Precession and Avalanches
Recently Deutsch has done work with Andreas Berger, formerly of Hitachi
Global Storage Technologies, and now Research Director of Nanogune,
to study the way the microscopic spins in a magnetic materials move,
such as materials that are used in hard disk drives. In particular,
we examined the
effects of precession and damping on avalanches in magnetic
materials. Previous work modeled avalanches in these systems mainly
by assuming relaxational dynamics, where a spin would just flip from
up to down, like a domino falling. In reality, spins precess and damping can be quite slow in
comparison with their precessional period. This means that energy in an
avalanche is not immediately dissipated and so can cause the spin degrees
of freedom to effectively heat up, which can cause distant neigbors to
avalanche as well. However we
showed that this process is much more analogous to an explosion than had
been previously thought. Instead of spins just flipping once from up
to down, they continue to spin around, that is, the spins get hot, and
in many materials they stay hot for a substantial amount of time. This
greatly alters the microscopic physics of the system, which means that
a change in one part of a magnet can effect the behavior much further
away. The hot region forms a growth front and the heat from it recruits
neighboring spins into the explosive region before they eventually cool
down. We analyzed this in detail using simulations and theoretical
models and were able to determine in what circumstances an explosion
gets extinguished and when it takes off.
On the right you can see an avalanche of a material with small damping.
Note in the above snapshots, how spins far away from the growth front
spontaneously avalanche. This is due to spin waves heating up
regions far ahead of front.
Further work with Andreas Berger showed how to incorporate damping in compuationally
efficient way to be able to better explore magnetic systems by simulation
techniques. We were able to alter the dyanamics of the Ising model to
include damping. The method was able to rigorously describe any system at
finite temperature this way by an algorithm that added non-gaussian
noise to system.
Using this technique we explored much larger systems than would otherwise
be possible. We showed that low damping systems can also alter
qualitatively the morphology seen in avalanching magnets. In some cases
disjoint avalanched cluseters are seen, as illustrated on the right.
We were also able to determine how the effective critical properties of avalanches
alter for low damping three dimensional systems. On small and intermediate
scales, They appear substantially different from relaxational dynamics.
Multicycles
Deutsch has worked with Onuttom Narayan on hysteresis curves in spin
systems. It had been assumed that at low temperatures,
an adiabatic hysteresis loop closes back on itself in steady state. They showed
that in many circumstances this is incorrect and the system goes
through multiple cycles before it returns to its initial state. Such
behavior may be observable in spin glass materials at low temperatures
and would show an interesting subharmonic response to an oscillating
magnetic field. Later in collaboration with Narayan and also a graduate
student, Trieu Mai, they showed
that in a realistic model of nanopillars,
it was possible to also see these multicyles.
Clicking on the picture to the right, you can see an mpeg movie of a set of
nanopillars in an applied field that is slowly varied between two moderate
values of field. Watch the blue third spin in the first column. It flips only
every other cycle.
Field Asymmetry in domain patterns
Experimental work using x-ray speckle techniques has discovered
a very surprising asymmetry
in patterns seen in a hysteresis loop.
A two dimensional thin film is placed in strong perpendicular magnetic
field which is slowly lowered. The speckle patterns are observed
as a function of the applied field. The same experiment is done
starting with the opposite field and raising it. The patterns seen
are statistically different. This is despite the fact that the
Hamiltonian is spin inversion symmetric.
The experiments have many other interesting features to them.
A range of films were used with different degrees of disorder.
At the lowest disorder, snake-like growth of domains was
observed to spontaneously occur at some threshold field
giving rise to a cliff in the hysteresis loop. This cliff
disappeared for higher disorder films.
Again in collaboration with Trieu Mai, Deutsch showed
that all the major features of these experiments could be understood
quite well using a model of this system. The key realization
is that precession causes a field asymmetry in the patterns
seen. This counter-intuitive result can be seen theoretically
and was confirmed by detailed numerical work.
The snake-like growth at low disorder could be understood
using this simulation, see the mpeg movie on the right,
and looks quite similar to experimental movies.
The asymmetry in patterns seen is also seen here and again
is similar to what is seen experimentally.
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