Electronic Properties of Nanopore Edges of Ferromagnetic Graphene Nanomeshes at High Carrier Densities under Ionic-Liquid Gating


Graphene edges with a zigzag-type atomic structure can theoretically produce spontaneous spin polarization despite being a critical-metal-free material. We have demonstrated this in graphene nanomeshes (GNMs) with honeycomb-like arrays of low-defect hexagonal nanopores by observing room-temperature ferromagnetism and spin-based phenomena arising from the zigzag-pore edges. Here, we apply extremely high electric fields to the ferromagnetic (FM) GNMs using an ionic-liquid gate. A large on/off-ratio for hole current is observed for even small applied ionic-liquid gate voltages (Vig). Observations of the magnetoresistance behavior reveal high carrier densities of ~1013 cm-2 at large Vig values. We find a maximum conductance peak in the high -Vig region and its separation into two peaks upon applying a side-gate (in-plane external) voltage (Vex). It is discussed that localized edge-π band with excess-density electrons induced by Vig and its spin splitting for majority and minority of spins by Vex (half-metallicity model) lead to these phenomena. The results must realize critical-element-free novel spintronic devices.

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T. Hashimoto, S. Kamikawa, Y. Yagi and J. Haruyama, "Electronic Properties of Nanopore Edges of Ferromagnetic Graphene Nanomeshes at High Carrier Densities under Ionic-Liquid Gating," Materials Sciences and Applications, Vol. 5 No. 1, 2014, pp. 1-9. doi: 10.4236/msa.2014.51001.

1. Introduction

The presence of spontaneously spin-polarized electrons has been theoretically reported at zigzag-atomic structure of edges of graphenes with flat energy bands [1-3]. We experimentally reported it at the hydrogen (H)-terminated pore edges of low-defect graphene nanomeshes (GNMs: Figure 1(a)) [1-15], which were fabricated using non-lithographic method (i.e., nanoporous alumina templates as etching masks [11]), by observing the ferromagnetism (i.e., ferromagnetic GNMs (FM-FNMs)) [1-9], the distribution of the polarized edge spins by magnetic force microscope [10], and some spin-based phenomena [10-15]. The spin polarization appeared because of the low-defect zigzag atomic structure of the pore edges [1-7] formed by edge reconstruction caused by critical-temperature annealing [12-14] and the assembly of narrow interpore regions (e.g., 10 ~ 20 nm width) corresponding to H-terminated zigzag graphene nanoribbons (GNRs: one-dimensional strip lines of graphene with edges on both longitudinal sides; Figure 1(a) [8,9]). A large ensemble of GNRs in a GNM enabled the emergence of large-magnitude ferromagnetism even at room temperature.

On the other hand, recently, several studies have reported achieving extremely high carrier densities on material surfaces (e.g., observing the transition from insulators to superconductors and carrier filling in higher energy bands) using electrolytic gates (e.g., ionic liquids and ionic solid-polymers: Figures 1(c) and (d)) [16-23]. The method enables the realization of a drop in the electric

Figure 1. Sample structures (a) Schematic top-view and (b) atomic force microscope image of hydrogen (H)-terminated zigzag GNMs, which gives a honeycomb-like array of lowdefect hexagonal nanopores. The mean pore diameter and interpore distance are ~80 nm and ~20 nm, respectively. The interpore regions can be H-terminated graphene nanoribbons (GNRs) with a width of ~20 nm and, thus, the GNM can be a large ensemble of H-terminated-zigzag GNRs, resulting in the appearance of large ferromagnetism. (c),(d) Hall-measurement pattern of the ~5-layer ferromagnetic (FM) GNM with an ionic-liquid gate using DEME-TFSI [19]. Side-gate electrode, which is located within ~500 mm distance from the GNM and is not covered by ionic liquid, was used for applying Vex.

field only at the interface of the material surface (e.g., only for a thickness of 1 nm) via the formation of a Debye layer (Figure 1(d)), thereby resulting in the concentration of an extremely high electric field at the surface. The method has been also applied to graphenes. For example, high carrier densities obtained by this method (1014 cm−2) have revealed the presence of the quantum distribution of two-dimensional (2D) acoustic phonons in graphenes. Further, the filling of the high-energy subbands has been observed along with high electron mobility in bilayer graphenes [16,17]. These results indicate the importance of the high carrier densities observed in graphenes (edges) in the light of examining novel electronic states and physical phenomena.

