In March 1981 G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel at the IBM Zürich Research Laboratory observed vacuum tunneling of electrons between a sharp tungsten tip and a platinum sample. Combined with the ability to scan the tip against the sample surface, the scanning tunneling microscope (STM) was born. Since then, this novel type of microscopy has continuously broadened our perception about atomic scale structures and processes. The STM allows one to image atomic structures directly in real space, giving us the opportunity to make the beauty of nature at the atomic level directly ‘visible’. Moreover, the sharp tip can be regarded as a powerful local probe which allows one to measure physical properties of materials on a small scale by using a variety of different spectroscopic methods. However, vacuum tunneling of electrons is not the only means by which local properties of matter can be probed. The development of the STM technique has triggered the invention of a whole family of scanning probe microscopies (SPM) which make use of almost every kind of interaction between a tip and a sample of which one can think.

Before we focus on the different modes of operation of a scanning tunneling microscope (STM) and the information which can be extracted, a historical review of earlier studies of tunneling phenomena is given in the following sections. This will serve as an introduction to tunneling experiments as well as motivation for a variety of experimental methods applied in STM. It will become clear later in this chapter that most of the special effects now studied in STM have already been investigated before by using planar metal–oxide–metal tunnel junctions.

Historical remarks on electron tunneling

Tunneling is an important mechanism of transport in condensed matter and across artificial junctions. In contrast to other transport mechanisms such as diffusion and drift, which can be described on the basis of classical physics, tunneling can only be understood in terms of quantum theory.

Consider a potential energy barrier and a microscopic particle, e.g. an electron, with an energy smaller than the potential barrier height. From the viewpoint of classical physics, this particle will never be able to traverse this barrier. However, in quantum theory, the wave–particle dualism may in fact allow this electron to traverse the barrier. The wave nature of microscopic particles (de Broglie, 1923) impinging upon a potential energy barrier is expressed in the experimental observation of a finite probability of finding the particles beyond the barrier and they are then said to have tunneled through it.

Condensed matter physics deals with systems containing a large number of atoms (typically 1023 cm−3) that form a dense aggregate. Theoretical treatment of such complex systems has traditionally been based on simplifying concepts.

1. The concept of totally neglecting the microscopic structure is used in phenomenological theories for macroscopic systems, such as thermodynamical or continuum mechanical descriptions.

2. The concept of a statistical theoretical treatment of a large number of atoms appears as a link between a macroscopic and microscopic description, where macroscopic observables are attributed to the average properties of the constituents of the whole aggregate, whereas fluctuations resulting from the individual behavior of single atoms are assumed to be negligible.

3. The concept of idealizing the microscopic structure of macroscopic systems has led to the foundation of modern condensed matter theory. Most notably, the concept of the perfect crystal, whose atoms are arranged in space with strict periodic order, has been used as a starting point for a profound description of real crystalline solids. The strict periodicity present in a perfect crystal allows rigorous theoretical treatment, leading to exact solutions of the Schrödinger equation. However, these solutions emphasize the collective properties of the many atoms chemically bound in the crystal, whereas the individuality of each atom is again lost.

The experimental techniques traditionally applied to investigation of the condensed state of matter, such as diffraction, specific heat, electrical transport or magnetization measurements, have also focused on average and collective properties of the many atoms in a macroscopic system.

Scanning probe methods, such as STM and SFM discussed in chapters 1 and 2, represent a novel approach to surface analysis and high-resolution microscopy. Traditional surface analytical and microscopical techniques are based on an experimental set-up schematically illustrated in Fig. 3.1(a). The sample in the center of an UHV chamber is probed by electrons, photons, ions or other particles which originate from corresponding sources, typically at a macroscopic distance from the sample surface. As a result of the interaction of the primary electrons, photons, ions etc. with the sample, secondary particles are created and eventually leave the sample together with scattered primary particles. They can be detected by appropriate detectors and analyzers which again are typically a macroscopic distance away from the sample surface. The direction of the emitted particles as well as their energy contain valuable information about the sample under investigation. The spatial resolution achievable is determined by the spatial extent of the primary beam as well as the interaction volume within the sample.

In contrast, scanning probe methods are based on a completely different experimental geometry depicted in Fig. 3.1(b). A sharp probe tip is brought into close proximity to the sample surface until interaction between tip and sample sets in. The interaction is spatially localized according to the shape of the probe tip and the finite effective range of the interaction.

Scanning tunneling microscopy (STM) and related scanning probe microscopies (SPM) have found numerous applications in various scientific disciplines and are already documented by thousands of publications devoted to this research field. It is certainly impossible to present a review of all that work which would in any sense be complete. Therefore, the second part of this book aims at a description and discussion of representative and important applications of STM and related SPM, rather than a comprehensive review of published work in this field. The selection of topics as well as the emphasis put on particular topics is mainly influenced by the number and significance of publications within a particular field of application. However, it naturally reflects the particular interests of the author of this book as well.

