  The magnetic properties of polycrystalline samples of Ba3Cu3In4O12 (In-334)
and Ba3Cu3Sc4O12 (Sc-334) are reported. Both 334 phases have a structure
derived from perovskite, with CuO4 squares interconnected to form half-twist
ladders along the c-axis. The Cu-O-Cu angles, ~ 90o, and the positive Weiss
temperatures indicate the presence of significant ferromagnetic (FM)
interactions along the Cu ladders. At low temperatures, T < 20 K, sharp
transitions in the magnetic susceptibility and heat capacity measurements
indicate three-dimensional (3D) antiferromagnetic (AFM) ordering at TN. TN is
suppressed on application of a field and a complex magnetic phase diagram with
three distinct magnetic regimes below the upper critical field can be inferred
from our measurements. The magnetic interactions are discussed in relation to a
modified spin-1/2 FM-AFM model and the 334 half-twist ladder is compared to
other 2-rung ladder spin-1/2 systems.