Indeed, a variety of spin-related phenomena have been predicted based on the study of the edge spins of graphene [6,24-28]. For instance, half-metallicity was predicted in GNRs with antiferromagnetic (AF) spin alignment at two zigzag edges [6]. In such a GNR, the gap for the spins with the same moment (e.g., up spins) between both edges disappears upon applying in-plane external electric fields (Vex), while the gap for the opposite-moment spins (e.g., down spins) increases. The occurrence of the (quantum) spin Hall effect was also predicted by resolving the double degeneration of edge spin bands (e.g., by introducing spin-orbit interactions) and controlling two spins with opposite moments existing in two different bands by applying electric fields [25,26]. In this light, a large spin current was experimentally observed using Zeeman splitting in high-quality bulk graphenes positioned on h-boron-nitride (BN) [27]. We have also reported possible spin-based phenomena arising from the pore edges of ~5-layer FM-GNMs [28].

In the present study, we fabricate an ionic-liquid gate on ~5-layer FM-GNMs with polarized spins at the pore edges, and we observe the changes in the pore-edge electronic and spintronic states induced by the applied ionic-liquid gate voltage Vig and also the side-gate voltage Vex via an electrode not connected to the ionic liquid.

2. Experimental Results and Discussions

2.1. Sample Fabrication

Figure 1 shows the top-view schematic (a) and atomic force microscope images (b) of H-terminated zigzag GNMs and the optical microscope image of the Hallmeasurement pattern on the fabricated GNM with an ionic-liquid gate (c), (d). The GNMs, which have honeycomb-like array of hexagonal nanopores, were fabricated on mechanically exfoliated graphenes via the nonlithographic method using a nano-porous alumina template (NPAT) as an etching mask [10,11].

The NPAT is easily fabricated through self-organization by anodic oxidation of pure (99.99%) aluminum films. The graphene was carefully etched by optimized low-power Ar gas (e.g., 200 - 600 V for 10 - 40 min) so as to avoid giving damages (Figure 1(d)) and the naomesh of the NPAT was transferred to graphene. Then, the NPAT was detached from the surface of the fabricated GNM, either mechanically or chemically.

The GNMs fabricated through these processes were annealed at a critical temperature 800˚C in high vacuum (10−6 Torr) for 0.5 - 3 days with continual pumping of gas and, then, in hydrogen gas by the field-emission-type radical CVD system under pressure >1 MPa at least for 3 h. The first annealing is for deoxidization of the pore edges with recovering all damages and defects and is the key to forming zigzag pore edges by edge atomic reconstruction [10,12-14], while the second annealing is the key for termination of the carbon atoms at the pore edges by hydrogen atoms for production of flat-band ferromagnetism.

It is to be noted that for electrical measurements, we employed ~5-layer graphenes, because monolayer GNMs exhibited poor electrical features. We have previously confirmed that even such thin-layer GNMs can exhibit ferromagnetism comparable with that of monolayer GNMs, although the amplitude reduces [1-3,22,23]. In fact, we have performed electrode fabrication and measurements after the confirmation of presence of the ferromagnetism.

The ionic-liquid gate was formed to apply Vig following ref. [19] by dropping N, N-diethyl-N-(2-methoxyethyl)-N-methylammonium bis-(trifluoromethylsulfonyl)- imide (DEME-TFSI) (Figures 1(c) and (d)). Applied Vig is consumed on at the interface of ionic liquid and the GNM, forming electrical-double layer within ~1 nm thickness (Figure 1(d)). Thus, it induces extremely high electric fields on the GNM surface. In the present experiment, side-gate electrode not exposed to the ionic liquid was used to apply the Vex.

