Effect of dimensionality on transition-metal elements of groups 3-7

We report theoretically on the effect of dimensionality on elementary low-dimensional systems of transition metals of groups 3-7 (Sc, Y; Ti, Zr, Hf; V, Nb, Ta; Cr, Mo, W; Mn, Tc, Re). This work completes the exploration on elementary low-dimensional systems of all transition metals, those of groups 8 to 12 being reported earlier. In contrast to the elementary low-dimensional systems of late transition metals, magnetic moment per atom (μ) predicted for some cases of early transition metals is very large. An interesting trend is observed for magnetic ordering as we go from group 3 to 7. The elementary low-dimensional systems of groups 3 and 4 prefer ferromagnetic ordering, with only Hf preferring to stay nonmagnetic as in bulk. Antiferromagnetic ordering is preferred by elementary low-dimensional systems of transition metals of groups 5 to 7. The maximum μ for ferromagnetic elementary low-dimensional systems ( 1.8μ_B for Sc linear chains) is much smaller than that for antiferromagnetic systems ( ∼3.4μ_B for linear chains of Cr and Mn). The antiferromagnetic ordering in two-dimensional systems is invariably accompanied by lattice expansion with respect to bulk. Our results are in accordance with available experimental and theoretical results. Magnetic linear chains of Sc, Ti, Zr (ferromagnetic in nature), and Cr, Re (antiferromagnetic in nature) are predicted to offer relative ease of formation experimentally and could be useful from an application point of view.