Figure 1

Tunneling density-of-states diagram for an Al-oxide-Ni tunnel junction showing the Al electrode for a BCS-type density of states split into spin-up (increased in energy by $\mu H$) and spin-down (decreased in energy by $\mu H$) parts and an assumed predominance of spin-down (magnetic moment parallel to the field) carriers at the Fermi surface of Ni. Arrows on density of states refer to spin direction. From 173.Reuse & Permissions

Figure 2

Normalized conductance of an $\mathrm{Al}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\text{−}\mathrm{Ni}$ tunnel junction measured as a function of the voltage applied to the Al film for three values of applied magnetic field. The asymmetry of the conductance peaks $a$, $b$, $c$, and $d$ $(H=33.7\mathrm{kOe})$ results from the spin polarization of the Ni carriers. From 173.Reuse & Permissions

Figure 3

Schematic potential diagram for two metallic ferromagnets separated by an insulating barrier. The directions of internal fields $h_A$ and $h_B$ within the magnets form an angle $\theta$. From 167.Reuse & Permissions

Figure 4

Schematic of STM geometry in the Tersoff-Hamann model. The probe tip is assumed to be locally spherical with radius of curvature $R$, where it approaches nearest the sample surface (shaded). The distance of nearest approach is $s$. The center of curvature of the tip is labeled ${\vec{r}}_0$. From 175.Reuse & Permissions

Figure 5

(Color) Principle of spin-polarized scanning tunneling microscopy (SP-STM): the spin-polarized tunneling current flowing between a magnetic tip and a magnetic sample depends on the relative alignment of the local magnetization of tip and sample as well as on the spin polarization of the electronic states of tip and sample contributing to the tunneling current.Reuse & Permissions

Figure 6

Schematic of a ferromagnetic tip scanning over alternately magnetized terraces separated by monatomic steps of height $h$. An additional contribution of spin-polarized tunneling leads to the observation of alternating step height values $h_1=h+\Delta s_1+\Delta s_2$ and $h_2=h-\Delta s_1-\Delta s_2$. From 202.Reuse & Permissions

Figure 7

Effective spin polarization of a $\mathrm{Cr}{\mathrm{O}}_2$-vacuum-Cr(001) tunnel junction as a function of sample bias voltage. The insets show the spin-up (upper part) and spin-down (lower part) density of states of $\mathrm{Cr}{\mathrm{O}}_2$ and the Cr(001) surface. From 200.Reuse & Permissions

Figure 8

Energetically lowest magnetic configuration of the end of a ferromagnetic amorphous metal tip. The inset shows the tip apex at higher magnification and reveals that the magnetization on the outer cone surface points along the tip axis. From 214.Reuse & Permissions

Figure 9

(Color) Schematic of the apex of a ferromagnetic (a) and an antiferromagnetic tip (b). In both cases, the spin state of the front atom determines the spin contrast in SP-STM. However, only in the case of an antiferromagnetic tip can the disturbing influence of long-range magnetic stray fields be avoided.Reuse & Permissions

Figure 10

Scanning electron micrograph of an electrochemically etched W tip after a high-temperature flash at $T>2200\mathrm{K}$ at (a) medium and (b) higher magnification revealing a tip diameter of about $1\mu \mathrm{m}$.Reuse & Permissions

Figure 11

(Color) Schematic of the magnetization distribution in magnetic thin-film tips, governed by magnetic interface anisotropy.Reuse & Permissions

Figure 12

(Color) Schematic of a simple preparation method for obtaining spin-sensitive probes. A nonmagnetic metallic tip is dipped into a magnetic sample and subsequently retracted. If the materials for tip and sample are chosen such that the magnetic sample material wets the tip, a stable SP-STM probe can be obtained.Reuse & Permissions

Figure 13

Constant-current STM topograph colorized with the spin-resolved spectroscopic $dI∕dU$ signal, showing domain walls in Fe double-layer nanowires grown on a W(110) substrate ([115]).Reuse & Permissions

Figure 14

(Color) Schematic experimental setup for modulated tip magnetization mode measurements with (a) an out-of-plane-sensitive magnetic tip and (b) an in-plane-sensitive ring-shaped magnetic probe.Reuse & Permissions

Figure 15

Comparison of the energy dependence of the measured spin polarization on a Gd(0001) sample using two different techniques: spin-polarized tunneling spectroscopy with an Fe-coated thin film tip (28) and spin-polarized inverse photoemission spectroscopy (66).Reuse & Permissions

