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1 Magnetic Exchange Force Microscopy with Atomic Resolution Uwe Kaiser, Alexander Schwarz and Roland Wiesendanger S1 AFM set-up Figure S1 shows the block diagram of the AFM data acquisition set-up using frequency modulation (FM) with a self-excited cantilever in the constant amplitude (CA) mode. It is also named non-contact AFM (NC-AFM). Amplitude A and frequency shift Δf are kept constant at an adjustable set-point by the A- and z-regulator, respectively. Four data channels can be recorded simultaneously during scanning line by line in the x-y-plane: the topography z(x,y) and its error signal, i.e., the frequency shift Δf(x,y), as well as the amplitude A(x,y) and its error signal, i.e., the excitation amplitude A exc (x,y), also known as dissipation. Additionally, a bias voltage U bias can be applied between tip and sample to minimize the electrostatic interaction and to characterize the conducting properties of the tip apex by performing Δf(U bias )-curves (see section S). Deflection Amplitude Frequency Sensor Detector Demodulator A-Regulator Cantilever Shaker A-Set-Point Tip A(x,y) Δf (x,y) A exc (x,y) U bias XYZ- z-regulator Scan Unit z (x,y) Figure S1: CA-FM-AFM data acquisition set-up. Sample Δf -Set-Point 1 1

2 S Tip characterisation The cleanliness of the evaporation procedure, which we use to coat our cantilevers with iron, has been checked by in situ Auger electron spectroscopy (AES) on the cantilever chip. No significant traces of oxygen or carbon were found. In addition to that, AES proves complete iron coverage, since no traces of silicon were detected. However, it is impossible to probe the nanometre sized tip apex, which is most relevant for MExFM, by AES. After iron evaporation mainly four possibilities have to be taken into account that would result in a non-magnetic tip apex. 1. Adsorbation of atoms from the residual gas at the tip apex. After iron evaporation a molecule from the residual gas in the vacuum system might adsorb at the tip end. Such an event is extremely unlikely, because in an ultra high vacuum system with a pressure below hpa, the impingement rate onto the foremost atom at the tip apex is below one molecule per day.. Insufficient iron coating. In this case the tip apex would be composed of the underlying insulating silicon oxide (after etching of the silicon cantilever a native oxide layer grows on it as indicated in figure S4). 3. Complete iron removal after a contact between tip and sample (cf., section S3). If all iron is lost the tip apex would be composed of the underlying insulating silicon oxide (see above). 4. Picking up sample material. During a contact between tip and sample a nickel oxide cluster could adhere to the tip apex. In the latter three cases, the tip apex would behave more like an insulator and not like a good metallic conductor as expected for a fully iron coated tip. Therefore, we prevalently record frequency shift versus bias curves Δf(U bias ) during our measurement sessions to determine whether the tip apex is well conducting, i.e., covered with iron. Δf(U bias )-curves are acquired at a certain (x,y)-position on the sample, i.e., without scanning. Then, the z-feedback is switched off and U bias is ramped from a preset starting value, e.g., +1 V, to its final value e.g., -1V, and back again. If both curves are regular and smooth parabolas as shown in figure S(a), it can be assumed that the whole tip is well conducting, and covered with iron. The voltage measured at the apex of the parabola is adjusted during subsequent imaging to minimize electrostatic tip-sample interactions. The particular curve displayed in figure S(a) was recorded directly after inserting the iron covered cantilever into the microscope. The cantilever was later used to obtain the MExFM data shown in figure of the letter. Two consecutively recorded parabolas that are shifted with respect to each other upon switching the direction of the bias voltage ramp as visible in figure S(b) are characteristic for a badly conducting tip apex. Such a hysteresis originates from slow charge relaxation time constants on an insulating tip apex. Discrete jumps in Δf(U bias )-curves as evident in figure S(c) indicate tunnelling events due to the presence of trapped states at an insulating tip apex. Tunnelling between tip and sample can be experimentally excluded by verifying that the number of tunnelling events is independent of the tip-sample distance. In principle, slow charge separation and tunnelling within the insulating nickel oxide sample could also be responsible for hysteresis or Δf-jumps. However, in this case we would not observe smooth Δf(U bias )-curves as in figure S(a) on insulating surfaces like nickel oxide. Moreover, we also found hysteresis and jumps on metallic surfaces, e.g., figure S(c), where charge relaxations