2.2. Changes in Electrical Properties and Extremely Large Ion/off upon Vig

Figure 2 shows the drain current (Ids) as a function of the back-gate voltage (Vbg) and Vig (i.e., before and after the formation of the ionic-liquid gate). Without the ionicliquid gate, the FM-GNM exhibits only n-type semiconductive behavior; Ids increases only with increasing Vbg (Figure 2(a)). Ids is zero even when Vbg is as small as −20 V. In contrast, with the ionic-liquid gating, Ids drastically increases with decreasing Vig (Figure 2(c)). Even when Vig is ~ −1 V, the p-type semiconductive behavior appears significantly. This can be attributed to hole doping by the partial oxygen-termination of the pore edges. Immediately before forming the ionic-liquid gate, the GNMs were exposed to an air atmosphere, because it is impossible to form the gate in high vacuum or a hydrogen atmosphere. Because the GNM is not covered by any passivation films, the pore edges are easily oxidized through this process, thereby resulting in the partial oxygen-termination and hole doping. Applying −Vig significantly enhances this hole doping via pore edges. This occurrence is different from the case of bulk graphene without edges. Otherwise, the ionic-liquid gate itself might cause oxygen-like termination.

Figures 2(b) and (d) show the logarithmic scales of Ids transformed from Figures 2(a) and (c). The subthreshold slope values (Vsub) are 5 V/decade for increasing Ids in the +Vbg region (Figure 2(b)) and 270 mV/decade for increasing Ids in the −Vig region (Figure 2(d)). The Vsub value reflects the on-off ratio of Ids (Ion/off) for the applied gate voltages and, hence, it is extremely important for field-effect transistor (FET) operation. The large Ion/off value directly leads to a high gain in the radio-frequency (RF) operation of FETs. The Vsub is inversely proportional to the Ion/off. Previously, we have reported on the electrical characteristics of high-quality and low-defect GNRs derived from the unzipping of carbon nanotubes (CNTs) combined with three-step annealing [8]. These GNR-FETs exhibited a large Vsub of 3 V/decade for a 20-nm width. The GNMs derived using polymer masks also exhibited a large Vsub of ~3 V/decade for a 7-nm


Figure 2. Electrical characteristics of GNM with back gate and ionic-liquid gate (a) Drain current (Ids) as a function of back-gate voltage (Vbg) and (b) its transformation to the logarithmic scale of Ids of the ~5-layer FM-GNMs. The GNMs show n-type semiconductive behavior and subthreshold slope values (Vsub) of 5 V/decade. (c) Ids as a function of ionic-gate voltage (Vig) after formation of the ionic gate and (d) its transformation to the logarithmic scale of Ids. A drastic increase in Ids in the −Vig region, indicative of p-type behavior, is observed with Vsub as small as 270 mV/decade.

interpore width (i.e., GNR width) [29]. Only the GNRs obtained from the unzipping of CNTs exhibited a small Vsub of 210 mV/decade but for a 2-nm width [9]. Thus, the present Vsub of 270 mV/decade for the 20-nm interpore width is extremely small compared with those of any other GNR-FETs. This strongly suggests the effectiveness of ionic-liquid gating in producing and modulating extremely high electric fields on the GNM surface and the interpore GNR regions.

2.3. Estimation of Carrier Densities by Magnetoresistance Observation and Large Geometrical Capacitance of Ionic-Liquid Gate

We investigate the charge density ns achieved upon applying Vig by observing the magnetoresistance (MR) behaviors in the FM-GNMs.

When magnetic fields (B) are applied perpendicular to the GNM plane, the electrons follow a cyclotron motion with the classical radius of the cyclotron orbit,

, where h and e denote Planck’s constant and the electron charge, respectively [28]. A variety of interesting MR phenomena has been observed depending on the correlation of 2Rc with (the pore diameter) and a (the diameter of the unit cell). For instancecommensurability MR peaks and Aharonov-Bohm (AB)- type oscillations (with an oscillation period , where S denotes the area of the unit cell) were observed around low B values at points where electrons encircle and localize around the nanopores (see Figure 3(a); 2Rc = a) for samples with large /a values and small interpore spacing (i.e., 2(a −)) that is insufficient to allow electron cyclotron motion. In contrast, at high B values, Shubnikov-de Haas (SDH) oscillations and consequent quantum Hall effects appeared for samples with small /a values and large interpore spacing that allowed for electron cyclotron motion with the small Rc values.

