  The chain-like system Ba_{3}Cu_{3}Sc_4O_{12} has potentially interesting
magnetic properties due to the presence of Cu^{2+} and a structure-suggested
low-dimensionality. We present magnetization M versus magnetic field H and
temperature T, T- and H-dependent heat-capacity C_{p}, ^{45}Sc nuclear magnetic
resonance (NMR), muon spin rotation ({\mu}SR), neutron diffraction measurements
and electronic structure calculations for Ba_{3}Cu_{3}Sc_{4}O_{12}. The onset
of magnetic long-range antiferromagnetic order at T_{N} ~16 K is consistently
evidenced from the whole gamut of our data. A significant sensitivity of T_{N}
to the applied magnetic field H (T_{N}~0 K for H=70 kOe) is also reported.
Coupled with a ferromagnetic Curie-Weiss temperature ({\theta}_{CW}~65 K) in
the susceptibility (from a 100 K-300 K fit), it is indicative of competing
ferromagnetic and antiferromagnetic interactions. These indications are
corroborated by our density functional theory based electronic structure
calculations where we find the presence of significant ferromagnetic couplings
between some copper ions whereas AF couplings were present between some others.
Our experimental data, backed by our theoretical calculations, rule out
one-dimensional magnetic behaviour suggested by the structure and the observed
long-range order is due to the presence of non-negligible magnetic interactions
between adjacent as well as next-nearest chains.