3 times are very fast and trapped states are absent. This demonstrates that Δf(U bias )-curves are able to probe the conducting properties of the tip apex. Figure S: Frequency shift versus bias curves to study the electrical properties of the tip apex. (a) Well conducing iron coated tip above a NiO(001) surface. The cantilever has been used to record the data of figure in the letter. (b) Hysteresis due to slow charge relaxation effects at the badly conducting tip apex on NiO(001). (c) Discrete jumps due to tunnelling events into localised states at an insulating tip apex recorded on Ni(111). S3 Reconfiguration of the tip apex due to a contact with the sample surface During scanning across a surface, the tip apex can be modified. Such modifications range from severe crashes to a slight change of the atomic configuration at the tip end. They can be recognized by abrupt changes in topography and dissipation images. Severe crashes can create large holes in the surface and lead to a complete break down of the oscillation. Less drastic tip-surface contacts usually produce small clusters with heights on the order of 1 nm or below. Iron from the sharp tip end is deposited onto the flat surface due to strong adhesion between the iron film on the sharp tip apex in front of a flat surface. Slight tip changes, i.e., a reconfiguration of atoms at the tip apex, can be detected by an abruptly changed atomic scale contrast, e.g., the corrugation amplitude can be either increased or reduced. If the atomic scale contrast is completely lost, the tip can be sometimes intentionally altered to attain atomic resolution again. Unwanted tip modifications often occur on sample areas with defects, e.g., step edges, adsorbates or vacancies. To ensure stable imaging, we avoided such areas during MExFM experiments. Imaging at small tip-sample separations, i.e., at large negative Δf set-points, also can result in spontaneous tip changes. They occur, because the frequency shift does not vary monotonically with distance, but changes its sign on the repulsive branch of the tip-sample interaction as sketched in figure S3. Note that the Δf(z)-relationship is not directly proportional to the force, but its shape reflects the same general distance dependence, i.e., Δf as well as the force between tip and sample is zero for infinite large distances, becomes negative at smaller distances due to the presence of long- and short- range attractive interactions and finally gets positive when the short-range repulsion dominates. Atomic resolution can be obtained in regime B, where the short-range forces dominate. Upon approaching further, the tip enters regime C, where the slope changes sign and the z-regulator starts to regulate in the wrong direction. Whenever this happens, a tip crash in inevitable. We observed that the imaging conditions are quite unstable during magnetic exchange contrast on NiO(001), i.e., unintentional tip changes occur relatively frequent. On the other hand, a purely chemical contrast on NiO(001) often remains stable for much longer time periods. Probably imaging at small distances close to the minimum is necessary to obtain a detectable magnetic exchange contrast on NiO(001), because the foremost iron atom at the tip apex has to probe the localized d-states at the nickel atoms. 3

4 Figure S3: Sketch of the distance dependence of Δf. Long-range forces, e.g., the magnetostatic force, are probed in regime A. Atomic resolution is obtained in the non-contact attractive regime B at tip-sample distances of about a few 100 pm. In this regime, the shortrange attractive tip-sample forces, which vary on the atomic scale, are probed. Hence the tipsample distance has to be adjusted by the z-regulator to keep Δf constant. The resulting z(x,y) map is the topography (cf., figure S1). On the left side of the minimum repulsive forces start to play a role and the slope of the Δf(z)-curve changes sign. If the tip-sample distance enters regime C, the z-regulation regulates in the wrong direction, which results in a tip-crash. Therefore, imaging conditions tend to be unstable at very small tip-sample separations. S4 Identification of atomic species On ionic surfaces, FM-AFM typically images only one species as protrusion. It can be either the anion or the cation. However, on NiO(001) a metallic tip will always interact stronger with oxygen than with nickel according to simulations presented in Ref. [19] and Ref. [0]. Only one class of tip has been proposed to image cations on ionic surfaces as protrusions. The tip apex has to be formed by a cluster picked up after a tip crash with the sample surface and the cluster (nickel oxide in our case) has to point with the anion (i.e., oxygen), towards the sample. As described