However, in complete contrast to this, reducing the width of scattering region results in the disappearance of plateau-like conductance spectra. This can be correlated to reduced efficiency of transmission eigenchannels to conduct the electrons, when the width of scattering region is smaller than the width of electrodes. However, in pristine GNR, due to absence of any back-scattering events, eigenchannels are fully conductive and yields plateau-like transmission with full efficiency. Thus, to further explicate the spin-polarized transmission with the reducing width, we employed ZGNRs in their low-lying ferromagnetic state. Table illustrates the evolution of energy difference between AFM and FM states with the reducing width of ZGNRH. On moving from 12ZGNRH to 4ZGNRH, the energy difference between AFM and FM states increases, while the smallest energy difference of 0.046 eV is observed for 2ZGNRH which represents a pentacene molecule connected between two ZGNR electrodes. We speculate that the increase in ∆E F M -AF M upon reducing width of ZGNR is related to the increase in spin-spin interactions between the magnetic moments localized on two opposite edges, as the distance between the edges is decreased from 12ZGNRH to 4ZGNRH. Further, the smallest energy difference for 2ZGNRH is also in correspondence to the smallest magnetic moment of 0.004 µ B on edge C-atoms of 2ZGNRH (tabulated in Table ). It is worthwhile to mention that although the energy difference is increasing upon reducing width of ZGNR, but it is still small enough to transform an AFM state to FM state under the application of external magnetic field or in presence of magnetic substrate. Apart from the energy difference, the change in average magnetic moment on the edge C-atoms of the electrode and scattering region with the reducing width is also tabulated in Table . It reveals a slight increase in average magnetic moment on the edge C-atoms of the electrode upon reducing width, on the other hand, a decrease is observed for edge C-atoms of the scattering region. For the case of 2ZGNRH, although molecular pentacene is non-magnetic in nature, The corresponding spin-polarized transmission spectra for the series of FM based ZGNRH models with reducing width is shown Figure . As discussed in the previous section, pristine 12ZGNRH shows a plateau of 3 e 2 /h in the energy range (-0.60 eV , -0.20 eV ), which reduces to ∼ 2 e 2 /h for 8ZGNRH and 10ZGNRH. This is accompanied by a simultaneous decrease in the plateau width and destruction of conductance plateaus to a certain degree in such a way that 8ZGNRH yields a linear transmission due to absence of any strongly localised states between (-1.80 eV , -0.80 eV ) and (0.80 eV , 1.80 eV ). Upon further reducing the width, conductance plateaus are strongly suppressed, and the conductance magnitude decreases such that 6, 4 and 2ZGNRH, yields a maximum transmission of one in the same energy range below Fermi level. This indicates that the number of effectively conductive eigenchennels decreases upon decreasing the width of ZGNRs. More interestingly, as the width of ZGNR is reduced, plateau-like conductance completely disappears and transmission spectra starts emerging in the form of narrow peaks.