Field induced multiple order-by-disorder state selection in antiferromagnetic honeycomb bilayer lattice

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In this paper we present a detailed study of the antiferromagnetic classical Heisenberg model on a bilayer honeycomb lattice in a highly frustrated regime in presence of a magnetic field. This study shows strong evidence of entropic order-by-disorder selection in different sectors of the magnetization curve. For antiferromagnetic couplings J₁=Jₓ=Jₚ/3, we find that at low temperatures there are two different regions in the magnetization curve selected by this mechanism with different number of soft and zero modes. These regions present broken Z₂ symmetry and are separated by a not fully collinear classical plateau at M=1/2. At higher temperatures, there is a crossover from the conventional paramagnet to a cooperative magnet. Finally, we also discuss the low temperature behavior of the system for a less frustrated region, J₁=Jₓ<Jₚ/3.