Sensing Noncollinear Magnetism at the Atomic Scale Combining Magnetic Exchange and Spin-Polarized Imaging.

Storing and accessing information in atomic-scale magnets requires magnetic imaging techniques with single-atom resolution. Here, we show simultaneous detection of the spin-polarization and exchange force with or without the flow of current with a new method, which combines scanning tunneling microscopy and noncontact atomic force microscopy. To demonstrate the application of this new method, we characterize the prototypical nanoskyrmion lattice formed on a monolayer of Fe/Ir(111). We resolve the square magnetic lattice by employing magnetic exchange force microscopy, demonstrating its applicability to noncollinear magnetic structures for the first time. Utilizing distance-dependent force and current spectroscopy, we quantify the exchange forces in comparison to the spin-polarization. For strongly spin-polarized tips, we distinguish different signs of the exchange force that we suggest arises from a change in exchange mechanisms between the probe and a skyrmion. This new approach may enable both nonperturbative readout combined with writing by current-driven reversal of atomic-scale magnets.

The ultimate goal of magnetic-based storage is to create ultrahigh density memory based on energy-efficient manipulation[1] of the remnant magnetization state of nanomagnets. Magnetic nanostructures[2−5] as well as magnetic atoms on surfaces[6−9] have emerged as candidates for atomic-scale magnetic storage. While it has recently been shown that the magnetic remanence can be greatly enhanced for a single magnetic atom on a surface[8,9] by utilizing a combination of weakly conducting surfaces, symmetry,[10] and the localized nature of 4f-derived moments,[8] the magnetic state of such nanoscale magnets are extremely sensitive to readout techniques based on spin-polarized current.[5−7,9,11] To this end, various remote readout schemes[9,12,13] based on spin-polarized tunneling have been developed in order to probe the intrinsic magnetization dynamics of a single atom supported on thin insulating films.[14,15] However, an atomic-scale sensing scheme, which has the freedom to operate with or without the flow of current and which can deconvolute magnetic, electronic, and structural variations, has not been shown so far.

Spin-polarized scanning tunneling microscopy (SP-STM)[16] has emerged as the leading technique for characterizing and manipulating the magnetization of surfaces at the atomic length scale. Despite its vast success, this technique faces some limitations: (1) the topographic, electronic, and magnetic contributions are convoluted;[17] (2) sensing requires current flow, which can unintentionally flip the magnetization;[6] (3) detection is often limited to orbitals that exhibit spin polarization far into the vacuum.[11] To this end, noncontact atomic force microscopy (NC-AFM)[18] is a complementary technique to STM, providing a high-resolution method for structural and orbital characterization[19,20] as well as chemical sensitivity[21] and operating without current flow. On the basis of NC-AFM, magnetic exchange force microscopy (MExFM)[22] provides an alternative means toward detecting magnetism, by directly measuring the exchange force between a magnetic probe and the sample. MExFM also provides the means of quantifying the exchange force via distance-dependent spectroscopy.[23] While SP-STM has been widely implemented, MExFM has thus far only been applied to few surfaces with the first studies focusing on antiferromagnetic structures.[22−25] Therefore, a clear advance in magnetic imaging of nanoscale magnets would be to not only expand the application of MExFM toward noncollinear magnetic structures but to combine SP-STM and MExFM simultaneously for a more complete picture of magnetism at the atomic scale.

Here, we demonstrate a new type of magnetic imaging based on combining both SP-STM and MExFM simultaneously, employing low-temperature STM/AFM based on a qPlus sensor[26] mounted with a ferromagnetic Fe tip, which we refer to as SPEX (spin-polarized/exchange) imaging. Using SP-STM as a starting point, we observe the well-known 2-fold magnetic structure of the face-centered cubic (fcc) monolayer of Fe on Ir(111).[4] Applying height-dependent imaging, we illustrate the onset of magnetic exchange contrast of the nanoskyrmion lattice, which emerges closer to the surface as compared to typical SP-STM imaging, and we compare this to the measured spin-polarized current at that height. We observe a positive correlation between the magnetic images in both imaging modes. By employing force and current spectroscopy, we quantify the spin polarization and exchange force as a function of distance from the surface, which illustrates that substantial spin polarization exists further out in the vacuum compared to the exchange force. For all probes, the spin polarization remains nearly constant. However, for probes that exhibit a stronger spin polarization, we observe a reversal in the magnetic exchange force with increasing tip–surface separation evidencing a detectable distance-dependent transition in the exchange mechanism between the surface and probe.