In a previous work on FM-GNMs with nearly identical structure parameters as those in the present one but without the ionic-liquid gate, a commensurability MR peak was observed at B ~ 1.2 T [28]. From the expression, we estimated and an elastic mean free path of (where D denotes the diffusion constant and vF denotes the Fermi velocity) ~800 nm. Based on this result, we can estimate ns under extremely high electric fields caused by applying Vig to FM-GNMs with an ionic-liquid gate.

Figure 3 shows the MR (Rxx) as a function of Vig. The commensurability MR peak can be observed at B ~ 1 T at Vig = 0 V. As Vig decreases, the peak shifts to larger B regions. The maximum peak position of B ~ 5 T is observed at Vig = −12 V. This indicates an increase in ns with decreasing Vig, because a large ns value requires a large B value in order to satisfy the condition for the commensurability peak:. Consequently, the maximum ns of ~1 × 1013 cm−2 can be estimated from the peak B value for Vig = −12 V.

This value is extremely large despite the small value of the assembled 20-nm-width GNR structure of the present GNM. This large value is attributed to the large electric field caused by Vig. Moreover, this result also implies the contribution of the induced edge-p states of the nanopores, in which high-density carriers localize at the pore edges even when B = 0 (i.e., the large peak around Vig = −12 V in Figure 4(b), explained later). These edge-localized carriers are added to the cyclotron electrons at Vig = −12 V, thereby resulting in extremely large values of ns. Indeed, it is noteworthy that the peak position moves to a lower B value and ns decreases at Vig = −16 V. This evidences the contribution of the edge-p electrons localized around the pore at Vig = −12 V. Furthermore, the extremely large ns value results in a small mean free path (le) of ~800 nm, which is considerably smaller than the circumferential length of the pore and cell (~250 nm). Thus, the present GNM is not within a ballistic charge transport regime, and no AB-type oscillations are observed in Figure 3(b).


Figure 3. Magnetoresistance behavior for various ionicliquid gate voltages (a) Schematic view of an electron orbit for a commensurability MR peak in a GNM. The peak appears at a B value where the electron cyclotron diameter (2Rc) is close to the unit cell diameter (a) and electrons localize in the unit cell. (b) MMR behavior (Rxx) in a perpendicular field as a function of Vig of FM-GNMs with ~5-layers at T = 1.5 K. The broad MR peaks at each Vig value indicate the commensurability MR peaks mentioned in (a). Change in the peak position is caused by the modulation of ns upon changing Vig. The peak B positions provide the ns values of the FM-GNM at each Vig, which includes the pore-edge localized electrons even for B = 0.

In addition to the extremely high value of ns, the other strong advantage of using the ionic-liquid gate is the obtainment of a large geometrical capacitance (Cgeo) [19], which allows the direct observation of the quantum capacitance (CQ). The large geometry of the ionic-liquid region (Figure 1(c)) provides an extremely large Cgeo. This capacitance allows the direct observation of the quantum capacitance (, where m* denotes the effective mass of carriers and D2 is the electronic density of states of the 2D layer), because the total capacitance is given by and the 1/Cgeo value is negligible. In fact, a previous work has reported on the possible detection of D2D at higher energy bands arising from the CQ of individual layers in monolayer to trilayer graphenes, using this method. Here, the capacitance of 2D systems is conventionally obtained from the Hall measurements (i.e., changes in ns as a function of). However, it is difficult to employ this method in our case because the scattering by the honeycomb-like nanopore array prevents Hall measurements.

Instead, we employ a GNR model in order to estimate Cgeo, and reconfirm the possibility of the direct observation of CQ, because the interpore regions are GNRs (Figure 1). The GNR models gives carrier mobility , where gm denotes the mutual conductance and L denotes the GNR length8. The gm value of ~500 mS at Vds = 0.8 V is observed in Figure 2(d), and L corresponds to the inter-electrode distance of 2500 nm in our fabricated GNM. In a previous report, we have also estimated μ < ~100 cm2/Vs in FM-GNMs from MR measurements [28]. Consequently, Cgeo for the side gate electrode is estimated to be ~12 μF/cm2.

