Theoretically, one often use the spin-spin correlation function (which is the sum of 3 terms in the x, y, z directions) to describe ferromagnetic (FM) or anti-ferromagnetic (AFM) order. For example, on the square lattice,
I want to know if there are other spin correlation functions that can help identify more complicated magnetic order, such as spin-canting and ferrimagnetism?
(Visualization of these orders can be found at, e.g. https://web.archive.org/web/20160611194326/http://magician.ucsd.edu/essentials/WebBookse18.html)