Intrinsic localized modes in a monatomic lattice with weakly anharmonic nearest-neighbor force constants

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Abstract
The frequencies of anharmonic local modes in one-, two-, and three-dimensional lattices have been obtained analytically by combining the rotating-wave approximation with some of the formalism used previously to characterize defect modes in harmonic crystals. For weak anharmonicity these modes become delocalized, while they take on the vibrational pattern of a small molecule when the anharmonicity becomes large. The first-order corrections to the rotating-wave approximation are found to be small for any anharmonicity parameter, verifying that this approximate method of analysis can be used to separate the equations of motion. This identification of the weak-anharmonicity limit permits us for the first time to address the question of the existence of anharmonic local modes in real crystals. With anharmonic parameters similar to those found in alkali-metal halide crystals, the energy needed to produce these modes in all three dimensions is estimated. We find that thermal motion alone does not provide enough amplitude to support these modes in a lattice with the anharmonicity of pure LiF. On the other hand, at some defect sites the requirements could be less severe, and anharmonic modes might be generated by a nonthermal process such as an optical excitation of the F center, which introduces an energy equivalent of ∼40-Debye phonons into the lattice. The large anharmonicities found in solid He and near ferroelectric systems should provide more friendly environments for these modes.