A variety of levitation techniques are available to the researcher to study high-temperature materials in the normal and supercooled states. The most widely practised techniques at the present time are aerodynamic levitation, in particular conical nozzle levitation (CNL), various kinds of magnetic levitation including electromagnetic levitation (EML), and electrostatic levitation (ESL). Other methods developed for specific applications such as acoustic levitation and gas-film levitation are less widely used and will be discussed only briefly.

In order for levitation to be useful in a scientific experiment, it is important not only to supply a force that can counteract the gravitational field but also to maintain the sample in a configuration that is sufficiently stable to allow the measurements to be performed. The issue of stability may be quite complex. A prime example is the Levitron®, a popular toy in which a spinning magnetic top is suspended above a flat surface of a magnetic material (http://www.levitron.com/). The levitating force is obvious, but the stability requires a complex physical analysis (Berry,1996; Berry & Geim, 1997).

The variety of methods in current use suggests that each one has particular advantages and disadvantages, depending on the application in hand. CNL is a relatively simple and versatile technique and can be readily incorporated into different kinds of experimental apparatus. EML is restricted to conducting samples, generally metals, in which case relatively large samples (up to 1–2 cm diameter if desired) can be levitated.

In this chapter we discuss some elements that are semiconducting in the solid state and that, because of their relatively high melting points and interest in their supercooled liquid states, have been the subject of investigation with levitation techniques. The first materials to be discussed – silicon, germanium and their alloys – in fact melt into metals, albeit, as we shall see, metallic liquids with quite unusual properties.

Silicon

Silicon crystal growth and crystal properties are important in the semiconductor industry. Silicon is the host material for the majority of semiconductor applications, and the properties of its crystalline, amorphous and liquid phases are of substantial interest. The atomic structure, electrical, optical and thermophysical properties of the liquid phase are key factors that determine the quality of crystals grown from the melt. Mito et al. (2005) have made numerical simulations of Czochralski growth of silicon crystals and found that the Peclet number and deflection of the melt–crystal interface, two important parameters in the growth process, are highly sensitive to the emissivity, thermal conductivity, temperature coefficient of surface tension in the liquid as well as the emissivity and thermal conductivity of the crystal. A graphic representation of the importance of thermophysical properties of the liquid for numerical modelling of crystal growth is given in Fig. 7.1.

The conductivity and other electrical transport properties of liquid Si and Ge have been measured by several authors in contained samples.

Introduction

The first part of this chapter describes the edge effects of patterned ferromagnetic films. The edge pole of the ferromagnetic film plays a significant role in the film properties, in particular, the magnetic energy state. Since the magnetic memory cells are made of tiny pieces of patterned film or film stack, the effects due to the end poles become a dominant factor governing the stability and switching behavior of the memory cell. The second part of this chapter deals with the switching properties of a small patterned film under an external magnetic field. A coherent switching model is introduced to describe the switching properties of the film. This is the basis of the write operation of the field-MRAM cells.

Edge poles and demagnetizing field

When a ferromagnetic thin film is patterned and etched into shapes, the magnetic poles at the edge of the film are exposed. Like the end of a bar magnet, magnetic flux emits from the poles at the edge of the thin film. Inside the film, the flux points in a direction opposite to the magnetization. The magnetic field associated with the end poles is called the demagnetizing field, HD. The magnitude of HD is position-dependent.

Consider a semi-infinite film of thickness t and saturation magnetization MS. The film extends from y = 0 in the +y-direction toward infinity and extends in both the +x- and –x-direction toward infinity (see Fig. 3.1).

Introduction

A short time after the discovery of magnetic tunneling devices, tunneling magnetoresistance (TMR) replaced giant magnetoresistance (GMR) read sensor in the hard disk drive. This marked the first successful commercialization of magnetic tunnel junction technology. The first mass production of the magnetic recording head based on a MgO tunnel barrier took place in 2006. In the same year, 4 Mb MRAM chips were commercialized, and it was the first field-MRAM product working in the toggle-write mode. The viability of MTJ technology at the product level is proven. Subsequently, electronic system designers started to consider seriously how to take advantage of this technology. Many new applications of MTJ technology begin to emerge. One of the new circuit elements is the non-volatile magnetic flip-flop device, which is used for the reduction of VLSI chip power as well as for run-time system re-configuration. Such new applications can only be realized with the unique properties of magnetic tunnel junction devices.

Other new applications are being explored in the field of healthcare. GMR and TMR chips are used for detecting biological molecules labeled with magnetic particles, and this could be a powerful platform for next-generation diagnostics. The sensitivity achievable with simple portable instrumentation can be orders of magnitude better than the current methods. Since this application is still in its infancy, it will not be discussed further here. Interested readers are referred to the references above.

SI magnetic units are easily related to the current, voltage and energy in MKS units, since the SI system was originally developed under the assumption that magnetism is originated from electric current. The dimensions of magnetic units are shown below; A = amperes, s = seconds, kg = kilograms and m = meters.

1. (1) newton (N) = kg m/s2;

2. (2) joule (J) = kg m2/s2;

3. (3) magnetic field (H) = A/m;

4. (4) henry (h) = kg m2/s2A2;

5. (5) tesla (T) = kg/s2A;

6. (6) weber (Wb) = kg m2/s2A.

Magnetism in cgs units is less transparent. The unit of magnetic moment m is the emu. The density of the magnetic moment MS is emu/cm3. The magnetic induction is given by B = H + 4πMS, where the magnetic field H is given in units of oersted (Oe) and B is given in gauss (G). (1 Oe = 1 G in air, since M = 0 in air.) Thus, the “4π” in 4πMS is not dimensionless. Its dimension is [G/(emu/cm3)], and it is equivalent to the inverse of susceptibility, so that the unit of 4πMS is [G/(emu/cm3)] · [emu/cm3] = G.

The dimension of “emu” can be understood from the dimension of energy. In Chapter 2, we discussed the magnetostatic energy per unit volume of magnetic material under a magnetic field H to be ∼MS · H. The dimension of MS · H is [emu · cm−3] · [Oe], which should be equivalent to [erg · cm−3]. Therefore, the dimension of emu is [erg/Oe] or [emu/G] in air.

Introduction

Magnetic ferrite core memory was invented and produced in the 1960s, prior to semiconductor memory. Ferrite cores are made from a paste of ferrite powers, which are sintered at high temperature. The process of forming a discrete core is not as scalable as the integrated circuit process on a silicon wafer. The product life of a magnetic core was short, and in the 1970s this technique was replaced by semiconductor memory. A similar fate happened to magnetic bubble memory, another type of magnetic memory, which was built on a magnetic garnet material substrate (gadolinium gallium garnet, Gd3Ga2(GaO4)3). The bit density of bubble memory technology is scalable since it is made with a planar process, similar to the silicon integration circuits. However, because it is on garnet, it is passive and cannot perform logic functions (such as address decoding), and it requires a companion silicon chip to provide the logic function to complete the memory access function. Even with better memory performance, magnetic bubble memory could not compete against magnetic hard disk and semiconductor memory, which continue to show a clear path of scaling for a lower cost. By the mid 1980s, commercial magnetic bubble production had ended.

Subsequent efforts in the development of magnetic memory have been focused on the integration of magnetic thin-film memory devices into silicon wafer processes. Magnetic memory devices exist in the form of thin-film stacks, which can easily be integrated into the back-end metal wiring metallurgy process.