Two-spin-wave spectra of easy-plane ferromagnetic chains
Peter S. Riseborough, Pradeep Kumar
The easy-plane ferromagnetic chain in an applied magnetic field is known to map onto a sine-Gordon field theory, in the classical continuum limit. The sine-Gordon field theory supports breather excitations which, when quantised, are identifiable as a hierarchy of bound states of several small-amplitude excitations. For increasing values of the interaction parameter, the highest members of the hierarchy become unstable to the emission of a soliton/anti-soliton pair. For a critical value of the interaction parameter, even the ground state of the quantised sine-Gordon theory becomes unstable. For the quantum spin system, the excitations corresponding to the two lowest members of the hierarchy of breathers are the single-spin-wave and the two-spin-wave bound states. The authors examine the two-spin-wave bound-state excitations of the quantum spin system directly, using a large-S approach. Although the method does rely on large S, they recover previously derived results valid for arbitrary S, such as the exact two-spin-wave bound states for the isotropic Heisenberg ferromagnet and the expansion in the anisotropy about this result. In the limit of large anisotropy the two-spin-wave bound state becomes unstable, in a manner suggestive of the instability of the quantum-sine-Gordon field theory.
Journal of Physics Condensed Matter•Oct 9, 1989•3 citations