Supporting online material
Ferromagnetism realized by hydrogenated graphene nanopore arrays
K. Tada1, J. Haruyama1*, H. Yang2, M. Chshiev2, T. Matsui3, H. Fukuyama3
1Faculty of Science and Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 252-5258, JAPAN
2SPINTEC, CEA/CNRS/UJF-Grenoble 1/Grenoble-INP,38054, Grenoble cedex 9, FRANCE
3Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JAPAN
*To whom correspondence should be addressed: E-mail:
(1)Fabrication of nano-porous alumina template (NPAT) masks
The NPAT (Fig.1), which consists of a honeycomb array of hexagonal-shaped antidots,was fabricated by the anodicoxidation of a pure aluminum (Al) substrate (Al = 99.99%) using electrochemical methods witha carbon electrode as thecathode16. Due to self-organization, a NPAT provides structure parameters (e.g.,pore diameter and interpore spacew)with exceptionally high regularity and high reproducibility. After the formation, the NPAT with an area of 1 cm2was detached from the Al substrate by alternating the polarity of the two electrodes. The detached NPATs were then placed onto the graphenes on Si(SiO2) substrateas etching masks (Supporting online material(3) below).SQUID measurements proved that the NPATs do not include any magnetic impurities.
(2) Fabrication of bulk graphenes
The thin-multilayer (< 10 layers) and monolayer graphene samples as the base for formation of GNPAs were extracted from bulk Kish graphite (Toshiba Ceramics) onto degenerately doped Si wafers with a 250-nm-thick SiO2 surface layer by means of mechanical exfoliation. Interference-induced color shifts in an optical microscope (3D-CCD), Raman spectroscopy, and cross-correlation with an AFM profile allowed us to identify the number of deposited graphene layers of all graphene flakes, which ranged from 1 to 10.
(3)Low power etching method of graphene for avoiding damage
Using the NPATas a mask, assembled graphenes(supplementary information (2)(11)) were etched by a carefully optimized conditions using low-power Ar gas (e.g., 200–600 V for 10 – 40 min) to avoid giving damage to the pore edges. We carried out the low-power etching step by step. Each after etching in 10 minutes, we performed FESEM (or AFM) observation and checked formation of nano-pores on Si-substrate under the NPAT mask. Until confirmation of formation of the nano-pores on Si-substrate, we repeated the slight etching.
(4)Three advantages of the present non-lithographic method
The three advantages of the present non-lithographic method using the NPAT mask in conjunction with low-power gas etching and high-temperature annealingcan be explained as follows:
①Because of the nonlithographic fabrication method, it ensures minimal damage to the nanopore edges.
②The honeycomb-like hexagonal nanopore array can result in the formation of a large number of GNRs with sufficient lengths (e.g., 40 nm in the present case) because of the presence of six boundaries among the neighboring six pores (Fig.1a) compared with that of lattices of the square- and round-shaped pores. In the actual GNPA, it is speculated that zigzag and armchair edges may exist with mixed states in one GNR (one boundary). Even in this case, a large number of GNRs in the present GNPAs can yield a large area of assembled zigzag-edge GNRs.
③From a topological reason, when the edge structure of one boundary of a hexagonal pore is aligned with the hexagonal carbon lattice of graphenes, the other five pore boundaries can have the same edge atomic structure such as pure zigzag (Fig. 1a). This also strongly contributes to the advantage mentioned in (2).
(5) Multi-layer graphenes for STM observation
For STM observations (Fig.1c), the substrates with 10-layer GNPAs were selected. This is because we could not get a large enough conductivity in monolayer GNPAs for the measurements.However, the results are consistent because the zigzag edge sates of the surface layer in the 10-layer GNPA at least are similar to those in monolayer GNPA (e.g., M. Otani et al., Phys. Rev. B 81,161403 (R)(2010)).
(6) Annealing foroxygen-terminated GNPAs
For observation of the features of oxygen-terminated GNPAs, after the observation of the feature in Fig.2, the sample was annealed at 800 C in high vacuum (10-6 Torr) for 3days for de-hydrogenationof the edges and thenin oxygen atmosphere for 1 hourforoxidizationof the pore edges. SQUID measurements were carried out right after the annealing.
(7) Disappearance of ferromagnetism in Oxygen-terminatedGNPAs
Some theories reported that the formation of a spin-paired carbon–oxygen (C–O) chemical bond drastically reduces the local atomic magnetic moment of carbon at the zigzag edge of GNRs and suppresses the emergence of ferromagnetism. The disappearance of ferromagnetism in our oxygen-terminated GNPAs is qualitatively consistent with this theory.
