Spin waves in itinerant multiple-spin-density-wave systems. I

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Abstract
The generalised susceptibilities for the itinerant antiferromagnetic spin structures corresponding to ground states of linear (LSDW) and multiple spin-density waves (MSDW) are derived within the random-phase approximation for a one-band Hubbard model. The problem has been made practicable by exploiting the magnetic group symmetry of the MSDW states. Whereas for an LSDW state the response functions decouple naturally into transverse and longitudinal dielectric blocks, in the MSDW state the terms transverse and longitudinal lose their meaning. Nevertheless the responses do decouple into four branches, of which three give rise to acoustic spin wave modes and the fourth gives rise to special mode corresponding to the non-linear spin wave mode found in a recent paper using the Heisenberg model. Explicit formulae are given from which spin wave dispersions can be evaluated. These are easily generalisable for the more realistic many-orbital case.

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