Center for Materials for Information Technology an NSF Materials Science and Engineering Center Understanding Magnetic Switching: Spin Wave Visualization P. B.Visscher, D. M. Apalkov, and X.Feng Department of Physics and Astronomy The University of Alabama Web version Narration is in notes (icon on lower left toolbar will give the notes window)| Movies will not play until they’ve been downloaded and correctly pointed to – it may be easier to play them from the web page (folder directory) directly. They have names like HUp.mov, HDown.mov, HHor.mov, OneCell Hz=Hk.mov, etc.

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Motivation We want to understand switching in magnetic media (e.g., hard disk). M Basic problem: switch to M Known mechanisms: Curling Buckling Nucleation at end

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Movie 1 Initial motion, just after reversing external field. See precession about field, then “breakup”. OR, spin-wave switching (Safonov & Bertram 1999):

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Switching Simulation Magnetization vs time for a 4  4  4 system: Movie 1 Movie 2

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Movie 2 After system has halfway switched from up to down. Lots of spin wave energy.

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Landau-Lifshitz equation without damping (not important in early stages of fast switching) thermal (Langevin) noise (small, k B T<<Zeeman energy) Basic equation for precession

Center for Materials for Information Technology an NSF Materials Science and Engineering Center We want to switch the magnetization so it points down -- try reversing magnetic field H from up to down:

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Precessional switching Since M precesses around H, the way to get M to swing down is to use a horizontal H:

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Anisotropy field (due to intrinsic crystalline anisotropy or to sample shape)

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Add a vertical component to H ext to cancel anisotropy field:

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Decrease H ext so it doesn’t quite cancel H K. Then precession around z has both signs, tends to cancel.

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Spin waves A homogeneous system can get near the “hard plane” but it will always come back (closed orbits). In spin wave switching simulations we saw inhomogeneity: spin waves. To understand spin waves we have to introduce exchange interactions: Neighboring spins (or magnetized finite elements) exert exchange fields on each other: MM’ H exch If all M’s are parallel the exchange field has no effect (MxH=0). But if they aren’t, M’s precess around each other (spin waves).

Center for Materials for Information Technology an NSF Materials Science and Engineering Center One spin wave ?? spin waves

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Fourier-transform to get spin wave amplitudes: Visualizing spin waves Each M(r) can be written as the sum of its Fourier components: where the Fourier component is Rather than display the complex vector M(k), we display all the individual components M k (r) for all cells r. (N vectors, not N 3.)

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Visualizing Spin Wave Amplitudes

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Superimposed spin waves

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Back to switching We found that a uniform system with an almost-downward H would get close to the equator, but not switch. Add exchange interactions (spin waves):

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Growth of spin-wave amplitudes

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Orbits during switching

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Why is it unstable? Calculating (FMR) precession frequency General formula for spin-wave frequency (=resonance frequency for FMR, if k=0) where D M is the demag+anisotropy factor along M and D t1 and D t2 are demag+anisotropy factors transverse to M In the simple case of M along the easy (z) axis, D M =2K/M s and D t1 = D t2 = 0, so  2 > 0 and  is real: we get circular precession. If M is along a hard axis, D t1 = 2K/M s and one factor can be negative, making  imaginary (exponentially growing instability). This is the origin of the switching instability.

Center for Materials for Information Technology an NSF Materials Science and Engineering Center History of hard-plane FMR Oddly enough, this instability was known experimentally as early as Along a hard axis, the frequency becomes As we lower the hard axis field H, this vanishes at a critical value H c = 2K/M s. Below H c, M will not remain along the hard axis, so we cannot do FMR. J. Smit and H. G. Beljers, Phillips Res. Rept. 10, 113 (1955), reproduced from “The Physical Principles of Magnetism”, A. H. Morrish, 1965.

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Simulation of simple hard-plane instability Below H c = 2K/M s, M will not remain along the hard axis, so we cannot do FMR, but we can do a short-time simulation:

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Back to switching We found that a uniform system with an almost-downward H would get close to the equator, but not switch. Add exchange interactions (spin waves):

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Summary We have identified the instability responsible for spin wave switching. Remaining to do: Consider samples with boundaries (everything here was with periodic b.c.’s) Add magnetostatic interactions (Fast Multipole Method) Determine which wavelengths are most unstable

Center for Materials for Information Technology an NSF Materials Science and Engineering Center

Center for Materials for Information Technology an NSF Materials Science and Engineering Center Why perpendicular recording? Perpendicular-recording head medium N S Longitudinal Larger write field in perpendicular case Smaller write field in longitudinal case Longitudinal