in the following, we do not have any indication for such a scenario. We carefully protocol the history of our cantilevers in a lab journal. With the particular cantilever used to acquire the data displayed in figure of the letter and figure S5 in section S6, we only observed slight tip modifications after evaporation of iron. One resulted in a tiny bump at the location where the tip change occurred. The volume of the material lost from the tip apex was much smaller than the amount evaporated onto the tip apex. Moreover, all Δf(U bias ) curves recorded during the measurement session with that particular cantilever were smooth parabolas similar to figure S(a) showing no hysteresis. Therefore, we infer an iron coated tip apex and identify maxima as oxygen atoms and minima as nickel atoms. S5 Magnetic polarisation of the tip According to the Heisenberg model, i.e., H = J 1 S 1 S, where J 1 is the exchange integral, the magnitude of the magnetic exchange interaction between two spins S 1 and S depends on the angle θ between them. Therefore, it is helpful to adjust the spins at the tip apex in a favourable manner with respect to the orientation of the sample spins - ideally in a parallel or antiparallel configuration. 4

5 In nickel oxide the spins are located at the nickel atoms and point along <11> orientations. In our instrument, we are able to generate an external magnetic flux density of up to 5 T perpendicular to the (001) surface of nickel oxide, which is too small to significantly influence the spin directions in an antiferromagnet. However, it is sufficient to manipulate the magnetic polarisation of the ferromagnetic iron film on the tip, since the saturation polarisation of bulk iron is about.1 T. Due to their shape anisotropy, thin iron films are polarised in-plane. Therefore, the preferred magnetic polarisation along the side faces of a sharp pyramidal tip is oriented nearly perpendicular with respect to the sample surface. However, at the tip apex the curvature results in a magnetic polarisation parallel to the surface. Note that within this plane, no preferred orientation exists. The situation is sketched in figure S5(a). In MFM experiments, such tips are even in zero fields mainly sensitive to the z-component of the magnetic stray field emanating from ferromagnetic domains. Due to the high aspect ratio and small tip radius the long-range magnetostatic dipolar tip-sample interaction is dominated by the magnetic material at the side faces leading to a large out-of-plane component of the magnetic polarisation. However, since MExFM detects the short-range magnetic exchange interaction between the spins of the foremost atom at the tip apex and the sample atom underneath, such tips are expected to be mainly sensitive to the in-plane components of the sample spins. All possible spin orientations in the different antiferromagnetic domains of nickel oxide exhibit a significant in-plane as well as out-of-plane component with respect to the (001) surface. As mentioned above, an in-plane polarised tip apex has no preferred orientation within the plane and can exhibit any angle with the in-plane component of the spins at the nickel atoms. In the worst case, the in-plane components of tip and sample spins are aligned perpendicular resulting in a vanishing magnetic exchange interaction. This situation is very unfavourable and therefore it is much better to rely on the out-of plane component of tip and sample spins, because they are always either parallel or antiparallel aligned. To ensure a significant magnetic exchange interaction, the preferred magnetic polarisation in the tip apex ought to be changed from in-plane to out-of-plane. This can be done by an external magnetic field as shown in figure S5(b). This controlled alignment of the spins at the tip apex into the favourable out-of-plane direction is the main difference compared to all previously performed experiments with magnetically coated tips on NiO(001). Note that the spin of the foremost atom at the tip apex is only oriented perfectly along the external field, if the Zeeman energy dominates all other relevant magnetic energy contributions, e.g., shape anisotropy energy and the local magnetocrystalline anisotropy energy due to spin-orbit coupling. Since the local magnetic properties at the tip end are unknown, we applied the strongest external field that our superconducting magnet could generate, to maximise the out-of-plane component at the tip apex. Figure S4: Influence of an external magnetic field on the magnetic polarisation of the tip. (a) Due to the shape anisotropy the preferred orientation without an applied field is in-plane and 5

