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Layered frustrated antiferromagnetic Heisenberg spin model: role of inplane frustration and interlayer coupling

We present an exact diagonalization study on layered $J_{1}-J_{2}$ antiferromagnetic Heisenberg spin model to examine the role of frustration induced by inplane next-nearest neighbor coupling $J_{2}$, in presence of interlayer antiferromagnetic coupling $J_{\perp}$. A finite lattice of 24 spins in layered geometry of $(4\times 3)\oplus (4\times 3)$ is considered and the resulting Hamiltonian matrix diagonalized using Davidson iterative algorithm to obtain the ground and a few low-lying excited states. The lattice size ($24$ spins with Hilbert space dimensionality of $2704156$ in $S_{z}^{tot}=0$ subspace) has been kept relatively small because of the large number of runs required to sample $J_{1}-J_{2}-J_{\perp}$ parameter space. Quantities like spin-gap, Shannon entropy, spin-spin correlation, static spin structure-factor, magnetic specific-heat and magnetic susceptibility are calculated for various values of spin-spin coupling parameters. With increase in interlayer coupling, the system is driven to states with long range order and the interval of quantum paramagnetically disordered state, sandwiched between Néel and collinear ordered states, narrows on the scale of inplane frustration parameter.