Potential-tuned magnetic switches and half-metallicity transition in zigzag graphene nanoribbons

TL;DR

This paper addresses how to induce and control ferromagnetism in carbon-based nanostructures by applying a potential drop to zigzag graphene nanoribbons (ZGNRs). It combines first-principles density functional theory with extended/simple-pi-orbital Hubbard models to show that potential drops stabilize ferromagnetic domains between inter-chain sites in the bulk when the nominal Van Hove filling is crossed, with a parallel mechanism in the tight-binding picture. The authors report a robust half-metallicity transition within the same magnetic state, where a spin-channel gap closes and reopens as $V$ is tuned, and even reverses which spin channel is metallic in wide ribbons. The results offer a route to manipulate spin in graphene nanostructures via gating or substrate engineering, with robustness against ribbon width, potential profile, and interaction strength, enabling potential room-temperature spintronic applications.

Abstract

Realizing controllable room-temperature ferromagnetism in carbon-based materials is one of recent prospects. The magnetism in graphene nanostructures reported previously is mostly formed near the vacancies, zigzag edges, or impurities by breaking the local sublattice imbalance, though a bulk chiral spin-density-wave ground state is also reported at van Hove filling due to its perfectly nested Fermi surface. Here, combining of the first-principles and tight-binding model simulations, we predict a robust ferromagnetic domain lies between the inter-chain carbon atoms inside the zigzag graphene nanoribbons by applying a potential drop. We show that the effective zigzag edges provide the strong correlation background through narrowing the band width, while the internal Van Hove filling provides the strong ferromagnetic background inherited from the bulk. The induced ferromagnetism exhibit interesting switching effect when the nominal Van Hove filling crosses the intra- and inter-chain region by tuning the potential drops. We further observe a robust half-metallicity transition from one spin channel to another within the same magnetic phase. These novel properties provide promising ways to manipulate the spin degree of freedom in graphene nanostructures.

Figures (15)

• Figure 1: (a) Schematic $15$-ZGNR in potential field. Upper panel: $15$-ZGNR with a fixed potential drop along the $x$-direction. The ferromagnetic domains in the $2^{\text{nd}}$ inter-chain state is highlighted (blue and red symbols). Low panel: the schematic potential field, $\alpha=0$ for homogeneous potential field, and $\alpha=15$ for the strongly attenuated potential field. (b) Distribution of magnetism in the $i^{\text{th}}$ inter-chain state simulated by the first-principles calculations, from top to bottom, $\Delta=0.6$, $1.4$, and$1.56$, respectively the isosurface value of the spin-polarized electron density is $0.003$$e$/Å$^{3}$, blue and red for spin-down and spin up, respectively. (c) Static spin susceptibility in respective channels in the non-interacting system, left for the $4^{\text{th}}$ inter-chain state with $V=12.5$ eV and right for the $4^{\text{th}}$ intra-chain state with $V=11.5$ eV. From top to bottom, data are the AB ($\chi_{A_{i}B_{i}}$), and BA ($\chi_{B_{i}A_{i+1}}$) channels, respectively. (d) Magnetic phase diagram in the potential-tuned $15$-ZGNR simulated by first-principles calculations, and (e) similar magnetic phase diagram simulated by the extend-$\pi$-orbital Hubbard model. (f) Width-potential ($N-V$) magnetic phase diagram simulated by the simple-$\pi$-orbital Hubbard model. The magnitude of magnetization shown here is the summation over the half-width ribbon (left) with $M_{t}=\sum_{i\in\text{left}}M_{i}$. The homogeneous potential drops ($\alpha=0)$ is assumed in all figures.
• Figure 2: (a) and (b), potential-tuned density of states, simulated by the first-principles calculations and the extend $\pi$-orbital Hubbard model. Here, the density of states is summed over a near Fermi energy interval $[-40,40]$ meV, integrated near the $k_{y}=\pi$ region ($k_{y}\in[\pi/2,3\pi/2]$). The $i^{\text{th}}$ inter-chain state (gray region) is highlighted by the colored notation, which corresponds to the colored region shown in (c) and (d). (c) and (d) are the charge distribution of respective sites simulated by the extend $\pi$-orbital and simplified $\pi$-orbital Hubbard model, respectively. From left to right are $A_{1}$ to $A_{6}$ (solid lines) and $B_{1}$ to $B_{5}$ (dash lines) in the lower panels, and the corresponding counterparts in upper panels. The color-shaded region highlights the inter-chain carbon sites ($1^{\text{st}}$ to $5^{\text{th}}$ from left to right). The dotted lines show the Van Hove filling of the bulk graphene. The homogeneous potential drops $(\alpha=0)$ are adoped in (a)-(d). (e)-(f) are the two typical low energy band structure for the $2^{\text{nd}}$ intra-chain state ($V=16.2$ eV) and the $2^{\text{nd}}$ inter-chain state ($V=21.3$ eV) in the normal state of $15$-ZGNR with strongly decayed potential ($\alpha=10$), respectively. Two inserts in each panel are the weight of the lowest valence and highest conduction bands highlighted in left panels, and the density of states contributed from the respective sites, as well as the total density of state. Here, the simplified $\pi$-orbital model is adopted for simplicity.
• Figure 3: (a) and (d) Spin resolved density of states simulated by the first-principles calcualtion and the extend $\pi$-orbital Hubbard model. Here, the density of states is an integration over $k_{y}\in[\pi/2, 3\pi/2]$ region. In (a), the upper panel is for the $2^{\text{nd}}$ intra-chain state ($\Delta=0.72$), and the lower two panels are for the $3^{\text{rd}}$ inter-chain state ($\Delta=0.8$ and $\Delta=1.0$). In (b), the top panel, and bottom panel in (b) is in the $2^{\text{nd}}$ intra-chain, and $3^{\text{rd}}$ intra-chain states, while the three middle panels are in the $2^{\text{nd}}$ inter-chain state, respectively. (c) The band gap (excluding the Dirac points) for respective spin channel simulated by the simple-$\pi$-orbital model in the $30$-ZGNR. The color region is the $2^{\text{nd}}$ inter-chain state. The gray circles is the magnetization summed over the half-width ribbon. Here, strong decay ratio $\alpha=15$ is assumed.
• Figure S1: Results in low potential drop of $15$-ZGNR in the framework of simple-$\pi$-orbital model simulations. From left to right panels are the charge density, magnetization, low-energy dispersion (only three lowest conducting and three highest valence bands are included), and the density of states, respectively. From top to bottom, the selected potential drop is $V=0$ eV, $V=0.81$ eV, and $V=1.6$ eV, respectively. The homogeneous potential drop ($\alpha=0$) is assumed.
• Figure S2: Evolution of the bandgap for spin-up and spin-down channel in low potential drops, simulated by the simple-$\pi$-orbital Hubbard model.