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The title compounds have dominant ferromagnetic (FM) exchange interactionswithin one-dimensional (1D) half-twist ladders of s =1/2 Cu2^{+} ions andantiferromagnetic(AFM) interactions between ladders, leading to ordered 3Dphases at temperatures below 20K. Here we show that a microscopic 1D model ofthe paramagnetic (PM) phase combined with a phenomenological model based onsublattice magnetization describes the observed temperature and field dependentmagnetism. The model identifies AFM, spin-flop (SF) and PM phases whoseboundaries have sharp features in the experimental magnetization M(T,H) andspecific heat CP(T,H). Exact diagonalization (ED) of the 1D model, possible for24 spins due to special structural features of half-twist ladders, yields themagnetization and spin susceptibility of the PM phase. AFM interactions betweenladders are included at the mean-field level using the field, HAF, obtainedfrom modeling the ordered phases. Isotropic exchange J1 = -135K and g-tensor g= 2.1 within ladders, plus exchange and anisotropy fields HAF and HA, describethe ordered phases, and are almost quantitative for the PM phase.

Spin-flop and antiferromagnetic phases of the ferromagnetic half-twist ladder compounds Ba3Cu3In4O12 and Ba3Cu3Sc4O12