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Electric Contributions to Magnetic Force Microscopy Response from Graphene and MoS2 Nanosheets

Magnetic force microscopy (MFM) signals have recently been detected from whole pieces of mechanically exfoliated graphene and molybdenum disulfide (MoS2) nanosheets and magnetism of the two nanomaterials was claimed based on these observations. However, non-magnetic interactions or artefacts are commonly associated with MFM signals, which makes the interpretation of MFM signals not straightforward. A systematic investigation has been done to examine possible sources of the MFM signals from graphene and MoS2 nanosheets and whether the MFM signals can be correlated with magnetism. It is found that the MFM signals have significant non-magnetic contributions due to capacitive and electrostatic interactions between the nanosheets and conductive cantilever tip, as demonstrated by electric force microscopy (EFM) and scanning Kevin probe microscopy (SKPM) analyses. In addition, the MFM signals of graphene and MoS2 nanosheets are not responsive to reversed magnetic field of the magnetic cantilever tip. Therefore, the observed MFM response is mainly from electric artefacts and not compelling enough to correlate with magnetism of graphene and MoS2 nanosheets.

Journal of Applied Physics 116, 213904 (2014). DOI: 10.1063/1.4903040 3 from graphene and MoS 2 nanosheets has been systematically investigated and the correlation between the MFM signals and magnetism is discussed.

II. EXPERIMENTAL
The graphene and MoS 2 nanosheets used in this work were exfoliated from HOPG (Ted Pella) and MoS 2 particles (Sigma-Aldrich) using the Scotch tape method. An Olympus BX51 optical microscope was used for the visualization of the few-layer graphene and MoS 2 nanosheets. A Cypher scanning probe microscope (Asylum Research) was used for the MFM, EFM and SKPM measurements. A Co/Cr coated magnetic cantilever with a spring constant of 2 N/m and coercivity of ~400 Oe (ASYMFM, Asylum Research) and Pt/Ti coated conductive cantilevers with a spring constant of 2 N/m (AC240TM, Asylum Research) were used. The magnetic cantilever tip was magnetized and also reversely magnetized by approaching it to a neodymium magnet either face-up or face-down.

