I. Introduction

The field of surface magnetism is the natural extension of the bulk magnetism studies. Surface science in general was inhibited for a long time because of the lack of sample preparation conditions adequate for performing reproducible experiments on well-defined systems. Since the ultra-high vacuum (UHV) equipment became widespread, the surface science research flourished. Techniques were developed to achieve atomic resolution in real-space imaging including the recent surge of scanning-probe microscopies, started with the invention of the Scanning Tunneling Microscope¹ (STM). The availability of structural data on the atomic level led to deeper understanding of the macroscopic phenomena and allowed the direct observation of microscopic effects. In magnetic measurements similar advances can be expected when imaging of magnetic moments of individual atoms or, at least direct observation of magnetic domain boundaries, becomes possible. Behavior of such domain boundaries is important both for "pure" research, such as the near phase transition phenomena, and for practical applications, such as imaging bits on magnetic storage devices.

Few magnetic microscopies² are available for imaging at progressively diminishing scale. Optical microscopes can be adapted to produce contrast using Kerr rotation of linearly polarized light reflected off domains with different magnetization³. The diffraction limit of the resolution is about 500 nm for optical techniques and can be somewhat overcome by near-field optical microscopy⁴. Magnetic Force Microscopy (MFM) measures the force that stray magnetic field of the surface exerts on the small magnetic tip. Magnetization then is probed indirectly via the magnetic poles of the sample⁵, and the resolution obtained is on the order of 10-50 nm. Electron-based microscopies push resolution further. Secondary-electron microscopy with polarization analysis (SEMPA) measures the spin polarization of secondary electrons emitted from a magnetized sample⁶ with resolution of about 20 nm. High-energy electron microscopes, such as Lorentz microscopy, where the deflection of the beam by magnetic domains is detected, can achieve resolution of 2 nm and can be used both as reflection and transmission techniques⁷. So far the only technique potentially capable of atomic resolution is spin-polarized scanning tunneling microscopy (SPSTM). While spin contrast is not yet obtainable on a routine basis, the recent advances described in the following sections suggest that SPSTM may become the ultimate magnetic microscopy technique.

II. Spin-Polarized Scanning Tunneling Microscopy Basics

The general principle behind SPSTM is the same as for regular STM. A piezo-electric crystal is used to accurately position an atomically sharp tip above a sample (Fig. 1). Changing the position in the lateral (x,y) plane allows to scan continuously across the sample surface and changing the vertical (z) position allows to maintain desired tip-sample distance. If that distance becomes small enough (10 - 0.1 Angstroms) and voltage is applied between the sample and the tip, the tunneling current (1 - 0.1 nA) can be observed. This current depends exponentially on the tip-sample separation. Therefore if a feedback loop is used to adjust the vertical position to keep the current constant (constant current scanning mode) tip-sample separation can be kept constant with great precision. Alternatively the z-coordinate can be held constant and the tunneling current recorded. Since the current is essentially proportional to the density of electronic states in the sample, the first method maps constant density of states contours and the second method maps the actual density of states.

Fig.1 Basic STM setup. Atomically sharp tip is mounted on 3 piezo crystals that allow precise positioning in 3 directions. Moving in (x,y) plane scans the tip across the sample, z piezo determines the tip-sample distance.

SPSTM uses the fact that if the tunneling electrons are spin-polarized, then the tunneling current strongly depends on the sample spin-state. The current increases when the two spin-polarizations are parallel and decreases when they are anti-parallel. Depending on the source of the spin-polarization of electrons we can have two types of SPSTM: magnetic (usually metallic) tip and optically pumped GaAs tip.

III. Spin-Polarized Tunneling

The single most important property of ferromagnetic materials is that electron energy bands are split into two subbands. The splitting is due to electrons' spin and it results in one of the subbands containing more electrons than the other. The two subbands are usually referred to as majority and minority subbands. Unequal population of the two subbands produces ferromagnetic materials that have non-zero magnetization without any external magnetic field.

