Exploration of Fermi-Pasta-Ulam Behavior in a Magnetic System

We study nonlinear spin motion in one-dimensional magnetic chains. We find significant differences from the classic Fermi-Pasta-Ulam (FPU) problem examining nonlinear elastic motion in a chain. We find that FPU behavior, the transfer of energy among low order eigenmodes, does not occur in magnetic systems with only exchange and external fields, but does exist if a uniaxial anisotropy is also present. The FPU behavior may be altered or turned off through the magnitude and orientation of an external magnetic field. A realistic micromagnetic model shows such behavior could be measurable.

Figure 1

Time evolution of the system started in the $n=1$ state but with different initial amplitudes. (a) $A=0.001$ and the system stays in the $n=1$ mode. (b) $A=0.1$ and the $n=1$ mode redistributes to multiple other modes but repeatedly goes back into mode 1. (c) $A=0.15$ and the simple periodic behavior seen in (b) has become much more complex (d) $A=0.5$ and the time evolution shows strongly nonlinear behavior where the system is approaching ergodicity.

Figure 2

Mode projections for identical systems with different applied fields. The initial state contains 95% $n=0$ and 5% $n=1$ and $A=0.1$ The time evolution in (b) and (c) shows FPU-like behavior.

Figure 3

The projection of the dynamic state onto the linear eigenmodes of the system when (a) the field is applied in plane, and (b) the field is applied out of plane. The applied field is $H_o=25\mathrm{kOe}$, and $A=0.1$.

Figure 4

The projection of the dynamic state onto the linear eigenmodes of the system when damping ($\alpha ={10}^{-4}$) is present. The remaining parameters are $H_o=5\mathrm{kOe}$, the initial state is $n=1$ with an amplitude of 0.25.