Spin heptamer excitations in the pyrochlore antiferromagnets MgCr₂O₄

In this study, we examine the spin heptamer excitations for the S = 3/2 systems of ACr2O4 (A=Mg, Zn). Using a Heisenberg spin-spin exchange Hamiltonian, we determined the exact representation for the energy eigenstates and inelastic neutron scattering structure factors for the S = 3/2 heptamer. The functional forms of inelastic neutron structure factors were calculated through an examination of the S = 1/2 heptamer. Since the individual structure factors are dependent on the excited sub-geometry of the cluster, not the total spin of the ions, the functional forms of the S = 3/2 excitations can be mapped on to similar S = 1/2 excitations. The mapping helps to reduce the fundamental basis set and allows one to calculate the closed form solutions. Therefore, we are able to clarify that the spin excitations of this pyrochlore antiferromagnet resemble discrete transitions of a spin heptamer.