Figure 16

Application of the spectroscopic mode of SP-STM. (a) Spin-resolved local density-of-states (LDOS) diagram for a tunnel junction with a rare-earth metal (0001) surface, exhibiting a spin-split electronic state close to $E_F$, and an Fe-coated tip with a constant spin-resolved LDOS. Due to spin-dependent tunneling, the differential tunneling conductance will be enhanced (reduced) at a bias voltage which corresponds to the energy of the surface state spin component parallel (antiparallel) to the tip’s preferred spin direction (b). This leads to a reversal in the magnitude of the spin-dependent $dI∕dU$ signal at the energies of the peak positions of the spin-split surface state upon magnetic switching of the sample by an external applied magnetic field. (c) This type of behavior was observed in the spin-resolved tunneling spectra measured with an Fe-coated tip above a Gd(0001) island. From 28.Reuse & Permissions

Figure 17

(Color) Application of SP-STS for magnetic domain imaging with subnanoscale spatial resolution: a thin Dy(0001) film (90 ML) grown epitaxially on a W(110) substrate (a) exhibits a domain structure (b) with six different in-plane orientations of the local magnetization. (c) The six different contrast values in the SP-STM image result from the six different projections of the local sample magnetization onto the local magnetization direction (quantization axis) of the Dy probe tip. From 107.Reuse & Permissions

Figure 18

(Color) Determination of magnetic domain wall widths. (a) Magnetization distribution of a 60 ML Dy(0001) film as measured with a Cr-coated W tip. The relatively high magnetic anisotropy of Dy leads to narrow magnetic domain walls of typically $2–5\mathrm{nm}$ width, as deduced from the corresponding line sections (b). From 14.Reuse & Permissions

Figure 19

SP-STM images ($dI∕d{m}_T$ signal) of the dendriticlike magnetic structure on a Co(0001) single-crystal surface at different length scales: (a) fractal-like domain-wall structure at large scale, (b) the end of a branch with a wall-like feature, and (c) detail of a sharp domain wall. (d) The corresponding topography of the same surface area as in (c). From 64.Reuse & Permissions

Figure 20

(Color) Thin film of 3.2 ML Fe on W(001) grown at a temperature $T\sim 525\mathrm{K}$. (a) Constant-current STM topograph showing that patches of 2, 3, and 4 ML Fe on W(001) are exposed at the surface. (b) Simultaneously measured spin-resolved $dI∕dU$ map showing three magnetic contrast levels (I–III) on the third monolayer and two magnetic contrast levels (1, 2) on the fourth monolayer. The derived magnetization axes for the third and fourth monolayers are sketched in (c). From 182.Reuse & Permissions

Figure 21

(Color) Application of SP-STM to nanocrystalline thin films. (a) STM topograph and (b) spectroscopic SP-STM image of a nanocrystalline Fe film showing the correlation between magnetic and grain structure at subnanometer-scale spatial resolution.Reuse & Permissions

Figure 22

(Color) Application of SP-STM to surfaces of antiferromagnets. (a) Spin-resolved differential tunneling conductance spectrum $dI∕dU$ measured with an Fe-coated W tip above differently magnetized terraces of a Cr(001) surface. A highly spin-polarized $d_{z^2}$-like surface state of Cr(001) close to the Fermi level provides a high spin-dependent $dI∕dU$ signal. (b) SP-STM line profiles measured in the constant-current mode reveal alternating step-height values whereas the spin-resolved spectroscopic $dI∕dU$ signal shows low and high levels, depending on the relative directions of magnetization of tip and surface terrace. (c) Spatially resolved spectroscopic SP-STM image $(1000\times 300{\text{nm}}^2)$ revealing the topological antiferromagnetic order of the Cr(001) surface. From 104, 103.Reuse & Permissions

Figure 23

(Color) Surface magnetic structure in the presence of defects. (a) STM topograph and spectroscopic SP-STM image of the Cr(001) surface revealing the magnetization distribution around a screw dislocation. (b) Large-scale STM and SP-STS images showing the presence of a domain wall connecting two screw dislocations. (c) Line profile across the domain wall observed in (b) yielding a domain-wall width of about $166\mathrm{nm}$. From 155.Reuse & Permissions

Figure 24

(Color) Large-scale view of the topological antiferromagnet Cr(001) in the presence of screw and edge dislocations. Several SP-STS images, each $1\mu {\mathrm{m}}^2$ in size, have been put together in order to reveal the magnetization distribution over an extended surface area and to show the degree of reproducibility of SP-STS imaging even when recording the data at room temperature as in the present case.Reuse & Permissions

