  Recently, based on the refined crystal structure of Pr0.6Ca0.4MnO3 from
neutron diffraction, Daoud-Aladine et al.[PRL89,97205(2002)] have proposed a
new ground state structure for the half-doped manganites R0.5Ca0.5MnO3, where R
is a trivalent ion like Bi,La,Pr,Sm or Y. Their proposal describes the CE
magnetic structure attributed to these materials as an arrangement of dimers
along the ferromagnetic Mn zig-zag chains that form it. However, the dimers'
proposal is in conflict with the Goodenough-Kanamori-Anderson rules, which give
a coherent description of many transition metal insulating compounds and
predict the coexistence of Mn3+ and Mn4+ ions in equal parts in the half-doped
manganites. On the other hand, Rivadulla et al.[PRB 66, 174432 (2002)] have
studied several single crystal samples of half-doped manganites and propose a
phase diagram in terms of the tolerance factor which contains both types of
structures. In the present work we have calculated the magnon dispersion
relations for the CE magnetic structure, arising for each type of proposal: the
charge ordered and the dimer phases, respectively. We consider a
three-dimensional unit cell containing 16 spins, and compare the magnetic
excitations along different paths in the first Brillouin zone. We conclude that
measurement of the magnon dispersion relations should allow a clear distinction
between the two proposals, predicting qualitative differences arising along
specific directions of propagation in the first Brillouin zone.
