Sensory-organ-like response determines the magnetism of zigzag-edged honeycomb nanoribbons

Abstract

We present an analytical theory for the magnetic phase diagram for zigzag edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter U . We show that the edge magnetic moment varies as ln U and uncover its dependence on the width W of the ribbon. The physics of this owes its origin to the sensory organ like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first order magnetic transition from an anti-parallel orientation of the moments on opposite edges to a parallel orientation occurs upon doping with holes or electrons. The critical doping for this transition is shown to depend inversely on the width of the ribbon. Using variational Monte-Carlo calculations, we show that magnetism is robust to fluctuations. Additionally, we show that the magnetic phase diagram is generic to zigzag edge terminated nanostructures such as nanodots. Furthermore, we perform first principles modeling to show how such magnetic transitions can be realized in substituted graphene nanoribbons.PACS numbers: 73.22.Pr Interest and activity in magnetic nanostructures has been driven by their possible application in nanoelectronic/spintronic devices, with graphene based systems grabbing a significant fraction of the attention. Magnetism at the zigzag terminated edges of graphene has been studied by first principles calculations [11,12], and by a simplified effective Hubbard model [13][14][15][16][17][18][19] described by a hopping parameter t and a site-local repulsion U . Ref. 15 showed that the magnetism in graphene is robust to "shape disorder" of the nanostructure, while ref. 17 studied finite width graphene nanoribbons including the effects of doping. There are also studies of defect induced magnetism [20,21] and of magnetism of other nanostructures [14,22]. There are encouraging recent experimental signatures of magnetism [23][24][25], along with suggestions [26] that extraneous effects such as reconstruction would render the magnetism fragile.The origin of magnetic moment in zigzag edge terminated honeycomb nanostructures has been attributed to the edge states[2, 27, 28] -localized electronic states which have most weight at the edges and die exponentially in the bulk. [29][30][31] These states are of topological origin [32] and have been experimentally observed using scanning tunneling microscopy. [33,34] Magnetism at the edges is attributed to the Stoner mechanism(see, e.g., [35]) and is best discussed in terms of a Landau theory.[35] The ground state energy of the system is expressed aswhere M is the magnetic order parameter, a, b > 0 are positive constants that depend on the microscopics, and U c is a critical value of the on-site repulsion. For U < U c , the energy is minimum when M = 0, i. e., system is non-magnetic. At U = U c , there is a quantum phase transition to the magnetic state, and for U > U c one finds |M | ∼ √ U − U c . Stoner theory [36], based on linear response...

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