  Thin ferromagnetic elements in the form of rectangular prisms are
theoretically investigated in order to study the transition from single-domain
to two-domain state, with changing the in-plane aspect ratio p. We address two
main questions: first, how general is the transition; second, how the critical
value p_c depends on the physical parameters. We use two complementary methods:
discrete-lattice calculations and a micromagnetic continuum approach. Ultrathin
films do not appear to split in two domains. Instead, thicker films may undergo
the above transition. We have used the continuum approach to analyze recent
Magnetic Force Microscopy observations in 30 nm-thick patterned Permalloy
elements, finding a good agreement for p_c.
