Observation of spin-wave characteristics in the two-dimensional ferromagnetic ordering of in-plane spins

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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(βT) 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.