6 therefore follows the curvature of the tip. (b) In a strong external magnetic field the magnetic polarisation is everywhere aligned along the field direction. S6 Exclusion of an oscillatory noise source as origin for the MExFM contrast A possible non-magnetic origin for a modulation on neighbouring rows of nickel atoms as observed in figure is an oscillatory noise source in phase with the atomic scale contrast. The phase relation can be changed by variation of the scan frequency or scan angle. The latter is demonstrated in figure S5, where the scan angle has been rotated by 30 with respect to figure (b) in the letter. The chemical and the magnetic exchange contrast are also rotated by 30, as visible in the raw data and the Fourier transform (see inset of figure S5). Therefore, we can exclude the presence of such an oscillatory noise source. Figure S5: Raw data topography image showing the MExFM contrast on neighbouring rows of nickel atoms by changing the scan angle by 30 relative to figure (b) in the paper. Nickel rows that appear lower are marked by arrows. The inset displays the Fourier transform with the two additional peaks stemming from the 1 magnetic surface unit cell. S7 Exclusion of a tip artefact as origin for the MExFM contrast A topographical image of a sample recorded with a probe is a convolution between tip and surface. Therefore, an image can contain tip artefacts, i.e., features that are more related to tip properties than sample properties. For example, monoatomic steps between surface terraces can appear doubled, if two nano-tips protrude from the tip apex (a so called double-tip). On the atomic scale the corrugation amplitude along equivalent crystallographic directions can be different, e.g., along [110]- and [-110]-directions on the quadratic chemical surface unit cell of NiO(001). This cannot be related to a sample property, but can be traced back to a nonspherical tip apex, where more than one atom contributes significantly to the short-range interaction. Such a tip could even produce a row-like contrast, i.e., the atomic corrugation is clearly visible along one direction, but nearly vanishes along the other. However, in this case the corrugation amplitude of neighbouring rows is identical and their distance corresponds to the structural surface unit cell. In general, it is impossible that a multiatom tip apex generates the observed modulation between neighbouring nickel rows on NiO(001) with a purely nonmagnetic tip-sample interaction, because alternating rows of nickel and oxygen atoms are chemically and structurally identical. Note that figure (a) exhibit an identical chemical contrast along equivalent crystallographic directions, which indicates a structurally very symmetric single atom tip apex. 6

7 S8 Previous experiments with magnetic tips on NiO(001) In Ref. [5] and [6] as well as in Ref. [7] high resolution experiments have been executed at low temperatures, with an excellent signal to noise ratio. However, no atomic scale magnetic contrast was observed. The same is true for the raw data acquired at room temperature, which have been presented in Ref. [8]. However, after adding the corrugations amplitudes of line sections along [110]- and [1-10]-directions across 85 unit cells present in their image data, the authors reported a tiny modulation on neighbouring maxima, i.e., oxygen sites. They defined a topographical asymmetry on chemically equivalent sites and determined a value of about 1%. Using their definition, the topographical asymmetry in our data would correspond to about 17% and is observed on the nickel atoms. In principle, such a contrast on oxygen rows is possible, because surface oxygen is slightly polarised according to Ref. [0]. Another possible explanation would be a kind of superexchange mechanism between second layer nickel spins and the spin at the foremost tip atom via surface oxygen. Although the authors of Ref. [8] observed the same kind of modulation and asymmetry also with non-magnetic tips and mention the possibility of a tip artefact as possible origin, they interpreted their finding with magnetic tips as an indication of a magnetic exchange contrast. However, they did not show Fourier transforms of their raw data and did not report any tests, like scan angle rotation (see section S6), to exclude an oscillatory noise source in phase with the atomic periodicity. Since their unit cell averaging procedure also exhibited a modulation if applied to image data recorded with non-magnetic tips, their evaluation technique is neither unambiguous nor reliable. The most obvious and best method to detect the presence of a small periodic signal in noisy image data is a Fourier transform. Therefore, we Fourier transformed our raw data to verify the presence of the periodic magnetic exchange contrast already visible in our raw data and only employed unit cell averaging to quantify the magnitude of the chemical and magnetic contrast. 7