Figure 25

Application of SP-STM to magnetic nanostripes. (a) Rendered perspective topographic STM image $(200\times 200{\mathrm{nm}}^2)$ of narrow Fe nanostripes ($\sim 6–7\mathrm{nm}$ wide) prepared on a stepped W(110) substrate, grayscale coded with the spin-resolved spectroscopic $dI∕dU$ signal as measured with an out-of-plane-sensitive Gd-coated tip. A dipolar antiferromagnetic coupling between the Fe double-layer nanostripes leads to an alternating spin contrast. However, if two double-layer stripes are too close to each other, the exchange interaction leads to a ferromagnetic coupling. In some cases, narrow domain walls can be observed along the double-layer nanostripes. (b) Schematic of the perpendicularly magnetized double-layer Fe stripes exhibiting an antiparallel dipolar coupling in order to reduce the magnetic stray field of the array. Within the domain walls, the Fe double-layer nanostripes locally exhibit an in-plane magnetization. From 145; 34.Reuse & Permissions

Figure 26

(Color) Multidomain magnetic nanostripes. (a) Rendered perspective topographic STM image $(200\times 200{\mathrm{nm}}^2)$ of $\sim 15\mathrm{nm}$ wide Fe nanostripes prepared on a stepped W(110) substrate, color coded with the spin-resolved spectroscopic $dI∕dU$ signal as measured with an out-of-plane-sensitive Gd-coated tip. A characteristic magnetic domain structure with a typical domain size of $15\times 20{\mathrm{nm}}^2$ can be observed. (b) Rendered perspective topographic STM image $(200\times 200{\mathrm{nm}}^2)$ of $\sim 15\mathrm{nm}$ wide Fe nanostripes prepared on a stepped W(110) substrate, color coded with the spin-resolved spectroscopic $dI∕dU$ signal as measured with an Fe-coated tip. In this case, a domain-wall contrast is achieved due to the sensitivity of Fe thin-film tips to the in-plane magnetization component. (c) Differential tunneling conductance spectra measured with a W tip, a Gd-coated tip, and an Fe-coated tip above Fe double-layer nanostripes exhibiting both out-of-plane and in-plane magnetization directions depending on the particular location. While the W tip is sensitive only to the change of electronic structure between the first and second layers of Fe on W(110), the use of Gd-coated tips as well as Fe-coated tips leads to a pronounced spin dependence of the measured tunneling conductance curves, particularly for a sample bias of $U=+0.7\mathrm{V}$. From 35.Reuse & Permissions

Figure 27

(Color) Series of spin-resolved spectroscopic $dI∕dU$ maps $(200\times 200{\text{nm}}^2)$ of an array of multidomain Fe double-layer nanostripes obtained in an increasing perpendicular magnetic field. Pairs of 180° walls are gradually forced together, which is equivalent to the formation and compression of 360° walls. At a field of $800\mathrm{mT}$, most of them have vanished, i.e., the Fe thin film is in magnetic saturation. From 116.Reuse & Permissions

Figure 28

(Color) Rendered perspective topographic STM image $(200\times 200{\mathrm{nm}}^2)$ of a closed Fe double layer prepared on a stepped W(110) substrate, color coded with the spin-resolved spectroscopic $dI∕dU$ signal as measured with an out-of-plane-sensitive GdFe-coated tip. The Fe thin film exhibits a stripe domain phase along the $\left[1\overline{1}0\right]$ direction with a magnetic periodictiy of about $50\mathrm{nm}$. From 110.Reuse & Permissions

Figure 29

(Color) Ultrasharp magnetic domain walls. (a) Spin-resolved spectroscopic $dI∕dU$ map $(400\times 400{\text{nm}}^2)$ of 1.25 ML Fe on a stepped W(110) substrate as measured with an in-plane-sensitive Fe-coated W tip. Monolayer stripes with in-plane magnetic anisotropy exhibit a domain contrast whereas the narrow double-layer stripes in between exhibit a domain wall contrast which is more clearly visible in the zoom-in SP-STS image of (b). A detailed analysis of line profiles across the domain walls of first- and second-layer Fe nanostripes, based on micromagnetic theory, leads to wall widths of $w_{\mathrm{DL}}=3.8\pm 0.2\mathrm{nm}$ for the narrow Fe double-layer nanostripe and $w_{\mathrm{ML}}=0.6\pm 0.2\mathrm{nm}$ for the Fe monolayer stripes (c). From 151.Reuse & Permissions

Figure 30

(Color) Schematic of a narrow domain wall where the magnetization rotates quasicontinuously on a lateral scale of several lattice sites (top part) and the case of an extremely narrow domain wall for which the spin-density orientation rotates between two atoms, where the spin density is minimal, leading to antiferromagnetically coupled neighboring lattice sites (bottom part).Reuse & Permissions

