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

The title compounds have dominant ferromagnetic exchange interactions within one-dimensional (1D) half-twist ladders of s = 1/2 Cu(2+) ions and antiferromagnetic (AFM) interactions between ladders, leading to ordered 3D phases at temperatures below 20 K. Here we show that a microscopic 1D model of the paramagnetic (PM) phase combined with a phenomenological model based on sublattice magnetization describes the observed temperature and field dependent magnetism. The model identifies AFM, spin-flop and PM phases whose boundaries have sharp features in the experimental magnetization M(T,H) and specific heat C(P)(T,H). Exact diagonalization of the 1D model, possible for 24 spins due to special structural features of half-twist ladders, yields the magnetization and spin susceptibility of the PM phase. AFM interactions between ladders are included at the mean-field level using the field, H(AF), obtained from modelling the ordered phases. Isotropic exchange J1 =- 135 K and g-tensor g = 2.1 within ladders, plus exchange and anisotropy fields H(AF) and H(A), describe the ordered phases and are almost quantitative for the PM phase.