Employing SP-STM in constant-current mode, we first characterize the prototype nanoskyrmion lattice of a monolayer of Fe on Ir(111),[4] which provides access to all magnetization directions. The Fe monolayer grows pseudomorphically on Ir(111) and forms two island types depending on the overall stacking of the atoms, referred to as fcc and hexagonal close-packed (hcp)[4,27] (Figure a). The prototypical nanoskyrmion lattice is found in the fcc islands.[4] Here, the magnetic ground state is composed of Néel-type skyrmions, characterized by a square symmetry with a calculated magnetic unit cell length of ac ≈ 1 nm (shown in Figure b for an out-of-plane spin-polarized tip).[4] The square magnetic unit cell is superimposed onto the three-fold-symmetric Fe/Ir(111) lattice, resulting in three rotational domains.[4] This nanoskyrmion lattice provides an opportunity to probe chiral magnetic structures with MExFM compared to the collinear antiferromagnets previously probed with MExFM.[22−25]

Figure 1

(a) Large-scale mapping (55 × 45 nm2) of mono- and bilayer islands of Fe on Ir(111) for SP-STM (Vs = 50 mV, It = 100 pA), merged with the Laplace-filtered image to highlight structural details (for raw data see Supporting Information Section S3). The labels hcp/fcc refer to the stacking of the monolayer islands, where fcc exhibits the square-symmetric magnetic nanoskyrmion structure, and 2L refers to the bilayer, where complex spin spirals can be observed. (b) Schematic atomic-scale view of the nanoskyrmion lattice. For the sake of clarity the commensurate representation is shown. (c) Constant frequency shift AFM topography revealing structural details of the surface such as adsorbates and subsurface defects (Δfset = −10.9 Hz, zmod = 64 pm, Vs = 0.6 mV, z = −0.22 ± 0.01 nm relative to the image in (a)). (d) Tunneling current map simultaneously recorded with the AFM topography in (c), which includes the spin-polarized signal for each layer. The lateral scale bars in all panels correspond to 5 nm. Color-scale ranges: (a) 0.33 to 1.1 nm, (c) 0.1 to 0.42 nm, (d) 3.5 pA to 213 pA.

In addition to the fcc Fe islands exhibiting the square-symmetric nanoskyrmion lattice, large-scale images also reveal regions with monolayer hcp islands as well as bilayer Fe islands (Figure a). Our SP-STM images allow for distinguishing the hcp islands from their fcc counterparts because of a three-fold-symmetric spin contrast, as expected.[27] Likewise, we detect the spin contrast on bilayer islands, which exhibit a complex spin-spiral network.[17] For the latter, three rotational domains coexist, which allows for calibrating the tip magnetization (Supporting Information Section S2). For all measurements shown here, we ensured that the tip dominantly exhibits an out-of-plane magnetization relative to the surface, although a small in-plane component cannot be ruled out.

