On the application of group theory to spinwaves in collinear magnetic structures

The application of group theory to spinwaves in collinear magnetic structures is discussed in close analogy with similar applications made in the case of lattice vibrations. Some of the basic features pertaining to magnetic space groups are first recalled and the spinwave equations for collinear magnetic systems are set up. The details of applying group theory are then described using the multiplier-representation approach, and finally the methodology is illustrated by working through in detail the classification of spinwaves in Fe₃O₄. The relationship of the present results to those given earlier by Brinkman and Elliott for the same crystal is also pointed out.