Figure 31

(Color) Magnetic behavior of Co nanostripes. (a) Spin-resolved spectroscopic $dI∕dU$ map $(130\times 130{\text{nm}}^2)$ of Co monolayer nanostripes prepared on a stepped Pt(111) substrate, as measured with an out-of-plane sensitive Cr-coated W tip. (b) Magnetic hysteresis curve extracted from SP-STS data of Co monolayer stripes on Pt(111) showing a coercive field of $0.25\pm 0.05\mathrm{T}$. From 130.Reuse & Permissions

Figure 32

(Color) SP-STS images showing the multidomain state of large nanoislands of Dy on a W(110) substrate. The island size is about (a) $800\mathrm{nm}$ and (b) $400\mathrm{nm}$.Reuse & Permissions

Figure 33

(Color) Application of SP-STM to magnetic vortex states. (a) Schematic of a magnetic vortex. Far away from the vortex core the magnetization continuously curls around the vortex center with an orientation in the surface plane. Toward the center of the vortex core the magnetization turns out of the surface plane until it is perpendicularly oriented. (b) SP-STS image revealing a magnetic vortex state in an Fe island with a size of about $200\mathrm{nm}$ and a thickness of about $8\mathrm{nm}$. A Cr-coated W-tip that is sensitive to the in-plane magnetization component was used.Reuse & Permissions

Figure 34

(Color) Magnetic vortex core contrast depending on the SP-STM tips being used. (a) High-resolution SP-STS image of the in-plane magnetization component of a magnetic vortex core state in an Fe island measured with an in-plane-sensitive Cr-coated W tip. (b) High-resolution SP-STS image of the out-of-plane magnetization component of a magnetic vortex core state measured with an out-of-plane-sensitive Cr-coated W tip. (c) Distorted SP-STS image of a magnetic vortex core obtained with an Fe-coated W tip.Reuse & Permissions

Figure 35

(Color) Magnetic vortex core contrast as function of external field direction. (a) Response of a magnetic vortex core to an external magnetic field: while the size of the vortex core is increased if the external field is applied parallel to the out-of-plane magnetization direction in the core region, the opposite behavior is observed for the antiparallel case. (b) The field dependence of line profiles across the vortex core, extracted from the experimental SP-STS data obtained with a Cr-coated tip, show good agreement with calculated line profiles based on micromagnetic theory. From 185.Reuse & Permissions

Figure 36

(Color) Magnetic vortex core state as function of nanoisland thickness. (a) SP-STS image $(400\times 400{\text{nm}}^2)$ showing a single-vortex state of an Fe island $7.5\mathrm{nm}$ thick. (b) Diamond (double-vortex) state observed by SP-STS on an Fe island of similar lateral size but slightly thicker $\left(8.5\mathrm{nm}\right)$ than the one in (a). (c) Magnetization distribution for the double-vortex state observed in (b). From 44.Reuse & Permissions

Figure 37

(Color) SP-STS data obtained with an Fe-coated W tip showing simultaneously in-plane magnetized, single-domain Fe nanoislands and the magnetic domain structure of an Fe monolayer (wetting layer) on a W(110) substrate. The magnetization directions of the Fe nanoislands and the magnetic domain structure of the Fe monolayer are strongly correlated. From 197.Reuse & Permissions

Figure 38

(Color) Magnetism of single-domain nanoislands as function of their lateral size. (a) SP-STS image$(400\times 400{\text{nm}}^2)$ of Fe double-layer nanoislands with a Fe monolayer in between. The data have been recorded with an out-of-plane-sensitive Gd-coated probe tip. (b) Zoom-in SP-STS image $(70\times 70{\text{nm}}^2)$ showing vanishing out-of-plane spin contrast on the smallest Fe double-layer nanoislands. (c) Magnitude of the spin-resolved $dI∕dU$ signal as a function of the islands’ lateral size.Reuse & Permissions

Figure 39

(Color) Exchange-coupled nanoislands. (a) Spin-resolved $dI∕dU$ map $(400\times 400{\text{nm}}^2)$ of nanoscale Fe islands of single-atomic height on a stepped Cr(001) substrate. The data were recorded at room temperature with an in-plane-sensitive Fe-coated tip. Due to an antiferromagnetic exchange coupling between the nanoscale Fe islands and the Cr(001) substrate, the Fe islands are magnetized in opposite directions relative to the underlying Cr(001) terraces and therefore exhibit opposite in-plane spin contrast. (b) Local spin-resolved differential tunneling conductance spectra as measured above differently magnetized Cr(001) terraces and corresponding Fe nanoislands located on top of these two types of Cr(001) terraces. The reversal of intensity levels of the differential tunneling conductance at the bias voltage corresonding to the energetic position of the $d_{z^2}$-like surface state of Fe(001) and Cr(001) indicates the antiferromagnetic coupling between the Fe islands and the Cr(001) substrate. From 156.Reuse & Permissions