(8) Disappearance of diamagnetism in GNPAs
In our oxygen-terminated GNPAs, even the diamagnetism of graphene mostly disappeared. One of the reasons is attributed to the formation of the nanopore array, because such an array drastically reduces the bulk graphene area available for presence of loop currents to produce diamagnetism at the currently applied magnetic-field range (i.e., corresponding to only GNRs with W 20 nm between nanopores; Fig. 1a). The radius of the cyclotron motion for electrons is given by Rc = (nS)1/2(h/2)/eB. By observing the magnetoresistance (i.e., commensurability[XJ1] peak), we calculate nSto be ~(4 × 1011) cm−2 in the present GNPAs. Based on this ns value, Rc is calculated to be as large as ~400 nm, even for the currently applied largest magnetic field of 1000 gauss. Indeed, this Rc value is 20 times larger than W 20 nm between the present nanopores, and it prohibits the emergence of loop currents for the formation of diamagnetism.
(9) Confirmation of no influence of parasitic factors
A large ensemble of monolayer GNPAs with a total area 4×1cm2 was finally prepared for magnetization measurements (Fig.2) (i.e., One sample at least consists of 4 substrates with monolayer GNPAs. The total area does not include the area of the nano-pores.The total number of measured samples was 11). In order to confirm no contribution of NPATs and Si-substrates, the magnetization of the Si-substrates assembled only with NPATs (i.e., without GNPAs) was measured as well as the [NPATs +Si-sub + bulk graphenes] and the absence of ferromagnetism was carefully confirmed.
(10) Hydrogen termination of zigzag edges and the emergence of ferromagnetisms
The following three types of hydrogen terminations are possible. (1) A GNR with a zigzag edge, at which all carbon atoms are each terminated by one hydrogen atom on both sides, provides a flat band for 2/3 k. Electrons are well localized at the edges andthis leads to an antiferromagnetic state. (2) In contrast, when all thecarbon atoms of a zigzag edge on one side of a GNR areeach terminated by two hydrogen atoms (so that the edge carbon atom becomes tetrahedrally coordinated; a bearded edge) with the carbon atoms on the opposite sideterminated by a single hydrogen atom, a flat band appears for 0 kresulting in a completely localized “on-bonding state” around the Fermi level (EF). This leads to the spin polarization of all carbon atoms and to the appearance of ferromagnetism. (3) The double hydrogen atom termination of the zigzag-edge carbon atoms on both sides of a GNR provides a flat band for 0 k 2/3 and creates a modified zigzag edge (a bearded edge).
In the text, we concluded the case (1) is the one that is applicable, because cases (2) and (3) are notquite reasonable for the observed ferromagnetism. In particular, for case (3), excess hydrogenation of edge carbon atoms will result in the suppression of edge-localized magnetization. This conclusion can be reconfirmed by increasing the time, temperature, and pressure of H2 annealing that the present annealing condition favors mono-H termination for large magnetization (Figs. 2).
Confirmation of the number of hydrogen atoms terminating the pore edges has not been confirmed in the present experiments (see (12) below). However, the ferromagnetism observed only in the hydrogen-annealed GNPAs (Fig.2) strongly suggests presence of the zigzag edges at the pore edges in comparison with many theories.
(11) How to estimate edge magnetization based on GNR model
(1) The total area ofassembled bulk graphenes used for the nanopore array formation is 4 cm2.
(2) The area of one hexagonal unitcell with a pore is S = 6(3−1/2/2)(a/2)2 4300 nm2, where a= [80 nm (pore diameter) + 20 nm (pore spacing)].
(3) Thus, the total number of nanopores is (4 cm2)/(4300 nm2) 1011 [(1)/(2)].
(4) The total number of dangling bonds perhexagonal pore is (40 nm)/(0.142 nm × 31/2) × 6 = 166 × 6 1000.
(5) The total number of edge dangling bonds of the GNPA used for the SQUID measurement is 1014 [(3) × (4)]. Therefore, using (5), the saturation magnetization per edge dangling bond is estimated to be 1.2 × 10−6 (emu) × 10−3/1014 = 1.2 × 10−23 (J/T). Thus, the magnetic moment per edge dangling bond is, therefore, estimated to be (1.2 × 10−23)/(B = 9.3 × 10−24) 1.3 B,where B is the Bohr magneton.