This value is in good agreement with those in previous reports on ionic-liquid (electrolytic) gates [19]. Conventional GNRs with widths of 2 ~ 20 nm placed on SiO2 substrates have Cgeo ~ 10−10 - 10−12 F for the source electrodes. Thus, the present Cgeo value is nearly 105 times greater than these reported values. Therefore, we can estimate CQ and D2D directly from the measurement results related to Ctot also in our GNM.

2.4. Observation of Differential Conductivity on Vig

Figure 4(a) shows the differential conductivity (dI/dV; Rxx−1) as a function of Vig in the low-Vig region when B = 0 T. Even in the present ~5-layer GNM, a Dirac-pointlike dip (zero-bias anomaly) is observed in the dI/dV curves. Moreover, as the absolute value of Vig increases, other dips and peaks appear. Such dI/dV anomalies due to Vig variation have been reported in tri-layer graphenes with ionic-liquid gates and attributed to carrier filling in higher energy bands (i.e., interband scattering). This is a advantage unique to the electrolytic gate method for the abovementioned reasons (i.e., introducing large electric fields and the presence of a large Cgeo). The curves in Figure 4(a) are qualitatively consistent with the abovementioned features. However, in Figure 4(a), the dI/dV anomalies observed at Vig ~ ±0.3 V are considerably more defined than those observed in the tri-layer graphenes. Moreover, the plateau of the second peak in the +Vig region is broad and consists of very small peaks. The presence of these peaks might suggest very strong interband scattering and the presence of a complicated higher-band structure in our ~5-layer FM-GNM.

In the large Vig region (Figure 4(b)), we observe many dI/dV peaks. In particular, a significantly large and broad dI/dV peak is observable around Vig ~ −12 V, when the side-gating Vex is 0 V (dotted line in Figure 4(b)). Although the dI/dV properties as a whole are very complicated, the observed large dI/dV values in the -Vig region at Vex = 0 V are consistent with the hole-dominant property in Figures 2(c) and (d). This consistency indicates

Figure 4. Conductivity behaviors for various ionic-liquid gate voltages Vig and side-gate (in-plane external) voltages Vex (a) Differential conductivity (dI/dV) as a function of Vig at low Vig values. (b) dI/dV curves in the high-Vig regions with side-gating Vex. The dashed vertical line indicates the location of the maximum peak and the dashed circle indicates its splitting into two peaks with increasing Vex. (c) The spin splitting voltage ΔVig estimated from the two peaks in Figure 4(b) as a function of side-gate Vex. (d) Peak ratio for left/right peaks as a function of Vex in Figs.4b and 4c. It should be noticed that the peak ratio starts to significantly increase from the critical Vex ~ 8 V due to the reduction in the height of the left peak, at which point ΔVig saturates in Figure 4(c). (e)-(g) Hal-metallicity-based schematics of changes in spin bands for majority and minority spins at both edges of a FM-GNR (corresponding to the interpore region) as a function of the in-plane Vex. Insets: The schematics of the two dI/dV peaks shown in Figure 4(b).

the significant appearance of p-type semiconductive behavior.

The dI/dV values typically have a strong correlation with D2D and ns, conventionally. A large D2D value around Fermi level results in a large dI/dV value [16,17]. Hence, the maximum dI/dV peak around Vig ~ −12 V (Figure 4(b)) should reflect the maximum D2D value of our FMGNM.

Because the edge-localized flat p band has the largest D2D values (edge states) and strongly contributes to the appearance of the ferromagnetism also in graphites [3, 21-23], the maximum dI/dV peak should correspond to this edge-p band. Theoretical works have proposed that the edge-magnetic moment arising from the edge-p state survives even in graphites with interlayer interaction (e.g., ABA stacking with mono-hydrogenated edges) [3,21-23]. Moreover, because the present FM-GNM has only ~5layers, the influence of interlayer coupling for suppressing the emergence of ferromagnetism is very weak.

