In ferromagnets or antiferromagnets made of a single or a few atomic layers, domain walls can be as sharp as a few atomic lattices, which are only accessible by SPSTM. Pratzer et al.^[11] measured the ultra-sharp domain walls of monolayer and double layer Fe grown on W(110). The magnetization direction of monolayer Fe is in-plane, while double layer Fe has an out-of-plane easy axis. When measuring with an in-plane sensitive magnetic tip, monolayer Fe shows oppositely magnetized domains separated by a domain wall as narrow as 0.6 nm, while double layer Fe does not show any magnetic contrast except at the domain wall region where the magnetization direction is tilted into the plane. This kind of sharp domain was also observed in layer-wise antiferromagnets. In general, the domain wall in an antiferromagnet is unfavored, which is usually accompanied by magnetic or structural defects. Schlickum et al.^[12] observed domain walls in layer-wise antiferromagnet Mn thin films induced by the atomic step of the Fe substrate. The magnetization directions of Mn are either parallel or antiparallel to the magnetization direction of the underlying Fe. On the surface, neighboring Mn terraces have the opposite magnetization direction. Thus, a frustrated region will be formed if an Fe atomic step is present underneath the Mn terraces. Neighboring Mn terraces show magnetic contrast that is clearly visible.^[13] In addition, the underlying Fe step creates magnetic contrast within a given Mn terrace. The width of the transition region can be directly measured, which increases from 2 to 7 nm as the thickness of Mn increases.^[12]

SPSTM also provides the capability to resolve the antiferromagnetic structure on the atomic scale, especially when operating in constant current mode. Corrugation of the surface magnetic superstructure decays much slower into a vacuum than the atomic structure;^[14] thus, the antiferromagnetic structure can be easily resolved with a magnetic tip. As an example, Bode et al.^[15] observed a checkboard antiferromagnetic spin structure in an Mn monolayer on W(001). Even an atomically sharp antiferromagnetic domain wall induced by structural defects was resolved. In fact, SPSTM was very successful in resolving magnetic states on the atomic scale. These results were cited in the very thorough review by Wiesendanger.^[4] Recently, STM was used in many new quantum systems. Enayat, et al.^[16] found a double-row antiferromagnetic structure in Fe_1+yTe, which is important in understanding the relationship between ubiquitous antiferromagnetism in parent compounds and their superconducting phase. Hänke et al.^[17] further studied the reorientation of magnetic moments at the surface compared to bulk Fe_1+yTe. Yang et al.^[18] studied magnetism of a magnetically doped topological insulator and found the surface states exhibit ferromagnetism owing to the energy resolution provided by SPSTM.

Beyond a simple collinear spin structure, noncollinear spin states are more common. The first class of noncollinearity originates from the topological arrangement of atoms, where the simple antiparallel alignment of neighboring atoms cannot be fully satisfied.^[19] These noncollinear states are more probable in more complex crystals. The second class of non-collinear spin states arises from higher order effects involving spin and orbital moments. The relativistic spinorbit coupling may lead to mixing of spin states and as a consequence to noncollinear states. Aside from the magnetocrystalline anisotropy, a well-known effect of spin–orbit coupling in systems with broken inversion symmetry is the anisotropic exchange or Dzyaloshinsky–Moriya interaction.^[20,21] This additional term may lead to a non-collinear ground state. A single measurement is insufficient to distinguish between a collinear and a non-collinear spin state. Instead, this requires a combination of spin configuration measurements with different quantization axes.

The classical example of topologically-driven noncollinear antiferromagnetic spin structure is an arrangement of antiferromagnetic atoms in a two-dimensional hexagonal lattice. In this lattice, it is impossible to align all the nearest neighbors such that they are antiparallel. Thus, a frustrated antiferromagnetic Néel structure with a 120° angle between neighboring magnetic moments forms, as shown in Fig. 1. Four energetically degenerate configurations of the 120° Néel structure were drawn and can be distinguished by the orientation of their moments. Direct experimental observation of this Néel structure was found in an Mn monolayer grown on Ag(111).^[22] The magnetic contribution in a constant current SPSTM image is proportional to the projection of the spin polarization of the sample on the spin polarization of the tip. If these spin structures are now imaged with a spin polarized tip, four different images can be obtained. If the tip spin polarization is parallel to that of one of the Mn atoms (Fig. 1(a)), the projection of four possible spin configuration results in two kinds of spin images with opposite contrast (Fig. 1(a)). In both images, the spin pattern shows six-fold rotational symmetry. If the tip spin polarization is perpendicular to one of the Mn moments (Fig. 1(b)), three atoms in the unit cell yield three different projections of their spin polarization on the tip spin polarization, thus leading to patterns with only three-fold rotational symmetry (Fig. 1(b)). This unambiguously demonstrates the 120° Néel structure in a monolayer Mn with a triangular lattice.^[23]

Fig. 1.

