatial confinement provided by the field-well determines the spectral separations between the various discrete localized modes. The four lowest-frequency localized modes are localized width modes LM1 (n = 1, m = 1), LM2 (n = 2, m = 1), a localized length mode LM3 (n = 1, m = 2), and a localized width mode LM4 (n = 3, m = 1) [16]. Figure 1(c) shows micromagnetic simulated mode profiles of the lowest-four localized modes in the 700 nm × 1 µm active region.…”

“…Spatial localization in, e.g., nanoconstrictions and planar nano-gap contacts [1,[7][8][9][10][11][12] produces discrete modes whose frequencies lie below the spin wave dispersion for the extended sample thus reducing scattering channels [1,5] and enabling auto-oscillation. Alternatively, a localized region of reduced internal magnetic field generated by the dipole field of a nearby micromagnetic particle confines the spin wave modes in a nanoscale magnetic field well [13][14][15][16] thus enabling auto-oscillation. Dipole-field localized modes offer advantages as spin-Hall oscillators [16]: First, in contrast to all previous geometrically confined oscillator modes which are fixed once fabricated, field confinement offers in-situ tunability.…”

“…Alternatively, a localized region of reduced internal magnetic field generated by the dipole field of a nearby micromagnetic particle confines the spin wave modes in a nanoscale magnetic field well [13][14][15][16] thus enabling auto-oscillation. Dipole-field localized modes offer advantages as spin-Hall oscillators [16]: First, in contrast to all previous geometrically confined oscillator modes which are fixed once fabricated, field confinement offers in-situ tunability. In particular, the lateral confinement and field well depth are tunable by particle parameters-size, moment, particlesample separation-the latter of which can be altered in-operando, and is continuously controllable if the particle is mounted on a cantilever whose height is variable.…”