We have already discussed in section 1.22 that a variety of forces act between the tip and the sample during STM operation with their strength depending on the tip–surface separation. These forces have been exploited to develop another type of scanning probe microscopy, namely scanning force microscopy (SFM), which no longer uses electron tunneling to probe local properties of sample surfaces, but rather the tip–sample force interaction. Since the force interaction does not depend on electrically conducting samples (and tips), SFM can be applied to insulators as well, thereby extending the applicability of local probe studies to an important class of materials which are difficult to investigate by electron microscopical and spectroscopical techniques due to charging problems. Before we focus on SFM, a brief historical review of surface force measurements and surface profilometry, which are closely related to SFM, is given in the next section.

Historical remarks on surface force measurements and surface profilometry

Surface force apparatus (SFA)

For two electrically neutral and non-magnetic bodies held at a distance of one to several tens of nanometers, the van der Waals (VDW) forces usually dominate the interaction force between them. The VDW forces acting between any two atoms or molecules may be separated into orientation, induction and dispersion forces. Orientation forces result from interaction between two polar molecules having permanent multipole moments, whereas induction forces are due to the interaction of a polar and a neutral molecule where the polar molecule induces polarity in the nearby neutral molecule.

Introduction

In previous Chapters, transfer of energy to and from a permanent magnet, and associated changes in energy of the external field have been discussed. For initial magnetization, the objective is to apply sufficient energy to the material to align its internal magnetization vectors Min a unique direction, for which the magnet is said to saturate at Msat. Optimum performance is achieved along this preferred axis, but the characteristics quantifying the material's properties have to be measured outside the magnet. The internal parameter M cannot in fact be measured directly, and although the intrinsic curve is the more fundamental characteristic of a magnet, it must be deduced from an external measurement of the normal B versus H loop.

This example illustrates a problem, which is commonly encountered by users of permanent magnets. Whereas they design a device to operate in a certain manner, it later appears that the real magnet does not meet these expectations. Later in this Chapter, we discuss various techniques that are used for measuring magnetic parameters - their application to the properties of magnets themselves will provide the basis for quality control. Unfortunately, the magnitude of applied field that is required to saturate a particular magnet is a somewhat empirical quantity.

Introduction

Permanent magnets have been employed in a wide range of electrical apparatus for a great many years, and it is well beyond the scope of this text to discuss their design for all current applications. However, the dramatic improvements in material properties that accompanied the evolution of rare earth magnets have focussed interest on certain electromechanical and electronic devices, in which these materials may be applied to advantage. With this in mind, we discuss a wide variety of applications, which reflect the scope of new design activity today. This includes devices whose extremely high production quantities continue to make low cost ceramic ferrite the dominant material in today's market, and high added value products, which exhibit significant performance benefits using high energy rare earth magnets.

The most important application for permanent magnet materials is in direct current (d.c.) rotating electric motors. Ceramic ferrites have long been used in these machines to provide a steady magnetic field from their stators, but more recently rare earth magnets have been employed to particular advantage to promote the evolution of electronically commutated brushless d.c. motors, in which the permanent magnet assembly usually becomes the rotating component. The high energy of rare earth magnets is often used to produce a greater air gap flux density in a d.c. motor, which yields a corresponding improvement in the motor's output torque. The magnet's high coercivity is also attractive, because this improves its resistance to demagnetization from the motor's own armature winding.

The original inspiration to write this book came when, after an electrical engineering training in the late 1960s, I embarked upon the design of a variety of permanent magnet electrical machines. I needed to know more about the behavior and performance of the different magnet materials than the electromechanical design texts provided, and significantly more applications data than the scientific books on magnetism contained. This shortcoming was exacerbated in the early 1970s when an entirely new class of magnet - the rare earths - was discovered, offering a vast array of new opportunities for permanent magnet devices, and new challenges to designers such as myself. As these new materials were developed, their properties exhibited dramatic improvements from year to year, reaching maturity in the early 1990s as a full range of samarium-cobalt and neodymium-iron-boron magnets. Until this had happened, I felt that any attempt to produce a comprehensive text including a description of these materials would have been premature. Now, with first-hand experience in most cases, I am able to describe their selection and design for a wide range of important applications.

The material for this book has evolved from courses given to students and practicing engineers while I was at the University of Cambridge and the University of Southern California, and from a variety of assignments to develop and design permanent magnet materials.

Introduction

When a designer specifies the use of a permanent magnet, he certainly hopes that its magnetization will indeed remain permanent, or at least a close approximation to this. Specifically, the designer requires the magnet's demagnetization curve, the second quadrant of the B versus H characteristic, to remain unchanged under normal operating conditions. Unfortunately, this is never the case, so it is important to understand the nature of the changes that may occur, so that any degradation of the magnetic properties reflected in the demagnetization curve may be accounted for in the design. Changes in a magnet after it has been manufactured and fully magnetized may be caused by any combination of external influences, such as temperature, pressure and applied field. These changes fall into three categories.