III. RESULTS AND DISCUSSION
The preparation procedure of graphene and MoS 2 nanosheets and experimental conditions for MFM measurements are similar to those reported in Ref. 21 . The graphene and MoS 2 nanosheets were prepared on silicon wafer covered with a 90 nm layer of silicon oxide (90 nm SiO 2 /Si) by the Scotch tape exfoliation and then visualized by optical microscope observation. [23][24][25] Figure 1a   The obtained MFM results are consistent with those in the previous report. 21 As shown in Figure 1c, the graphene nanosheets do show MFM phase shift/contrast compared to the nonmagnetic SiO 2 /Si substrate, especially the 1L graphene showing a relatively strong contrast (note that positive MFM phase shift is defined as "attractive" in Cypher AFM, which is opposite to the setting in most other AFMs, e.g. Bruker AFM). In addition, similar reduction of the MFM phase shift with the increase of the lift height was observed in our experiment ( Figure 1d-h), which was also reported in Ref. 21 .
Journal of Applied Physics 116, 213904 (2014). DOI: 10.1063/1.4903040 5 To test whether the observed MFM phase contrast is due to magnetic interactions or nonmagnetic artifacts, the following three additional tests were conducted. MFM signals are often associated with non-magnetic interactions, especially long-range electric forces such as electrostatic and capacitive forces, two of the strongest non-magnetic contributions in MFM. 22 These two electric interactions could be prevalent for all surfaces no matter that it is conducting, semiconducting or insulating. So the first test is to evaluate the electrostatic and  Fitting of the MFM phase shifts with respect to DC voltages can be used to estimate how significant the electric contributions are to the MFM images. If the cantilever frequency shift is smaller than its resonant frequency, the phase shift Δ can be written as: 26 Where / is the local force gradient or derivative of the force felt by the cantilever tip at a lift height z; k is the spring constant of the cantilever; and is the quality factor or Q factor of the cantilever. In the case of capacitive and electrostatic interactions, if the capacitive interaction between the cantilever tip and the sample is treated as an ideal capacitance and the sample surface is planar, the force gradient can be simplified as: 26,27 The first term relates to capacitive force, where C is the local capacitance between the cantilever tip and the sample surface; is the DC voltage applied to the cantilever tip; is the work function difference between the cantilever tip and the sample surface; is the effective surface potential proportional to the trapped charges on the sample surface. The second term associates with Coulombic (electrostatic) force due to charges, where is the charge-induced electric field applied to the cantilever tip. It can be seen that the capacitive part has a quadratic function to and the Coulombic part is linear to . Because the Coulombic force is normally much smaller than the capacitive force, the force gradient and thus phase shift (Δ ) due to capacitive and electrostatic forces generally show a parabola under varying . [28][29][30] Figure 2h shows that the measured phase shift values of the 1L and 10L graphene nanosheets can be well fitted using second degree polynomials, when dipolar water film, between the SiO 2 substrate and the graphene nanosheets or charge transfers between the substrate and the graphene. 29,32,33 The capacitive interaction relates to work function difference ( ), surface potential ( ) and local capacitance (C) (see Eq. 2). As discussed above, the work function difference among graphene nanosheets of different thicknesses is small and negligible, but the surface potentials due to trapped charges are quite different. In addition, it has been found that graphene nanosheets of different thicknesses have different capacitance. 34 So the capacitive contribution to the different phase shifts (i.e. force gradients) among graphene nanosheets of different thickness comes from their different surface potential ( ) and capacitance (C).
These are the origins of the different phase contrasts for graphene nanosheets of different thicknesses and also explain why MFM phase contrast can be observed from the graphene ( Figure 1c). The second test involves non-magnetic cantilever for "MFM" scans. A conductive but nonmagnetic cantilever coated by Pt/Ti was used to scan graphene nanosheets following the  Figure 3 shows that the EFM images are almost identical to the MFM images in Figure 2, except when = 0 (as in Figure 2d and 3d). The small difference is derived from the discrepancy of work function difference ( ) between the cantilever tip and the graphene nanosheets due to different cantilever coating materials (Co/Cr vs. Pt/Ti), and possibly different work function and built-in charges of the MFM and EFM cantilevers ( ) (see Eq. 2). In fact, we found that magnetic and conductive cantilevers produced in the same batch could give rise to slightly different MFM and EFM phase images ( = 0) of the same graphene nanosheets. 35 The reduced MFM phase signal with increased lift height (Figure 1e-i) can be also replicated by EFM, 35 because capacitive and electrostatic forces are also distance sensitive. It should be noted that similar EFM images from graphene have been reported before. 29,34,36 This test demonstrates that similar phase shift can be observed even when non-magnetic cantilever is used and re-confirms that strong capacitive and electrostatic interactions are present between conductive cantilever tip and the graphene on SiO 2 /Si substrate. The above tests clearly show that the reported MFM signals mainly, if not completely, derives from non-magnetic interactions or artefacts.   (Figure 4). In contrast, a floppy disk, as a control sample, did show expected MFM phase reverse after the magnetism of the same cantilever tip was reversed. 35 In addition, the effect of lift height on the MFM phase shift is identical for the reversed tip magnetism. 35 In fact, the reported MFM signals from whole pieces of graphene 21 are very different from the previously reported MFM signals from graphite which only shows magnetic signals at defects or edges, rather than from whole pieces of material. 3,5 These MFM results are therefore unlikely to be from magnetic interactions. (2.98 nm) and 23L (15.9 nm) are shown in Figure 5a and b, respectively. Similar to the case of graphene, the MFM phase images of the MoS 2 nanosheets of different thicknesses show different contrast: the thicker MoS 2 (23L) exhibits more phase shift than the 1L and 4L nanosheets, consistent with the previous MFM study. 21 However, the MFM phase images of the MoS 2 nanosheets with ranging from -2 to +2 V also show dramatic different phase shifts ( Figure 6). The comparison of the vertexes of the fitted phase shift among the 1L, 4L and 23L MoS 2 nanosheets shows that the 1L MoS 2 (red) has a larger minimum of phase shift than the 4L (blue) and 23L (black) nanosheets (Figure 6i). This trend is opposite to that of graphene (Figure 2i), which can be attributed to SiO 2 substrate's negative (electron) doping for MoS 2 and positive (hole) doping for graphene. 29,30 This suggests that in addition to capacitive interactions, Coulombic (electrostatic) interactions between MoS 2 and the cantilever tip is strong, as supported by SKPM analysis which shows a strong charge effect ( Figure 6j). 37 In addition, no MFM phase reverse was observed from the MoS 2 nanosheets under reversed tip magnetism either (Figure 7). So similar to the case of graphene, the MFM signals from MoS 2 nanosheets also have a significant non-magnetic contribution.

Effect of different cantilevers from the same batch
It is found that different cantilevers even from the same batch could give slightly different EFM results. Figure S1 shows the EFM images of the same piece of graphene nanosheets using two Pt/Ti coated conductive cantilevers produced in the same batch (same parameters, such as spring constant and coating material) with no voltage applied (V tip = 0V). It can be seen that the two EFM images are slightly different, which could be due to different trapped charges in the two cantilevers and their different tip structures, as discussed in Eq. 2. Figure S1. EFM images of the same piece of graphene nanosheets using two different cantilevers produced in the same batch. All the scanning conditions are identical.

Effect of lift height on EFM phase shift
The effect of lift height on the EFM phase images was shown in Figure 2, which also shows that the phase shift decreases with the increase of lift height, similar to that of the MFM phase images (Figure 1e-i). Figure S2. EFM phase images of the graphene nanosheets using different lift height (z). The scale range is 0.1° for all images.

MFM of a floppy disk before and after reverse of tip magnetism
MFM phase images were taken from a floppy disk with reversed direction of magnetic field of the magnetic cantilever tip. A particle on the surface of the floppy disk (* in Figure S3a) was used as a navigation mark to return to the same location after the reverse of tip magnetism. As expected, the phase shifts reversed with the reversed tip magnetism.

Lift height effect on MFM phase images of the graphene with reversed tip magnetism
The effect of lift height on the MFM phase images of the graphene is compared with reversed magnetism of the magnetic cantilever tip. Figure S4 shows that the MFM phase images at different lift heights (z = 35 to 125 nm) are identical before and after the tip magnetism was reversed. Figure S4. MFM phase images of the graphene nanosheets under the initial direction of magnetic field of the magnetic cantilever tip (upper row) and MFM images under the reversed tip magnetism (lower row).