Figure 40

(Color) Stacking-dependent spectroscopic contrast on Co nanoislands. (a) Spin-averaged $dI∕dU$ map $(60\times 60{\text{nm}}^2)$ of nanoscale Co islands [two layers high relative to the Cu(111) substrate] as measured with a nonmagnetic W tip. The strong spectroscopic contrast between different islands originates from a different stacking of the Co islands and is a pure electronic structure effect. It is not related to a different magnetization state of the Co islands. (b) Local (spin-averaged) differential tunneling conductance spectra obtained with a nonmagnetic W tip above differently stacked Co islands. While a $d_{z^2}$-like surface state related peak is found at a sample bias voltage of $-0.35\mathrm{V}$ for fcc-stacked Co islands, this peak is shifted to $-0.28\mathrm{V}$ for hcp-stacked Co islands. This difference gives rise to a stacking-dependent contrast in spatially resolved spectroscopic images. The third spectrum shown was measured above the Cu(111) substrate. It shows a conductance rise at $-0.46\mathrm{V}$ which is related to the onset of the free-electron-like $sp$-type surface state of the Cu(111) substrate. From 148.Reuse & Permissions

Figure 41

(Color) Disentangling stacking- and magnetic-state-dependent contrast of Co nanoislands. (a) Spin-resolved differential tunneling conductance spectra measured with an out-of-plane-sensitive Cr-coated W tip on differently stacked and differently magnetized double-layer Co nanoislands on Cu(111). (b) Energy-dependent “structural asymmetry” and “spin asymmetry” curves derived from the spin-resolved tunneling spectra presented in (a). By choosing sample bias voltages for which the spin asymmetry becomes large while the structural asymmetry is negligible, a clear and pure magnetic contrast can be achieved in spatially resolved SP-STS measurements (c). Image size: $60\times 60{\text{nm}}^2$.Reuse & Permissions

Figure 42

(Color) Set of SP-STS data $(150\times 150{\text{nm}}^2)$ showing the response of nanoscale Co islands on Cu(111) to an external magnetic field applied perpendicular to the sample surface plane. The SP-STS images were obtained with an out-of-plane-sensitive Cr-coated W tip which is not affected by the external field. From 148.Reuse & Permissions

Figure 43

(Color) Spin-averaged STS image $(60\times 60{\text{nm}}^2)$ showing 2D electronic confinement states in double-layer Co nanoislands on Cu(111) as well as scattering states of the Cu(111) surface state electrons at single Co adatoms and $\mathrm{Co}∕\mathrm{Cu}$ interfaces.Reuse & Permissions

Figure 44

(Color) SP-STS data $(60\times 60{\text{nm}}^2)$ revealing the spin dependence of the 2D electronic confinement states in nanoscale Co islands which manifests itself by a spin-dependent oscillation amplitude of the confinement states for differently magnetized Co nanoislands. From 150.Reuse & Permissions

Figure 45

(Color) Atomic-resolution spin mapping on an antiferromagnetic Mn monolayer. (a) Schematic of an antiferromagnetically ordered atomic layer with a bcc (110) lattice symmetry. The rectangular magnetic unit cell is twice larger than the diamond-shaped structural unit cell. (b) Atomic-resolution constant-current STM image $(2.7\times 2.2{\text{nm}}^2)$ of an atomic layer of Mn, pseudomorphically grown on a W(110) substrate. Since a nonmagnetic W tip was used in this case, the opposite orientation of magnetic moments of adjacent Mn atoms cannot be revealed. All Mn atoms therefore appear identical. (c) In contrast, the magnetic superperiodicity corresponding to the theoretically predicted $c(2\times 2)$ antiferromagnetic state of the atomic layer of Mn on W(110) can be revealed by an in-plane sensitive Fe-coated W tip. The insets in (b) and (c) show a comparison with simulated STM and SP-STM images based on density functional theory, respectively. From 88.Reuse & Permissions

Figure 46

(Color) Atomic-resolution spin mapping on an antiferromagnetic Fe monolayer. (a) SP-STM image showing the magnetic $(2\times 2)$ superstructure of (b) an antiferromagnetic monolayer of Fe on a W(001) substrate. Since an out-of-plane magnetized Fe-coated W tip has been used, one concludes that the Fe monolayer on W(001) exhibits an out-of-plane magnetic anisotropy, which was subsequently confirmed by DFT calculations. The inset in (a) shows an atomically resolved $(1\times 1)$ lattice as revealed either by a nonmagnetic or by an in-plane-sensitive probe tip. From 112.Reuse & Permissions

