Intrinsic Localized Spin Wave Modes
For a one-dimensional easy-axis antiferromagnetic chain of N classical spins the Hamiltonian is given by
where both J and D are positive. The equation of motion can therefore be written as
where the effective magnetic field is produced by the nearest-neighbor exchange interactions and the anisotropy, that is,
Since the effective field is soft in the sense that its magnitude decreases as the spin deviations increase, such discrete lattices can support intrinsic localized spin wave modes (ILSMs) with frequencies in the gap below the standard antiferromagnetic resonance frequency.
To find the eigenvector of an ILSM, the new variable
is introduced to make use of the uniaxial symmetry. Two types of stationary ILSMs can be found, either single-peaked or double-peaked. In an ILSM each spin precesses about the easy-axis with time-independent spin deviation. Frequencies of both types of ILSMs decrease with increasing the maximum spin deviation in the mode. However, the double-peaked ILSMs are dynamically unstable, evolving into single-peaked ILSMs under noise perturbation.
The above Java applet can launch molecular dynamics simulations of both types of ILSMs. If the "Perturbed?" box is checked, randomly perturbed eigenvectors would be used as the initial condition in MD simulations. Otherwise, the unpertubed eigenvectors would be used. It takes about 20 TAFMR for a perturbed double-peaked ILSM to evolve into a single-peaked one. You can also obtain updated magnetic dipole spectrum by clicking the "Power Spectrum" button.