# Magnetism in bipartite lattices

Suppose we have a bipartite lattice( A and B). By tuning some parameters in the Hamiltonian, we get a region of parameter space where sublattice magnetizations, $$m_{A}$$ and $$m_{B}$$ are both of same sign but not equal in magnitude. I mean to say , I have finite staggered magnetization, $$m_{s}=(m_{A}-m_{B})/2$$ as well as uniform magnetization, $$m_{f}=(m_{A}+m_{B})/2$$. Can I call it ferrimagnetic ?

Normally, if the sublattice magnetizations are oppositely oriented and there also happens to be some difference in their magnitudes, we call it ferri. But here I have $$m_{A},m_{B}$$ having same orientation but differing magnitudes.

According to my understanding, even if A and B have same direction of magnetizations but unequal magnitude, it means that A is more up, B is less up $$\equiv$$ B is more down. So, it can be called ferrimagnetic. Any clarification in this regard will be appreciated.

The typical, textbook definitions of ferrimagnetic do mention sublattices with unequal and opposite moments, so you should probably avoid calling it that. I think what you describe is better called a ferromagnet, albeit with a two-site unit cell. People have studied ferromagnetic mixed-spin Hamiltonians (e.g. chains coupling sites with magnetic moment $$S=3/2$$ to $$s=1$$ to $$S=3/2$$ and so on) and those systems tend to be called mixed-spin ferromagnets even though they will have unequal magnetization in the fully polarized case.