Spin-wave analysis of the ferromagnetic-ferromagnetic Heisenberg spin bilayer with intralayer single-ion anisotropy and interlayer antiferromagnetic interaction

In this paper, the spin wave theory is applied to the Heisenberg spin bilayer with intralayer ferromagnetic interaction [Formula: see text], intralayer single-ion anisotropy D and interlayer antiferromagnetic interaction [Formula: see text]. It is found that the effects of both D and [Formula: see text] on the thermodynamic quantities give rise to the two different low-temperature asymptotic behaviors with and without exponential law. For [Formula: see text], the interlayer antiferromagnetic interaction can induce the appearance of the maximum of the layer magnetization at finite temperatures. At the location of the layer magnetization maximum, the approximate behaviors (such as the power, linear, rational, exponential and logarithmic laws) which are driven by the temperature or the anisotropy, are obtained for the low-temperature thermodynamic properties. It is shown that the presence of antiferromagnetic interlayer interaction [Formula: see text] clearly induces more quantum fluctuations than the case where the interlayer interaction [Formula: see text] is ferromagnetic. Our results of the layer magnetization agree with the experimental data of the layered van der Waals crystal FeCl 2 at low temperatures. In the monolayer case of [Formula: see text], our results are in agreement with the findings obtained by the existing theories and the quantum Monte Carlo data.