  The AR$_2$O$_4$ family (R = rare earth) have recently been attracting
interest as a new series of frustrated magnets, with the magnetic R atoms
forming zigzag chains running along the $c$-axis. We have investigated
polycrystalline BaNd$_2$O$_4$ with a combination of magnetization, heat
capacity, and neutron powder diffraction (NPD) measurements. Magnetic Bragg
peaks are observed below $T_N$ $=$ 1.7 K, and they can be indexed with a
propagation vector of $\vec{k}$ $=$ (0 1/2 1/2). The signal from magnetic
diffraction is well described by long-range ordering from only one of the two
types of Nd zigzag chains, with collinear up-up-down-down intrachain spin
configurations. Furthermore, low temperature magnetization and heat capacity
measurements reveal two field-induced spin transitions at 2.5 T and 4 T for $T$
$=$ 0.46 K. The high field phase is paramagnetic, while the intermediate field
state may arise from a spin transition of the long-range ordered Nd chains,
resulting in an up-up-down intrachain spin configuration. The proposed
intermediate field state is consistent with the magnetic structure determined
in zero field for these chains by NPD, as both phases are predicted for the
classical Ising chain model with nearest neighbor and next nearest neighbor
interactions.