Figure 47

(Color) The upper part shows two SP-STM images of exactly the same surface location on a 1 ML $\mathrm{Fe}∕\mathrm{W}\left(001\right)$ sample which were obtained with the same Fe-coated W tip magnetized by an external field in two opposite out-of-plane directions. An atomic adsorbate was used for making an accurate registry between the two SP-STM images allowing the calculation of the sum (topographic contrast) and difference (magnetic contrast) images (lower part).Reuse & Permissions

Figure 48

(Color) Atomic-resolution spin mapping in the presence of surface defects. (a) Larger-scale SP-STM image of the antiferromagnetic Fe monolayer on W(001) with atomic resolution. In addition to the magnetic $(2\times 2)$ superlattice, atomic-scale defects (vacancies and impurities) as well as second-layer Fe islands (bright features) are visible. (b) Perspective view of several SP-STM images, each ${\left(50\mathrm{nm}\right)}^2$ in size, which have been put together in order to reveal the perfect Néel-type order of the Fe monolayer on W(001) over an extended surface area and show the degree of reproducibility of atomic-resolution SP-STM imaging.Reuse & Permissions

Figure 49

(Color) Domain wall in the antiferromagnetic Fe monolayer on W(001): comparison between the spin structure as derived from Monte Carlo simulations, simulated SP-STM image based on the calculated spin structure, and experimental atomic-resolution SP-STM data. From 42.Reuse & Permissions

Figure 50

(Color) Atomic-resolution spin mapping on an antiferromagnetic nitride surface. (a) Constant-current SP-STM image obtained with an in-plane-sensitive Mn-coated W tip showing the antiferromagnetically coupled rows of Mn1 sites on the ${\mathrm{Mn}}_3{\mathrm{N}}_2\left(010\right)$ surface. (b) Schematic of the spin structure of ${\mathrm{Mn}}_3{\mathrm{N}}_2\left(010\right)$ and a corresponding experimental SP-STM line profile obtained under constant-current conditions. The period of the magnetic modulation amounts to $1.2\mathrm{nm}$. From 169.Reuse & Permissions

Figure 51

Atomic-resolution spin mapping on a ferrimagnetic transition metal oxide surface. (a) Schematic structure model of different Fe-O(001) planes of magnetite $\left({\mathrm{Fe}}_3{\mathrm{O}}_4\right)$ exhibiting Fe rows of alternating ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ pairs. While the separation of the Fe rows is $0.6\mathrm{nm}$, the atomic spacing along the Fe rows is $0.3\mathrm{nm}$. The magnetic period along the Fe rows is expected to be four times larger than the atomic spacing, i.e., $1.2\mathrm{nm}$. (b) Schematic of the spin structure along the Fe rows of an Fe-O plane of magnetite and a corresponding experimental SP-STM line profile obtained under constant-current conditions. The observed period of $1.2\mathrm{nm}$ reflects the spin structure of alternating ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ pairs (205). (c) Constant-current SP-STM image of the ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(001\right)$ surface revealing the magnetic superstructure period of $1.2\mathrm{nm}$ along the Fe rows of an Fe-O(001) plane. From 106.Reuse & Permissions

Figure 52

(Color) SP-STS image showing Co monolayer stripes prepared by step-flow growth on a stepped Pt(111) substrate as well as individual Co adatoms on the bare Pt(111) terraces. Out-of-plane spin contrast of a Cr-coated W tip was verified by revealing the magnetic structure of the out-of-plane magnetized Co nanostripes and the response of the sample to an external magnetic field (see Fig. 31). From 132.Reuse & Permissions

Figure 53

(Color) SP-STS applied to individual magnetic adatoms. (a) Spin-resolved local differential tunneling conductance spectra measured with an out-of-plane-sensitive Cr-coated tip above individual Co adatoms adsorbed either on fcc or on hcp sites of the Pt(111) substrate. Depending on the relative alignment of the magnetic moments of the tip apex atom and the Co adatoms, different spin-resolved tunneling conductance curves are obtained (red spectra for the parallel case and green spectra for the antiparallel case). (b) The energy-dependent spin asymmetry curves calculated from the spin-resolved tunneling spectra in (a) show quite similar behavior for Co-adatoms adsorbed on fcc and on hcp sites, except for the energy range between $-0.2\mathrm{eV}$ and the Fermi level. From 132.Reuse & Permissions

