Spin configurations of π electrons in quasi-one-dimensional organic ferromagnets

Abstract

Based on a theoretical model proposed for quasi-one-dimensional organic polymer ferromagnets, the spin configuration of vr electrons in a~-conjugated carbon chain with a single and two side radicals, which contains unpaired electrons, is investigated.The strong electron-phonon interaction and electron-electron interaction in the one-dimensional system are taken into account self-consistently. It is found that around the unpaired electrons there appears a~-electron spin-polarization cloud with alternation of the sign and the amplitude of the spin density extending over a certain distance, which reduces rapidly with the increasing of electron-phonon coupling. In order to obtain ferromagnetic order in this kind of material, the number of carbon atoms, which is intermittent between two neighbor side radicals, should be odd. It is shown that the~-orbital alternation will result in a Peierls transition which stabilizes the magnetic order.

CDW Transition and Instability in Interchain Coupled Organic Ferromagnets with Next-Nearest Neighboring Hopping Interaction

“…In our calculation of the ferromagnetic order in the system we assume that the unpaired electrons at side radicals have up-spins (positive-spin). When the energy gap exists, the up-spin electrons and down-spin electrons occupying the energy levels have the same number, all the pelectrons along each main chain form an antiferromagnetic SDW while the unpaired electrons of side radicals form ferromagnetic order [13,14]. However, when the nextnearest neighboring hopping interaction exceeds the critical value, the energy gap disappears owing to the splitting of energy levels with respect to different spins and more electrons occupy the lower down-spin energy levels than the higher up-spin energy Fig.…”

“…They treated the p-electrons along the main carbon chain as an antiferromagnetic spin chain and assumed that there is an antiferromagnetic correlation between the p-electron spin and the residual spin of side radical. Recently, Fang et al [13,14] proposed a theoretical model to describe this kind of organic ferromagnet. They considered the itinerary of p-electrons, the Hubbard electron±electron correlation and the antiferromagnetic spin correlation between the p-electron and unpaired electron at side radicals.…”

Stability of Interchain Coupled Organic Ferromagnets with Non-Nearest Neighbor Hopping Interactions

“…(8) to (11) self-consistently. The starting geometry in the iterative optimization process is usually the one with y jl 0 and hn jila i hn jilb i 1=2, and by substituting them into Eqs.…”

“…The main chain consists of carbon atoms each with a p electron and R represents a kind of side radicals containing an unpaired electron. Recently, Fang et al [10,11] proposed a theoretical model to describe this kind of quasi-one-dimensional organic ferromagnets. They considered the itineracy of p electrons and strong electron±electron correlation.…”

Peierls-Extended Hubbard Model Study on an Organic- Inorganic Bipartite Lozenge Ferrimagnetic Chain

“…Figure 1a shows one example of an organic conjugated polymer ferromagnet to possess aligned spins due to the presence of molecular radicals R [7]. In a series of papers Yao et al [8][9][10] proposed a theoretical model, and studied the structure of poly-BIPO in Fig. 1a.…”