Mode- and Size-Dependent Landau-Lifshitz Damping in Magnetic Nanostructures: Evidence for Nonlocal Damping

Abstract

We demonstrate a strong dependence of the effective damping on the nanomagnet size and the particular spin-wave mode that can be explained by the theory of intralayer transverse-spin pumping. The effective Landau-Lifshitz damping is measured optically in individual, isolated nanomagnets as small as 100 nm. The measurements are accomplished by use of a novel heterodyne magneto-optical microwave microscope with unprecedented sensitivity. Experimental data reveal multiple standing spin-wave modes that we identify by use of micromagnetic modeling as having either localized or delocalized character, described generically as end and center modes. The damping parameter of the two modes depends on both the size of the nanomagnet as well as the particular spin-wave mode that is excited, with values that are enhanced by as much as 40% relative to that measured for an extended film. Contrary to expectations based on the ad hoc consideration of lithography-induced edge damage, the damping for the end mode decreases as the size of the nanomagnet decreases. The data agree with the theory for damping caused by the flow of intralayer transverse spin currents driven by the magnetization curvature. These results have serious implications for the performance of nanoscale spintronic devices such as spin-torque-transfer magnetic random access memory.

Nanowire spin torque oscillator driven by spin orbit torques

“…These results can be used to determine the values of saturation magnetization M s ¼ 608 emu cm À 3 , surface magnetic anisotropy K s ¼ 0.237 erg cm À 2 and edge dilution depth D ¼ 10 nm, where D is defined as the distance from the wire edge over which magnetization linearly increases from zero to the full film value 43 . These values of M s , K s and D are consistent with previous studies of thin Py nanomagnets [45][46][47] . Using these values of the nanowire magnetic parameters and assuming translational invariance along the nanowire axis, we perform micromagnetic simulations to find the spectrum of spin wave eigenmodes for magnetic field applied in the sample plane at b ¼ 85°.…”

Microwave magnetic dynamics in ferromagnetic metallic nanostructures lacking inversion symmetry

“…In that paper it was found that the S21 value for a stripline loaded by a thin ferromagnetic film scales as exp(Z r /Z 0 ), where Z 0 is the characteristic impedance of the stripline without the sample on its top and Z r is extra impedance inserted by the ferromagnetic resonance in the material. Equation (1) We also add an extra term - (1) S f -to this equation, in order to account for a linear slope seen in S(f) in some traces off-resonance. ( (1) S is also a complex number.)…”

“…Equation (1) We also add an extra term - (1) S f -to this equation, in order to account for a linear slope seen in S(f) in some traces off-resonance. ( (1) S is also a complex number.) This formula fits the experimental data very well.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12]). These materials are important for the emerging fields of magnonics [13], microwave spintronics [14][15][16][17], and for novel sensor applications [18][19][20][21].…”

Spin torque ferromagnetic resonance with magnetic field modulation

“…Optimization of MTJ performance for these applications requires quantitative evaluation of the spin torque (ST) vector [12], magnetic damping [13], voltagecontrolled magnetic anisotropy [14][15][16], and the spectrum of magnetic excitations of the MTJ [17,18]. A common techniques for quantitative measurements of these properties is ST ferromagnetic resonance (ST-FMR) [19,20].…”