  We investigate the connection between highly frustrated kagome based
Hamiltonians and a recently synthesized family of materials containing Ti3+
S=1/2 ions. Employing a combination of all electron density functional theory
and numerical diagonalization techniques, we establish the Heisenberg
Hamiltonians for the distorted kagome antiferromagnets Rb2NaTi3F12, Cs2NaTi3F12
and Cs2KTi3F12. We determine magnetization curves in excellent agreement with
experimental observations. Our calculations successfully clarify the
relationship between the experimental observations and the
magnetization-plateau behavior at 1/3 height of the saturation and predict
characteristic behaviors under fields that are higher than the experimentally
measured region. We demonstrate that the studied Ti(III) family of materials
interpolates between kagome strip and kagome lattice.
