Josh Deutsch Research Dynamics of Magnets

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.

Disjoint avalanche 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.