Now let us define spin-polarization of the tunneling current P as follows:

where n "up" and "down" are densities of electrons with spins parallel and antiparallel to magnetic field respectively. This definition suggests that the band splitting in ferromagnetic materials, described above, can be used to emit spin-polarized electrons. In fact they are produced in field emission and tunneling through metal-insulator-metal junction experiments. The simplest model for spin-dependent tunneling suggests that the spin-polarization of electrons extracted from the material is determined by the total density of states and thus can be both positive and negative. First experiments on spin-polarized field emission from well-defined facets of monocrystalline metals have been performed in late 1960s when this effect was observed for gadolinium⁸ and later for nickel⁹. Most surprising result was that the polarization turned out to be always positive and generally higher than the values predicted by the simple band-theory. Similar phenomena were observed in planar junction experiments¹⁰. Several attempts were made to explain the results in the framework of the bulk band structure¹¹, many-body effects and spin-dependent surface potential¹². Currently the two most generally accepted models were proposed by Slonczewski¹³ and by Stearns¹⁴ and Julliere¹⁵. Slonczewski's theory treats electrons as independent particles, and considers two separate currents of spin-up and spin-down electrons contributing to the total tunneling current. In this approach the conductance can vary greatly in magnitude and sign depending on the wave vectors k "up" and "down" inside the ferromagnet and attenuation coefficient k in the barrier. Model of Stearns and Julliere, regarded by some as more physical (Fig. 2), assumes that the tunneling current is proportional to the density of states of the highly-polarized itinerant d-like electrons. This theory easily explains the proportionality of spin-polarization to bulk magnetization - a very important experimental observation. However the polarization values are not well predicted for all ferromagnet-insulator-ferromagnet tunneling systems. At present data are too conflicting to confirm or rule out either of the models and SPSTM may make a significant contribution, providing results from well-characterized surfaces in UHV environment.

Fig. 2 Simplified version of Stearns-Julliere model of spin-polarized tunneling. N's are respective numbers spin-up, spin-down electrons in the two materials, a and a* are respective proportions of spin-up (that is aligned with the field) electrons.

IV. SPSTM with Magnetic Tip and Magnetic Sample

Even though their detailed observations and predictions vary significantly, spin-polarized tunneling experiments provide us with all the necessary tools for SPSTM. The idea is to use a single crystal ferromagnet with constant magnetization as an STM tip while imaging a sample that in the simplest case should be also a single crystal ferromagnet. If the tip has a properly chosen well-defined crystal plane at its end, when bias voltage is applied the tip becomes a source of spin-polarized electrons and a ferromagnet-insulator-ferromagnet junction is formed between the tip and the sample. The tunneling current then should depend on the orientation of the sample's magnetization with respect to the spin-polarization of tunneling electrons (Fig. 2). Direction of the local magnetization changes from domain to domain, thus magnetic structure can be imaged with nm and sub-nm resolution typical for STM.

Substantially polarized tunneling electrons are necessary to produce easily detectable variation (on the order of 10 %) of the tunneling current caused by the orientation of the sample magnetization. There are at least 4 ferromagnetic metals that can be sources of such polarized electrons (see table 1). A prototype SPSTM with single-crystal Ni tip was in fact built, tested and reproducible signals consistent with spin-polarized tunneling were reported¹⁶. However the first SPSTM results in vacuum were actually obtained by Wiesendanger et al¹⁷ using a different magnetic tip - CrO₂ covered cleaved Si(111). In that experiment a Cr(001) surface with atomic steps was imaged using non-magnetic (W) and then magnetic tip. Height of all the steps appeared to be the same (0.14 nm) while imaging with non-magnetic tip, but showed alternation between 0.16 and 0.12 nm with magnetic tip. Authors point out that this can be easily explained by the model where steps on Cr sample have alternating magnetization (see Fig. 3).

Fig. 3 Ferromagnetic tip scanning over alternately magnetized terraces separated by monoatomic steps. An additional contribution from spin-polarized tunneling leads to larger apparent height h₁ for parallel tunneling, compared to smaller h₂ for antiparallel tunneling. (adapted from Ref. 17)

Although still open for alternative explanations, taken at face value this observation suggests that use of SPSTM for imaging of magnetic structures is indeed possible. In this light, it is very encouraging that atomic resolution in magnetic tip - magnetic sample system has been reported²¹ by the same group 2 years after the first experiments. This sub-nm resolution has been achieved with an iron tip on (100) surface of magnetite (Fe₃O₄) where images show individual rows of iron ions (0.59 nm row spacing). More recently successful Scanning Tunneling Spectroscopy (STS) of Fe/W(110) system using iron covered tungsten tips was reported¹⁸ by the same group, opening the possibility for magnetically sensitive spectroscopy measurements.

Use of other tip materials can be advantageous for several practical reasons. First, significant increase in polarization of emitted electrons has been observed when metallic electrodes were covered with thin film of EuS. After the fisrt experiments¹⁹ in the 70's this "spin-filter" effect has been observed for few other similar materials and is generally attributed²⁰ to the effect of tunneling barrier caused by exchange splitting. Such splitting lowers the tunnel barrier energy for spin-up and raises it for spin-down electrons, leading to the preferential selection of spin-up electrons in the tunneling current.

