It is well known that the spin wave spectrum in the antiferromagnetic ordering is commonly written as e=sqrt(A(q)^2-B(q)^2), based on the linear spin wave theory. The magnetic interactions are included in A(q)^2 and B(q)^2.

Is there a similar equation in the case of collinear ferrimagnetic ordering? I searched for many literature, but unfortunately failed to find it. Could anybody give me some directions on it and recommend some literatures if possible?

Thank you for your help in advance!

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