Figure 54

(Color) SP-STM images of four Co adatoms on Pt(111) obtained with a parallel (left) or antiparallel (right) alignment of the magnetic moments of tip apex atom and Co adatoms. In this case, a sample bias voltage of $-0.1\mathrm{V}$ was chosen for which the electronic contrast, arising from the two inequivalent Co adsorption sites (fcc and hcp), is much stronger than the magnetic contrast arising from the different orientation of the Co moments in the left and in the right image. From 132.Reuse & Permissions

Figure 55

(Color) Set of two SP-STM images showing several Co adatoms on Pt(111) with their spins aligned either parallel (left) or antiparallel (right) with respect to the spin orientation of the tip apex atom. In this case, a sample bias voltage of $+0.3\mathrm{V}$ was chosen for which the observed contrast difference between the left and the right image is primarily dominated by the different magnetic states of the Co adatoms, while the inequivalent Co adsorption sites cannot be distinguished. From 132.Reuse & Permissions

Figure 56

(Color) Determination of atom-resolved magnetization curves by SP-STS. (a) Experimentally determined magnetization curves for individual Co adatoms on a Pt(111) substrate for two different temperatures: By recording the spin-resolved differential tunneling conductance signal above single Co adatoms as a function of the externally applied magnetic field and by fitting the experimental data according to Eq. (41), the magnetic moment of the Co adatoms can be extracted. (b) Magnetization curves measured at $0.3\mathrm{K}$ for Co adatoms adsorbed on fcc and on hcp sites. The inset shows the histograms of the extracted magnetic moments of 38 hcp adatoms and 46 fcc adatoms. The significant variation of the extracted magnetic moments is not caused by the difference in the adsorption sites, but must be related with a spin-dependent interaction among the Co adatoms mediated via the Pt substrate in combination with the statistical distribution of the Co adatoms on the substrate. From 132.Reuse & Permissions

Figure 57

(Color) Indirect magnetic exchange interaction between Co adatoms and a Co monolayer stripe on a Pt(111) substrate. (a)–(c) Magnetization curves measured on the Co monolayer (straight lines) and on three adatoms (dots) $A$, $B$, and $C$ visible in the inset topograph of (d). The black vertical arrows in (a)–(c) indicate the exchange bias fields $B_{\mathrm{ex}}$, which can be converted into exchange energy values as plotted in (d) as a function of distance of the Co adatoms from the Co monolayer stripe. The black line in (d) represents the dipolar interaction calculated from the stray field of a $10\text{−}\mathrm{nm}$-wide Co stripe, whereas the red, blue, and green lines are fits to 1D, 2D, and 3D range functions for indirect magnetic exchange interaction. From 132.Reuse & Permissions

Figure 58

(Color) SP-STS image showing a spin-dependent scattering state arising from a single oxygen atom chemisorbed on a Fe(110) substrate. The contrast originates from the scattering of minority-spin electronic states of $d$-like symmetry as revealed experimentally by the spatial distribution of the scattering state and the relative strength of the scattering for the minority- and majority-spin channels. The interpretation has been supported by ab initio spin-resolved electronic structure calculations. From 180.Reuse & Permissions

Figure 59

(Color) Time-resolved SP-STS on individual nanoislands. (a) Topographic STM image (bottom left) and 23 successive spin-resolved $dI∕dU$ maps of four superparamagnetic Fe nanoislands on Mo(110) labeled a–d. Magnetic switching events that were directly observed are marked by straight arrows while zigzag arrows indicate switching events that must have occurred when the tip did not scan across the particular islands. (b) Time- and spin-resolved $dI∕dU$ signal of the four nanoislands shown in (a). Since the position of the slow scanning direction is fixed, this direction represents the time rather than a lateral scale. The total observation time is about $40\text{min}$ with a $1\mathrm{s}$ increment. Five switching events of island $a$ can be recognized. (c) Averaged line profiles drawn along the time axis. The effect of the dipolar coupling between islands $a$ and $b$ is highlighted by the differently shaded regions. From 37.Reuse & Permissions

Figure 60

Discovery of a novel complex nanoscale magnetic structure in a Fe monolayer pseudomorphically grown on an Ir(111) substrate. (a) SP-STM image obtained with an in-plane-sensitive Fe-coated W tip showing no magnetic contrast. (b), (c) Magnetic superstructure of Fe on Ir(111) as revealed with an out-of-plane magnetized Fe-coated W tip in different external magnetic fields. (d) Spin structure model for the Fe monolayer on Ir(111) based on the experimental SP-STM data. (e) SP-STM image revealing all three possible rotational domains of the magnetic superstructure found on $\mathrm{Fe}∕\mathrm{Ir}\left(111\right)$. From 184.Reuse & Permissions

