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Calculation of the Spin Wave Energy Gap at k = o for a Simple Cubic Ferromagnet with Anisotropic Exchange Interactions
Author(s) -
Belorizky E.,
Casalegno R.,
Niez J. J.
Publication year - 1980
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221020135
Subject(s) - brillouin zone , condensed matter physics , physics , spin wave , spins , anisotropy , exchange interaction , cubic crystal system , ferromagnetism , lattice (music) , quantum mechanics , band gap , acoustics
Spin waves in a system of pseudo‐spins forming a simple cubic ferromagnetic lattice are analysed by considering the most general bilinear interaction between nearest neighbors allowed by a four‐fold order symmetry of the bond ℋ ij = J ∥ S iz S jz + J ⟂(S ix S jx +S iy S jy ) for a pair (i,j) oriented along the z axis. For that extended Heisenberg system, the excitation energy a t the center of the Brillouin zone is found to be zero with the usual theory, a result which violates the Goldstone theorem predicting a gap a t this point. This gap is calculated through two different but consistent methods and its variation with the anisotropy of the exchange parameters is determined numerically. It is seen that even for a small gap, strongly anisotropic exchange is possible.