After characterizing the sample using SP-STM, we subsequently perform AFM in constant frequency shift mode, or so-called AFM topography. As the frequency shift Δf is related to the average force gradient,[18] the AFM topography is sensitive to variations in short-range forces here. At larger tip–sample separations, the exchange interaction and other magnetic forces are negligible, as well as spatial variations arising from electrostatic and van der Waals interactions. Therefore, the AFM topography primarily reflects the structural variations on the surface, while SP-STM topography is sensitive to local changes in the electronic and magnetic structure. Therefore, the comparison of AFM and STM images offers the possibility to distinguish between structural and electronic effects. For the acquisition of an AFM topography, we move the tip closer to the surface to an offset position z = −0.22 ± 0.01 nm, where z = 0 nm is defined by the SP-STM stabilization parameters (Vs = 50 mV, It = 100 pA) and a negative value refers to a displacement toward the surface. We record the AFM topography at constant frequency shift (using zmod ≤ 110 pm) and simultaneously measure the spin-polarized current that results from a very small sample voltage (|Vs| < 1.7 mV). Various features are identified that can be attributed to adsorbates or structural defects in the Fe layer or beneath the surface (presumably in the iridium), which appear quite differently in the AFM versus STM images. For example, the AFM topography clearly reveals subsurface defects both underneath fcc and hcp islands (see arrows in Figure c). In the STM image (Figure a), these defects cannot be easily seen on the fcc islands, whereas they show up as pronounced depressions on hcp islands. This is also found in the spin-polarized current map (Figure d) simultaneously acquired with the AFM image.

In order to reveal the short-range magnetic exchange interaction in AFM topography, we have to move the tip closer to the surface. In the following, we focus on the fcc monolayer Fe islands exhibiting the square nanoskyrmion lattice (Figure ). Again, we first take an SP-STM image using the above-mentioned stabilization parameters that define z = 0 nm (Figure a). For the MExFM imaging, we change the tip offset roughly to z = −0.31 nm and take a constant frequency shift image (b) while simultaneously acquiring a current map (c). The constant frequency shift image reveals a square structure (Figure b) with a lattice constant a = 0.87 ± 0.4 nm, which is comparable to the values taken from the SP-STM images of the nanoskyrmion lattice (Figures a and 2a) and in reasonable agreement with previously reported experimental values.[4] An identical pattern is found in the simultaneously acquired current map (Figure c), resulting from the retained spin polarization of the current at this height. Line profiles at identical positions of both images reveal the clear correlation of both signals (Figure d). Therefore, we conclude that the constant frequency shift image corresponds to a MExFM image, that is, we detect the spatial variation in exchange force between tip and surface. We note that the tip magnetization is constant; in other words, we see no evidence that the tip magnetization flips as a function of distance or due to superparamagnetic fluctuations. Therefore, the image contrast corresponds to the difference in the attractive force between the aligned and antialigned orientation of the magnetic moments within the nanoskyrmion lattice relative to the tip moment. We discuss this in more detail below.

Figure 2

High-resolution mapping (8 × 6 nm2) of the nanoskyrmion lattice (a) SP-STM (Vs = 50 mV, It = 100 pA). The dashed square indicates the magnetic unit cell. (b) MExFM image in constant frequency shift mode (Δfset = −14.6 Hz, zmod = 102 pm, Vs = 0.2 mV, z = −0.31 ± 0.01 nm). (c) Simultaneously acquired current map. (d) Line profiles along the arrows indicated in (b,c). A simplified view of the magnetization of the nanoskyrmion lattice is shown below the line profile. The scale bar in all panels is 1 nm. The color scale ranges are (a) −10.2 to 12.2 pm, (b) 0.11 to 9.3 pm, and (c) −26 to 48 pA.

A quantitative comparison of the line profiles in Figure d reveals that the MExFM contrast between aligned and antialigned portions of the nanoskyrmion lattice are typically in the range of Δz = 1.0 ± 0.5 pm. As we detail below, the magnetic contrast corresponds to a frequency-shift difference of only Δf ≈ 0.1 Hz. This corrugation in the MExFM images is about a factor 10 smaller than reported for the antiferromagnetic Fe monolayer on W(001),[25] which suggests that the overall exchange force between the ferromagnetic tip and the nanoskyrmion lattice may be weaker for this system. We observe that a larger height corrugation in the MExFM images is correlated with a larger current.

