Ordering phenomena in a heterostructure of frustrated and unfrustrated triangular-lattice Ising layers

We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling $J_{\rm A}$ and the ferromagnetic (FM) one $J_{\rm B}$ for the respective layers, which are coupled by the interlayer interaction $J_{\rm AB}$ by using Monte Carlo simulations. When $J_{\rm A}$ and $J_{\rm B}$ are of the same order, the unfrustrated FM plane orders first at a high temperature $T_{c1} \sim J_{\rm B}$. The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below $T_{c2}$. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-like pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in $\propto \JA / T$ is controlled by a line of Gaussian fixed points at $T = 0$. In the crossover region, a continuous variation in the effective critical exponent $4/9 \lesssim \eta^{\rm eff} \lesssim 1/2$ is observed. The phase diagram by changing the ratio $J_{\rm A}/J_{\rm B}$ is also investigated.