However, the localization of the edge-electrons prohibits current flow and obstructs detection of the large D2D by dI/dV observation in the present case, even if the D2D value is very high. Nevertheless, we have reported certain MR behaviors (e.g., periodic MR oscillations [28] and saw-tooth-like MR oscillations [10]) originating from edge-localized p-electrons in similar ~5-layer FM-GNMs operating under a constant current mode in four-probe measurements. We have argued that certain numbers of pore-edge-localized electrons can travel between electrodes because of the constant current mode (i.e., under non-thermal equilibrium). Moreover, the ns value of ~1 × 1013 cm−2 around Vig ~ −12 V observed in our ionic-liquid-gated FM-GNMs is considerably larger than the ns value of conventional FM-GNRs. This result supports the strong contribution of the drastically induced pore-edge p-electrons, as mentioned above. In such a case, the excess p-electrons localizing at the pore edges can be transported considerably more efficiently under a nonthermal equilibrium condition and contribute to the dI/dV. Therefore, we can assume that the maximum dI/dV value directly reflects the edge-localized p band with the highest DOS via the excess p electrons, as seen from scanning tunnel microscopy observations of the DOS.

Such maximum dI/dV peaks cannot be observed in conventional electrolytic-gated bulk graphenes without nanopores (i.e., without edge states), which showed no FM behavior, and such behavior has not thus far been observed in measurements obtained by applying Vbg. These results strongly support the correlation of the observed maximum dI/dV peak with the induced pore-edge pelectrons in our ionic-liquid gated ~5-layer FM-GNMs.

On the other hand, several other dI/dV peaks are also observed in Figure 4(b). These should originate from other D2D states, which are sensitive to spin interference by 1) the spin alignment of both the edges of the interpore GNR regions [3], 2) large ensemble of the GNR regions, 3) the interlayer stack structures [22], and also 4) Vig and Vex. Thus, it is difficult to identify the origins of the individual peaks. For example, the second-largest peaks observed around Vig ~ −5 V and −12 V at Vex = 0 in Figure 4(b) may be associated with the σ band, because the present GNMs have ~5-layer. In the present work, we focus on the largest dI/dV peak observable around Vig ~ −12 V at Vex = 0 in Figure 4(b), because Figures 4(b)-(d) suggest its strong correlation with the edge-p band, as stated in next section.

2.5. Splitting of a Maximum Conductance Peak by In-Plane External Fields and Half-Metallicity Model

As mentioned above, we interestingly find that the maximum dI/dV peak around Vig ~ −12 V separates into two peaks upon increasing the Vex (Figure 4(b)). The splitting voltage ΔVig monotonically increases with increasing Vex and saturates at around Vex = 8 V with ΔVig ~ 3 eV (Figure 4(c)). At low values of Vex, the left peak is considerably more prominent than the right peak (Figure 4(b)), while the left peak height reduces for large Vex values, and eventually, the two peaks exhibit similar heights. The peak ratio for the left/right peaks after peak separation becomes equal with increasing Vex because of the decrease in the left-peak height (Figure 4(d)).

This spin splitting can be qualitatively understood by the resolving of the double spin degeneration of the edgelocalized flat p band (i.e., separating of the majorityand minority-spin bands, which correspond to the left and right peaks, respectively) by applying the side-gating Vex, which plays role like applying in-plane Vex. Because the contribution of the localized minority-spins to dI/dV is very small, the right-peak height is actually small throughout all the Vex regions (Figure 4(b)). Indeed, such a spin splitting upon the application of an electric field has been reported as an anomalous spin Hall effect in FM/non-FM hybrid materials (e.g., Pt/Ni-Fe). From the theoretical viewpoint, the presence of spin bands for the majority and minority spins has also been reported in FM-GNRs [3].