Next, after H2 annealing at hightemperature, edge dangling bonds of a GNR are terminated by H atoms(Supporting online material (8)). Basically, three terminations should be considered: (1) mono-H termination for both edges, (2) di-H termination for bothedges, and (3) mono-H termination for one edge and di-H termination for the other edge. From a theoretical viewpoint,case (1) results in the formation of sp2and orbitals, which yields a flat energy band at 2/3 k in the Brillouin zone with electron localization. In contrast,case (2) results in the formation of sp3and orbitalsbecause of the tetrahedral coordination of two H atoms. It forms a flat band at 0 k 2/3 with suppressed electron localization. Case (3)produces a flat band at 0 k with entirely localized electrons.
However, there is no specified reason for causing case (3) in our GNRs, since this case implies that two neighboring pore edges have a different number of H atoms for termination. Furthermore, case (2) with a suppression of the magnetic moment also does not explain the large total edge magnetic moment of 1.3 B. Thus, we argue that our case corresponds to case (1). Consequently, after mono-H termination, the mono-H termination of the dangling bond decreases its magnetic moment to one B. The magnetic moment of one localized-edge orbital is, therefore, estimated to be as large as (1.3B– 1B) = 0.3B. This isin fairly good agreement with the theoretical contribution of the -orbital state to the edge magnetic moment of 0.3 B in a zigzag-edged GNR within the ferromagnetically ordered spin configuration.
(12) Probability of pure zigzag edges and observation of edge atomic structures
There are three different edge structures: zigzag, armchair, and amixture of the two. Because the possibility of the formation of each structure is basically equal (33%), the[XJ2] value of 50% for formation of a zigzag edge in the inset of Fig.1e (samples 1-4) indicates that almost half of the edgesfor the case of the mixtures (i.e., 33%/2 = 17%), which are close to the behavior of a zigzag edge, can be reconstructed to a zigzag edge by annealing (i.e., 33% + 17% = 50%). The remaining 50% of the samples, as shown in the inset of Fig.1e, will have armchair edges (sample 5) or large-volume defects (samples 6–8).
Observation of edge atomic structures is indispensable for the present experiments. However, it is extremely difficult at thecurrent stage to do this, because for HRTEM observation, GNPAs cannot be fabricated on a TEM grid, and for STM observation, the GNPAs do not have a conductivity enough large for such measurements. The GNPAs formed on Cu substrates may solve this problem for STM observations, because such a substrate provides a high conductivity, although the edge atomic structures may be affected by the Cu substrate.
(13) Removal of multi-layer GNPA flakes.
All multi-layer graphene nano-pore array flakes (i.e., except for monolayer GNPAs), which existed under the NPAT, were entirely removed by plastic tweezers one by one to measure the magnetization of only the monolayer GNPAs.After removing, the absence of them was carefully reconfirmed following the supplementary information (2).
On the other hand, we have recently detected ferromagnetism like Fig.2 also in GNPAs fabricated on monolayer graphenes grown on SiC substrate.
(14) Annealing methods
All the GNPAs fabricated through these processeswere annealed at 800 C in high vacuum (10-6 Torr) for 0.5 - 3days and thenin hydrogen gas for 1-3 hours for all the measurements. The first annealing is for deoxidization of the pore edges and recovering all damages, while the secondannealing is for termination of the carbon atoms at the pore edges by hydrogen atoms. These annealing processes also give the pore edge states high chemical stability. Here, the three advantages of the present non-lithographic method using the NPAT mask are explained in supplemental material ( 4).
(15) Ferromagnetism by nitrophenyl fictionalization of delocalized -orbital of bulk graphenes
Recently, it has been reported that nitrophenyl fictionalization of delocalized -orbital of bulk graphenes can also lead to ferromagnetism with the same magnetization order (0.2B at T=2K) as the present our result19. It is surprising because it is associated with formation of sp3-hybrid orbital, in which magnetization is conventionally suppressed. Universal understanding with the present results, thus, is expected.
(16) Future possible applications; Magnet and spintronic devices
In a view of recent reports on the possibility of spin-filtering effect as below1 and (quantum) spin Hall effect (QSHE)2-4 using edge spin current of graphene, our observations pave a way towards realization of creation of novel spintronic devices as well as room-temperature flexible and transparent magnets.
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[XJ1]Millie says: Clarify this.
[XJ2]Millie says: Not sure if this is obvious – at least not obvious to me.