Generalization of polarized spin excitations for asymmetric dimeric systems

Through the use of Heisenberg spin-spin interactions, we provide analytical representations for inelastic neutron scattering eigenstates and excitation cross-sections of the general $S_1$-$S_2$ spin dimeric systems. Using an exact diagonalization approach to the spin Hamiltonian, we analyze various spin coefficients to provide general representations for the neutron scattering cross-sections of two interacting spins. We also detail a generalized method for the determination of $S_z$ polarized excitations, which provide an approximation for the excitations within an applied $z$-axis magnetic field. These calculations provide a general understanding of the interactions between two individual or compound spin systems, which can help provide insight into condensed matter systems like molecular magnets, quantum dots, and spintronic systems, as well as particle physics investigations into quark matter and meson interactions.