Microscopic study of interlayer magnetic coupling across the interface in antiferromagnetic bilayers

The enhancement of Neel temperature ($T_N$) of low-$T_{N}$ antiferromagnets in antiferromagnetic bilayers AF1/AF2, where the $T_N$ of AF1 is larger than AF2 (for example enhancement of $T_{N}$ of CoO in CoO/NiO or FeO in FeO/CoO), is a subject of considerable interest. One essential question needs to be answered in these bilayers: is the interfacial coupling a short-range one or long-range that mediates the effect of the AF1 layers on the magnetic properties of AF2 layer? To understand the systematics of the magnetic coupling across the interface, we investigate the plane-resolved magnetotransport properties of antiferromagnetic bilayers using an electron-hole symmetric one-band Hubbard model at half-filling, employing a semi-classical Monte Carlo method. In our model Hamiltonian calculations, we set Coulomb repulsion $U_{1} = 8$ to mimic high-$T_{N}$ AF1 layer, whereas we use $U_{2}$ = $2\times U_{1}$ to mimic the low-$T_{N}$ AF2 layer. Our calculations show that the $T_{N}$ of the low-$T_{N}$ antiferromagnet enhances substantially when it's thickness is small, similar to experiments, giving rise to single magnetic transition temperature of the bilayer system. These findings are well supported by a single peak in temperature-dependent specific heat. However, for larger thicknesses, the $T_{N}$ of the low-$T_{N}$ antiferromagnet approaches towards its bulk value and constituent antiferromagnetic layers align antiferromagnetically at two separate temperatures and two maxima are observed in specific heat data. Our calculations also show that the delocalization of moments is more or less confined near the interface indicating the short-ranged nature of the proximity effect. Our obtained results are consistent with the experimental observations. A detailed discussion of the modifications that will occur if we use $U_{1} = 8$ and $U_{2}$ = $0.5\times U_{1}$ will also be addressed.