  Square-lattice systems offer a direct route for realizing 2D quantum
magnetism with frustration induced by competing interactions. In this work, the
square-lattice materials YbBi2IO4 and YbBi2ClO4 were investigated using a
combination of magnetization and specific heat measurements on polycrystalline
samples. Specific heat measurements provide evidence for long-range magnetic
order below TN = 0.21 K (0.25 K) for YbBi2IO4 (YbBi2ClO4). On the other hand, a
rather broad maximum is found in the temperature-dependent magnetic
susceptibility, located at Tmax = 0.33 K (0.38 K) in YbBi2IO4 (YbBi2ClO4),
consistent with the quasi-2D magnetism expected for the large separation
between the magnetic layers. Estimation of the magnetic entropy supports the
expected Kramers' doublet ground state for Yb3+ and the observed paramagnetic
behavior is consistent with a well-isolated doublet. Roughly two-thirds of the
entropy is consumed above TN, due to a combination of the quasi-2D behavior and
magnetic frustration. The impact of frustration is examined from the viewpoint
of a simplified J1-J2 square lattice model, which is frustrated for
antiferromagnetic interactions. Specifically, a high-temperature series
expansion analysis of the temperature-dependent specific heat and magnetization
data yields J2/J1 = 0.30 (0.23) for YbBi2IO4 (YbBi2ClO4). This simplified
analysis suggests strong frustration that should promote significant quantum
fluctuations in these compounds, and thus motivates future work on the static
and dynamic magnetic properties of these materials.
