  The properties of two molecular-based magnetic helices, composed of 3$d$
metal Co and Mn ions bridged by Nitronyl Nitroxide radicals, are investigated
by density functional calculations. Their peculiar and distinctive magnetic
behavior is here elucidated by a thorough description of their magnetic,
electronic, and anisotropy properties. Metal ions are antiferromagnetically
coupled with the radicals, leading to a ferrimagnetically ordered ground state.
A strong metal-radical exchange coupling is found, about 44 meV and 48 meV for
Co- and Mn-helices, respectively. The latter have also relevant
next-nearest-neighbor Mn-Mn antiferromagnetic interactions (of $\sim$ 6 meV).
Co-sites are characterized by non-collinear uniaxial anisotropies, whereas
Mn-sites are rather isotropic. A key result pertains to the Co-helix: the
microscopic picture resulting from density-functional calculations allows us to
propose a spin Hamiltonian of increased complexity with respect to the commonly
employed Ising Hamiltonian, suitable for the study of finite-temperature
behavior, and that seems to clarify the puzzling scenario of multiple
characteristic energy scales observed in experiments.
