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The paper presents a computational study of the ground-state properties of aquantum nanomagnet possessing the shape of a finite two-legged ladder composedof 12 spins $S=1/2$. The system is described with isotropic quantum Heisenbergmodel with nearest-neighbour interleg and intraleg interactions supplementedwith diagonal interleg coupling between next nearest neighbours. All thecouplings can take arbitrary values. The description of the ground state isbased on the exact numerical diagonalization of the Hamiltonian. Theground-state phase diagram is constructed and analysed as a function of theinteractions and the external magnetic field. The ground-state energy andspin-spin correlations are extensively discussed. The cases of ferro- andantiferromagnetic couplings are compared and contrasted.

Ground-state magnetic properties of spin ladder-shaped quantum nanomagnet: Exact diagonalization study