The first category comprises those effects that result in a permanent change in the demagnetization curve, which persist even if the magnet is fully remagnetized. One should either avoid selecting a particular magnet type for an environment in which it will be exposed to conditions known to cause a permanent change, or provide protection for the magnet from this environment. Consider the case of alnico magnets, which, as described in Chapter 2, undergo a critical segregation of the ctl and a2 phases during their heat treatment between 550 and 650 ºC.

Introduction

The shape of the B versus H characteristic of a material reveals whether its magnetism is based upon magnetocrystalline or shape anisotropy. In either case, the ideal characteristics described in Chapter 1 were founded on the concept of spontaneous magnetization, and this theory is certainly a good approximation for single crystals; measurements in the preferred [1,0,0] direction for iron shown in Figure 1.6 confirm this. However, practical materials do not follow this theoretical ideal, as shown for comparison by the initial magnetization curves for a real sample of iron in Figure 2.1. A measurable external applied field H is required to magnetize and saturate this material, so this sample does not exhibit spontaneous magnetization. The same is true for samples of nickel, cobalt and all alloys that are used to produce permanent magnets.

While the magnetization curves for the single crystal in Figure 1.6 are dependent upon the crystallographic direction, the curve for a bulk sample of iron is not. A simple ferromagnetic material such as this is therefore isotropic with no preferred axis, and any enhanced properties in a specific direction will only be imparted to a magnet during its production process. Spontaneous magnetization still exists in the crystal lattice structure, so it must be explained how the theory of magneto crystalline anisotropy must be modified to predict the actual characteristics of permanent magnets. To do this, the model of a magnetic material must first be enhanced.

Introduction

Earlier texts on permanent magnets have opened with historical reviews of these materials (Hadfield, 1962; McCaig, 1977; Parker, 1990; Parker and Studders, 1962). In this book the design of modern permanent magnets is emphasized, and so initially the development of the relationships that are required to model today's materials for a variety of common applications is considered. To the extent that a historical review is provided in this chapter, it is of those fundamental equations of electromagnetism that are needed to understand the performance of magnets in circuits and devices.

There are many properties of a permanent magnet that are considered in its design for a magnetic device, but most often it is the demagnetization curve that initially determines its suitability for the task. Its shape contains information on how the magnet will behave under static and dynamic operating conditions, and in this sense the material characteristic will constrain what can be achieved in the device design.

The B versus H loop of any permanent magnet has some portions which are almost linear, and others that are highly non-linear. The shapes of these B versus H loops, or at least the demagnetization portions of them, tell the designer a lot about the suitability of the material for a given application. A brief derivation of the B versus H loop is presented, to illustrate the microscopic mechanisms that determine the macroscopic performance of a magnet.

Introduction

Analytical techniques, such as finite element analysis, provide accurate solutions for two- or three-dimensional field distributions in complex geometries, which in turn may be used to predict device performance with similar precision. However, these techniques require a detailed definition of the geometry and boundary conditions to be solved, which assumes that an initial design already exists. While providing an accurate field solution for a defined geometry, they will not optimize it - suggestions for changes to dimensions, materials, excitations, etc. must come from the designer, to be analyzed via a field solution. Consequently, while computer-based field analysis is an effective tool for simulating a known device, it is too cumbersome for design optimization.

Preliminary designs are usually performed using a magnetic circuit model of the device in which each component or magnetic flux path is represented by a discrete element. Equations representing the magnetic circuit components are derived in this Chapter, and the elements they define are used in an equivalent circuit (similar in many respects to an electrical analog circuit). This is a simple model, which can be easily optimized for any performance requirements. Thereafter, field analysis may be employed to verify the operation of the device, and to fine-tune the design.

Introduction

Using simplifications for the actual paths followed by flux in a magnetic device provides an approximate model as described in Chapter 4, which is useful both for preliminary selection of component materials and dimensions and for performing sensitivity analyses. Before building a prototype device, however, it is often desirable to perform a more detailed analysis of the flux distribution, to investigate the validity of the prior assumptions, and perhaps also to account for effects such as saturation and eddy currents. Depending upon the complexity of the design and the nature of the effects to be studied, a more accurate analytical solution of the field distribution may be attempted directly, or with the aid of commercially available computer software. The objective in this chapter is to provide the basis for the representation of magnetic fields in complex geometries, and an understanding of the most common techniques that are presently available.

The nature of the fields that occur in electromechanical devices may be categorized into three levels of complexity. The most straightforward are magnetostatic fields, which result from excitation at zero frequency. Nevertheless, materials may still be represented by non-linear characteristics in magneto static field solutions, as in the case of saturation. The next level of complexity involves alternating current excitation, which adds the effects of eddy currents to the field solution.