In combined STM/AFM imaging with a tuning fork, it is important to rule out potential cross-talk between the current and the frequency shift, where the tunneling current may introduce an interference with the deflection of the tuning fork. In order to account for that, we acquired constant height images of the frequency shift (Figure a) and the simultaneously measured current (Figure b). The resultant images both reveal the aforementioned skyrmion lattice. The constant height image qualitatively reproduces the contrast variations seen in constant frequency-shift imaging. In order to exclude cross talk, we changed the applied sample voltage during image acquisition with feedback off (arrows). While the change in voltage leads to a change in current, leading to a strong contrast variation, the measured frequency shift is not influenced by this strong perturbation (see also Supporting Information Section S8). This also holds for MExFM images (constant frequency shift mode, Figure c) and the simultaneously measured current in Figure d, allowing us to ascertain that both the frequency shift and current channels are independent.

Figure 3

(a) Frequency shift (smoothed by a Gaussian filter, see Supporting Information Section S8 for raw data) and (b) simultaneously current map acquired in constant height mode (zmod = 51 pm, z = −400 pm with the current-feedback loop opened above the bright position of the skyrmion lattice at Vs = 50 mV and It = 100 pA). At the line indicated by the arrow, the bias voltage was changed from Vs = 0.1 mV (upper part) to 0 mV (lower part). (c) MExFM image (smoothed by a 2-point Gaussian filter, see Supporting Information Section S8 for raw data) and (d) simultaneously measured current map in constant frequency shift mode (Δfset = −36 Hz, Vs = 0.0 mV (lower part), Vs = 0.4 mV (upper part), zmod = 180 pm)). At the scan line marked by the white arrow the voltage was increased from 0 to 0.4 mV. The scale bar is 1 nm in all images. Color scales: (a) −34.5 to −34.0 Hz, (b) −214 to 340 pA, (c) 14.5 to 17.8 pm, and (d) 0.9 to 1.8 nA.

To quantify the exchange force and spin polarization as a function of tip–surface separation, we perform distance-dependent measurements by moving the tip toward the surface and simultaneously recording the variations in frequency shift (using zmod = 40–80 pm) and current for dozens of different out-of-plane magnetized tips (representative curves are shown in Figure ; Supporting Information Section S7 for all data and the acquisition procedure). We perform these measurements at positions of maximum contrast, corresponding to aligned/antialigned magnetization orientation relative to the tip magnetization.[4] In order to exclude effects from a spatially dependent difference in tip height, the current feedback was opened prior to the movement toward the surface (SP-STM stabilization parameters Vs = 50 mV, It = 100 pA) and the tip was moved to the different lateral positions in constant height mode (see also Supporting Information Section S7). The variations in current as a function of distance exhibit the expected exponential dependence (Figure b) with the spin polarization between aligned and antialigned orientations varying slightly at all probed displacements. The negative frequency shift increases as the tip–sample separation is decreased (Figure a), indicating a stronger attractive force between the tip and the surface. At first glance, there is no obvious difference between the frequency-shift curves for aligned versus antialigned orientations on the nanoskyrmion lattice. However, as discussed above, the MExFM contrast is very small, whereas the overall Δf is a sum of the chemical, electrostatic, magnetic dipole, and exchange forces. Therefore, we revert to a previously applied method to extract magnetic exchange forces where the frequency shift due to antiferromagnetic exchange interaction has been defined by the difference between the bright and dark positions in the AFM topography, corresponding to antialigned and aligned magnetic moments between the iron atoms and the tip, respectively.[23] On the basis of this, we examine the difference between the bright (Δf↑(z)) and dark (Δf↓(z)) positions of the AFM topography, that is, Δfex(z) = Δf↑(z) – Δf↓(z), in order to quantify the magnetic exchange interaction between the different out-of-plane magnetization directions of the nanoskyrmion lattice. Figure c shows representative difference curves for three different tips. They reveal that Δfex(z) starts to decrease at z ≈ −0.2 nm, which indicates the onset of a significant exchange force between tip and surface. The frequency shift related to the magnetic exchange is on the order of 0.1 Hz, that is, about a factor of 400 smaller than the overall measured frequency shift (Figure a). We note that distance-dependent data acquired in between the positions of out-of-plane magnetization directions does not show any evidence of noncollinearity.