Magnetostatic interaction between a ferromagnetic tip and a ferromagnetic sample is another example of a practical problem that can be solved by using an alternative material - in this case antiferromagnetic tip! A wide range of conducting antiferromagnetic compounds was studied²¹ for that purpose and Cr, MnNi and MnPt tips produced atomic resolution imaging on non-magnetic samples during testing²¹.

V. Optically Pumped GaAs Tips

As promising as magnetic tip SPSTM is, it is not the only existing approach to obtain spin-polarized tunneling. Probably the most refined alternative is the use of optically pumped GaAs tips as sources of spin-polarized electrons. This technique can be used to study semitransparent (i.e. thin film) magnetic samples. An example of a possible experimental setup is summarized in Fig. 4. A GaAs tip is mounted on a regular STM and scanned across a sample. At the same time a beam of circularly polarized laser light is focused on the apex of the tip. To obtain the best possible polarization the laser light has to come perpendicular to the sample, that is why a semitransparent sample is used and laser beam is illuminating the tip through the sample. It has been shown²² that due to spin-orbit coupling and optical selection rules in GaAs, spin-polarized electrons can be induced by circularly polarized light. A bias voltage is applied between the tip and the sample, creating small tunneling current of these spin-polarized electrons. As it was illustrated in section III, the spin-polarized tunneling current depends on the direction of the sample's magnetization and therefore can be used to image the magnetic structure of the sample.

Fig. 4 SPSTM with optically pumped GaAs tip setup.

The practical implementation of that deceivingly simple scheme was thoroughly investigated in a series of papers^22,23 by Prince et al and recently observation of magnetic domains of Co films (see Fig. 5) was observed by Suzuki et al²⁴ using an STM with optically pumped GaAs tips.

Fig.5 (a) Topography image; (b) intensity modulation image; (c) polarization modulation response image. These 1x1 mm² images were recorded at the same sample location. (a) & (c) are simultaneous. (d) 1x1 mm² MFM image obtained on a typical sample with 10 nm gold-covered layer. (adapted from Ref. 24)

Topography image (Fig. 5a) shows the grainy structure of the sample (thin Co film on a 10 nm gold/mica substrate) due to the gold grains. The variation in laser beam intensity (Fig. 5b) does not affect that small-scale graininess of the image, but does not induce any larger-scale (few 100 nm) structure. However polarization image (Fig. 5c) does exhibit large-scale contrast that is very similar to a typical Magnetic Force Microscopy image (Fig. 5d) of the same type of sample. This result certainly does suggest that in fact the magnetic contrast was obtained, and leaves the possibility of nm and sub-nm resolution open. While obviously free of any problems due to magnetostatic tip-sample interactions (the tip is not magnetic!), this approach does have caveats of being limited to studies of thin films and of poor general understanding on the effects of the laser illumination on the nm scale, such as energy dependence and possible heating.

VI. SPSTM Questions and Answers

As it was noted repeatedly, SPSTM experiments are facing numerous technical difficulties, many of which were identified at the prototype stage¹⁶ and by various experimental groups^17,20,23,24:

• Thermal drift problems: sample and tip can be heated by the magnetic coils and illuminating laser light. Also in many cases scan speeds have to be low, which results in abnormally high thermal drifts.
• Magnetostriction of both the tip and the sample (even paramagnetic sample) can introduce significant uncertainty in tip-sample separation.
• Magnetostatic tip-sample interactions are poorly understood on nm scale
• Stray magnetic fields, non-stable laser light, and other sources of spurious noise
• Lack of a good test system (such as Si(111) 7x7 reconstructed surface for STM (Fig. 1))

None of the above problems however appear insurmountable at this point - alternative tip materials can fight the magnetic effects, faster and smaller STM's will help with drift, dealing with noises is every experimentalist's headache, but it never stopped anybody anyway, even the test system problem may be solved by stepped surfaces, for example. To make the long story short - there is certainly room for future developments, but the situation is far from desperate.

In addition, there exists a few other alternative SPSTM techniques, such as idea of Alvarado et al to combine the SEMPA⁶ technique and polarized fluorescence into STM-induced fluorescence with polarization analysis²⁵. These ideas are generally only on very preliminary stages right now, but so were the current favorites just a few years ago, and only the future will tell us which one them will be the first to reach the ultimate goal of magnetic microscopy with atomic resolution.

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