Multiscale magnetic study of Ni(111) and graphene on Ni(111)

We have investigated the magnetism of the bare and graphene-covered (111) surface of a Ni single crystal employing three different magnetic imaging techniques and ab initio calculations, covering length scales from the nanometer regime up to several millimeters. With low-temperature spin-polarized scanning tunneling microscopy we find domain walls with widths of 60–90 nm, which can be moved by small perpendicular magnetic fields. Spin contrast is also achieved on the graphene-covered surface, which means that the electron density in the vacuum above graphene is substantially spin polarized. In accordance with our ab initio calculations we find an enhanced atomic corrugation with respect to the bare surface, due to the presence of the carbon $p_z$ orbitals and as a result of the quenching of Ni surface states. The latter also leads to an inversion of spin polarization with respect to the pristine surface. Room temperature Kerr microscopy shows a stripelike domain pattern with stripe widths of 3–6 $\mu$m. Applying in-plane-fields, domain walls start to move at about 13 mT and a single domain state is achieved at 140 mT. Via scanning electron microscopy with polarization analysis a second type of modulation within the stripes is found and identified as 330 nm wide V lines. Qualitatively, the observed surface domain pattern originates from bulk domains and their quasidomain branching is driven by stray field reduction.

Figure 1

Ni(111), spin-averaged data. (a) Constant-current image ($U=-1$ V, $I=0.5$ nA) taken at $T=8$ K. (b) Atomically resolved image ($U=-4$ mV, $I=5$ nA) taken at RT. The diamond highlights the unit cell. (c) Height profile along the line displayed in (b). (d) The $dI/dU$ spectrum ($U_{s}tab=+1$ V, $I_{s}tab=2$ nA, $U_{m}od=80$ mV) is averaged over data taken at three different locations marked as red crosses in the $dI/dU$ map (inset).

Figure 2

Ni(111), spin-polarized data. Magnetic $dI/dU$ maps taken at (a) $B=0$ T and (b) $B=+50$ mT. Dashed lines show the shift of domain walls in the external magnetic field. (c) Line sections across domain walls marked by white box in (a). Gray circles and black lines represent experimental data and fitted profiles, respectively. (d) Magnetic $dI/dU$ map of 1.5 $\mu$m width taken at $B=0$ T. All data measured at $U=-200$ mV and $I=2.5$ nA.

Figure 3

Graphene on Ni(111), spin-averaged data. (a) Constant current overview image ($U=-1$ V, $I=0.5$ nA), taken at $T=8\pm 1$ K, showing flat terraces and four monatomic steps. (b) Zoom-in on a terrace ($U=+2.5$ mV, $I=5$ nA) showing the atomic lattice. (c) Height profile along the line depicted in (b). (d) Top and side views of the graphene/Ni top-fcc structure: Black color indicates carbon, blue color Ni atoms. Red dots indicate the positions of the empty spheres (see Sec. 5). The unit cell is highlighted by the diamond.

Figure 4

Graphene on Ni(111), spin-polarized data. Magnetic $dI/dU$ maps measured in (a) forward and (b) backward scan directions ($U=-200$ mV, $I=0.5$ nA). While the left wall is static, the right one is moved by the stray field of the tip (see text). (c) Line section as indicated in (a) and a fit of a general wall profile,[27, 28] yielding a wall width of about 50 nm. Data taken at $B=0$ T.

Figure 5

Simulated STM images calculated at a height of 3.6 Å over (a) clean Ni(111) and (b) graphene/Ni(111). The orientation of the graphene lattice is the same as in the unit cell depicted in Fig. 3d: The C atoms visible in the image belong to the B sublattice.

Figure 6

(a) Simulated STS spectrum at $3.6$ Å above the clean Ni(111) surface. (b) Spin contrast $\Delta \rho$ (see text) at $3.6$ Å over the pristine Ni(111) surface and the graphene-coated Ni(111) surface respectively.

Figure 7

Band structure of a clean 15-layer slab of Ni(111) for majority (a) and minority spin (b) components. The same slab, coated with graphene on one side, is shown in (c) for the majority and in (d) for the minority case. The projections of the bands onto empty spheres in the vacuum at 3.6 Å, averaged over their lateral position [red dots in Fig. 3d], are shown as fat bands. Here, the vacuum projections above the Ni are indicated by blue color, over graphene by red color. In (e) and (f) the contributions of each band to the corrugations measured in STM are visualized as fat bands [see Eq. (5)] in the same color code. For visualization purpose, the corrugation above Ni has been enhanced by a factor of 4.

Figure 8

Kerr microscopy images of the magnetic structure of the Ni(111) single crystal. The gray-scale amplitude of the images is proportional to the in-plane magnetization component which is indicated by a double arrow in the lower right corner.

Figure 9

SEMPA images of the magnetic structure of the Ni(111) surface at the same position, but with different surface preparations. Encoded in color is the direction of the in-plane magnetization, as defined by the 360${}^{\circ }$ color wheel. In (a) the surface is covered with graphene. (b) gives the signal from the clean Ni surface following sputter cleaning. For contrast enhancement, in (c) a thin iron layer has been deposited. To emphasize the changes in contrast, the lower right part of each image gives the $y$ component of the magnetization in a gray-scale representation.

Figure 10

High-resolution SEMPA images of the Néel-like walls at the Ni(111) surface. In (a) the in-plane distribution of the magnetization of the Ni(111) surface is shown. Encoded in color is the direction of the in-plane magnetization, as defined by the 360${}^{\circ }$ color wheel. In addition the direction is illustrated by the arrows. In (b) the $y$ component of the magnetization is shown in a gray-scale representation. The striped line indicates the path of the wall profile shown in (d). (c) Sketch of a section across a V line on the surface, illustrating the corresponding volume domain structure. The striped arrows indicate the branched structure of the corresponding domains. (d) The wall profile is fitted by Eq. (1) This fit yields a wall width $w$ $=$ 330 $\pm$ 6 nm.