One particular theory [6] has predicted the half-metallicity and spin-gap opening that can be realized upon applying the in-plane field Vex in zigzag-GNRs with AF spin alignment at both the edges (as mentioned in the introduction). In our fabricated FM-GNMs, the spin alignment at the two edges of the interpore GNR region is FM. However, when a similar mechanism is realized for the majority and minority spins with opposite moments for FM-GNRs assembled between the electrodes, the above mentioned spin splitting can be observed (Figures 4(e)- (g)), and it can be explained by assuming that the sidegate Vex plays the role of the in-plane field Vex. The predicted spin-gap opening as per the theory was Δtheory ~ 0.5 eV for Vex = 0.1 V/Å. In contrast, the abovementioned value of ΔVig ~ 3 eV for Vex = 8 V corresponds to a considerably larger ΔVig. As mentioned above, we have used the side-gating voltage Vex for this observation. When Vex = 8 V is applied from the side-gate electrode directly placed on the Si substrate, the voltage propagates via the substrate surface, thereby leading to a potential difference between both sides of the individual interpore GNR with 20-nm width. The potential difference can be estimated to be ~0.1 V/20nm, based on our previous work [8]. Thus, ΔVig ~ 3 eV for Vex = 8 V corresponds to ΔVig ~ 600 eV for Vex = 0.1 V/Å. This ΔVig value is considerably larger than the theoretical prediction Δtheory ~ 0.5 eV.

However, because this value of ΔVig ~ 600 eV is not the actual spin splitting energy in the GNM but corresponds to the Vig value applied to the side-gate electrode, the actual splitting energy ΔVsp needs to be calculated. The ΔVsp value corresponds to the energy in the singleparticle energy spectrum given by

Here, vF ~ 103 m/s denotes the Fermi velocity in our fabricated GNM, which is at least 1000 times smaller than that for bulk graphene [8] considering edge scattering. Using the previously estimated value of Cgeo ~ 12 μF/cm2, ΔVsp can be estimated to be ~0.54 eV. This value is quantitatively in good agreement with the abovementioned theoretical prediction of ΔVtheory ~ 0.5 eV. This estimation also implies that the edge-localized p band (i.e., the observed dI/dV peak at Vig ~ −12 V) exists at ~1.2 eV below the initial Fermi level position at Vig = 0 V. Because the FM-GNM consists of the assembled FM-GNRs, this might smear the dI/dV maximum and also its splitting by averaging. However, we assume that only the dominant some GNRs (interpore regions), of which the width-direction (i.e., both edges) locates in parallel with electrodes to apply Vex, and have perfect zigzag edges, strongly contribute to these phenomena.

Moreover, it should be noticed that the peak ratio starts to significantly increase from the critical Vex value of 8 V due to the reduction in the height of the left peak (Figure 4(d)), at which point ΔVig saturates (Figure 4(c)). This result supports the conclusions of the half-metallicity model [6]. Following this model, the saturation of ΔVig corresponds to the gap closing for one-moment spins existing at both edges of the GNRs (Figure 4(f)). Although this gap closing facilitates the same-moment spin current flow across the GNR, the localization of the edge electrons for the majority spin is suppressed by the spin current flow. A further increase in Vex results in a decrease in the amplitude of the edge states (i.e., resulting in a decrease in the excess ns) for the same-moment spins and, thus, the left-peak height decreases (Figure 4(g)) despite appearance of the current flow.

Consequently, we suggest that the applied side-gate Vex causes spin splitting of the edge-p band (for the majority and minority spins with opposite moments for FMGNRs) similar to that caused by the application of an inplane Vex following a theory [6]. This is because extremely large values of the D2D, which originate from the edge states of the nanopores induced by Vig, are highly sensitive to added external fields. In fact, we could observe no such Vex-dependent changes in the electronic states in the absence of Vig (in this case, we applied only the back-gate voltage and, consequently, we could not detect even edge-p states, as in Figure 4). Because the present GNM is placed on a SiO2 film, the side-gating Vex cannot directly modulate the interpore GNR edges. However, when the ionic-liquid gate is formed, the liquid faces the pore edges (i.e., both edges of an interpore GNR) and also the surface of SiO2 at the pore’s inner regions. We speculate that such conditions drastically change the large edge-electronic states even for a small potential difference existing between the two edges of the interpore GNR region caused by the side-gating Vex, and the Vex acts in a manner similar to the actual in-plane field Vex.

