Magnetism and magnetotransport in disordered graphene

We perform Monte Carlo simulations to study the interplay of structural and magnetic order in single layer graphene covered with magnetic adatoms. We propose that the presence of ripples in the graphene structure can lead to clustering of the adatoms and to a variety of magnetic states such as superparamagnetism, antiferromagnetism, ferromagnetism and spin-glass behavior. We derive the magnetization hysteresis and also the magnetoresistance curves in the variable range hopping regime, which can provide experimental signatures for ripple induced clustering and magnetism. We propose that the magnetic states in graphene can be controlled by gate voltage and coverage fraction.

Figure 1

(Color online) (a) Graphene sheet with random ripples. The color map represents the height increasing from blue to red in the interval $z∊\left[-z_{max},z_{max}\right]$. (b) and (c) graphene sheet covered with adatoms for a lower cutoff $h_0=0.28z_{max}$ and $h_0=0$ respectively (see main text). (d) Zoom in showing the adatoms on top of a hill (red rectangle).

Figure 2

(Color online) Spin configuration on top of a hill for (a) homogeneous coverage and (b)–(d) $h_0=-1$, 0 and $0.28z_{max}$ with adatom concentrations $x=0.5$, 0.11, and 0.02, respectively. In black, spin up; in orange, spin down. $\left(k_{B}T=0.01J_0\right)$.

Figure 3

(Color online) Left: (a) magnetization and (b) staggered magnetization as a function of an external magnetic field for a fully covered graphene sheet (black circles) and for $h_0=0$ (red squares) with $k_{B}T=0.01J_0$.

Figure 4

(Color online) Spin configurations for the same hill considered in Fig. 2 but with the random removal of nearest neighbors. (a) homogeneous honeycomb lattice, and (b)–(d) $h_0=-1$, 0, and $0.28z_{max}$, respectively. The adatom concentrations are (a) $x=0.24$ in the homogeneous lattice, (b) $x=0.22$, (c) $x=0.08$, and (d) $x=0.01$. In black, spin up; in orange, spin down $\left(k_{B}T=0.01J_0\right)$.

Figure 5

(Color online) Magnetization as a function of magnetic field for a lattice without first neighbors: homogeneous lattice (black circles), $h_0=0$ and $k_{B}T=0.01J_0$ (red squares) and $k_{B}T=0.05J_0$ (green triangles). Inset: $h_0=0$ and $k_{B}T=0.2J_0$ (blue diamonds).

Figure 6

The three columns show spin configurations (top), the details of the configuration for a small region of the system (middle) and total magnetization normalized by the value of saturation ($M_s$) versus magnetic field (bottom) for (a) $h_0=0.28z_{max}$, (b) $h_0=0$, and (c) a random distribution. The three systems contain the same concentration of adatoms, $x=0.05$.

Figure 7

(Color online) (a) Magnetoresistance for noninteracting spins at three different temperatures: $k_{B}T=0.01J_0$ (solid line), $k_{B}T=0.1J_0$ (dashed line), and $k_{B}T=0.2J_0$ (dotted line). (b) Magnetoresistance for the three different incorporation distributions shown in Fig. 6: $h_0=0.28z_{max}$ (black circles), $h_0=0$ (red squares) and a random distribution (blue diamonds). (c) Magnetoresistance in the case without first neighbor H atoms for $h_0=0$ and different temperatures: $k_{B}T=0.01J_0$ (red squares), $k_{B}T=0.05J_0$ (green triangles), and $k_{B}T=0.2J_0$ (blue diamonds). All curves are normalized by the corresponding zero-field resistance $R\left(H_{ex}=0\right)=1$ and are symmetric for $H_{ex}<0$.