Magnetoelectric Effect in Graphene Nanoribbons on Substrates via
Electric Bias Controlled Exchange Splitting
Zhuhua Zhang1, Changfeng Chen2 & Wanlin Guo1,2
1
Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing
210016, China
2
Department of Physics and High Pressure Science and Engineering Center, University
of Nevada, Las Vegas, Nevada 89154, USA
Supplimentary Information
FIG. S1 Spatial magnetization density and electronic structures of freestanding and
adsorbed GNRs on the Si(001) substrate.
FIG. S2 Mechanism for the magnetoelectric effect in the adsorbed bilayer Z7-GNR.
FIG. S3 Effect of interlayer stacking and spacing on the magnetoelectric effect.
FIG. S4 ME effect in bilayer GNR on simulated metastable adsorption site.
FIG. S5 Robustness of the magnetoelectric effect for GNRs on other types of substrate.
1
a
b
c
Up-spin
right edge Down-spin
left edge
0.6
I
II
Down-spin
right edge
0.19
Total DOS (a.u.)
-0.34
0.3
E-EF (eV)
III
up-spin
left edge
Epeak
FIG. S1. Spatial magnetization density and electronic structures of freestanding and
adsorbed GNRs on the Si(001) substrate. (a) Charge redistribution induced by adsorption
0.0
of the second Z7-GNR layer. Red (solid line) and blue (dot line) colors correspond to
charge accumulation and depletion regions, respectively. The contour spacing is set to be
80×10-3 e/Å3. (b) Total electron density of states of the freestanding (I), adsorbed
single-layer (II) and bilayer (III) Z7-GNRs. (c) Spin-polarized electronic structure for the
-0.3
ground state of system in (a) with the bands of top GNR layer around EF in solid lines;
the green dash lines denote the spin-polarized band structure of the freestanding Z7-GNR.
When a single-layer Z7-GNR is adsorbed on a Si(001) surface, it forms covalent Si-C
-0.6
bonds at both edges with two silicon dimers and the ribbon edge is perpendicular to the
-0.6
-0.3
dimer rows, leading to a bridge-like energetically most favorable configuration on the
substrate. When a second GNR layer is additionally placed on the system, there is a
spontaneous charge transfer from the bottom GNR layer to the top GNR layer as shown
in Fig. S1(a). Figure S1(b) shows that the sharp localized density of states (DOS) at the
Fermi level EF for magnetic instability in the freestanding magnetic ribbon is absent for
the adsorbed single-layer Z7-GNR. Interestingly, the localized edge states are regained in
a bilayer Z7-GNR adsorbed on the substrate, as indicated by the high DOS at EF shown in
Fig. S1(b). It is clear that the top layer remains a magnetic semiconductor, while the gap
is reduced from that of a freestanding GNR shown in Fig. S1(c).
2
J
E-
I
II
DOS
DOS
III
DOS
DOS
DOS
DOS
FIG. S2. Mechanism for the magnetoelectric effect in the adsorbed bilayer Z7-GNR.
Average local up-spin (red) and down-spin (blue) DOS of the left and right edge carbon
atom in the top Z7-GNR layer under electric field strengths of -0.6 (I), -0.3 (II) and 0.4
(III) V/Å.
3
a
p
n
b
Magnetic
Magnetic moment
(B) moment (B)
0.25
p
n
0.20
0.25
0.15
(V/Å)
0.20
FIG. S3. Effect of interlayer stacking and spacing on the ME effect in adsorbed bilayer
GNRs. Magnetic moment per edge carbon atoms of the top Z-GNR layer in the bilayer
0.10
Z6-GNR adsorbed on Si(001) substrate as a function of applied electric field at different
interlayer stacking (a) and spacing (b). The ME coefficient in the n-doped region, αn, is in
units of 10-12 Gcm2/V.
0.15
When the bilayer Z-GNR shows AA stacking, the ME modulation is nearly unchanged
within the calculation accuracy. On the other hand, when the interlayer spacing of the
adsorbed bilayer is compressed by 3%, it is shown that the ME coefficient is reduced
from uncompressed value of -0.66 (units of 10-12 Gcm2/V) to 0.58. The reason is that
decreasing the interlayer spacing will enhance the interaction between the bilayer, which
0.10
increases the band dispersion of the localized edge states in the top GNR layer. As a
result, the edge states are delocalized, following the reduction of ME coefficient and the
peak of edge moment in neutral as can be expected from the Stoner theory.
4
-0.8
a
0.14
p
Magnetic moment (B)
b
n
0 V/Å
-0.40
0.12
(V/Å)
0.10
0.57
FIG. S4. ME effect in bilayer GNR on simulated metastable adsorption site. (a) Bias
0.08
voltage dependent magnetic moment on the edge carbon atom of the second Z-GNR layer
in the bilayer Z6-GNR with 4 H atoms binding to the interior of bottom layer. (b) Charge
redistribution in the bilayer without the bias voltage. Red (solid lines) and blue (dot lines)
colors indicate charge accumulation and depletion, respectively, with the contour spacing
set to 80×10-3 e/Å3.
0.06
When the sp3 bonds are formed at ribbon interior, the interaction between the ribbon
edges of both the GNR layers is enhanced compared to that with sp3 bonds formed at
ribbon edges, which can be reflected by the distinct charge redistribution at the ribbon
edges as shown in Supplementary Fig. S3(b). This behavior enhances the asymmetry of
the top layer edges. Therefore, in this case the ME modulation is distinctly asymmetrical
for two ribbon edges. At zero field, the edge atoms at the left ribbon edge are p-doped,
while are n-doped at the right edge [see the charge redistribution shown in Fig. S3(b)].
Thus the n-to-p-type transition occurs at the positive and negative fields for the left and
right edges, respectively.
5
-0.
a
b
Magnetic moment
(B) moment (B)
Magnetic
0.25
p
0.20
0.25
n
0.15
0.20
0.10
(V/Å)
FIG. S5. Robustness of the ME effect for GNRs on other types of substrate. (a)
Magnetic moment per carbon atom at the left edge of a single-layer Z6-GNR on
0.15
0.05
H-terminated Si(001) substrate as a function of the applied bias voltage. (b) Magnetic
moment per edge carbon atom of the top layer in a bilayer Z6-GNR adsorbed on clean
Si(111) substrate as a function of the applied bias voltage.
0.10
0.05
-0.8
6