Figure 4

(a) Distance dependence of Δf(z) at two different locations with opposite contrast within the magnetic unit cell of the nanoskyrmion lattice (cf. areas circled in red (Δf↑(z)) and blue (Δf↓(z)) in the inset), acquired with an dominantly out-of-plane magnetized tip (z = 0 nm is defined by STM stabilization parameters Vs = 50 mV, It = 100 pA). (b) Simultaneously acquired distance dependence I(z) at the same two locations using the same tip. (c) Difference in frequency shift Δfex(z) = Δf↑(z) – Δf↓(z), revealing the magnetic exchange contribution, for three different tips (Savitzky-Golay filtered prior to subtraction). (d) Distance-dependent spin-polarized asymmetry () for the same three tips used in (c) (cf. color code). (e) Exchange force Fex(z) extracted from Δfex(z) using eq (prior to this, Δf(z) was smoothed using a Savitzky-Golay filter). The color code for (c) to (e) reflects low (blue) to high (red) spin asymmetry . The Supporting Information provides distance dependences for dozens of different tips (Section S7) to reflect the reproducibility and statistical spread.

The distance-dependent curves also permit to compare exchange-force frequency shifts Δfex with the spin polarization. For this, we plot the current asymmetry as a function of z (Figure d), which was simultaneously acquired with the Δfex curves using the same tips (as color-coded in Figures c,d). The plots show that increases only slightly as the tip height is decreased, indicating that the spin polarization does not reverse, and remains relatively constant. The small variation and constant sign of is further evidence that the tip magnetization remains nearly constant within the entire probed regime, allowing us to rule out that the increasing exchange interaction between tip and surface strongly affects the tip magnetization. The comparison of Δfex(z) with also illustrates the different height regimes at which SP-STM and MExFM work, illuminating the complementary information that can be acquired by both techniques.

Finally, to extract the magnetic exchange force Fex(z) from Δfex(z), we utilize the formula[28]with f0 and zmod being the resonance frequency and oscillation amplitude, respectively. The stiffness of the tuning fork (k ≈ 1800 N/m) was taken from literature.[26] The resultant is plotted in Figure e. The onset of the exchange force can be clearly seen at displacements z ≈ – 0.2 nm. All Fex(z) curves show a decrease of the force, down to −25 pN.

In addition to observing an onset of a strong exchange force (z ≈ −0.4 nm), resulting from direct exchange between Fe atoms, we see a significant exchange interaction of opposite sign character at larger separations for certain tips (z ≈ −0.3 nm). By cross-correlating the extracted exchange force Fex(z) with the spin-polarization , our data suggests that this force reversal is particularly evident for tips that exhibit a larger spin polarization (Figure d). Now we discuss the various mechanisms that can modify the exchange interaction between the probe and surface. In refs (29 and 30), it was shown that relaxation of the foremost atoms of a Cr tip can induce a modification in the exchange interaction. However, in that case the effect was strongest for Cr tips on Fe surfaces, whereas we have purely Fe probes here. Nevertheless, a sign reversal in the exchange energy was calculated and assigned to an indirect exchange mechanism[23,30] when the Cr tip was brought closer to the antiferromagnetic Fe layer on W(100). For that system, the probe can sense the exchange from additional neighboring atoms in addition to the atom beneath the tip at certain separations. The higher number of antialigned Fe atoms, compared to aligned Fe atom underneath the tip leads to an antiferromagnetic exchange between the probe and surface.[23] However, for the Fe skyrmion lattice studied here, the magnetization of nearest-neighbored atoms are only partially rotated with respect to the magnetization of the atom directly underneath the tip, due to the small pitch change in the skyrmion unit cell. Therefore, an antiferromagnetic interaction of neighboring Fe atoms on the surface is considered unlikely.

