  The role of dipolar interactions and anisotropy are important to obtain,
otherwise forbidden, ferromagnetic ordering at finite temperature for ions
arranged in two-dimensional (2D) arrays (monolayers). Here we demonstrate that
conventional low temperature magnetometry and polarized neutron scattering
measurements can be performed to study ferromagnetic ordering of in-plane spins
in 2D systems using a multilayer stack of non-interacting monolayers of
gadolinium ions. The spontaneous magnetization is absent in the heterogenous
magnetic phase observed here and the saturation value of the net magnetization
was found to depend on the applied magnetic field. The net magnetization rises
exponentially with lowering temperature and then reaches saturation following a
$T\ln(\beta T)$ dependence. These findings verify predictions of the spin-wave
theory of 2D in-plane spin system with ferromagnetic interaction and will
initiate further theoretical development.
