  The spin structure of wave functions is reflected in the magnetic structure
of the one-particle density matrix. Indeed, for single determinants we can use
either one to determine the other. In this work we discuss how one can simply
examine the one-particle density matrix to faithfully determine whether the
spin magnetization density vector field is collinear, coplanar, or noncoplanar.
For single determinants, this test suffices to distinguish collinear
determinants which are eigenfunctions of $\hat{S}_{\hat{n}}$ from noncollinear
determinants which are not. We also point out the close relationship between
noncoplanar magnetism on the one hand and complex conjugation symmetry breaking
on the other. Finally, we use these ideas to classify the various ways single
determinant wave functions break and respect symmetries of the Hamiltonian in
terms of their one-particle density matrix.
