  Motivated by the recent experimental observation of multi-component spinor
condensates via a time-dependent quadrupole-Ioffe-configuration trap (QUIC
trap), we provide a general framework for the investigation of nonadiabatic
Landau-Zener dynamics of a hyperfine spin, e.g., from an atomic magnetic dipole
moment coupled to a weak time-dependent magnetic (B-) field. The spin flipped
population distribution, or the so-called Majorona formula is expressed in
terms of system parameters and experimental observables; thus, provides much
needed insight into the underlying mechanism for the production of spinor
condensates due to nonadiabatic level crossings.