2.6. Rapid Degradation of Samples during Electrical Measurements

Subsequent to measurements performed over nearly three days, we observed a degradation of the electrical and magnetic characteristics of the FM-GNM. In particular, the appearance of single-electron charging effect was observed in the current channel region (Figure 5).

The staircase-like feature is confirmed in the Ids vs. Vds relationship in Figure 5. The inset shows dIds/dVds as a function of Vds. It exhibits a periodical oscillation with a period of 180 mV. It is well known that such a phenomenon is understood as the Coulomb staircase, which originates from the charging effect of a single electron in an extremely small dot area with a charging energy of Ec = e2/2Cdot ~ 180 meV, where Cdot denotes the capacitance of the dot area [30,31]. The Cdot value corresponds to ~10−18 F, which is a value that is considerably smaller than Cgeo and also any other capacitances of the present GNM-FET structure. This result strongly suggests the emergence of small defects in the current channel region due to degradation after the three-day measurements. Indeed, ref. [16] reported on the quick degradation of graphenes with electrolytic gates and the consequent importance of obtaining quick measurements.

Figure 5. Electrical characteristics after three-day measurements Ids-Vds relationship after the measurements through nearly three days. The sample was placed in a He-gas atmosphere in a Cryomag system (Oxford Inst.) at T = 1.5 K during the measurements. Inset: dIds/dVds as a function of Vds. The curve exhibits a periodical oscillation with a period of 180 mV, the so-called Coulomb staircase.

The sample was placed under high-vacuum conditions in a Cryomag system (Oxford Instruments) at T = 1.5 K during the measurements. Thus, we concluded that the edge degradation is due to the chemical reaction of the (frozen) ionic liquid with the GNM during the measurement. Because the H-terminated pore edges face the ionic liquid, they are most sensitive to such degradation. In the present edge-related measurements, a more careful treatment of the GNMs will be required, because it is well known that the edge-based phenomena are highly sensitive to edge degradation.

Moreover, in our previous works, we have reported observing AB-type MR oscillations [28] and saw-tooth like MR oscillations (i.e., the spin pumping effect [10]) arising from the localized electrons at the pore edges in ~5-layer FM-GNMs without ionic-liquid gating. On the other hand, in the present structure with ionic-liquid gates, these oscillations are hardly observed. This absence of oscillations might also be due to the partial degradation caused by the chemical reaction between the pore-edge carbon atoms and the ionic liquid.

3. Conclusions

Graphene edges with a zigzag-type atomic structure can theoretically produce spontaneous spin polarization despite being a critical-metal-free material. We previously demonstrated this in GNMs with honeycomb-like arrays of low-defect hexagonal nanopores by observing room temperature ferromagnetism and spin-based phenomena arising from the zigzag-pore edges.

In the present work, we applied extremely high electric fields to the FM-GNMs using an ionic-liquid gate. A large on/off-ratio for hole current was observed for even small applied Vig. Observations of the MR behavior revealed the carrier densities as high as ~1013 cm−2 under large Vig values, despite the assembly structure of narrow GNRs with ~20 nm width. Cgeo as large as ~12 μF/cm2 was also estimated. We observed a maximum conductance peak in the high −Vig region and its separation into two peaks upon applying a side-gate Vex. Based on halfmetallicity model, it was discussed that the localized edge-π band with excess-density electrons induced by Vig and its spin splitting for majority and minority spins caused by Vex led to these phenomena and that the applied Vex played a role similar to that of the in-plane field Vex under the application of Vig.

The present finding clarify that one can detect the localized edge bands via the excess-density electrons due to Vig by observing conductance and also the spin behaviors of the band within controlled manner by applying side-gate Vex. The results must be valuable for criticalelement-free novel spintronic devices.


The authors thank Y. Iwasa, K. Fujita, Y. Hashimoto, E. Endo, Y. Iye, S. Katsumoto, M. Yamamoto, S. Tarucha for their technical contribution, fruitful discussions, and encouragement. This work was partly supported by a Grant-in-Aid for Scientific Research (Basic research A: 24241046) under the aegis of MEXT, a Grant for Zeroemission Energy program by Kyoto University, and also an AFOSR grant.


Conflicts of Interest

The authors declare no conflicts of interest.


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