The stray field of the Fe tip may also modify the measured forces. As the spin-polarization of our probes is constant over the accessed distance range (Figure d), a stray field from the tip will add an offset and alone cannot change sign of the exchange force at larger separations. Finally, in the calculations in ref (31) for a single magnetic atom on top of a metallic surface, it is shown for certain probes that a sign change in the interaction can be observed as a function of probe-surface separation. In this case, the sign reversal is attributed to a change in direct overlap of s or p orbitals with the d orbitals, that is, a Zener model. We speculate that this last mechanism may be responsible for the observed sign reversal. However, we note that they predict a large change in the spin-polarization as a function of distance, which is inconsistent with our observations. We also note, however, that also a few tips with low spin polarization (Supporting Information Section S7) exhibit a reversal and a few tips with large do not, indicating that other effects, for example, the tip-apex geometry or relaxations, may also play a non-negligible role. The alignment of the tip magnetic moment with respect to the local moments of the skyrmion lattice, that is, the assignment of ferromagnetic/antiferromagnetic interactions, requires comparison to ab initio calculations in order to determine the relative orientations responsible for the imaged intensity variation in the magnetic unit cell.[23,29−32]

We employed a new method of magnetic imaging by combining SP-STM and MExFM based on STM/NC-AFM with a tuning fork. We illustrate that this new combination can be utilized to characterize chiral magnetic structures, as exemplified by the nanoskyrmion lattice. SPEX imaging could provide complementary information by deconvoluting structural features from electronic and magnetic properties, which is typically very difficult to decouple. For example, we see evidence in the bilayer of Fe/Ir(111) of strong vertical relaxations resulting in nonplanar structures in AFM imaging (Figure c), which may be related to the dislocation network that was previously reported in pure SP-STM imaging.[17,33] The combined method can provide more complete characterization toward understanding the impact of defects on the magnetic ground state, as well as a path toward studying multielement magnetic surfaces that can be difficult to delineate based on STM alone. Distance-dependent spectroscopy reveals the different height regimes at which spin polarization and various types of magnetic exchange can be detected above the surface. While the spin polarization is nearly constant for a given probe, we observed that the magnetic forces at large separations depend strongly on the absolute spin polarization of the tip. To this end, combining SPEX imaging with ab initio methods would be advantageous in revealing the relevant exchange mechanisms and surface atoms responsible for the measured force, and correlating this with the spin polarization of the tip.[32] Moreover, investigation of other noncollinear surfaces would be interesting in order to ascertain if the MExFM method can detect noncollinear exchange. The advantages of probing magnetism at closer distances compared to spin-polarized tunneling may also enable direct access to the strongly localized and elusive 4f orbitals[8,9] in future experiments where tunneling-based experiments have been inconclusive or could only indirectly probe 4f magnetism.[9,11] After preparation and submission of this manuscript, we became aware of similar work utilizing solely MExFM.[34]

Methods

Scanning probe microscopy was performed utilizing a commercial ultrahigh vacuum low-temperature STM/AFM from CreaTec Fischer & Co GmbH, which operates at a base temperature of T = 6.3 K. AFM measurements using a noncontact frequency-modulation mode were done utilizing a tuning fork-based qPlus sensor[26] with its free prong oscillating at its resonance frequency f0 ≈ 27.7 kHz. The force is indirectly measured by the shift of the resonance frequency Δf. Oscillation amplitudes zmod between 40 and 110 pm were used with zmod being half the peak-to-peak value. As we do not observe a minimum in Δf, all data is acquired in the attractive force regime. Further details on the experimental parameters, tip variations, and absence of crosstalk are available in Supporting Information Sections S1, S6, and S8, respectively.

The Ir(111) surface was prepared by repeated cycles of Ne+ sputtering and annealing (T ∼ 1800 K) in an oxygen atmosphere (p ∼ 4 × 10–6 mbar) followed by a final flash to 1800 K. The Fe was deposited from an e-beam evaporator onto Ir(111) kept at room temperature and subsequently annealed (T ∼ 630 K), leading to the formation of multilayer Fe islands, in which the first layer exhibits both hcp and fcc stacking.