Spin excitations used to uncover the nature of the magnetically ordered ground state of Pr0.5Ca0.5MnO3

We have used time-of-flight inelastic neutron scattering to measure the spin wave spectrum of the canonical half-doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$, in its magnetic and orbitally ordered phase. Comparison of the data, which cover multiple Brillouin zones and the entire energy range of the excitations, with several different models shows that only the CE-type ordered state provides an adequate description of the magnetic ground state, provided interactions beyond nearest neighbor are included. We are able to rule out a ground state in which there exist pairs of dimerized spins which interact only with their nearest neighbors. The Zener polaron ground state, which comprises strongly bound magnetic dimers, can be ruled out on the basis of gross features of the observed spin wave spectrum. A model with weaker dimerization reproduces the observed dispersion but can be ruled out on the basis of subtle discrepancies between the calculated and observed structure factors at certain positions in reciprocal space. Adding further neighbor interactions results in almost no dimerization, i.e. interpolating back to the CE model. These results are consistent with theoretical analysis of the degenerate double exchange model for half-doping.