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	Fig. 1. Four possible configurations of the 120° Néel structure (1, 2, 3, and 4). Panels (a) and (b) are two groups of constant current images taken with magnetic tips. The size of the images is about 2 nm × 2.5 nm. By assuming the magnetic orientation of the tip, projections of the four spin configurations on the tip magnetization direction results in different magnetic images.

Due to the nonproportional projection of the magnetic moments on different orientations of the noncollinear spin structure, it is quite straightforward to distinguish a noncollinear spin structure from a collinear spin structure. Similar or even more complex noncollinear spin structures have been observed in many topologically driven frustrated systems, such as Cr/Pd(111),^[24] Fe/Re(0001),^[25] Fe/Ir(111),^[26] and Fe/Rh(001).^[27] Nevertheless, determining the exact orientation of each atomic magnetic moment is rather challenging. The problem was solved by integrating SPSTM with a 3D external magnetic field. The magnetization direction of the ferromagnetic tip can be rotated to an arbitrary direction with the external field, which then can yield the 3D projection of the atomic magnetic moments. Figure 2 show an SPSTM image of a hexagonal FeSe surface, which is an antiferromagnetic semiconductor. When imaged with an Fecoated W tip, the magnetization direction can be aligned to the external magnetic field, thus yielding different SPSTM images. Taking Fig. 2(a) as an example, the contrast reverses when the tip magnetization changes from the +X to X direction. This can be seen from the line profiles in the two images, which were gathered along the same trajectory in each image. The apparent height difference between three neighboring atoms changes when the tip magnetization is reversed, indicating the spin polarization projected on the magnetization of the tip changes. A similar argument can also be applied to the Y and Z axes. Obviously, +Y and −Y images (Fig. 2(b)) also contain a large spin contribution. The appearance of the SPSTM images along the X direction are different from the images gathered along Y direction, indicating that the projection of spin polarization along X is not proportional to that on Y. This means that the surface has a noncollinear spin structure, while in the Z axis, the +Z image is nearly the same as the −Z image (not shown, see Ref. [28]), indicating a negligible spin polarization in the Z direction. This can also be seen from the corresponding line profiles. Thus, the spin orientation of individual atoms can be determined by vectorially adding the X and Y components, as shown in Fig. 2(c).

Fig. 2.

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Fig. 2. (a) and (b) Topographical images of a 4 nm × 4 nm region under an external field of X = +2T, X = −2T, Y = +2T, and Y = −2T, as marked in the images. Line profiles were drawn in the middle of panels (a) and (b). (c) The upper figure shows the topographic profile. The lower figure shows the magnetic components obtained by calculating the difference between the X and Y images. Arrows in the middle show the spin direction of each atom by taking a vector sum of the X and Y magnetic components.

Strong spin–orbit coupling could also induce a complex spin structure. A single Mn monolayer on the pseudo-hexagonal surface of W(110) was firstly found to have row-wise antiferromagnetic order.^[29] Interestingly, later on, a more detailed study found that there is a large scale periodic modulation of the contrast with a 6 nm period superimposed on the row-wise contrast.^[30] Interestingly, the observed SPSTM images change with the application of the external magnetic field. The areas of maximal corrugation move laterally excluding a spin density wave, thus implying that the spin structure is a non-collinear spiral. Ab initio calculations including the spin–orbit interaction indicate that the ground state of Mn on W(110) is indeed a cycloidal spin spiral.^[30] Nevertheless, it is difficult to determine the direction of the spin spiral without the in-plane directional sensitivity; on the other hand, this shows the importance of the vector field. Meckler et al.^[31] studied the magnetic structure of an Fe double layer on W(110) and found an inhomogeneous right-rotating cycloidal spin spiral that was not observed in the SPSTM measurement.^[11] There are only a few SPSTM instruments with vector fields that currently exist; some of these were recently developed and could facilitate measurements at temperatures as low as 25 mK,^[32] or could allow rotation of the scanning head rather than rotating the field.^[33] It is certain that SPSTM combined with ultralow temperature and a vector field has unique advantages in studying complex magnetic properties.

