Dynamical algebra of spin waves in localised-spin models
Subir Kumar Bose
The idea of the spectrum generating algebra (SGA) is used to study the low-lying excitations in various localised-spin models of ferromagnetic, ferrimagnetic and antiferromagnetic solids. The noncompact algebra SO(2,1) approximately SU(1,1) is found to generate the spin wave or the magnon spectrum for ferromagnetic, ferrimagnetic and antiferromagnetic Bravais lattices with nearest-neighbour exchange interactions (Heisenberg model). The ferromagnetic case is treated including dipolar interactions in the model. For a quadratic antiferromagnet with easy-plane anisotropy the SGA is found to be the direct product SO(2,1)(X)SO(2,1) approximately SO(2,2). For the XY and the Heisenberg-Ising models of an antiferromagnetic linear chain the SGA is the compact counterpart of SO(2,1), i.e. SO(3) approximately SU(2). It is concluded that if the magnons are quantised as bosons then the SGA is the noncompact algebra SO(2,1), and if they are quantised as fermions then the SGA is the compact angular momentum algebra SO(3).
Journal of Physics A Mathematical and General•Apr 21, 1985•12 citations