Figure 61

(Color) Electronic structure of the Fe monolayer on Ir(111). (a) Experimental $dI∕dU\left(U\right)$ spectrum for 1 ML of Fe on Ir(111) compared to the calculated vacuum LDOS of (b) an assumed ferromagnetic state and (c) for the mosaic spin structure model. From 184.Reuse & Permissions

Figure 62

(Color) Discovery of a surface-related spin spiral state by SP-STM. (a) SP-STM image of a single monolayer of Mn pseudomorphically grown on a W(110) substrate. In addition to the local antiferromagnetic order on the atomic scale, an additional long-wavelength modulation having a periodicity of about $6\mathrm{nm}$ is observed, which is due to a spin spiral state (32). (b) Schematic of the spin spiral having a unique sense of rotation, or chirality, with respect to the surface that is different from its mirror image. From P. Ferriani.Reuse & Permissions

Figure 63

(Color) Magnetic imaging through adsorption layers. (a) Spin-resolved $dI∕dU\left(U\right)$ spectra and spatially resolved SP-STM $(350\times 350{\text{nm}}^2)$ data of a clean Fe nanoisland in a magnetic vortex state prepared on a W(110) substrate. (b) Spin-resolved $dI∕dU\left(U\right)$ spectra and spatially resolved SP-STM data of a similar Fe nanoisland covered by a $c(3\times 1)$ sulfur layer. The adsorption of sulfur leads only to a weak perturbation of the spin-resolved electronic structure of the Fe nanoisland thereby still allowing the spin-resolved mapping of the magnetic vortex state through the adsorption layer. From 15.Reuse & Permissions

Figure 64

(Color) Application of NC-AFM to NiO(001). (a) Crystal structure of NiO with a (001) surface plane. The lattice constant of NiO is $a=0.417\mathrm{nm}$. (b) Atomically resolved NC-AFM image of NiO(001) showing only one atomic species as bright spots. In addition, a single adsorbate is visible on the right-hand side of the image. From 6. (c) Total valence charge density distribution for the NiO(001) surface indicating that the oxygen atoms should appear as protrusions (bright sites) in NC-AFM images whereas the Ni atoms should correspond to the dark sites. From 53.Reuse & Permissions

Figure 65

(Color) Atomic-resolution spin mapping by MExFM. (a) Schematic of the spin structure of antiferromagnetic NiO(001) probed by a spin-sensitive MExFM tip. (b) Spin-resolved image of NiO(001) with atomic resolution as obtained by MExFM after unit-cell averaging. (c) Fourier transform of the raw MExFM data showing two spots which correspond to the magnetic superstructure period of the antiferromagnetic spin ordering at the NiO(001) surface. From 99.Reuse & Permissions

Figure 66

(Color) Comparison of (a) an atomic-resolution image of NiO(001) as obtained by conventional NC-AFM exhibiting pure chemical contrast and (b) atomic-resolution MExFM data showing the additional superstructure due to the antiferromagnetic structure of NiO. The line section in (a) reveals an apparent height difference of $4.5\mathrm{pm}$ between nickel (dark) and oxygen (bright) sites, corresponding to a chemical contrast as explained in Fig. 64. In the MExFM image of (b) the oxygen atoms reveal the same contrast throughout the image while the nickel atoms with opposite spin orientations now show up with an apparent height difference of $1.5\mathrm{pm}$. This small height difference in the MExFM data results from the magnetic exchange force interaction between the magnetic atom at the tip apex and the magnetic atoms on the sample surface depending on the relative spin alignment. Unit-cell averaging has been employed in order to improve the signal-to-noise ratio in the data sets.Reuse & Permissions

Figure 67

(Color) Comparison of (a) atomic-resolution MExFM data on NiO(001) and (b) corresponding data set of the simultaneously recorded dissipation signal. The contrast in the dissipation data appears to be inverted compared to the MExFM image, i.e., the dissipation is highest above the Ni sites. Interestingly, the dissipation data also show contrast between different oxygen sites, which might be explained by the detection of superexchange interactions between the magnetic tip atom and subsurface Ni atoms via the surface oxygen atoms.Reuse & Permissions

Figure 68

(Color) Application of MExFM to magnetic metal surfaces. (a) Atomic-resolution MExFM data $(3.2\times 3.2{\text{nm}}^2)$ of an antiferromagnetic atomic layer of Fe grown on a W(001) substrate. (b) The Fourier transform of the MExFM data reveals two sets of spots corresponding to (c) the magnetic superlattice and (d) the atomic lattice periodicities. Therefore, both types of information are included in the raw data. (e) The MExFM image contrast is strongly dominated by the long-period magnetic superstructure compared to the short-period atomic lattice structure.Reuse & Permissions