SPSTM was not only applied to research into ferromagnetic or antiferromagnetic structures, but was also successfully used to investigate the magnetization of single molecules, defects, and atoms, which are promising building blocks for next generation magnetic functional devices on the atomic scale. The atomic resolution of SPSTM has a natural advantage in studying these nanoscale objects, including single molecules,^[34–37] dopants^[38] or defects,^[39] and single atoms.^[40,41]

Figure 3 shows an SPSTM measurement of an iron porphyrin (FePc) molecule.^[34] In this experiment, FePc was grown on Bi₂Te₃, resulting in the formation of a flat molecular layer. Figure 3(a) shows a detailed image of one FePc molecule, where the central Fe atoms and four ligands are clearly visible. curves (Fig. 3(b)) taken under opposite magnetic fields clearly show that Fe is spin-polarized. Magnetic hysteresis loops can be obtained by plotting the magnitude as a function of the applied field, with the magnetic field parallel and perpendicular to the film, as shown in Figs. 3(c) and 3(d), respectively. The overlap of the value when increasing and decreasing the field in both cases clearly shows paramagnetic behavior. The saturation field is, however, very different. The in-plane signal saturates at 0.3 T, while the out-of-plane signal does not saturate until the field strength reaches 3 T. These results clearly indicate that the magnetic moments of FePc when deposited on Bi₂Te₃, and FePc has an in-plane easy axis with a considerably large magnetic anisotropy.

Fig. 3.

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	Fig. 3. (color online) (a) Topography of a single FePc molecule where the central Fe atom and four ligands are clearly resolved. (b) curves under ±1 T at the same Fe atom, where the magnetic field is parallel to the abplane. Panels (c) and (d) show at a fixed energy versus the magnetic field of the atom with the magnetic field aligned parallel and perpendicular to the ab plane, respectively.

SPSTM is not limited to studying molecules, but magnetic defects can also be studied with SPSTM. One can deduce the bulk properties in addition to interesting magnetic properties of defects. Chen et al.^[39] studied the magnetic properties of an FeSe surface with Se vacancies at the surface. FeSe is the simplest Fe based superconductor whose parent phase is currently under debate. First of all, unlike the obvious antiferromagnetic superstructure observed with SPSTM in a similar system (Fe_1−yTe^[16]), no trace of a magnetic superstructure in the SPSTM images could be observed in FeSe. However, magnetic contrast was observed from Se vacancies, as shown in Fig. 4. Similar to measurement on FePc molecules, as discussed before, figure 4(a) shows magnetic hysteresis loops in an Se defect, as well as at the bare surface. At the Se site closest to the vacancy, the magnetic loop displays clear paramagnetic behavior under a perpendicular magnetic field (black curve in Fig. 4(a)) while, at the Se site far away from vacancy, the value does not show any change with the external magnetic field changes (red curve in Fig. 4(a)). From the fact that the magnetization of the Se vacancy follows perfectly with the applied magnetic field, it can be concluded that FeSe thin film is nonmagnetic. If this were not the case, magnetization of the Se vacancy would be pinned by magnetization of the film. Further evidence of a nonmagnetic FeSe thin film is conceived in the spatial distribution of the spin polarization around the Se vacancy. Figure 4(b) and 4(c) show constant current images taken at opposite magnetic fields of ±0.5 T. By subtracting Fig. 4(b) from Fig. 4(c), topographic information was eliminated and a net spin distribution was obtained, as shown in Fig. 4(d). One can see clearly that the four Se sites around the defects manifest nearly the same spin polarization, which is shown in the line profiles (Fig. 4(f)) across the defects. From the perspective of symmetry, the presence of any magnetic superstructure in the Fe layer will break the fourfold symmetry in the spin channel. Thus, FeSe films must be nonmagnetic and magnetization damps rapidly at larger distances from the vacancy, and ab initio calculations further confirm that the defects behave as a ferrimagnetic cluster.

Fig. 4.

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	Fig. 4. (color online) (a) Magnetization curve measured with SPSTM near and away from the vacancy. (b) and (c) Topographical images taken with a Cr tip under antiparallel 0.5-T magnetic fields. (d) Difference image of panels (b)–(c). Panels (e) and (f) show line profiles from panels (b), (c), and (d).

Finally, as an example of the magnetization of single atoms, Meier et al.^[40] investigated single Co atoms on Pt(111). They successfully obtained magnetization curves for single Co atoms, which show paramagnetic behavior even at 0.3 K, although the expected magnetic anisotropy is as high as 9.3 meV per atom. The absence of hysteresis was attributed to the temperature-independent switching process, such as quantum tunneling of magnetization or current-induced magnetization switching by inelastic processes. In addition, they measured the long-range coupling between Co adatoms and the Co monolayer. A damped oscillatory behavior was observed, which is concluded to occur via Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange through conduction electrons in the Pt substrate.

Balashov et al.^[42] used ISTS to observe magnon excitation in bulk Fe. The excitation energy is of the order of a few meV. To distinguish the origin of the excitation, i.e., magnons or phonons, they used a spin-polarized STM tip as a source for hot electrons. Depending on the relative orientation of tip and sample spin polarization, the inelastic spectrum is altered while the relative orientation between the tip and sample switched, confirming magnon excitation.

Beyond the lateral resolution, STM can also be used to determine the momenta and life times of magnons by measuring standing spin wave excitation. In bulk magnetic materials, magnons are free to travel in any direction, resulting in a continuous dispersion of magnon energy E as a function of momentum k. Magnons in thin films are confined normal to the film plane, and standing magnons are formed. Their dispersion relation is given by a series of spin wave branches quantized in normal to the film plane, while dispersion is continuous along the and directions. Gao et al.^[43] measured spectra of fcc-Mn ultrathin films on Cu₃Au(001), which is a layer-wise antiferromagnet.^[44] In agreement with simple quantization, a series of excitation peaks in the inelastic spectra was observed (Fig. 5(a)). The onset of every branch of standing magnons is observed as a peak in an ISTS measurement. From the thickness t of the Mn layer and the order of the peak, magnon dispersion can be computed using a simple conversion , as shown in Fig. 5(b), which agrees well with neutron scattering data from Nistabilized bulk fcc-Mn and ab initio calculations.^[43]

Fig. 5.

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	Fig. 5. (a) Thickness dependent inelastic tunneling spectra in Mn thin films. (b) Magnon dispersion curve extrapolated from (a) together with neutron scattering data.

The single atomic spin-flipping process was first observed by Heinrich et al.^[45] in 2004 on a single Mn atom on an Al₂O₃ substrate. The substrate is decoupled from a metal by a thin insulating layer, and Zeeman splitting energy can be measured by ISTS. This method was soon extended to other systems, including single atoms on both metallic^[46–48] and insulating^[49–51] substrates. Magnetic anisotropy energy can be directly obtained through ISTS measurements. The anisotropic energy is usually quite small on a metallic substrate, but it can be enhanced on heavy metals with large spin orbit coupling. The magnetic anisotropy can be significantly increased by hybridizing magnetic atoms with the molecular orbits of insulators. In fact, if a proper insulating layer is chosen, giant magnetic anisotropy energies as large as 58 meV per atom were observed in single Co atoms on a MgO substrate.^[49] This striking behavior originates from the dominating axial ligand field at the O adsorption site, which leads to out-of-plane uniaxial anisotropy while preserving the gas-phase orbital moment of Co.

The pursuit of high anisotropic single atomic systems is critical to realizing nanoscopic magnets for high-density magnetic data storage or quantum computing. Despite the high anisotropic energy, which is already far above room temperature, stable magnetization of a single atomic magnet is observable over the order of minutes, even at an extremely low temperature. Quantum mechanical fluctuations are believed to largely dominate the magnetic instability. Decoupling from the thermal bath of electrons, nuclear spins, and lattice vibrations can be reduced by inserting an insulating layer^[49–51] or using symmetry protection.^[48] It is still possible to further enhance the magnetic anisotropy by using 4d or 5d elements instead of 3d atoms,^[52] or by using a specially designed artificial atomic structure, such as a Co or Ir biatomic system on graphene.^[53] A recent experiment already shows that Ho on MgO can be stabilized for hours.^[54] In this experiment, the authors used single atom electron spin resonance measurements, which are capable of detecting single spins with minimal perturbations.^[55]